On the connection between the intergalactic medium and galaxies: the H i–galaxy cross-correlation at z ≲ 1★

Abstract

We present a new optical spectroscopic survey of 1777 ‘star-forming’ (‘SF’) and 366 ‘non-star-forming’ (‘non-SF’) galaxies at redshifts z ∼ 0-1 (2143 in total), 22 AGN and 423 stars, observed by instruments such as the Deep Imaging Multi-Object Spectrograph, the Visible Multi-Object Spectrograph and the Gemini Multi-Object Spectrograph, in three fields containing five quasi-stellar objects (QSOs) with Hubble Space Telescope (HST) ultraviolet spectroscopy. We also present a new spectroscopic survey of 173 ‘strong’ (10¹⁴ ≤ N_HI≲ 10¹⁷ cm⁻²) and 496 ‘weak’ (10¹³ ≲ N_HI < 10¹⁴ cm⁻²) intervening H i (Lyα) absorption-line systems at z ≲ 1 (669 in total), observed in the spectra of eight QSOs at z ∼ 1 by the Cosmic Origins Spectrograph and the Faint Object Spectrograph on the HST. Combining these new data with previously published galaxy catalogues such as the Very Large Telescope Visible Multi-Object Spectrograph Deep Survey and the Gemini Deep Deep Survey, we have gathered a sample of 654 H i absorption systems and 17 509 galaxies at transverse scales ≲50 Mpc, suitable for a two-point correlation function analysis. We present observational results on the H i–galaxy (ξ_ag) and galaxy–galaxy (ξ_gg) correlations at transverse scales r_⊥ ≲ 10 Mpc, and the H i–H i autocorrelation (ξ_aa) at transverse scales r_⊥ ≲ 2 Mpc. The two-point correlation functions are measured both along and transverse to the line of sight, ξ(r_⊥, r_∥). We also infer the shape of their corresponding ‘real-space’ correlation functions, ξ(r), from the projected along the line-of-sight correlations, assuming power laws of the form ξ(r) = (r/r₀)^−γ. Comparing the results from ξ_ag, ξ_gg and ξ_aa, we constrain the H i–galaxy statistical connection, as a function of both H i column density and galaxy star formation activity. Our results are consistent with the following conclusions: (i) the bulk of H i systems on ∼ Mpc scales have little velocity dispersion (≲120 km s⁻¹) with respect to the bulk of galaxies (i.e. no strong galaxy outflow/inflow signal is detected); (ii) the vast majority (∼100 per cent) of ‘strong’ H i systems and ‘SF’ galaxies are distributed in the same locations, together with 75 ± 15 per cent of ‘non-SF’ galaxies, all of which typically reside in dark matter haloes of similar masses; (iii) 25 ± 15 per cent of ‘non-SF’ galaxies reside in galaxy clusters and are not correlated with ‘strong’ H i systems at scales ≲2 Mpc; and (iv) >50 per cent of ‘weak’ H i systems reside within galaxy voids (hence not correlated with galaxies), and are confined in dark matter haloes of masses smaller than those hosting ‘strong’ systems and/or galaxies. We speculate that H i systems within galaxy voids might still be evolving in the linear regime even at scales ≲2 Mpc.

INTRODUCTION

Motivation

The physics of the intergalactic medium (IGM) and its connection with galaxies are key to understanding the evolution of baryonic matter in the Universe. This is because of the continuous interplay between the gas in the IGM and galaxies: (i) galaxies are formed by the condensation and accretion of primordial or enriched gas; and (ii) galaxies enrich their haloes and the IGM via galactic winds and/or merger events.

Theoretical analyses – under a Λ cold dark matter paradigm – suggest that: (i) the accretion happens in two major modes: ‘hot’ and ‘cold’ (e.g. Rees & Ostriker 1977; White & Rees 1978; White & Frenk 1991; Kereš et al. 2005; van de Voort et al. 2011); and (ii) galactic winds are mostly driven by supernova (SN) and/or active galactic nuclei (AGN) feedback (e.g. Baugh et al. 2005; Bower et al. 2006; Lagos, Cora & Padilla 2008; Creasey, Theuns & Bower 2013).

Models combining ‘N-body’ dark matter simulations (collisionless, dissipationless) with ‘semi-analytic’ arguments (e.g. Baugh 2006, and references therein) have been successful in reproducing basic statistical properties of luminous galaxies (e.g. luminosity functions, clustering, star formation histories, among others). However, in order to provide predictions for the signatures of ‘hot’/‘cold’ accretion and/or AGN/SN feedback in the IGM, a full hydrodynamical description is required.

In practice, hydrodynamical simulations still rely on unresolved ‘subgrid physics’ to lower the computational cost (e.g. Schaye et al. 2010; Scannapieco et al. 2012), whose effects are not fully understood. Therefore, observations of the IGM and galaxies in the same volume are fundamental to testing these predictions and helping to discern between different physical models (e.g. Fumagalli et al. 2011; Oppenheimer et al. 2012; Stinson et al. 2012; Ford et al. 2013a; Hummels et al. 2013; Rakic et al. 2013).

Although the IGM is the main reservoir of baryons at all epochs (e.g. Fukugita, Hogan & Peebles 1998; Cen & Ostriker 1999; Schaye 2001; Davé et al. 2010; Shull, Smith & Danforth 2012), its extremely low densities make its observation difficult and limited. Currently, the only feasible way to observe the IGM is through intervening absorption-line systems in the spectra of bright background sources, limiting its characterization to being one-dimensional. Still, an averaged three-dimensional picture can be obtained by combining multiple lines of sight (LOS) and galaxy surveys, which is the approach adopted in this work (see Section 1.2).

The advent of the Cosmic Origins Spectrograph (COS) on the Hubble Space Telescope (HST) has revolutionized the study of the IGM and its connection with galaxies at low-z (z ≲ 1). With a sensitivity ∼10 times greater than that of its predecessors, COS has considerably increased the number of QSOs for which ultraviolet (UV) spectroscopy is feasible. This capability has been exploited for studies of the so-called circumgalactic medium (CGM), by characterizing neutral hydrogen (H i)¹ and metal absorption systems in the vicinity of known galaxies (e.g. Tumlinson et al. 2011; Thom et al. 2012; Keeney et al. 2013; Lehner et al. 2013; Stocke et al. 2013; Werk et al. 2013).

Studies of the CGM implicitly assume a direct one-to-one association between absorption systems and their closest observed galaxy, which might not always hold because of incompleteness in the galaxy surveys and projection effects. Given that metals are formed and expelled by galaxies, a direct association between them seems sensible, in accordance with predictions from low-z simulations (e.g. Oppenheimer et al. 2012). However, the situation for neutral hydrogen is more complicated, as H i traces both enriched and primordial material.²

The nature of the relationship between H i and galaxies at low-z has been widely debated. Early studies have pointed out two distinct scenarios for this connection: (i) a one-to-one physical association because they both belong to the same dark matter haloes (e.g. Mo 1994; Lanzetta et al. 1995; Chen et al. 1998) and (ii) an indirect association because they both trace the same underlying dark matter distribution but not necessarily the same haloes (e.g. Morris et al. 1991, 1993; Mo & Morris 1994; Stocke et al. 1995; Tripp, Lu & Savage 1998). More recent studies have shown the presence of H i absorption systems within galaxy voids (e.g. Stocke et al. 1995; Grogin & Geller 1998; Manning 2002; Penton, Stocke & Shull 2002; Tejos et al. 2012), hinting at a third scenario: (iii) the presence of H i absorption systems that are not associated with galaxies (although see Wakker & Savage 2009).³

If we think of galaxies as peaks in the density distribution (e.g. Press & Schechter 1974), it is natural to expect high column density H i systems to show a stronger correlation with galaxies than low column density ones, owing to a density–H i column density proportionality (e.g. Schaye 2001; Davé et al. 2010; Tepper-García et al. 2012). Similarly, we also expect the majority of low column density H i systems to belong to dark matter haloes that did not form galaxies. Thus, the relative importance of these three scenarios should depend, to some extent, on the H i column density. Tejos et al. (2012) estimated that these three scenarios account for ∼15, ∼55 and ∼30 per cent of the low-z H i systems at column densities |$N_{\rm H\,\small {I}} \gtrsim 10^{12.5}$| cm⁻², respectively, indicating that the vast majority of H i absorption-line systems are not physically associated with luminous galaxies (see also Prochaska et al. 2011b for a similar conclusion).

Study strategy

In this paper, we address the statistical connection between H i and galaxies at z ≲ 1 through a clustering analysis (e.g. Morris et al. 1993; Chen et al. 2005; Ryan-Weber 2006; Wilman et al. 2007; Chen & Mulchaey 2009; Shone et al. 2010), without considering metals. We focus only on hydrogen because it is the best IGM tracer for a statistical study. Apart from the fact that it traces both primordial and enriched material, it is also the most abundant element in the Universe. Hence, current spectral sensitivities allow us to find H i inside and outside galaxy haloes, which is not the case yet for metals at low-z (according to recent theoretical results; e.g. Oppenheimer et al. 2012).

Focusing on the second half of the history of the Universe (z ≲ 1) has the advantage of allowing relatively complete galaxy surveys even at faint luminosities (≲L★; elusive at higher redshifts). Faint galaxies are important for statistical analyses as they dominate the luminosity function, not just in number density, but also in total luminosity and mass. Moreover, the combined effects of structure formation, expansion of the Universe, and the reduced ionization background, allow us to observe a considerable amount of H i systems and yet resolve the so-called H i Lyα forest into individual lines (e.g. Theuns, Leonard & Efstathiou 1998; Davé et al. 1999). This makes it possible to recover column densities and Doppler parameters through Voigt profile fitting.

One major advantage of clustering over one-to-one association analyses is that it does not impose arbitrary scales, allowing us to obtain results for both small (≲1 Mpc) and large scales (≳1–10 Mpc). In this way, we can make use of all the H i and galaxy data available, and not only those lying close to each other. Results from the small-scale association are important to constrain the ‘subgrid physics’ adopted in current hydrodynamical simulations. Conversely, results from the largest scales provide information unaffected by these uncertain ‘subgrid physics’ assumptions (e.g. Ford et al. 2013a; Hummels et al. 2013; Rakic et al. 2013). Moreover, the physics and cosmic evolution of the diffuse IGM (traced by H i) obtained by cosmological hydrodynamical simulations (e.g. Paschos et al. 2009; Davé et al. 2010) are in good agreement with analytic predictions (e.g. Schaye 2001). Our results will be able to test all of these predictions.

Another advantage to using a clustering analysis is that it properly takes into account the selection functions of the surveys. Even at scales ≲300 kpc (the typical scale adopted for the CGM), a secure or unique H i–galaxy one-to-one association is not always possible. This is because H i and galaxies are clustered at these scales and because surveys are never 100 per cent complete. Clustering provides a proper statistical description, at the cost of losing details on the physics of an individual H i–galaxy pair. Thus, both one-to-one associations and clustering results are complementary, and needed, to fully understand the relationship between the IGM and galaxies.

In this paper, we present observational results for the H i–galaxy two-point correlation function at z ≲ 1. Combining data from UV HST spectroscopy of eight QSOs in six different fields, with optical deep multi-object spectroscopy (MOS) surveys of galaxies around them, we have gathered a sample of 654 well-identified intervening H i absorption systems and 17 509 galaxies at projected separations ≲50 Mpc from the QSO LOS. This data set is the largest sample to date for such an analysis.

Comparing the results from the H i–galaxy cross-correlation with the H i–H i and galaxy–galaxy autocorrelations, we provide constraints on their statistical connection as a function of both H i column density and galaxy star formation activity.

Our paper is structured as follows. Sections 2 and 3 describe the IGM and galaxy data used in this work, respectively. The IGM sample is described in Section 4 while the galaxy sample is described in Section 5. Section 6 describes the formalisms used to measure the H i–galaxy cross-correlation and the H i–H i and galaxy–galaxy autocorrelations. Our observational results are presented in Section 7 and discussed in Section 8. A summary of the paper is presented in Section 9.

All distances are in comoving coordinates assuming H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_m = 0.3, Ω_Λ = 0.7, k = 0, unless otherwise stated, where H₀, Ω_m, Ω_Λ and k are the Hubble constant, mass energy density, ‘dark energy’ density and spatial curvature, respectively. Our chosen cosmological parameters lie between the latest results from the Wilkinson Microwave Anisotropy Probe (Komatsu et al. 2011) and the Planck satellite (Planck Collaboration 2013).

INTERGALACTIC MEDIUM DATA

We used HST spectroscopy of eight QSOs to characterize the diffuse IGM through the observations of intervening H i absorption-line systems. We used data from COS (Green et al. 2012) taken under HST programmes General Observer (GO) 12264 (PI: Morris), GO 11585 (PI: Crighton) and GO 11598 (PI: Tumlinson); and data from the Faint Object Spectrograph (FOS; Keyes et al. 1995) taken under HST programmes GO 5320 (PI: Foltz), GO 6100 (PI: Foltz) and GO 6592 (PI: Foltz).

Data from programme GO 12264 were taken to study the statistical relationship between H i absorption-line systems and galaxies at redshift z ≲ 1. We selected four QSOs at z_QSO ∼ 1 (namely J020930.7−043826, J100535.24+013445.7, J135726.27+043541.4 and J221806.67+005223.6) lying in fields of view that were already surveyed for their galaxy content by the Very Large Telescope (VLT) Visible Multi-Object Spectrograph (VIMOS) Deep Survey (VVDS; Le Fèvre et al. 2005, 2013) and the Gemini Deep Deep Survey (GDDS; Abraham et al. 2004). Data from programmes GO 5320, GO 6100, GO 6592 and GO 11585 contain spectroscopy of three QSOs (namely Q0107−025A, Q0107−025B and Q0107−0232) whose line of sights (LOS) are separated by ∼0.4–1 Mpc. This triple QSO field is ideal for measuring the characteristic sizes of the H i absorption systems but it can also be used to address the connection between H i systems and galaxies (e.g. Crighton et al. 2010). Data from programme GO 11598 were originally taken to investigate the properties of the CGM by targeting QSOs whose LOS lie within ≲150 kpc of a known galaxy. For this paper, we used one QSO observed under programme GO 11598 (namely J102218.99+013218.8), for which we have conducted our own galaxy survey around its LOS (see Section 3). Given that this LOS contains only one pre-selected galaxy, this selection will not affect our results on the IGM–galaxy statistical connection.

Table 1 summarizes our QSO sample while Table 2 gives details on their HST observations.

Data reduction

COS data

Individual exposures from COS were downloaded from the Space Telescope Science Institute (STScI) archive and reduced using calcos v2.18.5 in combination with python routines developed by the authors.⁴ A full description of the reduction process will be presented in Finn et al. (in preparation), here we present a summary.

Individual files corresponding to single central wavelength setting, grating offset position (FP-POS) and stripe (i.e. x1d files) were obtained directly from calcos. The source extraction was performed using a box of 25 pixels wide along the spatial direction for all G130M exposures, and 20 pixels for all G160M and G230L exposures. The background extraction was performed using boxes encompassing as much of the background signal as possible, whilst avoiding regions close to the detector edges. We set the background smoothing length in calcos to 1 pixel and performed our own background smoothing procedure masking out portions of the spectra affected by strong geocoronal emission lines (namely the H i Lyα and O i λλ1302, 1306) and pixels with bad data quality flags.⁵ We interpolated across the gaps to get the background level in these excluded regions. The background smoothing lengths were set to 1000 pixels for the far-ultraviolet (FUV)A stripes, 500 pixels for the FUVB stripes and 100 pixels for all near-ultraviolet (NUV) stripes, along the dispersion direction.

The error array was calculated in the same way as in calcos, but using our new background estimation. Each spectrum was then flux calibrated using sensitivity curves provided by STScI.

Co-alignment was performed by cross-correlating regions centred on strong Galactic absorption features (namely, C ii λ1334, Al ii λ1670, Si ii λ1260, Si ii λ1526 and Mg ii λλ2796, 2803 Å). For each grating, we pick the central wavelength setting and FP-POS position with the most accurately determined wavelength solutions from STScI as a reference. These are FP-POS = 3 for all gratings, central wavelengths of 1309 and 1600 Å for the G130M and G160M gratings, respectively, and 2950 Å (using only the ‘B’ stripe) for the G230L grating. All other settings for each grating are then cross-correlated on these ones, assuming that the reference and comparison settings both contain one of the absorption features specified. Wavelengths offsets are then applied to the comparison settings to match the reference ones. These offsets typically amount to a resolution element or less. For those settings that could not be aligned on any of the Galactic features specified, we manually searched for other strong absorption lines on which to perform the cross-correlation. Strong absorption lines were always found. We then scaled the fluxes of the comparison setting such that its median flux value matches that of either the reference or the already calibrated setting in the overlapped region.

At this point, we changed some pixel values according to their quality flags: flux and error values assigned to pixels with bad data quality flags were set to zero, while pixels with warnings had their exposure times reduced by a factor of 2. We then rescaled the wavelength binning of each exposure to have a constant spacing equal to the dispersion for the grating, using nearest-neighbour interpolation. The combined wavelength binning therefore consists of three wavelength scales, one for the G130M grating (λ < 1460 Å), one for the G160M grating (1460 ≤ λ < 1795 Å) and one for the G230L grating (λ ≥ 1795 Å).

The co-addition was then performed via modified exposure time weighting. Finally, the combined FUV and NUV spectra were rebinned to ensure Nyquist sampling (two pixels per resolution element). Both are binned on to a linear wavelength scale with spacing equal to 0.0395 Å for the FUV, and a spacing equal to 0.436 Å for the NUV.

FOS data

Individual exposures from FOS were downloaded from the STScI archive and reduced using the standard calfos pipeline. Wavelength corrections given by Petry et al. (2006) were applied to each individual exposure. As described by Petry et al., these corrections were determined using a wavelength calibration exposure taken contemporaneously with the G190H grating science exposures, and were verified using Galactic Al ii and Al iii absorption features. The shortest wavelength region of FOS G190H settings overlap with the longest wavelength COS settings, and we confirmed that the wavelength scales in these overlapping regions were consistent between the two instruments. Then we combined all individual exposures together, resampling to a common wavelength scale of 0.51 Å pixel⁻¹.

Continuum fitting

We fit the continuum of each QSO in a semi-automatized and iterative manner: (i) we first divide each spectrum in multiple chunks, typically of 12 Å at wavelengths shorter than that of the H i Lyα emission from the QSOs (at larger wavelengths we used much longer intervals but these are not relevant for this work); (ii) we then fit straight line segments through the set of points given by the central wavelength and the median flux values for each chunk; (iii) we then removed pixels with flux values falling three times their uncertainty below the fit value; (iv) we repeat steps (ii) and (iii) until a converged solution is reached; (v) we fit a cubic spline through the final set of median points to get a smooth continuum. The success of this method strongly depends on the presence of emission lines, and on number and positions of the chosen wavelength chunks. Therefore, we visually inspect the solution and improve it by adding and/or removing points accordingly, making sure that the distribution of flux values above the continuum fit is consistent with a Gaussian tail. We checked that the use of these subjective steps does not affect the final results significantly (see Section 4.4).

In Fig. 1, we show our QSO spectra (black lines) with their corresponding uncertainties (green lines) and continuum fit (red lines). We refer the reader to Finn et al. (in preparation) for further details on the continuum fitting process (including the continuum fit associated with the peaks of the broad emission lines).

GALAXY DATA

Our chosen QSOs are at z_QSO ∼ 0.7–1.3, so we aim to target galaxies at z ≲ 1, corresponding to the last ∼7 Gyr of cosmic evolution. The majority of these QSOs lie in fields already surveyed for their galaxy content. We used archival galaxy data from: VVDS (Le Fèvre et al. 2005, 2013), GDDS (Abraham et al. 2004) and the Canada–France–Hawaii Telescope (CFHT) MOS survey published by Morris & Jannuzi (2006). Despite the existence of some galaxy data around our QSO fields we have also performed our own galaxy surveys using MOS to increase the survey completeness.⁶ We acquired new galaxy data from different ground-based MOS, namely: VIMOS (Le Fèvre et al. 2003) on the Very Large Telescope (VLT) under programmes 086.A-0970 (PI: Crighton) and 087.A-0857 (PI: Tejos); the Deep Imaging Multi-Object Spectrograph (DEIMOS; Faber et al. 2003) on Keck under programme A290D (PIs: Bechtold and Jannuzi); and the Gemini Multi-Object Spectrograph (GMOS; Davies et al. 1997) on Gemini under programme GS-2008B-Q-50 (PI: Crighton). Table 3 summarizes the observations taken to construct our galaxy samples.

The following sections provide detailed descriptions of the observations, data reduction, selection functions and construction of our new galaxy samples. We also give information on the subsamples of the previously published galaxy surveys used in this work.

VIMOS data

Instrument setting

We used the low-resolution (LR) grism with 1.0 arcsec slits (R ≡ λ/Δλ ≈ 200) due to its high multiplex factor in the dispersion direction (up to 4). As we needed to target galaxies up to the QSOs redshifts (z_QSO ∼ 0.7–1.3), we used that grism in combination with the OS red filter giving coverage between 5500 and 9500 Å.

Target selection, mask design and pointings

We used R-band pre-imaging to observe objects around our QSO fields and SExtractor v2.5 (Bertin & Arnouts 1996) to identify them and assign R-band magnitudes, using zero-points given by the European Southern Observatory (ESO). For fields J1005, J1022 and J2218 we added a constant shift of ∼0.38 mag to match those reported by the VVDS survey in objects observed by both surveys (see Section 3.5.2 and Fig. 4). No correction was added to the Q0107 field. For objects in fields J1005, J1022 and J2218 we targeted objects at R < 23.5, giving priority to those with R < 22.5. For objects in field Q0107, we targeted objects at R < 23, giving priority to those with R < 22. We did not impose any morphological star/galaxy separation criteria, given that unresolved galaxies will look like point sources (see Section 5.3). The masks were designed using vmmps (Bottini et al. 2005) using the ‘Normal Optimization’ method (random) to provide a simple selection function. We targeted typically ∼ 70-80 objects per mask per quadrant, equivalent to ∼ 210-320 objects per pointing. We used three pointings of one mask each, shifted by ∼2.5 arcmin centred around the QSO.

Data reduction for field Q0107

The spectroscopic data were taken in 2010 and the reduction was performed using vipgi (Scodeggio et al. 2005) using standard parameters. We took three exposures per pointing of 1155 s, followed by lamps. The images were bias corrected and combined using a median filter. Wavelength calibration was performed using the lamp exposures, and further corrected using five skylines at 5892, 6300, 7859, 8347 and 8771 Å (Osterbrock et al. 1996; Osterbrock, Fulbright & Bida 1997). Finally, the slits were spectrophotometrically calibrated using standard star spectra (Oke 1990; Hamuy et al. 1992, 1994) taken at dates similar to our observations. The extraction of the one-dimensional spectra was performed by collapsing objects along the spatial axis, following the optimal weighting algorithm presented in Horne (1986). Our wavelength solutions per slit show a quadratic mean rms ≲ 1 Å in more than 75 per cent of the slits and a rms ≲ 2 Å in all the cases. We consider these as good solutions, given that the pixel size for the LR mode is ∼7 Å. These data were taken before the recent update of VIMOS charge-coupled devices (CCDs) on 2010 August, and so fringing effects considerably affected the quality of the data at ≳7500 Å. We attempted to correct for this with no success.

Data reduction for fields J1005, J1022 and J2218

The spectroscopic data were taken in 2011 and the reduction was performed using esorex v.3.9.6. All three pointings of fields J1005 and J1022 were observed, while only ‘pointing 3’ of J2218 was observed. Due to a problem with focus, data from ‘quadrant 3’ of ‘pointing 1’ and ‘pointing 3’ of field J1022 were not usable. ‘Pointing 2’ (middle one) of fields J1005 and J1022 were observed twice to empirically asses the redshift uncertainty (see Section 3.1.5). We took three exposures per pointing of 1155 s followed by lamps. The reduction was performed using a peakdetection parameter (threshold for preliminary peak detection in counts) of 500 when possible, and decreasing it when needed to minimize the number of slits lost (we typically lost ∼1 slit per quadrant). We also set the cosmics parameter to ‘True’ (cleaning cosmic ray events) and stacked our three images using the median. Wavelength calibration was further improved using four skylines at 5577.34, 6300.30, 8827.10 and 9375.36 Å (Osterbrock et al. 1996, 1997) with the skyalign parameter set to 1 (first-order polynomial fit to the expected positions). The slits were spectrophotometrically calibrated using standard star spectra (Oke 1990; Hamuy et al. 1992, 1994) taken at dates similar to our observations. The extraction of the one-dimensional spectra was performed by collapsing the objects along the spatial axis, following the optimal weighting algorithm presented in Horne (1986). Our wavelength solutions per slit show a quadratic mean rms ≲ 1 Å in more than 90 per cent of the cases, which we considered as satisfactory for a pixel size of ∼7 Å. These data were taken after a recent update to VIMOS CCDs in 2010 August, and so no important fringing effects were present.

Redshift determination

Redshifts for our new galaxy survey were measured by cross-correlating galaxy, star and QSO templates with each observed spectrum. We used templates from the Sloan Digital Sky Survey⁷ degraded to the lower resolution of our VIMOS observations. Galaxy templates were redshifted from z = 0 to 2 using intervals of Δz = 0.001. The QSO template was redshifted between z = 0 and 4 using larger intervals of Δz = 0.01. Star templates were shifted ±0.005 around z = 0 using intervals of Δz = 0.0001 to help improve the redshift measurements and quantify the redshift uncertainty (see below). We improved the redshift solution by fitting a parabola to the three redshift points with the largest cross-correlation values around each local maximum. This technique gives comparable redshift solutions (within the expected errors) to that obtained by decreasing the redshift intervals by a factor of ∼10, but at a much lower computational cost. Before computing the cross-correlations, we masked out regions at the very edges of the wavelength coverage (<5710 and >9265 Å) and those associated with strong sky emission/absorption features (among 5870–5910, 6275–6325 and 7550–7720 Å). For the Q0107 field, we additionally masked out the red part at >7550 Å because of fringing problems. We visually inspected each one-dimensional and two-dimensional spectrum and looked for the ‘best’ redshift solution (see below).

Redshift reliability

For each targeted object we manually assigned a redshift reliability flag. We used a very simple scheme based on three labels: ‘a’ (‘secure’), ‘b’ (‘possible’) and ‘c’ (‘uncertain’). As a general rule, spectra assigned with ‘a’ flags have at least three well-identified spectral features (either in emission or absorption) or two well-identified emission lines; spectra assigned with ‘c’ flag are those which do not show clear spectral features either due to a low signal-to-noise ratio (S/N) or because of an intrinsic lack of such lines observed at VIMOS resolution (e.g. some possible A, F and G type stars appear in this category); spectra assigned with ‘b’ flags are those that lie in between the two aforementioned categories.

Uncertainty of the semi-automatized process

The process includes subjective steps (determining the ‘best’ template and redshift, and assigning a redshift reliability). This uncertainty was estimated by comparing two sets of redshifts obtained independently by three of the authors (NT versus SLM and NT versus NHMC) in two subsamples of the data. We found discrepancies in ≲5 per cent of the cases, the vast majority of which were for redshifts labelled as ‘b’.

Further redshift calibration for fields J1005, J1022 and J2218

Even though the wavelength calibration from the esorex reduction was generally satisfactory, we found a ∼1 pixel systematic discrepancy between the obtained and expected wavelength for some skylines in localized areas of the spectrum (particularly towards the red end). This effect was most noticeable in quadrant 3, where the redshift difference between objects observed twice showed a distribution displaced from 0 to ∼0.001 (∼1 pixel). A careful inspection revealed that the other quadrants also showed a similar but less strong effect (≲0.5 pixel). We corrected for this effect using the redshift solution of the stars. For a given quadrant, we looked at the mean redshift of the stars and applied a systematic shift of that amount to all the objects in that quadrant. This correction placed the mean redshift of stars at zero, and therefore corrected the redshift of all objects accordingly.

Redshift statistical uncertainty for fields J1005, J1022 and J2218

In order to assess the redshift uncertainty for these fields, we measured a redshift difference between two independent observations of the same object. These objects were observed twice, and come mainly from our ‘pointing 2’ in fields J1005 and J1022, but there is also a minor contribution (≲10 per cent) of objects that were observed twice using different pointings. Fig. 2 shows the observed redshift differences for all galaxies and stars (top panel); galaxies with ‘secure’ and ‘possible’ redshifts (middle panel); and galaxies classified as ‘star-forming’ (‘SF’) or ‘non-star-forming’ (‘non-SF’) based on the presence of current, or recent, star formation (see Section 5.1; bottom panel). All histograms are centred around zero and do not show evident systematic biases. The redshift difference of all galaxies show a standard deviation of ≈0.0006. A somewhat smaller standard deviation is observed for galaxies with ‘secure’ redshifts and/or those classified as ‘SF’ (note that there is a large overlap between these two samples), and consequently a somewhat larger standard deviation is observed for galaxies with ‘possible’ redshift and/or classified as ‘non-SF’. This behaviour is of course expected, as it is simpler to measure redshifts for galaxies with strong emission lines (for which the peak in the cross-correlation analysis is also better constrained) than for galaxies with only absorption features (at a similar S/N). From this analysis we take |${\approx } 0.0006/\sqrt{2} = 0.0004$| as the representative redshift uncertainty of our VIMOS galaxy survey in these fields. This uncertainty corresponds to ≈ 120-60 km s⁻¹ at redshift z = 0-1. This uncertainty is ∼2 times smaller than that claimed for the VVDS survey (Le Fèvre et al. 2005).

Further redshift calibration for field Q0107

We did not see systematic differences between quadrants, as was seen for fields J1005, J1022 and J2218. VIMOS observations of the Q0107 field were reduced differently, and the data come mainly from the blue part of the spectrum. Therefore, such an effect might not be present or, if present, might be more difficult to detect. However, we did find a systematic shift between the redshifts measured from VIMOS compared to those measured from DEIMOS. Given the much higher resolution of DEIMOS, we used its frame as reference for all our Q0107 observations. Thus, we corrected the Q0107 VIMOS redshifts to match the DEIMOS frame. This correction was ∼0.0008 (≲1 VIMOS pixel) and the result is shown in the bottom panel of Fig. 3 (blue lines).

Redshift statistical uncertainty for field Q0107

In order to assess the redshift uncertainty, we used objects that were observed twice in the Q0107 field. We found a distribution of redshift differences centred at ∼0 with a standard deviation of ≈0.001 (see top panel of Fig. 3), corresponding to a single VIMOS uncertainty of |${\approx } 0.001/\sqrt{2} \approx 0.0007$|⁠. Another way to estimate the VIMOS uncertainty in the Q0107 field is by looking at the redshift difference for objects that were observed twice, once by VIMOS and another time by DEIMOS (44 in total; see bottom panel of Fig. 3). In this case, the distribution shows a standard deviation of ≈ 0.00084, corresponding to a single VIMOS uncertainty of |$\sqrt{0.00084^2-0.00013^2} \approx 0.0008$|⁠, given that the uncertainty of a DEIMOS single measurement is ≈0.00013 (see below). So, we take a value of ≈0.00075 as the representative redshift uncertainty of a single VIMOS observation in the Q0107 field. This uncertainty corresponds to ≈ 220-110 km s⁻¹ at redshift z = 0-1. This uncertainty is larger than that of fields J1005, J1022 and J2218, consistent with the poorer quality detector being used.

DEIMOS data

Instrument setting

We patterned our DEIMOS observations to resemble the Deep Extragalactic Evolutionary Probe 2 (DEEP2) ‘1 h’ survey (Coil et al. 2004). We used the 1200 line mm⁻¹ grating with a 1.0 arcsec slit giving a resolution of R ∼5000 over the wavelength range 6400-9100 Å.

Target selection

Data reduction

The observations were taken in 2007 and 2008. The reduction was performed using the DEEP2 DEIMOS Data Pipeline¹⁰ (Newman et al. 2013), from which galaxy redshifts were also obtained.

Redshift reliability

The redshift reliability for DEIMOS data was originally based on four subjective categories: (0) ‘still needs work’, (1) ‘not good enough’, (2) ‘possible’, (3) ‘good’ and (4) ‘excellent’. In order to have a unified scheme, we matched those DEIMOS labels with our previously defined VIMOS ones (see Section 3.1.5) as follows: DEIMOS label 4 is matched to label ‘a’ ({4}→ {‘a’}); DEIMOS labels 3 and 2 are matched to label ‘b’ ({3,2}→ {‘b’}); and DEIMOS labels 1 and 0 are matched to label ‘c’ ({1,0}→ {‘c’}).

Redshift statistical uncertainty for field Q0107

In order to assess the redshift uncertainty, we used objects that were observed twice in the Q0107 field. We found a distribution of redshift differences centred at ∼0 with a standard deviation of ≈0.00019 (see top panel of Fig. 3), corresponding to a single DEIMOS uncertainty of |${\approx } 0.00019/\sqrt{2} \approx 0.00013$|⁠. So, we take a value of ≈0.00013 as the representative redshift uncertainty of a single DEIMOS observation in the Q0107 field. This uncertainty corresponds to ≈ 40-20 km s⁻¹ at redshift z = 0-1.

GMOS data

Instrument setting

We used the R400 grating centred on a wavelength of 7000 Å with a 1.5 arcsec slit giving a resolution of R = 639.

Target selection, mask design and pointings

We used R-band pre-imaging to select objects around our Q0107 field. We used SExtractor v2.5 (Bertin & Arnouts 1996) to identify objects and assign them R-band magnitudes. The masks were designed using gmmps.¹¹ Top priority was given to objects with R < 22, followed by those with 22 ≤ R < 23 and last priority to those with 23 ≤ R < 24. We typically targeted ∼40 objects per mask. Six masks were taken, three around QSO C, two around QSO B and one around QSO A, where many objects had already been targeted in previous observations.

Data reduction

The observations were taken in 2008. Three 1080 s offset science exposures were taken for each mask, dithered along the slit to cover the gaps in the CCD detectors. Arcs were taken contemporaneously to the science exposures. We used the Gemini Image Reduction and Analysis Facility (iraf) package to reduce the spectra. A flat-field lamp exposure was divided into each bias-subtracted science exposure to remove small-scale variations across the CCDs, and the fringing pattern seen at red wavelengths. The dithered images (both arcs and science) were then combined into a single exposure. The spectrum for each mask was wavelength calibrated by identifying known arc lines and fitting a polynomial to match pixel positions to wavelengths. Finally, the wavelength-calibrated two-dimensional spectra were extracted to produce one-dimensional spectra. The typical rms scatter of the known arc line positions around the polynomial fit ranged from 0.5 to 1.0 Å, depending on how many arc lines were available to fit (bluer wavelength ranges tended to have fewer arc lines). A 0.75 Å rms scatter corresponds to a velocity error of 38 km s⁻¹ at 6000 Å.

Redshift determination and reliability

We determined redshifts by using the same method as that of VIMOS spectra: plausible redshifts were identified as peaks in the cross-correlation measured between GMOS spectra and spectral templates (see Section 3.1.5 for further details). Redshifts reliabilities were also assigned following the definitions in our VIMOS sample.

Further redshift calibration

We found a systematic shift of the redshifts measured from GMOS with respect to those measured from DEIMOS for the 40 objects observed by these two instruments. Given the much higher resolution of DEIMOS we used its frame as reference for our Q0107 observations. Thus, we corrected all GMOS redshifts to match the DEIMOS frame. This correction was ∼0.0004 (≲1 GMOS pixel) and the result is shown in the bottom panel of Fig. 3 (red lines).

Redshift statistical uncertainty for field Q0107

There were only three objects that were observed twice using GMOS (see top panel of Fig. 3), and so we did not take the uncertainty from such a small sample. Instead, we use objects observed by both GMOS and DEIMOS to estimate GMOS redshift uncertainty. The distribution of redshift differences for objects with both GMOS and DEIMOS spectra (see bottom panel of Fig. 3) shows a standard deviation of ≈0.00027. Given that the uncertainty of DEIMOS alone is ≈0.00013 we estimate GMOS uncertainty to be |${\approx } \sqrt{0.00027^2 -0.00013^2 }\approx 0.00024$|⁠. This uncertainty corresponds to ≈70–35 km s⁻¹ at redshift z = 0–1.

CFHT MOS data

We used the CFHT galaxy survey of the Q0107 field presented by Morris & Jannuzi (2006). There are 61 galaxies in this sample, 29 of which were also observed by our GMOS survey. We use only redshift information from this sample without assigning a particular template or redshift label. We refer the reader to Morris & Jannuzi (2006) for details on the data reduction and construction of the galaxy sample.

VVDS

Three of the QSOs presented in this paper (namely: J100535.24+013445.7, J135726.27+043541.4 and J221806.67+005223.6) were chosen because they lie in fields already surveyed for galaxies by the VVDS survey (Le Fèvre et al. 2005, 2013). For our purposes, we use a subsample of the whole VVDS survey, selecting only galaxies in those fields. We refer the reader to Le Fèvre et al. (2005) and Le Fèvre et al. (2013) for details on the data reduction and construction of these galaxy catalogues.

Redshift reliability

The redshift reliability for VVDS data was originally based on six categories: (0) ‘no redshift’, (1) ‘50 per cent confidence’; (2) ‘75 per cent confidence’; (3) ‘95 per cent confidence’; (4) ‘100 per cent confidence’; (8) ‘single emission line’ and (9) ‘single isolated emission line’ (Le Fèvre et al. 2005, 2013). They expanded this classification system for secondary targets (objects which are present by chance in the slits) by the use of the prefix ‘2’. Similarly, the prefix ‘1’ means ‘primary QSO target’, while the prefix ‘21’ means ‘secondary QSO target’. In order to have a unified scheme, we matched those VVDS labels with our previously defined VIMOS ones (see Section 3.1.5) as follows: VVDS label 4, 3 and their corresponding extensions are matched to label ‘a’ ({4,14,24,214,3,13,23,213}→ {‘a’}); VVDS labels 2, 9 and their corresponding extensions are matched to label ‘b’ ({2,12,22,212,9,19,29,219}→ {‘b’}) and VVDS labels 1, 0 and their corresponding extensions are matched to label ‘c’ ({1,11,21,211,0,10,20,210}→ {‘c’}).

Consistency check between our VIMOS and VVDS sample

We performed a consistency check by comparing the redshifts and R-band magnitudes obtained for galaxies in common between our VIMOS sample and the VVDS survey in fields J1005 and J2218 (the only ones with such an overlap). We found a good agreement in redshift measurements between the two surveys, with a mean of the distribution being ≈0.0003 and a standard deviation of σ_Δz ≈ 0.001. This standard deviation is consistent with the quadratic sum of the typical VVDS uncertainty (⁠|${\sim } 0.0013/\sqrt{2}$|⁠) and our VIMOS one (⁠|${\sim } 0.0006/\sqrt{2}$|⁠), as |${\sim } \sqrt{0.0006^2+0.0013^2}/\sqrt{2} \approx 0.001$|⁠. In order to place all galaxies in a single consistent frame, we shifted the VVDS redshifts by 0.0003. The left-hand panel of Fig. 4 shows the distribution of these redshift differences after applying the correction.

The right-hand panel of Fig. 4 shows the distribution of R-band magnitude differences. We also see a good agreement in the magnitude difference distribution (by construction, see Section 3.1), with a mean of ≈0.006 and a standard deviation of σ_ΔR ≈ 0.09. We note that this standard deviation is greater than |$\sqrt{2}$| times the typical magnitude uncertainty as given by SExtractor of ∼0.02. Thus, we caution the reader that our reported R-band magnitude uncertainties might be underestimated by a factor of ∼3.

GDDS

One of the QSOs presented in this paper (namely: J020930.7−043826) was chosen because it lies in a field already surveyed for galaxies by the GDDS survey. For our purposes, we use a subsample of the whole GDDS survey selecting only galaxies in this field. We refer the reader to Abraham et al. (2004) for details on data reduction and construction of this galaxy catalogue.

Redshift reliability

The redshift reliability for GDDS data was originally based on five subjective categories: (0) ‘educated guess’, (1) ‘very insecure’; (2) ‘reasonably secure’ (two or more spectral features); (3) ‘secure’ (two or more spectral features and continuum); (4) ‘unquestionably correct’; (8) ‘single emission line’ (assumed to be O ii) and (9) ‘single emission line’ (Abraham et al. 2004). In order to have a unified scheme, we matched those GDDS labels with our previously defined VIMOS ones (see Section 3.1.5) as follows: GDDS label 4 and 3 are matched to label ‘a’ ({4,3}→ {‘a’}); GDDS labels 2, 8 and 9 are matched to label ‘b’ ({2,8,9}→ {‘b’}); and GDDS labels 1 and 0 are matched to label ‘c’ ({1,0}→ {‘c’}).

IGM SAMPLES

Absorption-line search

The search of absorption-line systems in the continuum normalized QSO spectra was performed manually (eyeballing), based on an iterative process described as follows: (i) we first searched for all possible features (H i and metal lines) at redshift z = 0 and z_QSO, and labelled them accordingly. (ii) We then searched for strong H i absorption systems, from z = z_QSO until z = 0, showing at least two transitions (e.g. Lyα and Lyβ or Lyβ and Lyγ, and so on). This last condition allowed us to identify (strong) H i systems at redshifts greater than z > 0.477 even for spectra without NUV coverage (λ > 1795 Å). (iii) When an H i system is found, we labelled all the Lyman series transitions accordingly and looked for possible metal transitions at the same redshift. (iv) We then performed a search for ‘high-ionization’ doublets (namely: Ne viii, O vi, N v, C iv and Si iv), from z = z_QSO until z = 0, independently of the presence of H i. (v) We assumed the remaining unidentified features to be H i Lyα and repeated step (iii), unless there is evidence indicating otherwise (e.g. no detection of the Lyβ transition when the spectral coverage and S/N would allow it). For all of the identified transitions, we set initial guesses in number of velocity components, column densities and Doppler parameters, for a subsequent Voigt profile fitting.

This algorithm allowed us to identify the majority but not all the absorption-line systems observed in our QSO spectral sample. The remaining unidentified features are typically very narrow and inconsistent with being H i (assuming a minimum temperature of the diffuse IGM of T ∼ 10⁴ K, implies a |$b_{\rm H\,\small {I}}\sim 10$| km s⁻¹; e.g. Davé et al. 2010), so we are confident that our H i sample is fairly complete.

Voigt profile fitting

We fit Voigt profiles to the identified absorption-line systems using vpfit.¹² We accounted for the non-Gaussian COS line spread function (LSF), by interpolating between the closest COS LSF tables provided by STScI¹³ at a given wavelength. We used the guesses provided by the absorption-line search (see Section 4.1) as the initial input of vpfit, and modified them when needed to reach satisfactory solutions. For intervening absorption systems, we kept solutions having the least number of velocity components needed to minimize the reduced χ².¹⁴ For fitting H i systems, we used at least two spectral regions associated with their Lyman series transitions when the spectral coverage allowed it. This means that for H i systems showing only Lyα transition, we also included their associated Lyβ regions (even though they do not show evident absorption) when available. This last step provides confident upper limits to the column density of these systems. For strong H i systems, we used regions associated with as many Lyman series transitions as possible, but excluding spectral regions of poor S/N (S/N ≲ 1). We refer the reader to Finn et al. (in preparation) for further details on the Voigt profile fitting process.

In the following, we will present only results for H i systems; a catalogue of metal systems will be published elsewhere.

Absorption-line reliability

For each H i absorption system, we assigned a reliability flag. We used a scheme based on three labels.

• Secure (‘a’): systems at redshifts that allow the detection of either Lyα and Lyβ or Lyβ and Lyγ transitions in a given spectrum, whose |$\log N_{\rm H\,\small {I}}$| values are greater than 30 times their uncertainties as quoted by vpfit.

• Probable (‘b’): systems at redshifts that only allow the detection of the Lyα transition in a given spectrum, whose |$\log N_{\rm H\,\small {I}}$| values are greater than 30 times their uncertainties as quoted by vpfit.

• Uncertain (‘c’): systems at any redshift, whose |$\log N_{\rm H\,\small {I}}$| values are smaller than 30 times their uncertainties as quoted by vpfit. Systems in this category will be excluded from the correlation analyses presented in this paper.

Consistency check of subjective steps

The whole process of finding and characterizing IGM absorption lines involves subjective steps. We checked that this fact does not affect our final results by comparing redshift, column density and Doppler parameter values for H i systems obtained independently – including the continuum fitting – by two of the authors (NT versus CWF) in the J020930.7−043826 QSO spectrum. We found values consistent with one another at the 1σ level in ∼90 per cent of cases for |$\log N_{\rm H\,\small {I}}$| and |$b_{\rm H\,\small {I}}$|⁠, and in 100 per cent of cases for redshifts. The vast majority of discrepancies were driven by weak absorption systems close to the level of detectability, for which the differences in the continuum fitting are more important.

N_HI and b_HI distributions and completeness

In Fig. 5 we show the observed H i column density (⁠|$N_{\rm H\,\small {I}}$|⁠; left-hand panel) and Doppler parameter (⁠|$b_{\rm H\,\small {I}}$|⁠; middle panel) distributions for ‘secure’ systems (‘a’ label; black solid lines), ‘secure’ plus ‘probable’ systems (‘a+b’ labels; dashed black lines) and ‘uncertain’ systems (‘c’ label; dotted red lines; see Section 4.3). We see sudden decreases in the number of systems at |$N_{\rm H\,\small {I}} \lesssim 10^{13}$| cm⁻² and |$b_{\rm H\,\small {I}} \lesssim 10$| km s⁻¹, which indicate the observational completeness limits of our sample and/or our selection (shown as grey shaded areas in Fig. 5).

Theoretical results point out that the H i column density distribution is well described by a power law of the form |$f(N_{\rm H\,\small {I}}) \propto N_{\rm H\,\small {I}}^{-\beta }$| with β ∼ −1.7-1.8, extending significantly below ∼10¹³ cm⁻² (e.g. Theuns et al. 1998; Paschos et al. 2009; Davé et al. 2010; Tepper-García et al. 2012). This has been observationally confirmed from higher S/N data (S/N ∼ 20-40) at least down to |$N_{\rm H\,\small {I}} \sim 10^{12.3}$| cm⁻² (Williger et al. 2010). Our current |$N_{\rm H\,\small {I}}$| completeness limit is therefore not physical, and driven by the S/N of our sample. Indeed, using the results from Keeney et al. (2012), the expected minimum rest-frame equivalent width for H i lines detected in the FUV-COS – in which the majority of weak lines are detected – at the 3σ confidence level (c.l.), for our typical S/N (S/N ∼ 10; see Table 2), is ∼40 mÅ. This limit corresponds to |$N_{\rm H\,\small {I}} \sim 10^{13}$| cm⁻² for a typical Doppler parameter of |$b_{\rm H\,\small {I}} \sim 30$| km s⁻¹, which is consistent with what we observe.

The same theoretical results point out that the H i Doppler parameter distribution for the diffuse IGM peaks at ∼ 20-40 km s⁻¹, with almost negligible contribution of lines with |$b_{\rm H\,\small {I}} < 10$| km s⁻¹ (Paschos et al. 2009; Davé et al. 2010; Tepper-García et al. 2012). Given that the FUV-COS data have spectral resolutions of about ∼16 km s⁻¹, these samples should include the vast majority of real H i systems at |$N_{\rm H\,\small {I}} \gtrsim 10^{13}$| cm⁻². On the other hand, the NUV-COS and FOS data (see Table 2) have spectral resolutions of about ∼100 km s⁻¹, which introduces some unresolved lines. Unresolved blended systems also add some unphysically broad lines in all our data. This observational effect explains, in part, the tail at large |$b_{\rm H\,\small {I}}$| (see middle panel of Fig. 5). We note that very broad lines can also be explained by physical mechanisms, such as temperature, turbulence, Jeans smoothing and Hubble flow broadenings (e.g. Rutledge 1998; Hui & Rutledge 1999; Theuns, Schaye & Haehnelt 2000; Davé et al. 2010; Tepper-García et al. 2012). There are a total of 58/766 ∼ 8 per cent of systems with |$b_{\rm H\,\small {I}} \ge 80$| km s⁻¹. Such a small fraction does not affect our results significantly.

We also note that the typical |$b_{\rm H\,\small {I}}$| uncertainties are of the order of ∼10 km s⁻¹, and so scatter of a similar amount is expected in the |$b_{\rm H\,\small {I}}$| distributions. This explains the presence of lines with |$b_{\rm H\,\small {I}} \lesssim 10$| km s⁻¹, all of which are consistent with 10 km s⁻¹ within the errors. However, as we do not use the actual |$b_{\rm H\,\small {I}}$| values in any further analysis, this uncertainty does not affect our results.

The right-hand panel of Fig. 5 shows the distribution of |$b_{\rm H\,\small {I}}$| as a function of |$\log N_{\rm H\,\small {I}}$| for ‘secure’ plus ‘probable’ systems (‘a+b’ labels; grey circles) and ‘uncertain’ systems (‘c’ label; red open triangles; uncertainties not shown). We see that there are not strong correlations between these values, apart from the presence of the upper and lower |$b_{\rm H\,\small {I}}$| envelopes. The upper envelope is consistent with an observational effect, as higher |$N_{\rm H\,\small {I}}$| values are required to observe lines with larger |$b_{\rm H\,\small {I}}$|⁠, for a fixed S/N (e.g. Paschos et al. 2009; Williger et al. 2010). The lower envelope is consistent with a physical effect, driven by the temperature–density relation of the diffuse IGM: H i systems with larger |$N_{\rm H\,\small {I}}$| probe, on average, denser regions for which the temperature – a component of the |$b_{\rm H\,\small {I}}$| – is also, on average, larger (e.g. Hui & Gnedin 1997; Schaye et al. 1999; Theuns et al. 1999; Paschos et al. 2009; Davé et al. 2010; Tepper-García et al. 2012). A proper analysis of these two effects is beyond the scope of this paper.

Column density classification

One of our goals is to test whether the cross-correlation between H i absorption systems and galaxies depends on H i column density. To do so, we split our H i sample into subcategories based on a column density limit. We define ‘strong’ systems as those with column densities |$N_{\rm H\,\small {I}} \ge 10^{14}$| cm⁻², and ‘weak’ systems as those with |$N_{\rm H\,\small {I}} < 10^{14}$| cm⁻². The transition column density of 10¹⁴ cm⁻² is somewhat arbitrary but was chosen such that: (i) the H i–galaxy cross-correlation for ‘strong’ systems and the galaxy–galaxy autocorrelation have similar amplitudes and (ii) the ‘strong’ systems sample is large enough to measure the cross-correlation at relatively high significance. A larger column density limit (e.g. ∼10^{15 − 16} cm⁻²) does indeed give a stronger H i–galaxy clustering amplitude, but it also increases the noise of the measurement.

We note that there might not necessarily be a physical mechanism providing a sharp lower |$N_{\rm H\,\small {I}}$| limit for the H i–galaxy association. However, recent theoretical results (e.g. Davé et al. 2010) suggest that there might still be a physical meaning for such a column density limit. We will discuss more on this issue in Section 8.2.5.

Summary

Our IGM data are composed of HST data from COS and FOS instruments taken on eight different QSOs (see Table 1 and 2). We have split our H i absorption-line system sample into ‘strong’ and ‘weak’ based on a column density limit of 10¹⁴ cm⁻². Our survey is composed of a total of 669 well-identified (i.e. ‘a’ or ‘b’) H i systems with N ≳ 10¹³ cm⁻².¹⁵ Table 4 shows a summary of our H i survey. Tables A1 to A8 present the survey in detail.

GALAXY SAMPLES

In this section, we describe our galaxy samples. In the following, we will refer to our new galaxy surveys in terms of the instrument used (VIMOS, DEIMOS and GMOS), to distinguish them from the VVDS or GDDS surveys.

Spectral type classification

One of our goals is to test whether the cross-correlation between H i absorption systems and galaxies depends on the galaxy spectral type (either absorption- or emission-line dominated; e.g. Chen et al. 2005; Chen & Mulchaey 2009). To do so, we need to classify our galaxy sample accordingly.

We took a conservative approach by considering only two galaxy subsamples: those which have not undergone important star formation activity over their past ∼1 Gyr and those which have. In terms of their spectral properties, the former type has to show a strong D4000 break and no significant emission lines (including Hα and [O ii]). The latter type are the complementary galaxies, i.e. those with measurable emission lines. We henceforth name these subsamples as ‘non-star-forming’ (‘non-SF’) and ‘star-forming’ (‘SF’) galaxies, respectively, deliberately avoiding the misleading terminology of ‘early’ and ‘late’ types. Summarizing,

• Non-SF galaxies: those galaxies which show no measurable star formation activity over their past ≳1 Gyr (e.g. early, bulge, elliptical, red luminous galaxy and S0 templates).

• SF galaxies: those galaxies which show evidence of current or recent (≲1 Gyr) star formation activity (e.g. late, Sa, Sb, Sc, SBa, SBb, SBc and starburst templates).

We note that we are not classifying galaxies on morphology, even though the template names might suggest that. Our classification is based solely on the presence or absence of spectral features associated with star formation activity. As an example, Fig. 6 shows eight galaxies with a variety of S/N, redshifts, redshift reliabilities and spectral classifications.

This template matching scheme was used only for our VIMOS and GMOS galaxies because in both the redshifts were determined using template matches. For the rest of our data, we used different approaches, described in the following sections.

DEIMOS data

The DEIMOS reduction pipeline provides three weights from a principal component analysis: w₁ (‘absorption like’), w₂ (‘emission like’) and w₃ (‘star like’). Thus, for DEIMOS data we use these weights to define SF and non-SF galaxies as follows: if max (fw₁, w₂) = fw₁ we assigned that object to be a ‘non-SF’ galaxy; if max (fw₁, w₂) = w₂ we assigned that object to be an ‘SF’ galaxy; and if z < 0.005 we assigned that object to be a ‘star’ (this last condition takes precedence over the previous ones). We used f = 0.2 to be conservative in the definition of ‘non-SF’ galaxies. This value also minimizes the ‘uncertain-identification rate’ in field Q0107 (see below). We did not use the information provided by w₃ because we found seven objects with z > 0.005 (galaxies) showing max (w₁, w₂, w₃) = w₃, probably because of their low S/N spectra.

CFHT data

In the case of the CFHT survey, we did not perform a spectral type split, and so we will only use these galaxies for results involving the whole galaxy population. We note that there is a large overlap between our GMOS and the CFHT samples and that the CFHT sample is comparatively small (61 galaxies). Thus, this choice does not compromise our analysis.

VVDS data

In the case of the VVDS survey, we used a colour cut to split the sample into red and blue galaxies. We chose this approach because the current VVDS survey does not provide spectral classification for galaxies in the fields used in this work. We used a single colour limit of B − R = 2.15 (no ‘k-correction’ applied)¹⁶ to split our sample. Thus, galaxies with B − R < 2.15 were assigned to our ‘SF’ sample, whereas those with B − R ≥ 2.15 were assigned to our ‘non-SF’ sample. We chose this limit as it gives the same proportion of ‘non-SF’/‘SF’ galaxies as in the rest of our sample. Objects with no B − R colour measurement were left out of this classification, and so these will only contribute to the results involving the whole galaxy population.

GDDS data

The GDDS survey provides spectral classification based on three binary digits, each one referring to ‘young’ (‘100’), ‘intermediate-age’ (‘010’) and ‘old’ (‘001’) stellar populations (Abraham et al. 2004). The GDDS spectral classification also allowed for objects dominated by one or more types, so ‘101’ could mean that the object has strong D4000 break and yet some strong emission lines. In order to match GDDS galaxies to our spectral classification, we proceeded in the following way. Galaxies classified as ‘old’ were matched to our ‘non-SF’ sample ({‘001’}→ {‘non-SF’ }); and galaxies classified as not being ‘old’ were matched to our ‘SF’ sample ({|$\not=$|‘001’}→ {‘SF’ }).

Uncertainty in the spectral classification scheme

We quantified the uncertainty in this spectral classification by looking at the ‘uncertain-classification rate’, i.e. the fraction of (duplicate) galaxies that were not consistently classified as either ‘SF’ or ‘non-SF’ over the total number of (duplicate) galaxies. For fields J1005, J1022 and J2218 this uncertain classification rate corresponds to 11/667 ∼ 2 per cent. None of these uncertainly classified galaxies show redshift differences ≳ 0.005 (catastrophic). For the Q0107 field, this uncertain-classification rate corresponds to 25/280 ∼ 9 per cent. From these, 4/25 show redshift differences ≳ 0.005, all of which are galaxies labelled as ‘b’ (‘possible’); and 19/25 were driven by observations using different instruments. The higher uncertain-identification rate for Q0107 is therefore mostly driven by the inhomogeneity of our samples.

For fields J1005 and J2218, we also checked whether the colour cut limit used to split the VVDS sample (see Section 5.1.3) gives consistency with the actual spectral classification of our VIMOS sample, for common objects observed by these two surveys. In this case, the uncertain-classification rate corresponds to 2/40 ∼ 5 per cent, all of which were conservative in the sense that the VVDS classification (uncertain) was ‘SF’ whereas the VIMOS one (reliable) was ‘non-SF’.

Treatment of duplicates

For objects observed with different instruments and/or showing different redshift confidences, we combined their redshift information considering the following priorities.

• Redshift label priority: we gave primary priority to redshifts labelled as ‘a’, ‘b’ and ‘c’, in that order.

• Instrument priority: we gave secondary priority to redshifts measured with DEIMOS, GMOS, VIMOS and CFHT, in that order. We based this choice on spectral resolution.

We therefore chose the redshift given by the highest priority and took the average when two or more observations had equivalent priorities. The spectral classification of uncertainly classified objects (i.e. being classified as both ‘SF’ and ‘non-SF’) was set to be ‘SF’, ensuring a conservative ‘non-SF’ classification.

Star/galaxy morphological separation

Our DEIMOS observations deliberately avoided star-like (unresolved) objects, based on the CLASS_STAR⁹ parameter provided by SExtractor (Section 3.2). We found that this selection misses a number of faint, unresolved galaxies and so it might introduce an undesirable bias selection (see also Prochaska et al. 2011a). This motivated our subsequent VIMOS and GMOS selection, for which no morphological criteria were imposed (see Section 3.1 and 3.3). Here, we summarize our findings regarding this issue.

The left-hand panel of Fig. 7 shows CLASS_STAR values as a function of R-band magnitude for objects with spectroscopic redshifts: ‘SF’ galaxies (big blue open circles), ‘non-SF’ galaxies (small red open triangles) and stars (small green squares). The sudden decrease of objects at R ∼ 22.5, 23.5 and 24.5 mag are due to our target selection (see Section 3). The fraction of ‘non-SF’ with respect to ‘SF’ galaxies is higher at brighter magnitudes (see Section 5.4). We see a bimodal distribution of objects having CLASS_STAR ∼0 (resolved) and CLASS_STAR ∼1 (unresolved). The vast majority of resolved objects are galaxies but some stars also fall in this category due to the non-uniform point spread function that varies across the imaging field of view. On the other hand, the vast majority of bright unresolved objects are stars, but a significant fraction of faint ones are galaxies. The right-hand panel of Fig. 7 shows a histogram of objects with CLASS_STAR ≥ 0.97 as a function of R-band magnitude. Such objects are typically excluded from galaxy spectroscopic surveys. We find unresolved galaxies over a wide range of magnitudes, but more importantly at R ≳ 21. At R ≳ 22 unresolved galaxies dominate over stars, and so a CLASS_STAR <0.97 criteria indeed introduces an undesirable selection bias. Even at magnitudes brighter than R ∼ 21, where the fraction of unresolved galaxies is small, this morphological bias is still undesirable for galaxy–absorber direct association studies. In our survey, 2(7) out of 33(82) R ≤ 21 (R ≤ 24) unresolved galaxies lie at ≤300 kpc (physical) from a QSO LOS which might have been left out based on a morphological selection. As mentioned, our DEIMOS survey is indeed affected by this selection effect, but our VIMOS and GMOS surveys are not, which allowed us to overcome this potential problem in all our fields, including Q0107.

Neither the VVDS nor the GDDS data are affected in this way. The VVDS survey targeted objects based only on magnitude limits, while the GDDS survey used photometric redshifts to avoid low-z galaxies, with no morphological criteria imposed.

Completeness

The completeness of a survey is defined as the fraction of detected objects with respect to the total number of objects that could be observed given the selection criteria. In the case of our galaxy survey, the completeness can be decomposed in: (i) the fraction of objects with successful redshift determination with respect to the total number of targeted objects; (ii) the fraction of targeted objects with respect to the total number of objects detected by SExtractor; and (iii) the fraction of objects detected by SExtractor with respect to the total number of objects that could be observed. In the following, we will focus only on the first of these terms for our new galaxy data. For the completeness of VVDS, GDDS and CFHT surveys, we refer the reader to Le Fèvre et al. (2005, 2013), Abraham et al. (2004) and Morris & Jannuzi (2006).

In Fig. 8, we show the success rate of assigning redshifts as a function of R-band apparent magnitude, for all objects (first column panels) and for galaxies and/or stars (second column panels). We present them separately for each of our new galaxy surveys because of their different selection functions. From top to bottom: VIMOS (J1005, J1022 and J2218), VIMOS (Q0107), DEIMOS (Q0107) and GMOS (Q0107). All of these fractions are computed for objects whose redshifts have been measured at high (label ‘a’, solid lines) and/or any confidence (label ‘a+b’, dashed lines). We see that our surveys have a ∼70–90 per cent success rate for objects with R ≲ 22 mag, and a ≲40 per cent success rate for objects with 22 ≲ R ≲ 24, except for our VIMOS survey of fields J1005, J1022 and J2218, which shows a ∼ 70-90 per cent success rate even for faint objects. As mentioned in Section 3 our VIMOS, GMOS and DEIMOS surveys were limited at R = 23–23.5, 24, 24.5, respectively, and so the small contribution of objects fainter than those limits correspond to untargeted objects that happened to lie within the slits. These objects correspond to a very small fraction of the total, and so we left them in. The higher success rate for brighter objects is expected given the higher S/N of those spectra. For objects brighter than R ∼ 22 mag, the fraction of identified galaxies is ≳50 per cent, and the fraction of identified stars varies: from ∼0 per cent in our DEIMOS survey (by construction; see Section 3.2), ≲10 per cent in our GMOS survey, to ∼20–10 per cent in our VIMOS surveys. The fraction of identified galaxies and stars at fainter magnitudes is ≲50 and 10 per cent, respectively.

Fig. 8 also shows how the galaxy completeness depends on our galaxy spectral type classification (see Section 5.1). The third and fourth column panels show the fraction of galaxies classified as ‘SF’ (blue lines) and ‘non-SF’ (red lines) over the total number of galaxies as a function of R-band magnitude and redshift, respectively. Excluding magnitude bins with <10 galaxies, we see that the fraction of ‘non-SF’ galaxies decreases with R-band apparent luminosity, consistent with the higher S/N spectra for the brighter objects. The fraction of ‘SF’ galaxies shows a flatter behaviour because the redshift determination depends more on the S/N of the emission lines than the S/N of the continuum. The fraction of ‘non-SF’ galaxies dominates over ‘SF’ ones at R ≲ 19 (see also left-hand panel Fig. 7), with a contribution of ∼50–70 per cent, although these bins have typically <20 objects. At fainter magnitudes (R ≳ 20), ‘SF’ galaxies dominate over ‘non-SF’ ones with a contribution of ∼60–90 per cent. Despite these magnitude trends, we see that our galaxy sample is dominated by the ‘SF’ type over the whole redshift range (except for the one galaxy observed at z > 1.4 in DEIMOS survey), as might have been expected from our conservative spectral classification (Section 5.1). ‘SF’ (‘non-SF’) galaxies account for ∼60–80 per cent (∼20–30 per cent) of the total galaxy fraction at z ≲ 1, with a mild decrease (increase) with redshift. This redshift trend is most apparent in our VIMOS survey of fields J1005, J1022 and J2218, which we explain as follows. The D4000 Å break becomes visible at 5500 Å for redshifts ∼0.4 and moves towards wavelength ranges of higher spectral quality (∼6000–7500 Å) at z ∼ 0.7–0.9. Simultaneously, Hα and [O iii] emission lines are shifted towards poor quality spectral ranges (≳ 8000 Å; due to the presence of sky emission lines) at z ∼ 0.2 and 0.6, and are out of range at z ≳ 0.4 and 0.8, respectively. At z ≳ 1 the only emission line available is [O ii] which explains the rise in the fraction of low-redshift confidence (‘b’ labels) ‘SF’ galaxies.

Summary

Our galaxy data are composed of a heterogeneous sample obtained from four different instruments (see Table 3), taken around eight different QSO LOS in six different fields (see Fig. 9 and Table 1). For fields with observations from more than one instrument, we have made sure that the redshift frames are all consistent. We have also split the galaxies into “SF’ and ‘non-SF’, based on either spectral type (for those lying close to the QSO LOS, i.e. VIMOS, DEIMOS, GMOS and GDDS samples) or colour (VVDS sample). Table 5 shows a summary of our galaxy survey. Tables A9 to A12 present our new galaxy survey in detail. We refer the reader to Le Fèvre et al. (2005, 2013), Abraham et al. (2004) and Morris & Jannuzi (2006) for retrieving the VVDS, GDDS and CFHT data, respectively.

Our final data set comprises 19588 (11133) galaxies with good (excellent) spectroscopic redshifts at z ≲ 1 around QSO LOS with 669 (453) good (excellent) H i absorption-line systems. This is currently the largest sample suitable for a statistical analysis on the IGM–galaxy connection to date.

CORRELATION ANALYSIS

The main goal of this paper is to address the connection between the IGM traced by H i absorption systems and galaxies in a statistical manner. To do so, we focus on a two-point correlation analysis rather than attempting to associate individual H i systems with individual galaxies.

The two-point correlation function, ξ(r), is defined as the probability excess of finding a pair of objects at a distance r with respect to the expectation from a randomly distributed sample.¹⁷ Combining the results from the H i–galaxy cross-correlation with those from the H i–H i and galaxy–galaxy autocorrelations for different subsamples of H i systems and galaxies, we aim to get further insights into the relationship between the IGM and galaxies.

Two-dimensional correlation measurements

Given that peculiar velocities add an extra component to the redshifts (in addition to cosmological expansion), our (X, Y, Z) will be affected differently, producing distortions even for actually true isotropic signals. This is because the X coordinate is parallel to the LOS, while the Y and Z coordinates are perpendicular to it. Let R(z) be the radial comoving distance at redshift z (equation 2) and Δθ a small (≪1) angular separation in radians. The transverse comoving separation can be then approximated by ≈R(z)Δθ, implying that our X coordinate will be affected by a factor of ≈1/Δθ times that of the Y and Z coordinates for a fixed redshift difference. As an example, a redshift difference of Δz = 0.0007 at z = 0.5 (≈140 km s⁻¹) will roughly correspond to a radial comoving difference of ≈2 Mpc, while only to a ≲0.02 Mpc difference in the transverse direction for comoving separations ≲20 Mpc. We therefore measured the auto and cross-correlations both along and transverse to the LOS, ξ(r_⊥, r_∥), independently. In terms of our Cartesian coordinates, we have that r_∥,ij ≡ |X_i − X_j| and |$r_{\perp ,ij} \equiv \sqrt{|Y_i - Y_j|^2 + |Z_i- Z_j|^2}$| are the along the LOS and transverse to the LOS distances between two objects at positions (X_i, Y_i, Z_i) and (X_j, Y_j, Z_j), respectively. Deviations from an isotropic signal in our (r_⊥, r_∥) coordinates can then be attributed to redshift uncertainties and peculiar velocities, including large-scale structure (LSS) bulk motions between the objects in the sample.

This approach makes the random samples a crucial component of the analysis. A detailed description of the random generator algorithms is presented in Section 6.2.

Another way to reduce the ‘shot noise’ is by using large bin sizes for counting the cross-pairs, but this will limit the spatial resolution of our ξ measurements. Therefore, we have chosen to compute the cross-pairs at scales r_⊥ < 10 Mpc using a linear grid of 0.5 Mpc in both (r_⊥, r_∥) coordinates and apply a Gaussian filter of 0.5 Mpc standard deviation (in both directions) to smooth the final counts distribution obtained from equation (13) before applying equations (4), (6) and (8). We treated the edges of the grid as if they were mirrors for the smoothing. As an example, Fig. 10 shows the number of cross-pairs between H i absorption systems and galaxies for our ‘Full Sample’ (defined in Section 7) using our adopted binning and smoothing.

An isotropic smoothing is desirable to avoid introducing artificial distortions, especially at the smallest scales. The use of a smoothing filter is justified by assuming that the underlying matter distribution that gives rise to H i absorption systems and galaxies (and hence to the data-data cross-pairs) is also smooth. Our approach offers a compromise between reducing the ‘shot noise’ while keeping a relatively small bin size. We caution though, that if the geometry of H i clouds does contain sharp edges at scales smaller than our adopted binning or smoothing length, then we would not be able to detect such a feature.

Random samples

One of the crucial steps for a correlation analysis is the construction of the random samples. In order to cancel out any possible bias, we preserved the sensitivity function of the real survey in our random samples. A detailed description of the random generator algorithms for H i absorption systems and galaxies is presented in the following sections.

Random absorption lines

We created random samples for individual observations made with a given instrument and/or instrument setting (i.e. resolution, wavelength coverage, etc.). This means that we treat the two channels of COS (FUV and NUV) independently for the creation of the random samples, and also for FOS. For a given absorption system with (RA, Dec., z_abs, |$N_{\rm H\,\small {I}}$|⁠, |$b_{\rm H\,\small {I}}$|⁠) we create α_abs random ones, varying the redshift but preserving the rest of its parameters.

Even though we have direct measurements of the equivalent widths for the real absorption systems, we do not use them directly in order to avoid confusion from blended systems. We use instead the approximation given by Draine (2011, see his equation 9.27) to convert the inferred |$N_{\rm H\,\small {I}}$| and |$b_{\rm H\,\small {I}}$| to a |$W_{\rm H\,\small {I}}^{\rm obs}$|⁠. Note that passing from |$W_{\rm H\,\small {I}} \rightarrow (N_{\rm H\,\small {I}},b_{\rm H\,\small {I}})$| is not always robust because of the flat part of the curve of growth, but passing from |$(N_{\rm H\,\small {I}},b_{\rm H\,\small {I}}) \rightarrow W_{\rm H\,\small {I}}$| is.

We mainly based our search of H i absorption systems on the Lyα transition (for which λ₀ = 1215.67 Å), but in some cases we extended it to Lyβ in spectral regions with no Lyα coverage. For the Lyβ detected systems, we applied the same method described above but changing the transition parameters accordingly.

Fig. 11 presents the redshift distribution of real (black lines) and random (red lines) absorbers in each of our independent fields using α_abs = 200.

Random galaxies

The random galaxies were created for each field and instrument independently. This means that we treat different galaxy surveys independently for the creation of the random samples, even when the galaxy surveys come from the same field. For a given observed galaxy with (RA, Dec., z_gal, magnitude, spectral type, etc.) we create α_gal random ones, varying the redshift, but preserving the rest of its parameters. This approach ensures the selection function is well matched by the random galaxies.

The random redshifts (⁠|$z_{\rm gal}^{\rm rand}$|⁠) were chosen based on the observed redshift distribution. We made sure that our randoms resembled the observed galaxy distribution independently of the observed magnitude of the galaxies. To do so, we selected multiple subsamples of galaxies at different magnitude bins, whose empirical redshift distributions are used as proxies for the redshift selection function. We used magnitude bins of size 1, shifted by 0.5 mag, ranging from 15 to 25. For the brighter and fainter ends of the subsamples we increased the magnitude bin sizes to ensure a minimum of 20 galaxies. For each magnitude subsample, we computed histograms using redshift bins of Δz = 0.01 (arbitrary), which were then smoothed with a Gaussian filter of standard deviation σ = 0.1 (roughly corresponding to a comoving scale of ≈300 Mpc at redshift z = 0.5). This large smoothing length is important to get rid of the LSS spikes and valleys present in the real redshift distributions. The final redshift probability distribution of a given magnitude bin is obtained by cubic spline interpolation over the smoothed histograms. Thus, for a given galaxy with observed magnitude m, we placed α_gal randoms according to the spline fit associated with the subsample of galaxies centred on the closest magnitude bin to m. We also imposed the redshifts of the random galaxies to lie between |$z_{\rm min}<z_{\rm gal}^{\rm random}<z_{\rm max}$|⁠, where z_min and z_max are the minimum and maximum galaxy redshifts of the real sample.

Fig. 12 presents the redshift distribution of real (black lines) and random (red lines) galaxies in each of our independent fields using α_gal = 20. Similarly, Fig. 13 presents the distribution in transverse separations of real (black lines) and random (red lines) galaxies with respect to their respective QSO LOS.

Projected correlations along the line of sight

Relations between auto- and cross-correlations

Adelberger et al. (2003) showed a third possibility: |$\xi _{\rm ag}^2$| exceeding ξ_ggξ_aa for correlation functions measured from discrete and volume limited samples. In the hypothetical case of an H i–galaxy one-to-one correspondence, then ξ_gg = ξ_aa, but ξ_ag will appear higher at the very small scales because in the case of autocorrelations we exclude the correlation of an object with itself, whereas in ξ_ag that correlation is present (Adelberger et al. 2003, see their appendix A). Such a behaviour between auto and cross-correlations will indicate that the two populations of objects are indeed the same physical entities. The geometry of our survey might not be suitable for testing this idea, as we are only mapping H i absorption systems along single LOS for which the completeness level of galaxies close to these absorbers is low. Still, we will bear this result in mind for the interpretation of our results.

Uncertainty estimation

As an example, Fig. 14 shows these four uncertainty estimations (square root of the variances) for our measurements of |$\xi _{\rm ag}^{\rm LS}(r_{\perp },r_{\parallel })$|⁠. From left to right: Δ_LS, Δ_JK, Δ_BS and Δ_DD. All these uncertainty estimations are within ∼1 order of magnitude consistent with each other, but systematic trends are present. Δ_LS and Δ_BS give the largest uncertainties while Δ_JK and Δ_DD give the smallest. We also observe that Δ_LS, Δ_JK and Δ_BS peak at the smallest scales (where the correlation amplitudes are greater) while Δ_DD does not. Similar behaviours are observed for the uncertainties associated with our |$\xi _{\rm gg}^{\rm LS}(r_{\perp },r_{\parallel })$| measurements (not shown).

Fig. 15 shows these four uncertainty estimations for our measurements of the projected correlations Ξ(r_⊥), for both H i–galaxy (squares) and galaxy–galaxy (circles): Δ_LS (green lines), Δ_JK (red lines), Δ_BS (blue lines) and Δ_DD (yellow lines). The top panel shows the absolute values for these different uncertainties, while the bottom panel shows the ratio of a given uncertainty estimation and Δ_BS. As before, we observe systematic trends, but all uncertainties are consistent within ∼1 order of magnitude of each other. In contrast to the two-dimensional uncertainties, Δ_BS is the largest in this case. Focusing on the smallest scales (where the correlation amplitudes are greater) we see that Δ_JK and Δ_LS are in closer agreement to Δ_BS than Δ_DD.

These results suggest that Δ_LS is preferable over Δ_DD and even over Δ_JK (at least when the number of independent fields is small, like in our case). A more in depth study of the error estimation for auto (e.g. Norberg et al. 2009) and cross-correlations is beyond the scope of this paper.

For the results of this paper, we will adopt uncertainties given by Δ_BS. As has been shown, Δ_BS gives, in general, the most conservative uncertainty estimation at all scales. An exception to this rule was found for ξ_aa(r_⊥, r_∥) and ξ_aa(r_⊥), in which Δ_LS > Δ_BS. This is due to the combination of the special survey geometry in which ξ_aa is measured. Thus, for such a sample we adopted Δ_LS as the uncertainty.

Calibration between galaxy and H i absorbers redshift frames

Before computing the final two-point correlation functions, we calibrated the redshift frames between our H i absorption systems and galaxies, using the idea presented by Rakic et al. (2011): that in an isotropic Universe, the mean H i absorption profile around galaxies should be symmetric. Thus, we measured the H i–galaxy cross-correlation using r_∥,ij ≡ X_i − X_j instead of r_∥,ij ≡ |X_i − X_j|, and applied a constant redshift shift to all our galaxies such that the cross-correlation appears symmetric with respect to the r_∥ = 0 axis at the scales involved in this analysis. This redshift shift corresponded to +0.0002 (smaller than the galaxy redshift uncertainty). Note that this shift has not been added to the redshifts reported in Tables A9 to A12. The final two-point correlation functions were still calculated using r_∥,ij ≡ |X_i − X_j| in order to reduce the ‘shot noise’.

RESULTS

In this section, we present the results of the two-point correlation analysis, following the formalisms described in Section 6. We used the H i and galaxy samples described in Sections 2–5, but excluding: (i) H i and galaxies falling in their respective ‘c’ categories (see Sections 3.1.6 and 4.3); (ii) H i and galaxies at z < 0.01 and at z > 1.3; (iii) H i systems at redshifts within 5000 km s⁻¹ of the redshift of the QSO in which the absorption line was observed; and (iv) galaxies at projected distances greater than 50 Mpc from the centre of their closest field. We will refer to this sample as the ‘Full Sample’, which comprises: 654 H i absorption systems, of which, 165 are classified as ‘strong’ and 489 as ‘weak’ (see Section 4.6 for definitions); and 17 509 galaxies, of which, 8293 are classified as ‘SF’ and 1743 as ‘non-SF’ (see Section 5.1 for definitions).

Table 6 summarizes relevant information regarding our ‘Full Sample’. The following results were computed with random samples 200 times and 20 times larger than the real H i and galaxy samples, respectively. Even though we have galaxies up to 50 Mpc from the QSO LOS, we will focus only on clustering at scales r_⊥ < 10 Mpc, as at larger scales our results get considerably noisier. Galaxies at r_⊥ > 10 Mpc are still used for the galaxy–galaxy autocorrelation though. In the case of the H i–H i autocorrelation, we only focus on scales r_⊥ < 2 Mpc, as we have no data sampling larger transverse scales.

Two-dimensional correlations

Full sample

In Fig. 16, we show the two-dimensional correlation functions (top panels) and their respective uncertainties (bottom panels) for our ‘Full Sample’ of H i-absorption systems and galaxies. The first three panels, from left to right, show the H i–galaxy cross-correlation (⁠|$\xi _{\rm ag}^{\rm LS}$|⁠; equation 8), the galaxy–galaxy autocorrelation (⁠|$\xi _{\rm gg}^{\rm LS}$|⁠; equation 4) and the H i–H i autocorrelation (⁠|$\xi _{\rm aa}^{\rm LS}$|⁠; equation 6), respectively. We see that the amplitudes of ξ_ag and ξ_aa are comparable (within the uncertainties), whereas the amplitude of ξ_gg is greater than these two (see also Table 7). Also, the fact that both ξ_gg and ξ_ag peak at the smallest separations confirms that the redshift frames for H i absorption systems and galaxies are self-consistent (by construction; see Section 6.6). The decrease in the ξ_aa signal at the smallest r_∥ separations is because we cannot always resolve two real absorption systems separated by less than the typical width of an absorption feature. This width corresponds to ∼16 km s⁻¹ (∼100 km s⁻¹) for FUV (NUV) data, which in comoving distance correspond to ∼0.26 Mpc (∼1.6 Mpc) at z = 0.5.

Our sample of H i absorption systems is not large enough to measure ξ_ag or ξ_aa anisotropies at a high c.l. Still, we can obtain qualitative features by looking at the corresponding ‘isocorrelation’ contours. We observe deviations from an isotropic signal in both ξ_ag and ξ_gg. Apart from a decrease of the ξ_aa signal at the smallest r_∥ separations, we do not see significant anisotropies in ξ_aa. The typical uncertainty for our single galaxy redshift determination, |$\Delta z_{\rm gal} \approx 0.0006/\sqrt{2}$|⁠, is equivalent to ∼ 1.7-1.4 Mpc at z = 0.1-0.5, which corresponds to an ‘anisotropy ratio’ of ∼3 : 1 for pixels of 0.5 Mpc each. If the observed anisotropies are dominated by redshift uncertainties, we should expect the ξ_ag contours to be consistent with this ratio (neglecting the much smaller contribution from the H i redshift uncertainty) and the ξ_gg one to be ∼4 : 1 (greater by a factor of |$\sqrt{2}$|⁠). These expectations are consistent with what we see in our ‘Full Sample’ for the smallest scales, whereas for scales ≳4 Mpc the anisotropy looks somewhat reduced. We do not detect compression along the LOS at larger scales either (e.g. Kaiser 1987). The only anisotropy observed can be fully explained by galaxy redshift uncertainties.

The fourth panel of Fig. 16 shows the ratio, |$(\xi ^{\rm LS}_{\rm ag})^2/(\xi ^{\rm LS}_{\rm gg}\xi ^{\rm LS}_{\rm aa})$|⁠. We see that the majority of the bins at the smallest scales have values (ξ_ag)²/(ξ_ggξ_aa) < 1. This result suggests that, contrary to what is usually assumed, the population of H i absorption systems (as a whole) and galaxies do not linearly trace the same underlying dark matter distributions (see Section 6.4).

In the following, we will split the H i absorber sample into ‘strong’ (⁠|$N_{\rm H\,\small {I}} \ge 10^{14}$| cm⁻²) and ‘weak’ (⁠|$N_{\rm H\,\small {I}}< 10^{14}$| cm⁻²), and the galaxy sample into ‘SF’ and ‘non-SF’. In this way, we can isolate the contribution of each subpopulation of H i and galaxies to the correlation functions, and to the (ξ_ag)²/(ξ_ggξ_aa) ratio.

‘Strong’ H i systems and ‘SF’ galaxies

Fig. 17 is analogous to Fig. 16 but for ‘strong’ H i systems (⁠|$N_{\rm H\,\small {I}} \ge 10^{14}$| cm⁻²) and ‘SF’ galaxies. We see that in this case the ξ_ag, ξ_gg and ξ_aa are all comparable within the errors (see also Table 7). Anisotropy signals behave in the same way as for our ‘Full Sample’, i.e. they are dominated by our galaxy redshift uncertainty and with no detected compression along the LOS at large scales.

In this case, the ratio (ξ_ag)²/(ξ_ggξ_aa) is consistent with 1, suggesting that ‘SF’ galaxies and |$N_{\rm H\,\small {I}}$| ≥10¹⁴ cm⁻² systems do trace the same underlying dark matter distribution. The comparable clustering amplitudes may also indicate that they typically belong to dark matter haloes of similar masses. We will address these points more quantitatively in Section 7.2.

‘Strong’ H i systems and ‘non-SF’ galaxies

Fig. 18 shows the correlation functions for ‘strong’ H i systems (⁠|$N_{\rm H\,\small {I}} \ge 10^{14}$| cm⁻²) and ‘non-SF’ galaxies. In this case, ξ_ag, ξ_gg and ξ_aa are all comparable within the errors (see also Table 7), but ξ_gg appears systematically larger. As before, the anisotropy is dominated by the galaxy redshift uncertainty and no (significant) compression along the LOS at large scales is detected.

Interestingly, there is a displacement in the ξ_ag peak relative to the smallest bin. This signal also appears symmetric with respect to the r_∥ = 0 axis, after computing ξ_ag using r_∥,ij ≡ X_i − X_j (not plotted) instead of r_∥,ij ≡ |X_i − X_j|. We also checked that the signal remained using only ‘a’ labelled H i systems and galaxies. This suggests that this feature might be real. A similar (although more uncertain) feature was observed by Wilman et al. (2007), from their observation of the H i-‘absorption-line-dominated galaxy’ cross-correlation (see their fig. 4).¹⁹ Pierleoni, Branchini & Viel (2008) also reported a similar signal from hydrodynamical simulations (see their fig. 7), although their samples of H i and galaxies are not directly comparable to our ‘strong’ and ‘non-SF’ ones. A more detailed comparison between our results and those from previous studies will be presented in Section 8.1.

The ratio (ξ_ag)²/(ξ_ggξ_aa) seems also consistent with 1, which suggests that ‘non-SF’ galaxies and |$N_{\rm H\,\small {I}}$| ≥ 10¹⁴ cm⁻² systems trace the same underlying dark matter distribution linearly.

Comparing Figs. 17 and 18 we see that ξ_gg for ‘non-SF’ galaxies is larger than that of ‘SF’ galaxies (as has been shown by many authors). Given that ξ_aa is the same in both cases, one would expect ξ_ag to be also larger for ‘non-SF’ than that of ‘SF’ galaxies. Although within the uncertainties our results indicate that the ξ_ag amplitude is independent of galaxy type, we do see a somewhat larger cross-correlation signal for ‘non-SF’ galaxies (see Table 7). We will address these points more quantitatively in Section 7.2.

‘Weak’ H i systems and galaxies

Figs 19 and 20 show the two-dimensional correlation functions for ‘weak’ H i absorption systems (⁠|$N_{\rm H\,\small {I}} < 10^{14}$| cm⁻²) and ‘SF’ and ‘non-SF’ galaxies, respectively. These results are dramatically different than those for ‘strong’ H i systems and galaxies. In particular, ξ_ag is significantly weaker than ξ_gg but also weaker than ξ_aa, for both types of galaxies. Consequently, the ratios (ξ_ag)²/(ξ_ggξ_aa) are both smaller than 1. This is a very strong indication (given the comparatively smaller uncertainties) that the underlying baryonic matter distributions giving rise to ‘weak’ H i absorption systems and galaxies are not linearly dependent. Given that the signal in the ξ_ag is marginally consistent with zero, we do not observe anisotropies either.

To summarize, ‘strong’ systems and galaxies are consistent with tracing the same underlying dark matter distribution linearly, whereas ‘weak’ systems are not. Therefore, the fact that (ξ_ag)²/(ξ_ggξ_aa) < 1 in the ‘Full Sample’ should be primarily driven by the presence of H i systems with |$N_{\rm H\,\small {I}} < 10^{14}$| cm⁻². We also note that the amplitude of ξ_aa is weaker for ‘weak’ systems than that for ‘strong’ systems.

Because redshift uncertainties affect ξ_ag, ξ_gg and ξ_aa in different ways, the interpretation of the two-dimensional (ξ_ag)²/(ξ_ggξ_aa) is not straightforward. In the following, we present the results for the projected correlation functions, which are not affected by velocity distortions along the LOS, and have smaller statistical uncertainties.

Correlations projected along the line of sight

Full sample

Fig. 21 shows the projected (along the LOS; see equation 16) correlation functions divided by the transverse separation, Ξ(r_⊥)/r_⊥, for our ‘Full Sample’ of H i absorption systems and galaxies. Different symbols/colours show our different measurements: the blue squares correspond to the H i–galaxy cross-correlation (ξ_ag), the black circles to the galaxy–galaxy autocorrelation (ξ_gg) and the red triangles to the H i–H i autocorrelation (ξ_aa; slightly shifted along the x-axis for the sake of clarity). The lines correspond to the best power-law fits (equation 20) to the data, from a non-linear least-squares analysis. The parameters r₀ and γ correspond to those of the real-space correlation function, ξ(r), when described as a power law of the form presented in equation (19). Uncertainties in these fits include the variances and covariances of both parameters. From this figure, we see that a power-law fit is a good description of the data, hence justifying the use of equations (19) and (20).²⁰ Table 8 summarizes the best power-law fit parameters for our different samples.

We find that ξ_ag(r) has a correlation length of |$r_0^{\rm ag} = 1.6 \pm 0.2$| Mpc and slope γ^ag = 1.4 ± 0.1, whereas ξ_gg(r) and ξ_aa(r) have correlation lengths of |$r_0^{\rm gg} = 3.9 \pm 0.1$| Mpc and |$r_0^{\rm aa} = 0.3 \pm 0.3$| Mpc, and slopes γ^gg = 1.7 ± 0.1, γ^aa = 1.1 ± 0.1, respectively. Thus, the clustering of H i absorption systems and galaxies is weaker than the clustering of galaxies with themselves, and the clustering of H i systems with themselves is weaker still. We also see that the slopes are inconsistent with each other at the 1σ c.l., which is in tension with the assumption that these objects trace the same underlying dark matter distribution linearly (see Section 6.4). Moreover, the slope of the ξ_aa(r) is consistent with γ = 1, indicating that this distribution is at the limit in which the methodology adopted here is valid (see Section 6.3).

As was the case for the two-dimensional results, in the following we will split the H i and galaxy samples into ‘weak’ and ‘strong’, and ‘SF’ and ‘non-SF’, respectively, in order to isolate different contributions from these subpopulations into the observed correlations.

‘Strong’ H i systems and ‘SF’ galaxies

The top-left panel of Fig. 22 shows the projected correlation functions for our ‘strong’ H i systems (⁠|$N_{\rm H\,\small {I}} \ge 10^{14}$| cm⁻²) and ‘SF’ galaxies. In this case, we find that the ξ_ag(r) has a correlation length of |$r_0^{\rm ag} = 3.8 \pm 0.2$| Mpc and slope γ^ag = 1.7 ± 0.1, whereas ξ_gg(r) and ξ_aa(r) have correlation lengths of |$r_0^{\rm gg} = 3.9 \pm 0.1$| Mpc and |$r_0^{\rm aa} = 3.1 \pm 0.7$| Mpc, and slopes γ^gg = 1.6 ± 0.1, γ^aa = 1.3 ± 0.4, respectively (see also Table 8). Thus, all have correlation lengths and slopes agreeing with each other at the 1σ c.l. The fact that all have comparable correlation lengths and slopes supports the hypothesis that ‘strong’ H i systems and ‘SF’ galaxies do trace the same underlying dark matter distribution.

‘Strong’ H i systems and ‘non-SF’ galaxies

The bottom-left panel of Fig. 22 shows the projected correlation functions for our ‘strong’ H i systems (⁠|$N_{\rm H\,\small {I}} \ge 10^{14}$| cm⁻²) and ‘non-SF’ galaxies. In this case, we find that ξ_ag(r) has a correlation length of |$r_0^{\rm ag} = 4.0 \pm 0.3$| Mpc and slope γ^ag = 1.7 ± 0.1, whereas ξ_gg(r) has a correlation length of |$r_0^{\rm gg} = 6.2 \pm 0.2$| Mpc and slope γ^gg = 1.6 ± 0.1 (see also Table 8). The parameters for ξ_aa(r) are the same as in the previous case (see Section 7.2.2). The fact that the slopes are all consistent supports the idea that ‘strong’ H i systems and ‘non-SF’ galaxies also trace the same underlying dark matter distribution. This is an expected result in view of what was observed for the case of ‘strong’ H i systems and ‘SF’ galaxies, and because it is well known that ‘SF’ and ‘non-SF’ do trace the same underlying dark matter distribution. We also see that the galaxy–galaxy autocorrelation is significantly larger than the H i–galaxy cross-correlation and the H i–H i autocorrelation. The most simple explanation for such a difference is that the linear bias (see Section 6.4) of ‘non-SF’ is greater than that of ‘SF’ galaxies. This has been commonly interpreted as ‘non-SF’ galaxies belong, on average, to more massive dark matter haloes than ‘SF’ galaxies. The fact that the correlation length for the ‘strong’ H i–galaxy cross-correlation is (marginally) larger for ‘non-SF’ than ‘SF’ galaxies is also expected because the H i population is the same in both cases. However, we will see in Section 7.2.5 that this length is smaller than what is expected from the linear dependence hypothesis.

‘Weak’ H i systems and galaxies

The top-right panel of Fig. 22 shows the projected correlation functions for our ‘weak’ H i systems (⁠|$N_{\rm H\,\small {I}} < 10^{14}$| cm⁻²) and ‘SF’ galaxies. In this case, we find that ξ_ag(r) has a correlation length of |$r_0^{\rm ag} = 0.2 \pm 0.4$| Mpc and slope γ^ag = 1.1 ± 0.3, whereas ξ_aa(r) has a correlation length of |$r_0^{\rm aa} = 0.3 \pm 0.1$| Mpc and slope γ^aa = 1.0 ± 0.1 (see also Table 8). The parameters for ξ_gg(r) are the same as in Section 7.2.2. These results are dramatically different from those involving ‘strong’ H i systems. In particular for the H i–galaxy cross-correlation, not only is the power-law fit questionable, but also the correlation length is smaller than both galaxy–galaxy and H i–H i autocorrelations. Moreover, the correlation length of the cross-correlation is consistent with r₀ = 0, i.e. no correlation.

The results for ‘weak’ H i systems and ‘non-SF’ galaxies are even more dramatic. The bottom-right panel of Fig. 22 shows the projected correlation functions for these samples. In this case, we find that ξ_ag(r) has a correlation length of |$r_0^{\rm ag} = 0.0 \pm 0.8$| Mpc and slope γ^ag = 1.0 ± 1.6. Although consistent within errors with the ‘weak’ H i –‘SF’ galaxy cross-correlation, this correlation length is even smaller. This result goes in the opposite direction to what would be expected in the case of linear dependency, because the clustering of ‘non-SF’ galaxies with themselves is stronger than that of ‘SF’. Therefore, these results are a strong indication that ‘weak’ H i systems and galaxies do not trace the same underlying dark matter distribution linearly.

Ratio (ξ_ag)²/(ξ_ggξ_aa)

Fig. 23 shows the ratio (ξ_ag)²/(ξ_ggξ_aa) for our different samples. The black circles correspond to our ‘Full Sample’; blue and red symbols correspond to ‘SF’ and ‘non-SF’ galaxies, respectively; and the squares and triangles correspond to ‘strong’ (⁠|$N_{\rm H\,\small {I}} \ge 10^{14}$| cm⁻²) and ‘weak’ (⁠|$N_{\rm H\,\small {I}} < 10^{14}$| cm⁻²) H i absorption systems, respectively. The left-hand panel shows the results from our adopted Gaussian smoothing of 0.5 Mpc standard deviation. Given that the points are all correlated, we expected this ratio to be roughly independent of the scale, at least below ≲2 Mpc. Thus, we attribute the large variation seen in the left-hand panel of Fig. 23 to ‘shot noise’ and repeated the calculation using a Gaussian smoothing of 1 Mpc standard deviation. The right-hand panel of Fig. 23 show the results from this last calculation. We note that the smoothings were applied to the cross-pairs only, before calculating the different Ξ and the corresponding ratios (see Section 6 for details), and that the uncertainties were obtained directly from the ‘bootstrap’ resampling of our independent fields (see Section 6.5).

These results are consistent with what we found for the two-dimensional correlations. We see that the ‘Full Sample’ have ratios inconsistent with 1. Taking the bin at 1.25 Mpc as representative, we find that (ξ_ag)²/(ξ_ggξ_aa) ≈ 0.2 ± 0.2, which gives a high c.l. (>3σ) for ruling out the hypothesis of linear dependency between the underlying matter distribution giving rise to H i and galaxies. The same is true for our samples of ‘weak’ H i systems and ‘SF’ galaxies, for which (ξ_ag)²/(ξ_ggξ_aa) ≈ 0.0 ± 0.2. In the case of ‘weak’ H i systems and ‘non-SF’ galaxies, we find (ξ_ag)²/(ξ_ggξ_aa) ≈ 0.0 ± 0.3 which is also inconsistent with 1, but the significance is somewhat reduced. Apart from the fact that ‘weak’ systems and galaxies have this ratio inconsistent with 1, it is also interesting to note that all are consistent with 0. This result supports the conclusion that many ‘weak’ H i systems are not correlated with galaxies on scales ≲2 Mpc.

On the other hand, in the case of ‘strong’ H i systems and ‘SF’ galaxies, this ratio is (ξ_ag)²/(ξ_ggξ_aa) ≈ 1.1 ± 0.6. Thus, we find consistency with the linear dependency hypothesis, although with large uncertainty. The ratio for ‘strong’ H i systems and ‘non-SF’ is (ξ_ag)²/(ξ_ggξ_aa) ≈ 0.5 ± 0.3, which is consistent with neither 1 nor 0 (at least at the 1σ c.l.). Given the large uncertainty in this case, no strong conclusion can be drawn. Still, if we believe this ratio to be <1, it would mean that a fraction of ‘non-SF’ galaxies would not be correlated with ‘strong’ H i systems either. This fraction can be estimated from the actual value of (ξ_ag)²/(ξ_ggξ_aa) (e.g. see Section 8.2.4).

Results assuming a fixed slope γ = 1.6

As mentioned in Section 6.4, if we assume that H i and galaxies do trace the same underlying dark matter distribution linearly, then we can use the different correlation lengths to obtain the relative linear biases between populations (e.g. Mo et al. 1993; Ryan-Weber 2006). For this method to work, we require the slopes of the correlation functions to be the same. Even though we have shown that this assumption is not always valid (at a >3σ c.l.), in this section we fix the slope of the real-space correlations and repeat the analysis. We do this for illustrative purposes, so these results should not be taken as conclusive.

Fig. 24 is the same as Fig. 22, but using a fixed slope of γ = 1.6. Judging from the plots, the fits work reasonably well for the galaxy–galaxy autocorrelations and the H i–galaxy cross-correlations for the ‘strong’ H i systems, but they fail to represent the H i–H i autocorrelations and the ‘weak’ H i–galaxy cross-correlations. These are expected results given what we observed in the previous analysis.

The bottom-left panel of Fig. 24 shows the results for our samples of ‘strong’ H i systems and ‘non-SF’ galaxies. We see that ξ_ag(r) has a correlation length of |$r_0^{\rm ag} = 3.8 \pm 0.2$| Mpc, whereas ξ_gg(r) has a correlation length of |$r_0^{\rm gg} = 6.2 \pm 0.1$| Mpc. The correlation length for ξ_aa(r) is the same as before. In contrast to the ‘SF’ case, the correlation length of ‘non-SF’ galaxies with themselves is significantly larger (>3σ c.l.). In this case, the ratio (ξ_ag)²/(ξ_ggξ_aa) ≈ 0.8 ± 0.1. Consequently, equation (28) is at the limit of its validity. Applying this equation, we find that b_g:b_a ∼ 1.8–2.2.

The top-right panel of Fig. 24 shows the results for our samples of ‘weak’ H i systems and ‘SF’ galaxies. We see that ξ_ag(r) has a correlation length of |$r_0^{\rm ag} = 1.1 \pm 0.1$| Mpc, and ξ_aa(r) also has |$r_0^{\rm aa} = 1.1 \pm 0.1$| Mpc. The correlation length for ξ_gg(r) is the same as previously mentioned (two paragraphs above). In this case, the ratio (ξ_ag)²/(ξ_ggξ_aa) ≈ 0.3 ± 0.1. Consequently, equation (28) should not hold. Still, if we apply this equation anyway, we find that b_g: b_a ∼ 2.6-7.6.

The bottom-right panel of Fig. 24 shows the results for our samples of ‘weak’ H i systems and ‘non-SF’ galaxies. We see that ξ_ag(r) has a correlation length of |$r_0^{\rm ag} = 0.1 \pm 0.5$| Mpc. The parameters for ξ_aa(r) and ξ_gg(r) are the same as previously mentioned (one and two paragraphs above, respectively). In this case, the ratio (ξ_ag)²/(ξ_ggξ_aa) ≈ 0.0 ± 0.1. Consequently, equation (28) should not hold either. Still, if we apply this equation, we find that b_g: b_a ∼ 4–700.

Consistency checks

In order to check whether our results are robust, we have repeated the analysis using only H i systems and galaxies in their respective ‘a’ categories (i.e. best quality; see Sections 3.1.6 and 4.3). We found qualitative agreement with all our previous results, but a systematic increase in the correlation amplitudes by ≲10 per cent (with larger statistical uncertainties) was observed. Such a difference is expected due to the presence of random contamination in our ‘Full Sample’ (e.g. catastrophic failures, missidentification of H i systems, etc.). Still, within the uncertainties, the results from both analyses are fully consistent.

We also checked the effect of the Gaussian smoothing by repeating the analysis without smoothing at all (but still using the same linear grid). As expected, the new results for r₀ and γ had increased statistical uncertainties but were all consistent with our previously reported values. We note that the slopes obtained from this new analysis were systematically larger by ∼10 per cent in most of the cases, but a ∼30 per cent increase was found for γ^aa and γ^ag in samples involving ‘weak’ H i systems.

DISCUSSION

Comparison with previous results

In this section, we compare our results with those published in other recent studies considering the H i–galaxy two-point correlation function at z ≲ 1.²¹

Comparison with Ryan-Weber (2006) results (z ∼ 0)

Ryan-Weber (2006) measured the H i–galaxy cross-correlation at z < 0.04 using H i data from the literature (Impey, Petry & Flint 1999; Penton, Shull & Stocke 2000; Bowen, Pettini & Blades 2002; Penton, Stocke & Shull 2004; Williger et al. 2006) and galaxy data from the H i Parkes All Sky Survey (HIPASS; Doyle et al. 2005). Their total sample comprised 129 H i absorption systems with |$10^{12.5} \lesssim N_{\rm H\,\small {I}} \lesssim 10^{15}$| cm⁻², from 27 QSO LOS, and 5317 gas-rich galaxies.

Our results are in contrast with theirs. First, they found a strong ‘finger-of-god’ signal in the two-dimensional H i–galaxy cross-correlation, extending up to ∼10 |$h^{-1}_{100}$| Mpc (see their fig. 3), corresponding to an ‘anisotropy ratio’ of ∼10 : 1. This anisotropy signal is also larger than they observed for the galaxy–galaxy auto- correlation (see their fig. 2), meaning that it cannot be explained by the galaxy redshift uncertainties. This result is in contrast to ours in that we do not see such a significant ‘finger-of-god’ signal, and the only anisotropy that we observe is consistent with being due to the galaxy redshift uncertainty.

Another difference between our results and theirs is the correlation length of the real-space correlations. They found |$r_0^{\rm ag} = 7.2 \pm 1.4$| |$h^{-1}_{100}$| Mpc (which in our adopted cosmology corresponds to |$r_0^{\rm ag} \approx 10.3 \pm 2.0$| |$h^{-1}_{70}$| Mpc) imposing γ^ag to be equal to that of the ξ_gg(r), γ^ag ≡ γ^gg = 1.9 ± 0.3. Although the slope is marginally consistent with what we find (see Section 7.2), the correlation length is more than 3σ c.l. larger than any of our values. If we set the slope of our correlations to be γ = 1.9, then we do not find consistency either (also note that a power-law fit for such a slope is not a good representation of our data). Ryan-Weber (2006) used this result to rule out ‘mini haloes’ for the confinement of H i absorption systems. In view of our new results, we consider that this conclusion must be revisited (see Section 8.2.6).

Another intriguing result from Ryan-Weber (2006) is the fact that the amplitude of ξ_ag(r) is greater than that of ξ_gg(r). They found a ξ_gg(r) correlation length of |$r_0^{\rm gg} = 3.5 \pm 0.7$| |$h^{-1}_{100}$| Mpc (≈5.0 ± 1.0 |$h^{-1}_{70}$| Mpc), which is somewhat larger but marginally consistent with our findings. In order to explain the larger |$r_0^{\rm ag}$| value with respect to |$r_0^{\rm gg}$|⁠, ξ_aa(r) should be greater than both ξ_gg(r) and ξ_ag(r). This hypothesis is difficult to understand within the current cosmological paradigm, and in fact, it is not supported by our results on the H i–H i autocorrelation either.

We note that the surveys have important differences, in particular regarding the galaxy samples. HIPASS selected galaxies based on H i emission, i.e. containing significant amounts of neutral gas. It also includes low surface brightness galaxies that might be lacking in ours. The clustering of these galaxies is expected to be lower than that of brighter galaxies in our sample though, which goes in the opposite direction of what is needed to reconcile our results with those of Ryan-Weber (2006). The much lower redshift range in their sample might also have an impact on the clustering, as structures are more collapsed. This might help to increase the correlation lengths, but it should not make the ξ_ag(r) amplitude greater than ξ_gg(r) by itself. Another possibility is that this might be a case in which the ratio (ξ_ag)²/(ξ_ggξ_aa) > 1, meaning that the H i and galaxies observed actually correspond to the same physical objects (see Section 6.4). Such an effect should be most noticeable at the smallest scales, but this is not supported by their results. Indeed, there is a flattening in their reported Ξ_ag(r_⊥)/r_⊥ at ≲1 |$h^{-1}_{100}$| Mpc (see their fig. 5) which makes the H i–galaxy cross-correlation consistent with the galaxy–galaxy autocorrelation at these scales.²²

Comparison with Wilman et al. (2007) results (z ≲ 1)

Wilman et al. (2007) measured the H i–galaxy cross-correlation at z ≲ 1 using data from Morris & Jannuzi (2006). Their total sample comprised 381 H i absorption systems with |$10^{13} \lesssim N_{\rm H\,\small {I}} \lesssim 10^{19}$| cm⁻², from 16 QSO LOS and 685 galaxies at ≲2 |$h^{-1}_{100}$| Mpc from the QSO LOS, of which, 225 were classified as ‘absorption-line dominated’ and 406 as ‘emission-line dominated’.

We find qualitative agreement with their observational results in the following sense: (i) no strong ‘finger-of-god’ effect is seen in the observed H i–galaxy cross-correlation; (ii) the larger the |$N_{\rm H\,\small {I}}$|⁠, the stronger the clustering with galaxies; and (iii) no evidence that ‘emission-line-dominated’ galaxies cluster more strongly with H i systems than ‘absorption-line-dominated’ ones (in contrast to what was reported by Chen & Mulchaey 2009, see below).

Wilman et al. (2007) also performed a comparison with a cosmological hydrodynamical simulation. In contrast to their observational results, they did find a strong ‘finger-of-god’ effect (similar to that found by Ryan-Weber 2006) in their simulated data (see their fig. 6). This prediction is not supported by our observations, as we do not detect such a strong anisotropy feature.

Comparison with Pierleoni et al. (2008) results (simulations)

Pierleoni et al. (2008) investigated the observational results from Ryan-Weber (2006) and Wilman et al. (2007) in the context of a cosmological hydrodynamical simulation. They selected samples of simulated H i absorption systems and galaxies, trying to match those from Ryan-Weber (2006).

Contrary to the Ryan-Weber (2006) observational results (and the prediction from Wilman et al. 2007), they did not find a strong ‘finger-of-god’ signal in the mock H i–galaxy cross-correlation (see their fig. 7), which agrees with our observational result. In contrast, they find a compression along the LOS at scales ≳4 |$h^{-1}_{100}$| Mpc, similar to the expectation from the ‘Kaiser effect’ (Kaiser 1987). We did not detect such a feature but note that our survey was not designed to do so.

They also found that the peak in the two-dimensional H i–galaxy cross-correlation was offset along the LOS by about ∼1 |$h^{-1}_{100}$| Mpc. A similar signal was observed in our sample of ‘strong’ H i systems and ‘non-SF’ galaxies (see Fig. 18), but these two results are not directly comparable. Indeed, we do not observe such a feature in our ‘Full Sample’. Still, we caution the reader that a ∼1 |$h^{-1}_{100}$| Mpc displacement in the LOS direction is comparable to our galaxy redshift uncertainty ( ∼ 1.4-1.7 |$h^{-1}_{70}$| Mpc), and so such a signal might get easily diluted.

Another qualitative agreement between our results and those from Pierleoni et al. (2008) is that the amplitude of the H i–galaxy cross-correlation is smaller than that of the galaxy–galaxy autocorrelation, and that the H i–H i autocorrelation is smaller still (see their figs 3 and 9). Quantitatively, they found that ξ_ag(r) and ξ_gg(r) have correlation lengths of |$r_0^{\rm ag} = 1.4 \pm 0.1$| |$h^{-1}_{100}$| Mpc (≈2.0 ± 0.1 |$h^{-1}_{70}$| Mpc) and |$r_0^{\rm gg} = 3.1 \pm 0.2$| |$h^{-1}_{100}$| Mpc (≈4.4 ± 0.2 |$h^{-1}_{70}$| Mpc), and slopes γ^ag = 1.29 ± 0.03 and γ^gg = 1.46 ± 0.03, respectively. These values are marginally consistent with our findings (see Table 8). Moreover, they predict a flattening of ξ_aa(r) at scales ≲1 |$h^{-1}_{100}$| Mpc, which is also consistent with our observations.

Finally, we also find agreement in the sense that the amplitude of the H i–galaxy cross-correlation significantly increases for high column density absorbers, but little variation is observed for different galaxy samples selected by mass (see their fig. 4). Even though we do not have direct measurements of galaxy masses in our galaxy samples, the significantly larger autocorrelation amplitude of ‘non-SF’ galaxies with respect to ‘SF’ suggests that, on average, ‘non-SF’ galaxies typically belong to more massive dark matter haloes than ‘SF’ galaxies (see also Section 8.2.6).

Comparison with Chen & Mulchaey (2009) results (z ≲ 0.5)

Chen & Mulchaey (2009) measured the H i–galaxy cross-correlation at z ≲ 0.5 from their own H i and galaxy survey (including data from Chen et al. 2005). Their total sample comprised 195 H i absorption systems with |$10^{12.5} \lesssim N_{\rm H\,\small {I}} \lesssim 10^{16}$| cm⁻², from 3 QSO LOS; and 670 galaxies at ≲4 |$h^{-1}_{100}$| Mpc from the QSO LOS, of which 222 are classified as ‘absorption-line dominated’ and 448 as ‘emission-line dominated’.

In this case, we find both agreements and disagreements. Our results agree with theirs in the sense that the clustering of ‘strong’ H i systems (⁠|$N_{\rm H\,\small {I}} \ge 10^{14}$| cm⁻²) with galaxies is stronger than that of ‘weak’ H i systems and galaxies (see their fig. 13), and that ‘strong’ H i systems and ‘emission-line-dominated’ galaxies have comparable clustering amplitudes. However, our results disagree with their claim that ‘strong’ H i systems cluster more strongly with ‘emission-line dominated’ than with ‘absorption-line dominated’ (see their fig. 13). In fact, our findings are consistent with the amplitude of the H i–galaxy cross-correlation being independent of spectral type (within the statistical uncertainties). Moreover, we find that the H i–galaxy cross-correlation for ‘non-SF’ galaxies is systematically stronger than that of ‘SF’ galaxies, which is the opposite to what Chen & Mulchaey (2009) found.

Quantitatively, they reported a ∼6 times smaller clustering amplitude between ‘strong’ H i absorption systems and ‘SF’ galaxies than that of ‘non-SF’ galaxies with themselves, whereas we find this difference to be a factor of ∼2 only. We note that their quoted statistical errors are Poissonian, which underestimate the true uncertainties. The Poissonian uncertainty in our survey is typically ∼1 order of magnitude smaller than our adopted ‘bootstrap’ one (see Section 6.5). Thus, there is still room for their results to agree with ours after taking this fact into account. There is also the possibility that sample/cosmic variance is significantly affecting their results. We note that one of the three QSO LOS used by them passes at ∼2  Mpc from the Virgo cluster. Even though this single cluster is not likely to explain the discrepancy, any sightline passing through it is also probing an unusually high overdensity in the local Universe (which extends beyond the Virgo cluster itself).

Comparison with Shone et al. (2010) results (z ∼ 1)

Shone et al. (2010) measured the H i–galaxy cross-correlation at 0.7 ≲ z ≲ 1.5 from their own H i and galaxy survey. Their total sample comprised 586 H i absorption systems with |$10^{13.2} \lesssim N_{\rm H\,\small {I}} \lesssim 10^{17}$| cm⁻², from 2 QSO LOS; and 193 galaxies at ≲4 |$h^{-1}_{70}$| Mpc from the QSO LOS (196 absorber–galaxy pairs used).

They found the peak in the two-dimensional H i–galaxy cross-correlation to be |$\xi _{\rm ag}^{\rm peak} = 1.9 \pm 0.6$| (although displaced from the smallest separation bin by ∼5 |$h^{-1}_{70}$| Mpc along the LOS; see their fig. 12), whereas |$\xi _{\rm gg}^{\rm peak} = 10.7 \pm 1.4$| for the galaxy–galaxy autocorrelation (see their fig. 13). Our results agree with theirs qualitatively in the sense that the clustering of H i and galaxies is weaker than that of the galaxies with themselves.

Summary

In summary, we have found agreements and disagreements with previously published results. We consider the majority of the discrepancies to be driven by the inherent difficulty of addressing uncertainties in this type of analysis, which often lead to an underestimation of the errors.

Interpretation of the results

In this section, we provide our preferred interpretation of our observational results.

Probabilistic interpretation (model independent)

The clustering analysis provides an essentially model independent statistic. The amplitude of the two-point correlation function corresponds to the probability excess of finding a pair compared to the Poissonian expectation. Thus, our results point towards the following conclusions.

• The probability of finding an ‘SF’ galaxy at a distance ≲5 Mpc from another ‘SF’ galaxy, is ∼2 times smaller than that of finding a ‘non-SF’ galaxy at that same distance from another ‘non-SF’ galaxy.

• The probability of finding an H i absorption system with |$N_{\rm H\,{\small {I}}} \ge 10^{14}$| cm⁻² at a distance ≲5 Mpc from an ‘SF’ galaxy, is approximately the same as that of finding an ‘SF’ galaxy at that same distance from another ‘SF’ galaxy.

• The probability of finding an H i absorption system with |$N_{{\rm H\,{\small {I}}}} < 10^{14}$| cm⁻² at a distance ≲5 Mpc from an ‘SF’ galaxy, is ∼10 times smaller than that of finding an ‘SF’ galaxy at that same distance from another ‘SF’ galaxy.

• The probability of finding an H i absorption system with |$N_{{\rm H\,{\small {I}}}} \ge 10^{14}$| cm⁻² at a distance ≲5 Mpc from a ‘non-SF’ galaxy, is ∼2 times smaller than that of finding a ‘non-SF’ galaxy at that same distance from another ‘non-SF’ galaxy.

• The probability of finding an H i absorption system with |$N_{{\rm H\,{\small {I}}}} < 10^{14}$| cm⁻² at a distance ≲5 Mpc from a ‘non-SF’ galaxy, is ≳100 times smaller than that of finding a ‘non-SF’ galaxy at that same distance from another ‘non-SF’ galaxy.

• The probability of finding an H i absorption system with |$N_{{\rm H\,{\small {I}}}} < 10^{14}$| cm⁻² at a distance ≲2 Mpc from another |$N_{\rm H\,\small {I}} < 10^{14}$| cm⁻² system is ∼4 times smaller than that of finding a |$N_{\rm H\,\small {I}} \ge 10^{14}$| cm⁻² system at that same distance from another |$N_{\rm H\,\small {I}} \ge 10^{14}$| cm⁻² system.

Any physical model aiming to explain the connection between H i absorption systems and galaxies at z ≲ 1 will need to take these constraints into account.

Velocity dispersion between H i and galaxies

We find that the two-dimensional H i–galaxy cross-correlations do not show detectable velocity distortions along the LOS larger than those expected from the galaxy redshift uncertainties. As mentioned, the typical uncertainty for our single galaxy redshift determination is |$\Delta z_{\rm gal} \approx 0.0006/\sqrt{2}$|⁠, which is equivalent to rest-frame velocity differences of Δv ∼ 120-60 km s⁻¹ at z = 0.1-1, respectively. Any velocity dispersion between H i systems and galaxies greater than, or of the order of, this value, would have been noticeable in the two-dimensional H i–galaxy cross-correlation signals. Therefore, we conclude that the bulk of H i systems on ∼ Mpc scales, have little velocity dispersion (≲120 km s⁻¹) with respect to the bulk of galaxies. Hence, no strong galaxy outflow or inflow signal is detected in our data.

We emphasize that our results are based on H i only. Given that H i does not exclusively trace gas originating in galaxy outflows or inflows, we do not necessarily expect to find the same signatures as those traced by metals (e.g. Ford et al. 2013b). Moreover, our results are dominated by scales somewhat larger than those typically associated with the CGM, in which the outflow or inflow signal is expected to be maximized. In view of these considerations, it is not surprising that no strong outflow or inflow signal is detected in our data.

We also emphasize that the cross-correlation analysis provides an averaged statistical result; individual galaxies having strong H i inflows/outflows might still be present, but our results indicate that these do not dominate the cross-correlation signal at z ≲ 1.

Spatial distribution of H i and galaxies

The absolute and relative clustering amplitudes of our different populations of H i and galaxies can be used to give us an idea of their spatial distribution. Our conclusions on this are as follows.

• The fact that ‘strong’ H i systems and ‘SF’ galaxies have similar amplitudes and slopes for the auto and cross-correlation, indicates that these are distributed roughly in the same locations.

• The fact that the autocorrelation of ‘non-SF’ has also the same slope but a larger amplitude, indicates that there are sublocations (within those where galaxies and ‘strong’ H i systems reside) with a higher density of ‘non-SF’ galaxies than ‘SF’ galaxies and/or ‘strong’ H i systems. This interpretation also explains the fact that the ratio (ξ_ag)²/ξ_ggξ_aa for ‘strong’ H i systems and ‘non-SF’ galaxies is consistent with neither 1 nor 0 (see Section 8.2.4).

• The suggestion that the self-clustering of ‘weak’ systems is not zero, and the fact that ‘weak’ H i systems and galaxies have a ratio (ξ_ag)²/ξ_ggξ_aa ≈ 0, indicate that these are not distributed in the same locations. Therefore, there are locations containing ‘weak’ H i systems but roughly devoid of ‘strong’ H i systems and galaxies of any kind.

This picture fits well with the recent results presented in Tejos et al. (2012), from their study of the distribution of H i absorption systems within and around galaxy voids at z ≲ 0.1. They showed that galaxy voids are not empty, and in fact contain about ∼ 20-40 per cent of H i absorption line systems with |$N_{\rm H\,\small {I}} \gtrsim 10^{12.5}$| cm⁻². The remaining ∼ 60-80 per cent were found at the edges of galaxy voids, hence sharing locations with galaxies.

Even though it seems natural to identify our ‘weak’ systems with those systems found in galaxy voids, not all ‘weak’ systems need to be unassociated with galaxies. Despite the fact that Tejos et al. (2012) reported a (tentative) difference in the column density distributions between H i absorbers within and around galaxy voids (at the ∼2σ c.l.), they did not find sharp |$N_{\rm H\,\small {I}}$| transitions between their samples. The most important difference came from the presence of ‘extremely weak’ H i systems, |$N_{\rm H\,\small {I}} \lesssim 10^{13}$| cm⁻², that were present within galaxy voids but not outside (see their figs 2 and 3). Such a low column density is at the limit of our current completeness (see Section 4.5) and so we are not able to give confident results on the clustering of these ‘extremely weak’ H i systems either with themselves or with galaxies. Restricting the column density range to |$10^{13}\le N_{\rm H\,\small {I}} < 10^{14}$| cm⁻², there are 19/50 ∼ 40 per cent systems within galaxy voids in the Tejos et al. (2012) sample. In the following, we will estimate the fraction of ‘weak’ systems that could still be associated with galaxies in our current sample.

H i and non-SF galaxies

Our proposed scenario aims to approximate what might be the case for galaxy clusters, which contain an important fraction of ‘non-SF’ galaxies but whose diffuse IGM or CGM can get destroyed by baryonic physics (e.g. Morris et al. 1993; Lopez et al. 2008; Padilla et al. 2009; Yoon et al. 2012). In such a case, |$\xi _{g_2g_2}/\xi _{g_1g_1} \gg 1$| because galaxy clusters represent the most massive dark matter haloes. Measurements and predictions for the autocorrelation of galaxy clusters point towards correlation lengths of |$r_0^{\rm cc}\sim 20{\rm -}30$| Mpc (e.g. Colberg et al. 2000; Estrada, Sefusatti & Frieman 2009; Hong et al. 2012), which would imply a |$\xi _{g_2g_2}/\xi _{g_1g_1} \sim 10 \pm 5$| (assuming a slope of γ = 1.6). Using this value together with (ξ_ag)²/(ξ_aa)(ξ_gg) = 0.5 ± 0.3, we find the fraction |$f_{g_1} \approx 0.75 \pm 0.15$| and consequently |$f_{g_2} \approx 0.25 \pm 0.15$|⁠.²³

Therefore, our results suggest that an important fraction of ‘non-SF’ galaxies ( ∼ 60-90 per cent) trace the same underlying dark matter distribution as ‘strong’ H i systems and ‘SF’ galaxies at scales ≲ 2 Mpc. This is in contrast with what can be inferred from the results reported by Chen & Mulchaey (2009), in which ‘strong’ H i systems cluster more weakly with ‘non-SF’ than ‘SF’ galaxies (see Section 8.1.4). In such a case, (ξ_ag)²/(ξ_aa)(ξ_gg) ≈ 0,²⁴ implying a fraction close to |$f_{g_1} \sim 0$|⁠.

Our simple interpretation agrees quite well with the recent observational results presented by Thom et al. (2012). These authors found that 11/15 ∼ 70 per cent of their sample of ‘non-SF galaxies’ at low-z, have H i absorption with rest-frame equivalent widths, W_r >0.3 Å (equivalent to ≳10¹⁴ cm⁻²), within 300 km s⁻¹ from their systemic redshifts, and at impact parameters ≲200 kpc (see their figs 2 and 3). By definition, these H i systems should be associated with the CGM of these galaxies. However, because of incompleteness in the galaxy surveys, it is not certain that this gas is purely associated with these ‘non-SF galaxies’ (less luminous ‘SF galaxies’ could have been missed by their target selection; e.g. Stocke et al. 2013). Still, both Thom et al. (2012) and our results point towards the conclusion that a significant fraction of ‘non-SF galaxies’ share locations with ‘strong’ H i systems at scales ≲2 Mpc. Thus, our results indicate that the ‘cold gas’ (traced by ‘strong’ H i) around ‘non-SF’ galaxies could be the rule rather than the exception.

Column density limit

Our choice of a 10¹⁴ cm⁻² limit was somewhat arbitrary (see Section 4.6). As mentioned, when we increase the limit for dividing ‘strong’ versus ‘weak’ systems from 10¹⁴ to ∼10^{15 − 16} cm⁻², we get larger cross-correlation amplitudes and slopes (although with larger uncertainties due to the reduced number of systems above such limits in our sample) for ‘strong’ compared to those from ‘weak’ systems. Similarly, when we decrease the limit from 10¹⁴ to ∼10¹³ cm⁻², we observe a decrease in the cross-correlation amplitudes and slopes of ‘strong’ systems. In this section, we explore more on this issue.

In order to quantify the H i–galaxy cross-correlation dependence on H i column density, we have repeated the analysis using subsamples of the H i absorption systems based on |$N_{\rm H\,\small {I}}$| limits, together with all galaxies in our ‘Full Sample’. We used 16 |$N_{\rm H\,\small {I}}$| bins of 1 dex width each, shifted by 0.1 dex, starting from [10¹³, 10¹⁴] through [10^14.5, 10^15.5] cm⁻². Fig. 25 shows the correlation lengths (top panel) and slopes (bottom panel) from the best power-law fits of the ‘real-space’ correlation functions of the form presented in equation (19), for each of those |$N_{\rm H\,\small {I}}$| bins. Different symbols/colours show our different measurements: the blue squares correspond to the galaxy-H i cross-correlation (ξ_ag); the black circles to the galaxy–galaxy autocorrelation (ξ_gg; slightly shifted along the x-axis for the sake of clarity); and the red triangles to the H i –H i autocorrelation (ξ_aa; slightly shifted along the x-axis for the sake of clarity). Note that points associated with the galaxy autocorrelation are independent of H i column density, and that points and uncertainties are both correlated. As expected, we see an overall monotonic increase in the correlation length and slopes with increasing |$N_{\rm H\,\small {I}}$|⁠. Such a behaviour can be explained by assuming that the fraction of H i systems that are not correlated with galaxies decreases with an increase in the minimum column density limit. Any change in the amplitude of the correlation functions can be understood as a change in the ‘linear bias’ and/or the fraction of ‘random contamination’ present. Changes in the slope of the correlations (like the one we have marginally observed in this work) would require the addition of baryonic physics, assuming a fixed underlying dark matter slope. We also observe that the ξ_ag and ξ_gg have comparable amplitudes (within 2σ) for column density bins centred at 10^14.5 cm⁻² and above, which corresponds to |$N_{\rm H\,\small {I}} \gtrsim 10^{14}$| cm⁻². As mentioned, this is one of the reasons that motivated our adopted limit of 10¹⁴ cm⁻² for splitting our H i sample (see Section 4.6).

These results show that there is a dramatic change in the H i–galaxy cross-correlation signal, where the correlation length changes from being consistent with 0 Mpc at |$N_{\rm H\,\small {I}}$| ∈ [10¹³, 10¹⁴] cm⁻², to being consistent with the ξ_gg value of ∼4 Mpc at |$N_{\rm H\,\small {I}}$| ∈ [10¹⁴, 10¹⁵] cm⁻². The slope of the H i–galaxy cross-correlation also follows the same trend. This is an important change occurring in about one order of magnitude column density range. Given the 1 dex binning used for this analysis (needed to reduce the statistical uncertainties), we cannot rule out an even sharper transition occurring within the ∼ 10¹³-10¹⁴ cm⁻² range with our current analysis.

Recent theoretical results also suggest that a 10¹⁴ cm⁻² limit might have a physical meaning. Davé et al. (2010) used a cosmological hydrodynamical simulation to study the properties of H i absorption systems from z = 2 to 0. They found an interesting bimodality in the distribution of |$\log N_{\rm H\,\small {I}}$| per unit path length at 〈z〉 ≈ 0.25, where |$N_{\rm H\,\small {I}}<10^{14}$| cm⁻² systems are dominated by the diffuse IGM and |$N_{\rm H\,\small {I}}>10^{14}$| cm⁻² are dominated by the condensed IGM associated with galaxy haloes (see their fig. 10). This theoretical result is supported by our observations of the similar clustering amplitudes of all ξ_ag, ξ_aa and ξ_gg albeit at a somewhat larger limit of |$N_{\rm H\,\small {I}} \sim 10^{14.5}$| cm⁻² (see Fig. 25).

Dark matter halo masses hosting H i systems and galaxies

It is common practice to compare the observed clustering amplitudes of extragalactic objects (e.g. galaxies, galaxy clusters, IGM absorbers, etc.) with that of the expected theoretical (cold) dark matter in a given cosmological framework, in order to infer a typical dark matter halo mass for the confinement of such objects (e.g. Mo et al. 1993; Ryan-Weber 2006). This method is model dependent, and it is only applicable over narrow cosmological epochs (narrow redshift ranges).

Our sample is composed of objects at 0 ≲ z ≲ 1, which corresponds to about half of the history of the Universe. Thus, a direct link between the clustering amplitudes reported in this paper with a single dark matter halo mass is not meaningful. Still, simple reasoning leads to the conclusion that the typical dark matter haloes for the confinement of H i systems and galaxies, should follow the same trends as the amplitudes of their correlation functions. Therefore, the most massive ones should correspond to ‘non-SF’ galaxies, followed by ‘SF’ galaxies, ‘strong’ H i systems (both comparable) and ‘weak’ H i systems, in that same order.

Fig. 26 is the same as Fig. 22 but including the prediction for the dark matter clustering at z ≲ 1 (thick dashed line). The shaded regions enclose the expected dark matter clustering between redshift z = 1 (lower envelope) and 0 (upper envelope), while the dashed lines correspond to the expectation at z = 0.5. These predictions were obtained from the dark matter power spectrum²⁵ provided by camb²⁶ (Lewis et al. 2000), with (thick dashed lines and dark shaded regions) and without (thin dashed lines and light shaded regions) the non-linear corrections of Smith et al. (2003), for our adopted cosmological parameters and σ₈ = 0.8. We see that the shape of the correlations for ‘strong’ H i systems and galaxies are approximately consistent with that of the predicted dark matter in the non-linear regime. Their somewhat larger amplitudes hint towards ‘absolute biases’ b ≳ 1. On the other hand, the shape of the ‘weak’ H i is marginally in disagreement with that of the dark matter expectation in the non-linear regime. In this case, the lower amplitude compared to that of the dark matter hints towards an ‘absolute bias’ b < 1. We note that for the case of ‘weak’ systems, a linear approximation for the dark matter clustering (i.e. neglecting the correction of Smith et al. 2003), gives a somewhat better match in terms of slopes, although still with amplitudes marginally above our observed ones. If a significant fraction of ‘weak’ H i systems reside in underdense regions (i.e. within galaxy voids), a linear evolution should be expected even at z ≈ 0. We speculate that H i systems within galaxy voids are still evolving in the linear regime, even at scales ≲ 2 Mpc.

In view of these results, we revisit the claim by Ryan-Weber (2006) that H i absorption systems with ≲ 10¹⁵ cm⁻² reside preferentially in dark matter halo of masses M ∼ 10^13.6-10^14.5|$h^{-1}_{100}$|M_⊙, analogous to those of massive galaxy groups. Given the significantly lower clustering amplitude of our full sample of H i systems compared to that of galaxies, we conclude that H i absorption systems are preferentially found in dark matter haloes of masses smaller than those populated by galaxies. At most, ‘SF’ galaxies and ‘strong’ H i systems are typically found in dark matter haloes of similar masses. Moreover, a significant fraction of ‘weak’ H i systems might reside in underdense regions with ‘absolute biases’ b < 1.

Three types of relationships between H i and galaxies

We have reported a significant (>3σ c.l.) rejection of the hypothesis that H i absorption systems and galaxies (as a whole) trace the same underlying dark matter distribution linearly (see Section 7). We have found that this is mostly driven by H i absorption systems with column densities |$N_{\rm H\,\small {I}}<10^{14}$| cm⁻² (‘weak’ systems), which show little (consistent with 0) correlation with galaxies. On the other hand, H i systems with |$N_{\rm H\,\small {I}} \ge 10^{14}$| cm⁻² (‘strong’ systems) are consistent with such an hypothesis. Thus, this indicates the presence of, at least, two types of relationships between H i and galaxies: (i) linear correlation and (ii) no correlation.

A third type of relationship comes from the fact that at small enough scales, H i systems and galaxies are a different manifestation of the same physical object; a galaxy is also a very strong H i absorption system and, depending on the galaxy definition, the other way around also applies. Our survey was not designed for studying scales ≲ 0.5 Mpc, and so it is not surprising that we do not observe a characteristic signal of a one-to-one association (see Section 6.4). Thus, we cannot neglect the fact that this relationship exists and should be included in our interpretation. Still, the contribution of this one-to-one correlation between H i absorption systems and luminous galaxies to the total fraction of H i systems at |$10^{13} \lesssim N_{\rm H\,\small {I}} \lesssim 10^{17}$| cm⁻² is quite low.

This picture fits well with what was presented early by Mo & Morris (1994), and is in contrast to the commonly adopted interpretation presented by Lanzetta et al. (1995) which claims that the majority of low-z H i systems belong to the extended haloes of luminous galaxies.

Prospects and future work

In this section, we will enumerate some of the projects that are directly linked to our current study, but that we have not performed here either because of lack of observational data or limited time. We aim to address them in the near future.

Comparison with simulations

Even though many of our results are in good agreement with those presented by Pierleoni et al. (2008, see Section 8.1.3), others have not been properly compared with the predictions from simulations yet. For instance, one of our key results is the fact that ‘weak’ H i systems and galaxies cluster more weakly than ‘weak’ H i systems with themselves, or than galaxies with themselves. As discussed in Section 8.2.3, this would imply that ‘weak’ H i systems and luminous galaxies do not trace the same underlying matter distribution linearly. It is still to be seen if current cosmological hydrodynamical simulations can reproduce this and all our observational results.

Cosmological evolution

A complete picture of the relationship between the IGM and galaxies requires understanding not only their statistical connection at a given epoch, but also their cosmological evolution. Combining our results with those from higher redshifts (z ∼ 2-3; e.g. Adelberger et al. 2003, 2005; Crighton et al. 2011; Rakic et al. 2012; Rudie et al. 2012; Tummuangpak et al. 2013), such an evolution can be studied. It is important to keep in mind that: (i) galaxy samples in these high-z studies are strongly biased against ‘non-SF galaxies’, and (ii) the lower the redshift, the higher the (average) overdensity traced by a fixed |$N_{\rm H\,\small {I}}$| limit (e.g. Schaye 2001; Davé et al. 2010, see equation 37). Thus, any evolutionary analysis has to properly take into account such differences.

We also note that because of observational limitations, the redshift range between z ∼ 1 and 2 is currently unexplored for studies of the IGM–galaxy connection. This is a very important cosmological time, as it is when the star formation density starts to decline (e.g. Hopkins & Beacom 2006). We hope this will be covered in the near future.

Dependence on H i Doppler parameter

In our current analysis, we have completely ignored the information provided by the Doppler parameters of the H i systems. Current hydrodynamical simulations suggest that above a limit of |$b_{\rm H\,\small {I}}\sim 50$| km s⁻¹, an important fraction of H i lines trace the warm–hot intergalactic medium (WHIM; e.g. Davé et al. 2010, see their fig. 11). The WHIM is currently the best candidate to host the majority of the ‘missing baryons’ at low-z (e.g. Cen & Ostriker 1999; Davé et al. 2010; Shull et al. 2012; Tepper-García et al. 2012). However, because of their expected large |$b_{\rm H\,\small {I}}$| and low |$N_{\rm H\,\small {I}}$| (≲ 10¹³ cm⁻²), its direct observation through H i has been extremely difficult. In fact, H i can appear undetectable in such conditions (Savage et al. 2010). Still, the H i–galaxy cross-correlation could provide an indirect way to observe the WHIM by splitting the samples by |$b_{\rm H\,\small {I}}$|⁠, and applying a similar reasoning as that presented in Section 8.2.4.

Cross-correlations for the CGM

Our current statistical results seem adequate for constraining the H i–galaxy connection on scales ∼ 0.5-10 Mpc. An obvious improvement would be to increase the galaxy completeness level at scales ≲ 0.5 Mpc. In this way, the two-point correlation function results can be directly linked to the studies of the CGM based on one-to-one absorber–galaxy associations (e.g. Prochaska et al. 2011b; Tumlinson et al. 2011; Thom et al. 2012; Stocke et al. 2013; Werk et al. 2013). Correlations between metals and galaxies will also provide a useful complement for such studies. Similarly, a better characterization of the galaxies (e.g. stellar masses, specific star formation rates, morphology, etc.) in these samples will allow us to isolate their relative contributions (and hence importance) to the observed correlation amplitudes.

‘Extremely weak’ H i systems

Our current data quality is not high enough to observe ‘extremely weak’ H i systems (⁠|$N_{\rm H\,\small {I}} \lesssim 10^{13}$| cm⁻²), but studying the H i–galaxy cross-correlation at such low column densities is clearly worth exploring. There is strong observational evidence that the vast majority of these absorbers reside within galaxy voids (e.g. Manning 2002; Tejos et al. 2012). In such a case an anti-correlation between ‘extremely weak’ H i absorption systems and galaxies should be expected, but this has not yet been observationally confirmed (or refuted). There is also the interesting possibility that these absorbers may represent a completely different type of H i absorption systems than those found co-existing with galaxies. If true, such systems are good candidates for testing our current galaxy formation paradigm (e.g. Manning 2002, 2003).

SUMMARY

We have presented a new optical spectroscopic galaxy survey of 2143 galaxies at z ≲ 1, around three fields containing five QSOs with HST UV spectroscopy.²⁷ These galaxies were observed by optical MOS instruments such as DEIMOS, VIMOS and GMOS, and were mostly selected based on magnitude limits (R ∼ 23-24 mag; no morphological criteria imposed). This selection also led to the detection of 423 stars and 22 AGN within those fields. Out of our new 2143 galaxies, 1777 have detectable star formation activity within their past ∼1 Gyr (referred to as ‘SF’), while the remaining 366 have not (referred to as ‘non-SF’).

We have also presented a new spectroscopic survey of 669 well-identified intervening H i absorption-line systems at z ≲ 1, observed in the spectra of eight QSO at z ∼ 1. These systems were detected in high-resolution UV HST spectroscopy from COS and FOS. Out of these 669 H i systems, 173 have column densities |$10^{14} \le N_{\rm H\,\small {I}}\lesssim 10^{17}$| cm⁻² (referred to as ‘strong’), while the remaining 496 have |$10^{13} \lesssim N_{\rm H\,\small {I}} < 10^{14}$| cm⁻² (referred to as ‘weak’).

Combining these new data with previously published galaxy catalogues from the VVDS (Le Fèvre et al. 2005, 2013), GDDS (Abraham et al. 2004) and Morris & Jannuzi (2006) surveys, we have gathered a sample of 17 509 galaxies with redshifts between 0.01 < z < 1.3, and at transverse separations <50 Mpc from their respective field centres; and 654 H i absorption systems at redshifts between 0.01 < z < z_max, where z_max is the redshift corresponding to 5000 km s⁻¹ blueward of the redshift of their respective QSOs. Out of those 17 509 galaxies, 8293 were classified as ‘SF’ and 1743 as ‘non-SF’; while out of those 654 H i systems, 165 were classified as ‘strong’ and 489 as ‘weak’.

Using these data, we have investigated the statistical connection between the IGM and galaxies through a clustering analysis. This data set is the largest sample to date for such an analysis. We presented observational results for the H i–galaxy cross-correlation and both the galaxy–galaxy and H i–H i autocorrelations at z ≲ 1. The two-point correlation functions have been measured both along and transverse to the LOS, ξ(r_⊥, r_∥), on a linear grid of 0.5 Mpc in both directions. We have measured the H i–galaxy (ξ_ag) and galaxy–galaxy (ξ_gg) correlations at transverse scales r_⊥ ≲ 10 Mpc, and the H i–H i autocorrelation (ξ_aa) at transverse scales r_⊥ ≲ 2 Mpc. We have integrated these correlations along the LOS up to 20 Mpc, and used the projected results to infer the shape of their corresponding ‘real-space’ correlation functions, ξ(r), assuming power laws of the form ξ(r) = (r/r₀)^−γ. By comparing the results from the H i–galaxy cross-correlation with the H i–H i and galaxy–galaxy autocorrelations, we have provided constraints on their statistical connection, as a function of both H i column density and galaxy star formation activity. We summarize our observational results as follows.

• Two-dimensional correlations, ξ(r_⊥, r_∥).

• Full sample: the H i–galaxy two-dimensional cross-correlation has comparable clustering amplitudes to those of the H i–H i autocorrelation, which are lower than those of the galaxy–galaxy autocorrelation. The peaks of these correlation functions were found to be ξ_ag = 2.3 ± 0.9, ξ_aa = 2.1 ± 0.9 and ξ_gg = 5.7 ± 0.7, respectively.

• ‘Strong’ H isystems and ‘SF’ galaxies: the H i–galaxy, H i–H i and galaxy–galaxy two-dimensional correlations all have comparable amplitudes. The peaks of these correlation functions were found to be ξ_ag = 8.3 ± 2.2, ξ_aa = 7.5 ± 2.3 and ξ_gg = 6.1 ± 0.6, respectively.

• ‘Strong’ H isystems and ‘non-SF’ galaxies: the H i–galaxy two-dimensional cross-correlation has comparable clustering amplitudes than those of the galaxy–galaxy autocorrelation, which are marginally higher than those of the H i–H i autocorrelation. The peaks of the correlation functions were found to be ξ_ag = 10.3 ± 5.6, ξ_gg = 12.6 ± 3.0 and ξ_aa = 7.5 ± 2.3, respectively.

• ‘Weak’ H isystems and ‘SF’ galaxies: the H i–galaxy two-dimensional cross-correlation has much lower amplitudes than those of the galaxy–galaxy and H i–H i autocorrelations. The H i–H i autocorrelation has also lower amplitudes than those of the galaxy–galaxy autocorrelation. The peaks of the correlation functions were found to be ξ_ag = 0.9 ± 0.6, ξ_gg = 6.1 ± 0.6 and ξ_aa = 1.9 ± 0.9, respectively.

• ‘Weak’ H isystems and ‘non-SF’ galaxies: the H i–galaxy two-dimensional cross-correlation has much lower amplitudes than those of the galaxy–galaxy and H i–H i autocorrelations. The H i–H i autocorrelation has also lower amplitudes than those of the galaxy–galaxy autocorrelation. The peaks of the correlation functions were found to be ξ_ag = 0.6 ± 0.5, ξ_gg = 12.6 ± 3.0 and ξ_aa = 1.9 ± 0.9, respectively.

• Real-space correlations, ξ(r) ≡ (r/r₀)^−γ.

• Full sample: the H i–galaxy cross-correlation has comparable clustering amplitudes than those of the H i–H i autocorrelation, which are lower than those of the galaxy–galaxy autocorrelation. The correlation lengths and slopes are found to be |$r_0^{\rm ag} = 1.6 \pm 0.2$| Mpc and γ^ag = 1.4 ± 0.1, |$r_0^{\rm aa} = 0.3 \pm 0.3$| Mpc and γ^aa = 1.1 ± 0.1, and |$r_0^{\rm gg} = 3.9 \pm 0.1$| Mpc and γ^gg = 1.7 ± 0.1, respectively.

• ‘Strong’ H isystems and ‘SF’ galaxies: the H i–galaxy, H i–H i and galaxy–galaxy correlations have all comparable amplitudes. The correlation lengths and slopes are found to be |$r_0^{\rm ag} = 3.8 \pm 0.2$| Mpc and γ^ag = 1.7 ± 0.1, |$r_0^{\rm aa} = 3.1 \pm 0.7$| Mpc and γ^aa = 1.3 ± 0.4, and |$r_0^{\rm gg} = 3.9 \pm 0.1$| Mpc and γ^gg = 1.6 ± 0.1, respectively.

• ‘Strong’ H isystems and ‘non-SF’ galaxies: the H i–galaxy cross-correlation has comparable clustering amplitudes than those of the galaxy–galaxy autocorrelation, which are higher than those of the H i–H i autocorrelation. The correlation lengths and slopes found to be |$r_0^{\rm ag} = 4.0 \pm 0.3$| Mpc and γ^ag = 1.7 ± 0.1, |$r_0^{\rm gg} = 6.2 \pm 0.2$| Mpc and γ^gg = 1.6 ± 0.1, and |$r_0^{\rm aa} = 3.1 \pm 0.7$| Mpc and γ^aa = 1.3 ± 0.4, respectively.

• ‘Weak’ H isystems and ‘SF’ galaxies: the H i–galaxy cross-correlation has much lower amplitudes than those of the galaxy–galaxy and H i–H i autocorrelations. The H i–H i autocorrelation has also lower amplitudes than those of the galaxy–galaxy autocorrelation. The correlation lengths and slopes are found to be |$r_0^{\rm ag} = 0.2 \pm 0.4$| Mpc and γ^ag = 1.1 ± 0.3, |$r_0^{\rm gg} = 3.9 \pm 0.1$| Mpc and γ^gg = 1.6 ± 0.1, and |$r_0^{\rm aa} = 0.3 \pm 0.1$| Mpc and γ^aa = 1.0 ± 0.1, respectively. We note however that a power-law fit for H i–galaxy cross-correlation might not be a good description of the observations.

• ‘Weak’ H isystems and ‘SF’ galaxies: the H i–galaxy cross-correlation has much lower amplitudes than those of the galaxy–galaxy and H i–H i autocorrelations. The H i-H i autocorrelation has also lower amplitudes than those of the galaxy–galaxy autocorrelation. The correlation lengths and slopes are found to be |$r_0^{\rm ag} = 0.0 \pm 0.8$| Mpc and γ^ag = 1.0 ± 1.6, |$r_0^{\rm gg} = 6.2 \pm 0.2$| Mpc and γ^gg = 1.6 ± 0.1, and |$r_0^{\rm aa} = 0.3 \pm 0.1$| Mpc and γ^aa = 1.0 ± 0.1, respectively. We note, however, that a power-law fit for the real-space H i–galaxy cross-correlation might not be a good description of the observations.

(iii) Amplitudes.

• H i–galaxy cross-correlations: the H i–galaxy cross-correlation amplitudes are systematically higher for ‘strong’ systems than for ‘weak’ systems, and are also higher for ‘non-SF’ galaxies than for ‘SF’ galaxies, with a much stronger dependence on H i column density than galaxy star formation activity. This is true for both the two-dimensional and the real-space correlations (see numbers above).

• Galaxy autocorrelations: the galaxy–galaxy autocorrelation amplitudes are systematically higher for ‘non-SF’ galaxies than for ‘SF’ galaxies. This is true for both the two-dimensional and the real-space correlations (see numbers above).

• H iautocorrelations: the H i–H i autocorrelation amplitudes are systematically higher for ‘strong’ systems than for ‘weak’ systems. This is true for both the two-dimensional and real-space correlations (see numbers above).

(iv) Velocity distortions.

• The two-dimensional H i–galaxy cross-correlations do not show significant velocity distortions along the LOS, apart from those expected by the galaxy redshift uncertainties.

• The peak in the two-dimensional H i–galaxy cross-correlation for ‘strong’ systems and ‘non-SF’ galaxies appears shifted by ∼1 Mpc along the LOS from 0, and there is marginal evidence (not significant) that this might be a real feature.

(v) Two-dimensional ratios, (ξ_ag)²/(ξ_ggξ_aa) on scales <2 Mpc.

• Full sample: the ratio (ξ_ag)²/(ξ_ggξ_aa) appears marginally inconsistent with 1.

• ‘Strong’ H isystems and galaxies: the ratio (ξ_ag)²/(ξ_ggξ_aa) appears roughly consistent (large uncertainties) with 1, irrespective of the galaxy star formation activity.

• ‘Weak’ H isystems and galaxies: the ratio (ξ_ag)²/(ξ_ggξ_aa) appears inconsistent with 1, irrespective of the galaxy star formation activity.

(vi) Projected along the LOS ratios, (ξ_ag)²/(ξ_ggξ_aa) on scales <2 Mpc.

• Full sample: we find (ξ_ag)²/(ξ_ggξ_aa) ≈ 0.2 ± 0.2. This rules out the hypothesis that H i systems and galaxies (as a whole) trace the same underlying dark matter distribution linearly, at a high statistical significance (>3σ c.l.).

• ‘Strong’ H isystems and ‘SF’ galaxies: we find (ξ_ag)²/(ξ_ggξ_aa) ≈ 1.1 ± 0.6. This is consistent (large uncertainties) with the hypothesis that ‘strong’ H i systems and ‘SF’ galaxies trace the same underlying dark matter distribution linearly.

• ‘Strong’ H isystems and ‘non-SF’ galaxies: we find (ξ_ag)²/(ξ_ggξ_aa) ≈ 0.5 ± 0.3. This marginally rules out the hypothesis that ‘strong’ H i systems and ‘non-SF’ galaxies trace the same underlying dark matter distribution linearly (only at the ∼2σ c.l.).

• ‘Weak’ H isystems and ‘SF’ galaxies: we find (ξ_ag)²/(ξ_ggξ_aa) ≈ 0.0 ± 0.2. This rules out the hypothesis that ‘weak’ H i systems and ‘SF’ galaxies trace the same underlying dark matter distribution linearly, at a high statistical significance (>3σ c.l.).

• ‘Weak’ H isystems and ‘non-SF’ galaxies: we find (ξ_ag)²/(ξ_ggξ_aa) ≈ 0.0 ± 0.4. This marginally rules out the hypothesis that ‘weak’ H i systems and ‘non-SF’ galaxies trace the same underlying dark matter distribution linearly (only at the ∼2σ c.l.).

(vii) ‘Absolute biases’.

• ‘Strong’ H isystems and galaxies: their ‘absolute biases’ are consistent with b ≳ 1.

• ‘Weak’ H isystems: their ‘absolute biases’ are consistent with b < 1.

Our interpretation of these results has led us to the following conclusions.

• The bulk of H i systems on ∼ Mpc scales have little velocity dispersion (≲120 km s⁻¹) with respect to the bulk of galaxies. Hence, no strong galaxy outflow or inflow signal is detected in our data.

• The vast majority (∼100 per cent) of ‘strong’ H i systems and ‘SF’ galaxies are distributed in the same locations. We have identified these locations with the ‘overdense large-scale structure’.

• A fraction of ‘non-SF’ galaxies are distributed in roughly the same way as ‘strong’ H i systems and ‘SF’ galaxies but there are sublocations – within those where galaxies and ‘strong’ H i systems reside – with a much higher density of ‘non-SF’ galaxies than ‘strong’ H i systems and/or ‘SF’ galaxies. We have identified such locations as galaxy clusters. We estimated that only a 25 ± 15 per cent of ‘non-SF’ galaxies reside in galaxy clusters and that the remaining 75 ± 15 per cent co-exist with ‘strong’ H i and ‘SF’ at scales ≲ 2 Mpc, following the same underlying dark matter distribution, i.e. the ‘overdense large-scale structure’.

• An important fraction of ‘weak’ systems could reside in locations devoid of galaxies of any kind. We have identified such locations as galaxy voids, i.e. the ‘underdense large-scale structure’. At a limit of |$N_{\rm H\,\small {I}} \ge 10^{13}$| cm⁻², we have estimated that roughly ∼50 per cent of ‘weak’ systems reside within galaxy voids. At lower |$N_{\rm H\,\small {I}}$| limits this fraction is likely to increase.

• The vast majority (∼100 per cent) of ‘strong’ H i absorption systems at low-z reside in dark matter haloes of masses comparable to those hosting the galaxies in our sample.

• At least ∼50 per cent of ‘weak’ H i absorption systems with |$N_{{\rm H\,{\small {I}}}} \ge 10^{13}$| cm⁻² reside in dark matter haloes less massive than those hosting ‘strong’ H i systems and/or the galaxies in our sample. At lower |$N_{\rm H\,\small {I}}$| limits this fraction is likely to increase.

• We speculate that H i systems within galaxy voids at z ≲ 1 might be still evolving in the linear regime even at scales ≲ 2 Mpc.

• We conclude that there are at least three types of relationship between H i absorption systems and galaxies at low-z: (i) one-to-one physical association; (ii) association because they both follow the same underlying dark matter distribution and (iii) no association at all.

We thank the anonymous referee for helpful comments and suggestions which improved the paper. We thank Pablo Arnalte-Mur, Rich Bielby, John Lucey, Peder Norberg and Tom Shanks for helpful discussions. We thank Pablo Arnalte-Mur for his help in obtaining the prediction for the dark matter clustering at z ≲ 1. We thank Mark Swinbank for his help in the reduction of GMOS data.

We thank contributors to SciPy,²⁸ Matplotlib²⁹ and the python programming language³⁰; the free and open-source community and the NASA Astrophysics Data System³¹ for software and services.

NT acknowledges grant support by CONICYT, Chile (PFCHA/Doctorado al Extranjero 1^a Convocatoria, 72090883). SLM was partially supported by STFC Rolling Grant PP/C501568/1 Extragalactic Astronomy and Cosmology at Durham 20082013. JB acknowledges support from HST-GO-11585.03-A and HST-GO-12264.03-A grants. ERW acknowledges support by Australian Research Council DP1095600. We also thank funding by STFC Grant ST/I001573/1.

This work was mainly based on observations made with the NASA/ESA Hubble Space Telescope under programmes GO 12264 and GO 11585, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555; and on observations collected at the European Southern Observatory, Chile, under programmes 070.A-9007, 087.A-0857 and 086.A-0970. Some of the data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the NASA. The authors wish also to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. This work was partially based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the NSF (United States), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência, Tecnologia e Inovação (Brazil) and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina).

REFERENCES

APPENDIX A: DATA TABLES

SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this article:

Table A9. Spectroscopic catalogue of objects in the Q0107 field.

Table A10. Spectroscopic catalogue of objects in the J1005 field.

Table A11. Spectroscopic catalogue of objects in the J1022 field.

Table A12. Spectroscopic catalogue of objects in the J2218 field (Supplementary Data).

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