FAR-ULTRAVIOLET NUMBER COUNTS OF FIELD GALAXIES

In order to measure the number counts of galaxies in our sample, we used the method developed in Gardner et al. (2000a). Because there are variations in depth across the FUV images, each FUV source would not necessarily be detectable over an entire image. For each source we must calculate the total area in which it would have been detected in each image. We use the rms error maps, produced from the weight maps of the drizzled SBC images, to determine these areas. Small-scale variations created during the image drizzling process are accounted for by smoothing the rms maps with a 04 × 04 median filter. AB magnitude and size of each source are required to calculate the total detection area in an image for that source. FUV AB magnitudes (FUV_AB) of the sources in all observed fields were obtained from photometric catalogs produced with SExtractor as described in Section 2. The size of each source was determined from the SExtractor segmentation maps used for the catalog photometry. Using the size and magnitude of each source, we calculate the maximum rms error of a pixel at 3σ in the following way: flux/(3$\times \sqrt{{\rm size}}$). Pixels in the rms map with errors less than or equal to this value make up the total area over which the source would have been detected at 3σ.

In order to be consistent, and not overestimate the detection area of the other sources, we cut down the edges of each rms map by a length equal to the radius of the circular area of each removed source (discussed in Section 2) before calculating their detection areas. This includes both the outer edges of images as well as edges on the inner parts of the images where drizzled fields do not overlap in the HUDF and HDF-N. In any given magnitude bin, there might be a failure to detect low surface brightness objects that are actually there. This effect can become larger toward fainter magnitudes. Thus, number count measurements must be adjusted for such incompleteness biases. To correct for incompleteness, we use two independent methods, bootstrap-sampling, and detection of artificially introduced galaxies. For the first method we bootstrap-sample the size distribution of the version 2.0 GOODS-S V-band catalog⁸ starting with a randomly generated FUV galaxy sample. First, 1000 FUV magnitudes are randomly generated for each FUV magnitude bin. Next, following the procedure in Gardner et al. (2000a), we use the mean and standard deviation parameters of a Gaussian distribution fit to the FUV–V color distribution in the HUDF between 24 ⩽m_AB ⩽ 28 to randomly generate FUV–V colors. Even though the completeness correction is ultimately applied to all magnitude bins from 21.5 to 29.5, this range (24 ⩽m_AB ⩽ 28) is selected for determining the Gaussian distribution because the magnitude distribution of the FUV sample drops off at ∼28.5, and there are very few galaxies in the HUDF with magnitudes brighter than 24. Thus, including bins brighter or fainter than these magnitudes would introduce unwanted errors into the distribution. Because the Gaussian color distribution does not vary greatly between the different SBC fields we only sample the HUDF. With these random FUV magnitudes and FUV–V colors, we calculate the optical magnitudes of the randomly generated sample and match them to the closest optical magnitudes of sources in the GOODS-S V-band catalog. The sizes of these objects are then sampled from segmentation maps produced from public GOODS-S V-band images with SExtractor using 0.8σ isophotes to define the source areas. These are isophotes within which each pixel in the V-band images is 0.8σ above the background noise. We use a 0.8σ size isophote because the same is used to define the source areas for the FUV photometry. From the sizes and FUV magnitudes of the random sample, we then calculate the maximum rms pixel error below which each simulated object would be detected and proceed to calculate the total detection area for each simulated object in the SBC rms maps. Finally, to get the completeness correction factor for each magnitude bin, we average per magnitude bin the detection areas of the simulated objects (including galaxies with zero detection area) and take the ratio with the average detection area of all real FUV sources in corresponding bins.

The second incompleteness correction method introduces 500 artificial FUV galaxies into the SBC data for each magnitude bin and recovers them with the same photometry algorithm used for the real data. We simulate these sources using the IRAF task ARTDATA in the NOAO package. We also simulate 500 V-band galaxies using the same software in order to use their isophotal sizes to provide the area in which to measure the flux of the artificial FUV sources. This approach mimics the procedure of the actual FUV photometry. To determine the correct magnitudes of the artificial V-band galaxies, we use the parameters of the same Gaussian FUV–V color distribution discussed above. An FUV artificial source that has sinal-to-noise ratio >3.5 is a detection, and the detection ratio equals the number of sources recovered over 500. Finally, to correct for incompleteness the number counts are divided by the detection ratio in each magnitude bin.

Both methods yield similar incompleteness corrections, within a few percent of one another, in each bin. An average of these two methods is used for the final correction to the number counts.

In Figure 4, we present the completeness corrected and the raw FUV number counts from this work and past FUV number counts from the literature. Their measured values, errors, completeness, and detection areas per magnitude bin are provided in Table 1. Small number Poisson statistical errors are calculated for each point from Gehrels (1986) at the 1σ level. The filled circles represent our completeness corrected counts. The open circles represent the raw counts. The upside-down triangles represent counts done with SBC images of the HDF-N from Teplitz et al. (2006). The asterisks represent counts done with HST STIS in the HDF-N and HDF-S from Gardner et al. (2000a). The squares represent counts done with GALEX from Xu et al. (2005, hereafter XU05 fields), and the upright triangles represent counts done with GALEX from Hammer et al. (2010, hereafter HAM10 field). No color corrections are made between the SBC filter which has a central wavelength of 1614 Å (filter peak is λ = 1500 Å) and the STIS and GALEX filters that have FUV central wavelengths at 1595 Å and 1530 Å,  respectively. As discussed in Teplitz et al. (2006), the color correction between the SBC and GALEX FUV filters would be significant for galaxies at z > 0.50 because the SBC filter is sensitive to a larger volume (∼30%) than the GALEX filter. This color difference results in no more than a factor of ∼2 (∼half a magnitude) between the SBC and GALEX number counts. They also discuss that Lyα emitting sources at z < 0.15 could have the opposite effect resulting from the bluer wavelength coverage of the GALEX filter. About 54% of our FUV sample with z_phot are at z_phot > 0.50 and ∼2.3% are at z_phot < 0.15. The majority (98%) of sources at z_phot > 0.5 are not comparable to GALEX bins because they have fainter magnitudes (FUV_AB > 24). Thus, comparisons with GALEX FUV number counts are not largely affected by ignoring the filter color correction.

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Our galaxy sample probes the faint end of the FUV number counts, with the majority of sources occupying magnitude bins 23.5–28.5. This is reflected in the error bars of these plotted points. The three faintest objects in our sample have FUV_AB = 29.19, 29.21, and 29.33. Although these sources are fainter than the magnitude drop-off of the FUV data (∼28.5), they are detected in the GOODS V-band catalog and above the detection threshold of 0.8σ. Thus, they are included in these number counts. However, due to the few sources detected, the measurement does not accurately represent the number counts at this faint level. On average our number counts are ∼35% and ∼36% lower than the faint HST FUV counts from Gardner et al. (2000a) and Teplitz et al. (2006), respectively. The differences in the measurements are likely the result of cosmic variance which is discussed in more detail in Section 3.4.

At the 22.5 mag bin, the slope of our number counts intersects the faint end of the GALEX HAM10 field counts but not the XU05 field counts, remaining higher than these at all overlapping magnitudes. It is not well understood why the GALEX counts diverge from each other after FUV_AB ∼ 21.25, but Hammer et al. (2010) show that the divergence cannot be due to their source detection/photometry methods, active galactic nuclei (AGNs), or cosmic variance between fields. Also, while cluster members in the HAM10 field bias the bright bins of these number counts, they only compose ∼2% of objects in the faintest bin, which represents the limiting depth of the survey. However, massive clusters are known to be associated with many filaments and the number of filaments is directly correlated with cluster mass (Pimbblet et al. 2004). Thus, Hammer et al. (2010) do not rule out large-scale structure behind the massive Coma Cluster as the culprit of their excess galaxy counts.

A primary use of galaxy number counts is to test and constrain models of galaxy evolution. In Figure 4, we compare our FUV number counts with two different models, a simple luminosity evolution model from Xu et al. (2005) and a cosmological semi-analytic model (SAM) from Somerville et al. (2011, hereafter SGPD11). The first model is the SB4/Lyα-flat SED model. This model is characterized by a UV luminosity evolution, L*∼ (1+ z)^2.5, and is constructed from a local FUV luminosity function (Wyder et al. 2005) with an estimated K-correction based on the UV SB4 SED from Kinney et al. (1996) with a flat spectrum between 1200 Å and 1000 Å. It was selected as an initial check that our measured number counts were reasonable since this model is in good agreement with evolution models derived from observed luminosity functions at high-z (Arnouts et al. 2005). When plotting the SB4/Lyα-flat SED model we did not color correct the model from the GALEX FUV effective wavelength at 1530 Å to the SBC effective wavelength at 1614 Å (see the further discussion in Section 3.2).

The second model, SGPD11, makes use of the latest version of the SAMs developed by Somerville and collaborators (Somerville et al. 2008, 2001; Somerville & Primack 1999). The backbone of these SAMs is dark matter ``merger trees" representing the hierarchical build-up of structure in the Λ cold dark matter (ΛCDM) paradigm. The model shown here is the ``fiducial WMAP5" model presented in SGPD11 and adopts cosmological parameters consistent with the five-year Wilkinson Microwave Anisotropy Probe (WMAP) analysis (WMAP5; Ω_m = 0.2383, Ω_Λ = 0.7617, $\mathit {h}$ = 0.732, σ₈ = 0.82). The physical processes included in the model include radiative cooling of gas, photoionization squelching, star formation in quiescent and burst modes, morphological transformation via mergers, supernovae feedback, chemical evolution, black hole growth, AGN-driven winds, and radio-mode feedback. The UV luminosities for the SAM galaxies are calculated from synthetic SEDs created by convolving the star formation and chemical enrichment histories for each galaxy with Bruzual & Charlot (2003) stellar population models using a Chabrier initial mass function. A two-component model for extinction by dust in diffuse cirrus and in dense ``birth clouds," following Charlot & Fall (2000), is also applied (for details see SGPD11). SGPD11 found, in agreement with other studies, that they had to adopt dust parameters that varied with redshift in order to match the UV and B-band luminosity functions at high redshift. We note that unlike simple pure luminosity evolution models, SAMs have many physical sources of scatter in galaxy number densities and properties.

We compare our number counts to the SGPD11 model for several reasons. This model includes what are believed to be the key physical processes that shape galaxy formation and evolution. In particular, the FUV number counts are expected to provide an important constraint on the processes that trigger and regulate star formation, which are highly uncertain. The FUV number counts are also highly sensitive to dust extinction, which is another uncertain ingredient in the SAMs.

Our measured FUV number counts are broadly consistent with the SGPD11 and the SB4/Lyα-flat SED model over all magnitudes. As seen in Figure 4, the SB4/Lyα-flat SED model appears lower than the SGPD11 SAM up to FUV_AB ∼ 26.5 after which the trend is reversed and the SGPD11 model is lower. The differences in the bright end of the models are most likely due to the fact that the SB4/Lyα-flat SED model is derived from a single SED. Both sets of GALEX counts are lower than the SGPD11 model at the bright end, however the HAM10 field counts start to coincide with the models at FUV_AB > 22.5. This is consistent with the fact that the SGPD11 model is known to overproduce bright galaxies compared to GALEX data (Gilmore et al. 2009; Somerville et al. 2011), due to a small degree of residual "overcooling" in massive halos. Our number counts do not match the SB4/Lyα-flat SED model at all magnitudes, but begin to coincide with it after 24.5 mag. As discussed by Teplitz et al. (2006), the discrepancies with this model, especially toward bright magnitudes, may suggest a need for number density evolution in FUV galaxy number count models because this model only takes into account luminosity evolution.

Uncertainties in measurements of galaxy number counts can arise as a result of overall large-scale structure variation or cosmic variance (Somerville et al. 2004). The observations used for this study were designed to significantly reduce the effects of cosmic variance by including data from various sight lines and covering a larger area than any previous FUV number counts study at these wavelengths and magnitudes. Our observations cover a total area of 15.9 arcmin², while the Gardner et al. (2000a) STIS observations in the HDF-N and S cover only 1.54 arcmin² and the Teplitz et al. (2006) SBC observations in the HDF-N cover only ∼3.77 arcmin². Also, the HDF-N has galaxy overdensities at z ∼ 0.45 and z ∼ 0.8 (Cohen et al. 2000) that bias the number counts in that field. To demonstrate the effects of cosmic variance, we have compared in Figure 5 our total FUV number counts with the number counts calculated in the GOODS-N and GOODS-S SBC fields separately. The red circles represent the total number counts, blue upside-down triangles represent the number counts in the GOODS-S area, and the orange squares represent the number counts in the GOODS-N area. The counts in the GOODS-N area are consistently higher than those in GOODS-S in every magnitude, bin except 22.5. The total number counts are a clear average of the number counts in these two fields over the entire magnitude range. This result demonstrates that using large areas and various sight lines to make measurements of number counts reduces bias due to cosmic variance, and ideally these types of data sets provide the best comparisons for SAMs.

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The total UV background light is composed of several ingredients, broadly including emissions from Earth's atmosphere, or airglow, Galactic emissions, and extragalactic emissions. The Galactic component has been shown to be dominated by interstellar UV radiation scattered isotropically by dust, but also includes molecular hydrogen fluorescence, H ii two-photon emission, and hot gas line emission, in smaller quantities (Murthy 2009; Bowyer 1991). The extragalactic component is dominated by UV flux from resolved sources (i.e., galaxies), but may also include weak emission from the IGM. Measurements of the resolved UV EBL can be determined from catalogs of extragalactic sources and can be interpreted as an average measurement of the star formation rate density over cosmological time, setting a lower limit for the total UV background light. Commonly, measurements of the UV background radiation that do not directly include these resolved sources are termed "diffuse background" measurements. Earlier studies making measurements of the diffuse FUV background are discussed in thorough reviews by Bowyer (1991) and Henry (1991), while more recent work has been reviewed by Murthy (2009). The definition of FUV wavelength coverage for each study varies between 912 and 1740 Å, depending on the detector used.

Several techniques have been imparted in order to measure the diffuse FUV background. First, many studies have measured Galactic dust scattering, removing airglow effects, and fitting models to diffuse observations, extrapolating the signal down to zero column density ($N_{\rm H\,\mathsc{i}}$ = 0) which provides levels for what is interpreted as the FUV extragalactic background (i.e., galactic sources and potentially diffuse IGM emission). Henry & Murthy (1993) used this technique to reanalyze data from the Johns Hopkins Ultraviolet Explorer experiment for observations above |b| = 40° (where b is Galactic latitude). An improved model simulating scattering of diffuse galactic light in the ISM was developed and used by Witt & Petersohn (1994) to re-measure the extragalactic background in Dynamic Explorer 1 observations from Fix et al. (1989). This same model was used by Witt et al. (1997) to re-evaluate the extragalactic background extrapolation from Far-Ultraviolet Space Telescope observations (Sasseen et al. 1995). Schiminovich et al. (2001) derived the extragalactic FUV background with data from the Narrowband Ultraviolet Imaging Experiment, the first experiment primarily designed to map the FUV background. Most recently, this extrapolation technique has been used by Seon et al. (2010) to measure the FUV extragalactic background with the Spectroscopy of Plasma Evolution from Astrophysical Radiation instrument. A second technique, that measures the truly diffuse extragalactic background, has been imparted by Brown et al. (2000) who masked the resolved FUV sources down to m_AB = 29 in HST STIS HDF-N and S, and HDF-N parallel imaging (Gardner et al. 2000a). They found a large unresolved diffuse background component that may include contributions from airglow.

Other studies have used FUV spectra and imaging from large data sets to map the FUV background over a large range of Galactic latitudes, revealing patchy skymaps of the background due to variations in intensities of the flux at different latitudes. Murthy et al. (1999) mapped the FUV background over the sky from 17 years of Voyager observations with the Voyager Ultraviolet Spectrometer, unique in that they are not partial to airglow effects, and Murthy & Sahnow (2004) mapped the FUV background intensity with Far-Ultraviolet Spectroscopic Explorer observations in 71 independent fields. Most recently, Murthy et al. (2010) used archival GALEX imaging to map the diffuse FUV background over ∼75% of the sky. This technique is used to put an upper limit on the extragalactic FUV background from values determined in the darkest areas of these data sets, primarily, but not necessarily, found in the vicinity of the Galactic poles. These FUV background skymaps have also revealed that some of the brightest FUV intensities are correlated with Galactic structures such as molecular clouds and nebulae. Detailed analysis to disentangle components of and effects on the diffuse FUV background in the vicinity of these structures have been carried out by determining correlations with H i column, H₂ fluorescence, Galactic extinction, and dust scattering, in some cases, resulting in measurements of an FUV extragalactic background component (Sujatha et al. 2005, 2007; Lee et al. 2006). Measurements of the diffuse FUV background are complimented by measurements of the resolved FUV background from extragalactic sources.

In this study, we calculate the FUV EBL from resolved sources in the FUV data used for number counts, and these results are given in Table 2. We use both sets of bright GALEX number counts in our calculation, giving us two possible values for the integrated EBL. First, we fit a slope of 0.13 ± 0.05 with an intercept of 0.68 ± 1.23 to our FUV number counts for magnitudes 24.5–28.5, including only the faint end of the SBC/FUV number counts distribution. We also fit a slope of 0.53 ± 0.01 with an intercept of −9.11 ± 0.28 to the XU05 GALEX counts for magnitudes 14.2–23.7. For the HAM10 field GALEX counts, we use the slope of 0.5 fitted to the FUV data by Hammer et al. (2010) with an intercept of −8.7 ± 0.81 for magnitudes 17.25–23.25. Next, these slopes, as well as the number counts, are converted to units of EBL per magnitude bin, erg s⁻¹ cm⁻² Hz⁻¹ sr⁻¹, using the formula from Madau & Pozzetti (2000):

$$\begin{equation} I_{\nu } = 10^{-0.4(\rm FUV_{{\rm AB}} + 48.6)}N(\rm FUV_{{\rm AB}}). \end{equation} \tag{ 1 }$$

Finally, we integrate under each function. For the combined fit of the faint-end SBC/FUV data with the XU05 data (hereafter EBL I), we set FUV_AB = 24.67 as the upper limit for the integral of the XU05 function and the lower limit for the integral of the SBC/FUV function, because this magnitude is the maximum in integrated light. From this model, we measure the integrated EBL for the magnitude range FUV_AB = 14–30 of $\nu \mathit {I_{\nu }}$ = 1.3^+0.2_{− 0.2} nW m⁻² sr⁻¹, or in photon units, $\mathit {I_{\lambda }}$ = 65.9⁺⁸_{− 8} photons s⁻¹ cm⁻² sr⁻¹ Å⁻¹. The errors are 1σ uncertainties on the number counts. The models and data are plotted in Figure 6. The model for the GALEX data between FUV_AB = 14–24.67 accounts for 66.5% of EBL I, measuring more of the resolved background light than our faint-end number counts. For the combined fit of the faint-end SBC/FUV data with the HAM10 data (hereafter EBL II), we set FUV_AB = 24.28 as the upper limit for the integral of the HAM10 function and the lower limit for the integral of the SBC/FUV function. From this model we measure the integrated EBL for the magnitude range FUV_AB = 17–30 of $\nu \mathit {I_{\nu }}$ = 1.6^+0.2_{− 0.2} nW m⁻² sr⁻¹, or in photon units, $\mathit {I_{\lambda }}$ = 82.6⁺¹²_{− 12} photons s⁻¹ cm⁻² sr⁻¹ Å⁻¹. Again, the GALEX portion of the model measures more resolved background light than our number counts, accounting for 66% of EBL II, very similar to XU05. This similarity is due to a caveat in the data included from these two studies in that XU05 cover a larger magnitude range than HAM10, and the latter has higher I_ν. This can be clearly seen in Figure 6.

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One of the first attempts at determining the FUV background from light emitted by galaxies was carried out by Martin & Bowyer (1989). They obtained data from an FUV imaging experiment that used a rocket mounted detector to observe signatures of galaxies in the integrated FUV background. The experiment covered wavelengths 1350–1900 Å and determined a 1σ upper limit for the summed FUV intensity coming from sources ∼50 photons s⁻¹ cm⁻² sr⁻¹ Å⁻¹, that is ∼25%–40% lower than our measurements. The UV EBL was measured at 2000 Å by Milliard et al. (1992) from FOCA number counts and by Armand et al. (1994) from predictions of number counts (Armand & Milliard 1994). While our measurements are well within the range of 40–130 photons s⁻¹ cm⁻² sr⁻¹ Å⁻¹ predicted by Armand et al. (1994), they are much higher than the 23 photons s⁻¹ cm⁻² sr⁻¹ Å⁻¹ determined from the FOCA number counts between magnitudes 15.0 and 18.5. Comparing our measurements to those from Gardner et al. (2000a), EBL I and EBL II are ∼54%–66% and ∼43%–58% lower, respectively, than their measurements of 2.9^+0.6_{− 0.4}–3.9^+1.1_{− 0.8} nW m⁻² sr⁻¹ (144⁺²⁸_{− 19}–195⁺⁵⁹_{− 39} photons s⁻¹ cm⁻² sr⁻¹ Å⁻¹) at 1595 Å. Xu et al. (2005) extrapolated models fit to the GALEX FUV number counts (1530 Å), integrated these functions to zero flux, and measured the total FUV EBL to be 1.03 ± 0.15 nW m⁻² sr⁻¹ which is ∼21% lower than EBL I, ∼37% lower than EBL II, and also below the Gardner et al. (2000a) range. The conclusion that can be drawn from our measurements is that the resolved EBL is unlikely to be much greater than ∼100 photons s⁻¹ cm⁻² sr⁻¹ Å⁻¹, and therefore other diffuse EBL measurements with significantly higher values (Schiminovich et al. 2001; Brown et al. 2000; Witt et al. 1997; Witt & Petersohn 1994; Henry & Murthy 1993) almost certainly include Galactic contributions and potentially smaller contributions from airglow. All values for the resolved FUV EBL discussed in this section are summarized in Table 2.