Far-infrared line emission from high-redshift galaxies

Abstract

1 INTRODUCTION

High-z galaxies are mainly discovered by means of their Lyman α emission line (Lyman alpha emitters; LAEs; e.g. Malhotra et al. 2005; Shimasaku et al. 2006; Hu et al. 2010; Ouchi et al. 2010) or through drop-out techniques (Lyman break galaxies; e.g. Steidel et al. 1996; Castellano et al. 2010; Bouwens et al. 2011; McLure et al. 2011). Both methods are plagued with intrinsic limitations: the Lyα detection is hampered by the increasingly neutral intergalactic medium, while the source redshift cannot be precisely determined with drop-out techniques; in addition, the rest-frame optical/ultraviolet (UV) radiation is strongly affected by the presence of dust. It is then important to assess whether other probes, as the far-infrared (FIR) metal lines ([C ii], [O i] and [N ii]) originating from the interstellar medium (ISM) of galaxies, could be used to detect new distant sources or better determine the properties of those already discovered. These lines are not affected by H i or dust attenuation, can deliver the precise redshift of the emitter and open a window to investigate the structure of the galactic ISM.

Among FIR lines, the ²P_3/2 → ²P_1/2 fine-structure transition of ionized carbon [C ii], a major coolant of the ISM, is by far most widely used to trace the diffuse neutral medium (e.g. Dalgarno & McCray 1972; Stacey et al. 1991; Wolfire et al. 1995; Lehner, Wakker & Savage 2004). Up to now, high-redshift (z > 4) detections of [C ii] lines have been obtained mainly in sources with high star formation rates (SFRs) (e.g. Cox et al. 2011; De Breuck et al. 2011) or in those hosting active galactic nuclei (e.g. Maiolino et al. 2005; Gallerani et al. 2012). Recently, Walter et al. (2012) put upper limits on the [C ii] luminosity arising from a gamma-ray burst host galaxy and two LAEs with moderate SFR. Other interesting fine-structure lines are [O i] 63 μm, tracing neutral (higher density) gas, and [N ii] 122 μm probing the ionized ISM phase. [O i] detections have been reported in two lensed ultraluminous infrared galaxies at z = 1.3 and z = 2.3 (Sturm et al. 2010); z > 4 nitrogen lines (including the [N ii] 205 μm) have been detected in quasars and submillimetre galaxies (Ferkinhoff et al. 2011; Combes et al. 2012; Decarli et al. 2012; Nagao et al. 2012). The unprecedented sensitivity of ALMA will revolutionize the field allowing the detection of FIR lines from the known ‘normal’ population of high-z galaxies (e.g. Carilli & Walter 2013, and references therein) as in the case of [C ii] detections in two z = 4.7 LAEs presented by Carilli et al. (2013). Therefore, developing models to predict FIR line luminosities and relate them to other physical features such as metallicity, Z, and SFR is fundamental to design and interpret future experiments.

In this work, we present the first detailed predictions for the intensity of several FIR emission lines ([C ii] 158, [O i] 63 and [N ii] 122 μm) arising from the ISM in high-z star-forming galaxies. Our work is similar in spirit to that of Nagamine, Wolfe & Hernquist (2006), who computed the [C ii] galaxy luminosity function based on a smoothed particle hydrodynamics (SPH) simulation coupled with a subgrid multiphase model of the ISM. We improve upon Nagamine et al. (2006) work in at least two ways: (a) we concentrate on a single prototypical high-z galaxy, a z = 6.6 LAE, hence reaching a sufficiently high resolution to properly describe the ISM small-scale density structure and (b) we implement radiative transfer (RT) which is crucial to model the intensity of the galactic UV field and the gas ionization structure.

2 NUMERICAL SIMULATIONS

We run cosmological SPH hydrodynamic simulations using gadget-2 (Springel 2005). We use the recent Wilkinson Microwave Anisotropy Probe 7+BAO+H₀ cosmological parameters: Ω_m = 0.272, Ω_Λ = 0.728, Ω_b = 0.0455, h = 0.704 and σ₈ = 0.807 (Komatsu et al. 2011). We simulate a (10 h^{− 1} Mpc)³ comoving volume with 2 × 512³ baryonic+dark matter particles, giving a mass resolution of 1.32 (6.68) × 10⁵ M_⊙ for baryons (dark matter) and gravitational softening ϵ = 2 h⁻¹ kpc. We select a snapshot at redshift z = 6.6, and we identify the most massive halo (total mass M_h = 1.17 × 10¹¹ M_⊙, r_vir ≈ 20 kpc) by using a Friend-of-Friend algorithm. We select a (0.625 h⁻¹ Mpc)³ comoving volume around the centre of the halo, and post-processed UV RT using licorice (Baek et al. 2009). licorice uses a Monte Carlo ray-tracing scheme on an adaptive grid. We set the adaptive grid parameter to have a minimum RT size of 0.61 h⁻¹ kpc. Starting from the density field provided by gadget, we recompute gas temperature including atomic cooling from the initial temperature T₀ = 10⁴ K. The initial ionization fraction is set to |$x_{\rm H\,\small {II}}=0$|⁠.

To define the position of the ionizing sources, we assume that stars form in those cells which are characterized by a gas density ρ ≥ ρ_th. We choose ρ_th = 1 cm⁻³, in order to reproduce the typical size (∼1–2 kpc) of star-forming regions at z ≈ 6 (Bouwens et al. 2004; Ouchi et al. 2009), as inferred by UV continuum emitting images. The projected position of stellar sources is shown in white in the upper-left panel of Fig. 1. A central large stellar cluster is clearly visible, along with other three minor stellar clumps displaced from the centre. We use the population synthesis code starburst99 (Leitherer et al. 1999) to obtain the ionizing spectrum of the galaxy. Theoretical works suggest that high-z galaxies might be relatively enriched (Z ≳ 0.1 Z_⊙) galaxies (Dayal et al. 2009; Salvaterra, Ferrara & Dayal 2011). We adopt Z = Z_⊙ as a fiducial value for our study, but we also consider a lower metallicity case, i.e. Z = 0.02 Z_⊙. We assume a Salpeter initial mass function with a slope of α = 2.35 in the mass range 1–100 M_⊙ and a continuous SFR of 10 M_⊙ yr⁻¹, obtained from the SFR–M_h relation at z = 6.6 (Baek et al. 2009; Baek, Ferrara & Semelin 2012). Ionizing UV luminosity is about L_UV ≈ 7 × 10⁴³ erg s^{− 1}. RT calculations are performed until equilibrium between photoionizations and recombinations is achieved; this occurs within ≈10 Myr. The public version of gadget-2 used in this work does not include the star formation process, neither the radiative cooling nor supernova (SN) feedback. The inclusion of radiative cooling may affect the baryon density profile, enhancing the density towards the centre of the galaxy, whereas SN feedback tends to smooth out density inhomogeneities. We have checked that the baryon density profile resulting from the simulations used in this work fits well with our previous low-resolution simulations which include all these processes (Baek et al. 2009). Finally, we note that the large gravitational potential of massive galaxies reduces the effects of SN feedback on star formation, as exemplified by fig. 1 of Vallini, Dayal & Ferrara (2012) and related discussion. We interpolate all gas physical properties around the halo centre on a fixed 512³ grid using the SPH kernel and smoothing length, within a (0.156 h⁻¹ Mpc)³ comoving volume. We achieve a higher resolution by interpolating on a finer grid as shown in fig. 6 of Baek et al. (2012). This method also allows us to have a continuos probability distribution function of the density, at low- and high-dense regions and thus increases the maximum density by about 50 per cent from 64³ grid to 512³ grid. The resulting hydrogen column density map is shown in the upper-right panel of Fig. 1.

Figure 1.

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Upper panels: the projected stellar distribution (left) and hydrogen column density (right). Lower panels: warm (left) and cold (right) neutral medium column density. The distribution of WNM is more diffuse compared to that of CNM which is predominantly found in small (D ≤ 2 kpc) clumps far from star-forming regions.

3 MULTIPHASE ISM MODEL

In the lower panels of Fig. 1, we show the WNM and CNM column densities. The WNM distribution closely traces regions of high (N_H ≈ 10²² cm^{− 2}) total hydrogen column density that are sufficiently far from the central star-forming region in order not to become ionized; cold gas lies instead only in small (D ≤ 2 kpc) overdense clumps at the periphery of the galaxy. The maps show that cold gas clumps are surrounded by diffuse haloes of WNM.

3.1 FIR emission lines

4 RESULTS

In Fig. 2, we show the predicted [C ii] 158, [O i] 63 and [N ii] 122 μm emission for the spectral resolution of our simulations (1.0 km s⁻¹), a beam resolution of 0.1 arcsec and Z = Z_⊙, along with the maps obtained by integrating the spectra over the full velocity range −200 < v < 300 km s⁻¹.

Figure 2.

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Left-hand column: the total (CNM+WNM) and WNM only (orange) spectrum of [C ii], [O i] and [N ii] binned in 1.0 km s⁻¹ channels. Right-hand column: [C ii], [O i] and [N ii] maps in mJy km s⁻¹ with a resolution of 0.1 arcsec and integrated over the entire spectral velocity range. The contribution of clump A to the [C ii] spectrum is plotted in grey.

The [C ii] spectrum contains considerable structure due to the presence of several emitting CNM clumps distributed over the entire galaxy's body (∼20 kpc). The individual sizes of the clumps are however much smaller (≲3 kpc). The peak of the spectrum reaches ∼2.5 mJy and it is displaced from the centre of the galaxy by about 100 km s⁻¹. This is due to the fact that the gas within the central kpc of our galaxy is highly ionized by the massive stars that form there. We find that 95 per cent of the total [C ii] flux originates from the CNM, and only 5 per cent from the WNM. For the [C ii] emission line, we obtain a flux of 185 mJy km s⁻¹, integrating over ∼500 km s⁻¹.

In Fig. 2, we plot in grey the spectrum extracted by integrating over a circular area of ∼2 kpc radius, centred on the component labelled ‘A’ in the map. It dominates the peak of the [C ii] spectrum (30 per cent contribution to the total emission), with the remaining ∼70 per cent coming from less luminous substructures. This is an important point as with high spatial resolution observations a substantial fraction of the [C ii] emission may remain undetected. The full width at half-maximum of the main peak is ∼50 km s⁻¹, consistent with the marginal detection of [C ii] in high-z LAEs (Carilli & Walter 2013). We have computed FIR line intensities also for a metallicity Z = 0.02 Z_⊙. In this case, the [C ii] and [O i] intensities drop by a factor of ∼1000 and ∼300, respectively, whereas the [N ii] flux is reduced by a factor of 50. While the WNM emission is ∝Z, at very low Z, CNM is practically absent, since the lower metal content makes the CNM phase thermodynamically unfavourable. A thorough analysis of the relative fraction of the emission arising from CNM and WNM as a function of Z will be addressed in a forthcoming paper.

The [O i] spectrum has a shape similar to that of [C ii], since for both emission lines we are taking into account the emission arising from the neutral phase of the ISM. In the case of [O i], 75 per cent of the total flux arises from the CNM and 25 per cent from the WNM. The maximum value of the [O i] flux is ∼0.35 mJy. The [N ii] emission line reaches a maximum flux of 0.022 mJy at v = 0. This line traces the ionized phase of the ISM, and the bulk of its emission arises from the centre of the galaxy where the ionizing field intensity is higher. In conclusion, the [O i] and [N ii] fluxes are ∼6 and ∼90 times lower than the [C ii] one.

5 COMPARISON WITH OBSERVATIONS

5.1 LAE observations

As pointed out in the introduction, FIR line observations in high-z sources have been carried out mainly in quasars and submillimetre galaxies. Recently, Walter et al. (2012) have tried to detect the [C ii] emission in Himiko, one of the most luminous LAEs at z = 6.6 (Ouchi et al. 2009). However, they end up only with a 1σ upper limit of 0.7 mJy km s⁻¹.

The large size of the Himiko Lyα emitting nebula (≥17 kpc) makes this object one of the most massive galaxies discovered at such high redshifts (Ouchi et al. 2009; Wagg & Kanekar 2012). From this point of view, Himiko's properties closely resemble those of the prototypical galaxy selected from our simulation. Moreover, the radius of the region within which we distributed the stars (∼1–2 kpc) is consistent with the Himiko half-light radius (1.6 kpc) observed by Ouchi et al. (2009). Other properties of Himiko are poorly constrained. The SFR is highly uncertain and its value strongly depends on the diagnostics used to infer it: SED fitting gives ≳ 34 M_⊙ yr⁻¹, UV luminosities yields |$25^{+24}_{-12}\,{\rm M_{{\odot }}\,yr^{-1}}$| and the Lyα line implies 36 ± 2 M_⊙ yr⁻¹. As for the metallicity, Ouchi et al. (2009) suggest Z = [1–0.02] Z_⊙ as a plausible range, i.e. consistent with the one we have chosen for our analysis.

For a fair comparison with the Plateau de Bure interferometer (PdBI) data by Walter et al. (2012), we smooth our [C ii] simulations to a beam resolution of 2.27 arcsec × 1.73 arcsec, and produce channel maps of 200 km s⁻¹ width. In Fig. 3, we show the map with the largest signal achieved. We find that for Z = Z_⊙ the maximum intensity is ∼0.72 mJy km s⁻¹, slightly exceeding the observed upper limit by Walter et al. (2012); thus, we can put a solid upper limit on Himiko's metallicity Z < Z_⊙. This shows the potential of FIR lines in obtaining reliable metallicity measures in high-z galaxies.

Figure 3.

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Synthetic map of [C ii] emission in mJy km s⁻¹ integrated over a velocity channel of width = 200 km s⁻¹ and smoothed to an angular resolution of 2.27 arcsec × 1.73 arcsec to allow comparison with Walter et al. (2012) observations.

5.2 Low-redshift observations

Haro 11 (H11), a nearby (z ∼ 0.02) dwarf galaxy (Cormier et al. 2012), is considered a suitable local high-z galaxy analogue. Through PACS observations of the [C ii], [O i] and [N ii] lines, Cormier et al. (2012) measured a size of ∼3.9 kpc for the H11 star-forming region, a value which is comparable to the size of the clump A shown in the uppermost right panel in Fig. 2. These authors also estimate the relative contribution to the observed FIR lines from the diffuse (neutral/ionized) medium and PDRs. They found that ∼80 per cent of the [C ii] and [N ii] emissions come from the diffuse medium, while the [O i] mostly originates from PDRs. We scale the luminosities of the predicted FIR emission lines to the H11 luminosity distance (D_L ∼ 88) and metal abundances (Cormier et al. 2012). For a fair comparison with the data taken from table 2 of Cormier et al. (2012), we compute [C ii], [O i] and [N ii] spectra by integrating over a region of ∼12 kpc in diameter, which corresponds to an angular size of 30 arcsec at the H11 redshift. For [C ii] and [N ii] lines, our model predicts a flux corresponding to 20 per cent of the observed one. For what concerns [O i], we recover only 3 per cent of the observed flux. However, we recall that the contribution of PDRs, not included in our model, might be non-negligible.

6 ALMA PREDICTIONS

In Table 1, we plot the expected total fluxes for the FIR emission lines considered, varying the metallicity between Z_⊙ and 0.02 Z_⊙. In the solar metallicity case, a [C ii] ∼5σ detection over four 25 km s^{− 1} channels requires a sensitivity of 0.2 mJy, which translates into an observing time of t_ON = 1.9 h with the ALMA full array. We note that the predicted fluxes are sensitive to the actual value of Z, implying that a [C ii] line detection can strongly constrain LAE metallicities. On the other hand, this implies that LAEs characterized by metallicities Z < 0.5 Z_⊙ would require a long observing time (t_ON > 7.7 h) to be detected even with the ALMA full array.

7 SUMMARY AND CONCLUSIONS

We have presented the first attempt to predict the intensity of several FIR emission lines ([C ii] 158, [O i] 63 and [N ii] 122 μm) arising from the ISM of high-z star-forming galaxies. We combined RT simulations of a z = 6.6 galaxy with a subgrid multiphase model to predict the density and temperature of the cold and warm neutral phase of the diffuse ISM. We find that WNM lies in overdense regions located sufficiently far from the central star-forming clump where the strong ionizing UV field does not allow the presence of neutral gas. Cold gas resides instead in more dense clumps. The physical properties of the CNM and WNM deduced here are in agreement with previous studies (e.g. W95; W03): the mean density and temperature of the CNM and WNM gas are 〈n_CNM〉 = 50 cm⁻³, 〈T_CNM〉 = 250 K and 〈n_WNM〉 = 1.0 cm⁻³, 〈T_WNM〉 = 5000 K, respectively.

Assuming Z = Z_⊙, our model predicts for the [C ii] emission line a flux of 185 mJy km s⁻¹, integrating over ∼500 km s⁻¹. The [O i] and [N ii] fluxes are ∼6 and ∼90 times lower than the [C ii] one, respectively. We have also investigated the case of Z = 0.02 Z_⊙. At this metallicity, the [C ii] and [O i] intensities drop by a factor of ∼1000 and ∼300, respectively, while the [N ii] flux is reduced by a factor of 50.

In the case of Z = Z_⊙, we have found that 95 per cent (75 per cent) of the [C ii] ([O i]) emission arises from the CNM of the ISM, and the remaining 5 per cent (25 per cent) from the warm neutral phase. In the lower metallicity case, the fluxes of the [C ii] and [O i] emission lines drop abruptly since the lower metal content does not allow the presence of CNM phase. As a caveat, we note that the [O i] 63 mμ line could be optically thick (e.g. Vasta et al. 2010). The intensity of the [N ii] line, instead, scales linearly with the metallicity, since it arises from the ionized medium.

Interestingly, the [C ii] and [O i] lines are shifted with respect to the [N ii] line, as a consequence of the fact that they originate from different regions: while the ionized medium, which is traced by the [N ii] line, is located close to the centre of the galaxy, the neutral gas, from which the [C ii] and [O i] lines originate, is predominantly located at large galactocentric radii. This result can explain the shift between the [C ii] and [N ii] lines observed in some high-z galaxies (e.g. Nagao et al. 2012). We have compared our predictions with observations of FIR emission lines in high-z and local star-forming galaxies. At Z = Z_⊙, our model slightly exceeds the 1σ = 0.7 mJy km s⁻¹ upper limit on the [C ii] intensity found in Himiko through PdBI observations (Walter et al. 2012). This result suggests that the gas metallicity in this source must be subsolar. Our results are also marginally consistent with [C ii], [O i] and [N ii] observations of H11 (Cormier et al. 2012), a suitable high-z galaxy analogue in the local Universe. In this case, our model predicts a flux which is ∼20 per cent (∼3 per cent) of the observed one in the case of [C ii] and [N ii] ([O i]) emissions.

We underestimate that the observed flux in H11 as a non-negligible fraction of their flux may be provided by dense PDRs not included yet in our study. In particular, the [O i] line is expected to originate primarily from PDRs (Cormier et al. 2012). We defer the inclusion of PDRs in a forthcoming paper.

According to our findings, the [C ii] emission line is detectable with the ALMA full array in 1.9 < t_ON < 7.7 h in star-forming, high-z galaxies with Z_⊙ > Z > 0.5 Z_⊙. We emphasize again that our predictions provide a solid lower limit to the expected FIR emission lines flux.

Finally, the results presented in this work might be very useful to FIR line intensity mapping studies. In fact, our model represents a valid tool to calibrate the intensity of these lines depending on the different properties of the first galaxies, such as the metallicity and the SFR. Since the mass of the CNM increases in weaker FUV radiation field environments, it is likely that the specific emission from FIR emission lines as the [C ii] and [O i] could increase towards fainter galaxies. We leave a dedicated study of this effect to future work.

We thank F. Combes, D. Cormier, S. Madden and T. Nagao for useful discussions and comments.

REFERENCES