Investigating the [C ii]-to-H i Conversion Factor and the H i Gas Budget of Galaxies at z ≈ 6 with Hydrodynamic Simulations

One of the most fundamental baryonic matter components of galaxies is the neutral atomic hydrogen (H i). At low redshifts, this component can be traced directly through the 21 cm transition, but to infer the H i gas content of the most distant galaxies, a viable tracer is needed. We here investigate the fidelity of the fine-structure transition of the (2 P 3/2 − 2 P 1/3) transition of singly ionized carbon C ii at 158 μm as a proxy for H i in a set simulated galaxies at z ≈ 6, following the work by Heintz et al. We select 11,125 star-forming galaxies from the simba simulations, with far-infrared line emissions postprocessed and modeled within the Sigame framework. We find a strong connection between C ii and H i, with the relation between this C ii-to-H i relation (β [C II]) being anticorrelated with the gas-phase metallicity of the simulated galaxies. We further use these simulations to make predictions for the total baryonic matter content of galaxies at z ≈ 6, and specifically the H i gas mass fraction. We find mean values of M H I/M ⋆ = 1.4 and M H I/M bar,tot = 0.45. These results provide strong evidence for H i being the dominant baryonic matter component by mass in galaxies at z ≈ 6.


INTRODUCTION
In the process of galaxy formation, the infall of neutral atomic hydrogen (H I) is a necessary, fundamental ingredient in the formation of stars.Reservoirs of H I gas condense into molecular hydrogen (H 2 ), which serves as fuel for star formation.As such, H I is a crucial component for the assembly of galaxies, and thus governs the first epoch of galaxy formation.At higher redshifts (z > 3) H I can also reveal large-scale structure of the universe by tracing the precursors to superclusters of galaxies (e.g.Scott & Rees 1990).
The main tracer of H I is the λ = 21 cm line, which arises from transitions between the hyperfine structure levels in the ground state of the hydrogen atom.There are many benefits, in theory, of utilizing the 21 cm line -for instance, it does not suffer from dust extinction and attenuation like other lines, and kinematic information about the emitting gas can be derived from its Doppler shift (Walter et al. 2008).Even though H I has been observed within our own galaxy (e.g.Kalberla et al. 2005) and for many galaxies locally (e.g.Thuan & Martin 1981;Swaters et al. 2002;Walter et al. 2008), few detections of the 21-cm line emission have been made beyond z ≈ 0.3 (Bera et al. 2019), mainly due to the weakness of the transition and the limited sensitivity (Carilli & Walter 2013).The current most distant estimate for a single galaxy has reached z = 0.376 (Fernández et al. 2016), with other recent works examining the average 21-cm signal from a stack of a few thousand galaxies out to z ≈ 1 (Chowdhury et al. 2020(Chowdhury et al. , 2021)).Although the evolution of the H I budget across redshift has been modeled via theoretical predictions (Madau & Dickinson 2014), our understanding of the fueling of star formation rate across cosmic time is incomplete without an understanding of how the contribution of H I to the total composition of galaxies evolves with redshift, from the epoch of reionization until today.
To infer the H I gas content of even more distant galaxies, it is clear that a suitable tracer has to be identified as a proxy.This is similar to how observations of in particular CO and [C I] has been used as tracers of the molecular gas content of galaxies through most of cosmic time (e.g.Papadopoulos & Greve 2004;Bolatto et al. 2013).We here investigate the 158 µm (1900.5 GHz) fine-structure transition of singly-ionized carbon ([Cii]) as a potential tracer of H I. This particular transition was suggested by Morton & Hu (1975) early on to be a strong cooling line within H I regions.Further work by Tielens & Hollenbach (1985); Wolfire et al. (1995); Hollenbach & Tielens (1999); Wolfire et al. (2003) chemically examined the role of [C II] in the cooling of photodissociation regions (PDRs) and the cold and warm neutral medium (CNM and WNM, respectively).Observationally, Madden et al. (1993) found that extended [C II] emission in NGC 6946 likely emerged from cold, atomic hydrogen clouds.Madden et al. (1997) investigated a correlation between [C II] luminosity and the H I gas mass (M H I ) in the local irregular galaxy IC 10, finding that while most [C II] emission arose from dense photodissociation regions (PDRs), ∼ 20% of the emission could arise from atomic hydrogen regions in the interstellar medium (ISM) of the galaxy.More recent work relying on hydrodynamical simulations of galaxies (e.g., Vallini et al. 2015;Lupi & Bovino 2020;Ramos Padilla et al. 2021, 2022) have constrained the fraction of [C II] originating from different ISM phases, showing that it is more predominantly produced in neutral H I regions at higher redshifts.As [C II] is one of the strongest cooling lines in the ISM, it is one of the brightest farinfrared lines and thus easily observable at high redshifts (Stacey et al. 2010).This makes it a natural candidate as a potential proxy for H I at z ≈ 6.With the further evidence to support it as a tracer of H I in the local universe, and the strong connection found in high-redshift gamma-ray burst (GRB) sightlines (Heintz et al. 2021), we here wish to further explore the feasibility of [C II] as a tracer of H I based on simulations to a) clarify and further investigate the viability of [C II] as a proxy for H I, b) make predictions for the H I gas mass fraction in galaxies at z ≈ 6, c) examine the underlying physics which drive this correlation.
The paper is structured as follows: In Section 2 we describe the observational and hydrodynamical simulation samples utilized for the purposes of this work.In Section 3 we describe the [C II]-HI relation both in equation form and in terms of a single conversion factor, β [C II] , and analyze the effect of metallicity on β [C II] .In Section 4 we investigate the H I gas budget at z ≈ 6.We conclude this work in Section 5.

SIMULATIONS & OBSERVATIONAL SAMPLES
This work uses a set of simba (Davé et al. 2019) galaxy simulations at z = 5.93, with line emission simulated and post-processed using v2 of Sígame (Olsen et al. 2017).The simba simulation set consists of three cubical volumes of 25, 50 and 100 cMpc h −1 on a side, all of which are used in this work to search for galaxies at z ∼ 6.For each volume, a total of 1024 3 gas elements and 1024 3 dark matter particles are evolved from z = 249.Within these three volumes, a total of 11,137 galaxies were selected via the yt (Turk et al. 2011)-based package caesar; yt is a Python package used to visualize & analyze volumetric data, and caesar is a sixdimensional friends-of-friends algorithm which is applied to the simulated gas and stellar particles to identify and select simba galaxies.The galaxy properties derived with caesar include star formation rate (SFR), computed by dividing the stellar mass formed over a 100 Myr timescale (Leung et al. 2020), SFR surface density, stellar mass (M ), and a SFR-weighted gas-phase metallicity (Z).The ionized, molecular, and atomic gas masses are calculated via caesar to be equal to the total mass of all gas particles associated with each respective phase (we refer to Olsen et al. 2017;Vizgan et al. 2022, for further description of how these gas "particles" are defined and constructed).
Our final sample consists of 11,125 galaxies, with [C II] luminosities in the range L [CII] = 10 3.82 − 10 8.91 L and a molecular gas masses M mol = 10 6.25 −10 10.33 M , with a mean M of 10 8.07 M , mean SFR of 1.9 M /yr, and mean metallicity of 0.18 Z .We refer to Leung et al. (2020) and Vizgan et al. (2022) for further description and detailing of simba, Sígame, caesar, and the simulation sample.
In this work, we define the total H I gas mass in each galaxy to be equal to the sum of its ionized and atomic hydrogen gas mass, independent of galactic region or radius.Molecular clouds have been shown observationally to also consist of a substantial fraction of H I and will thereby also contribute to the total H I gas mass.The fraction of H I in molecular clouds has been measured to vary between 20 to 80% in our Galaxy (Burgh et al. 2010), so here we assume that ∼50% of the total molec-ular gas in our simulations is H I. Similarly, a significant H I volume filling fraction of ≈ 50% has been derived for interstellar H I within the warm neutral medium in the solar neighborhood (Heiles & Troland 2003).The way that Sígame classifies gas particles as "ionized" in this gas-phase is by requiring that its electron-to-hydrogen fraction is x e − > 0.5; consequently, a gas particle in Sígame will be considered completely ionized beyond x e − > 0.5, and otherwise neutral.This is not realistic when considering a real galaxy and we thus assume ∼50% of the ionized gas will contribute to the atomic gas mass because of this classification.Because of this assumption, the gas masses derived from simulations should technically be treated as upper limits on the neutral gas budget.
We supplement our simulation sets with some observational samples of [C II] observations from the literature.We use H I gas masses (Cormier et al. 2015) of main-sequence dwarf galaxies with [C II] observations in the local Herschel Dwarf Galaxy Survey (Madden et al. 2013), which serve as high-redshift analogs.In addition, we use the X-shooter GRB afterglow legacy sample (XS-GRB; Selsing et al. 2019), which cover a redshift range between 0.059 and 7.84 and which were detected with the Swift satellite.(1) with a root-mean-square (rms) scatter of 0.39 dex.For comparison, we examine the relation between L [CII] and M mol and SFR within these simulations.We find that scatter is notably tighter than L [CII] vs. M mol (0.45 dex) and than L [CII] vs. SFR (0.50 dex) for our simulations (Vizgan et al. 2022).This is further support of [C II] being most tightly connected to H I, and thus a more reliable tracer of this gas-phase.Figure 2 2019) (see also Heintz et al. 2021), while the orange points are the galaxies from Cormier et al. (2015).

The metallicity dependence of the [C II]-to-H I conversion factor
Defining the [C II]-to-H I conversion factor as (Heintz et al. 2021), we derive a median log β [C II] = 1.7 +0.4 −0.3 M / L for our set of simulated galaxies at z ≈ 6. Heintz et al. (2021) This [C II]-to-H I relation is derived from a combination of high-z GRB afterglows, assuming that their pencilbeam sightlines probe representative regions of the starforming ISM, and was found to show remarkable consistency with direct observations of local galaxies (Heintz et al. 2021).
In Fig. 2 we examine the evolution of β [C II] with metallicity within our simulations.For comparison, we overplot the measurements at z = 1.7 − 6.3 from the GRB sightlines (Heintz et al. 2021) and the local set of observations (Cormier et al. 2015).We find an anti-correlation between β [C II] and Z with our simulations (with r/pearson coefficient = −0.20), in strong agreement with Heintz et al. (2021) and the local galaxy sample.Additionally, there appears to be a slight correlation between β [C II] and star formation rate.The anticorrelation of β [C II] is mostly a result of the definition; i.e. [C II]/H I is a proxy to carbon/hydrogen, hence the galaxies which are more-metal rich will have more carbon available, both in the neutral and ionized states.
With this set of simulations, we further make predictions of the H I gas mass fraction of galaxies at z ≈ 6. Defining the H I gas mass excess as M H I /M , we find a mean and median M H I /M = 1.4 and 1.2 +0.9 −0.6 , respectively.We also predict the fraction of H I by mass to the total baryonic matter content M bar,tot = M H I + M H2 + M .We find a mean and median fraction of M H I /M bar,tot = 0.45 and 0.46 +0.12 −0.13 , respectively.By comparison, the mean M H2 /M bar,tot is 0.17 and median 0.15 +0.10 −0.06 ; the mean M /M bar,tot is 0.38, and the median is 0.37 +0.14 −0.11 .We thus predict that H I is the dominant, baryonic matter component in galaxies at z ≈ 6.
Several observational works (e.In Figure 3 we investigate the evolution of the H I gas mass budget, comparing the data from the ALPINE [C II] survey (e.g.Dessauges-Zavadsky et al. 2020) with our simulations.The H I gas masses in the ALPINE data are derived first by deriving metallicities from their SFRs and stellar masses via the high-redshift massmetallicity relation in Curti et al. (2020), and then by using Equation 2 in this work (also see Heintz et al. 2021).We find that the ALPINE data are in reasonable agreement with the simulations; direct metallicity measurements from the ALMA sources, which were not available in the data, would allow for better constraints on the H I gas mass.Nonetheless, the ALPINE data are consistent with the prediction from simulations that the H I gas mass content should dominate the ISM at high-redshift.As the ALPINE team used the work from Zanella et al. (2018) 2020) For the ALPINE data, we derive gasphase metallicities from their M and SFRs using the massmetallicity relation in Curti et al. (2020).From there, we use Equation 2 to derive estimates of their H I gas mass content.
the H I, H 2 , or both gas masses, as it appears to be a good tracer of both the neutral and molecular gas reservoirs which occupy the ISMs of high-redshift galaxies.

CONCLUSIONS
Previously, [C II] has been used as a tracer of SFR in galaxies (e.g.De Looze et al. 2014), and more recently as a tracer of H 2 gas mass (e.g.Zanella et al. 2018;Madden et al. 2020;Dessauges-Zavadsky et al. 2020;Vizgan et al. 2022).In this work, we use a set of simulated galaxies at z 6 (Vizgan et al. 2022) to investigate the utility of [C II] luminosity as a tracer of atomic (i.e.diffuse) hydrogen gas mass, following the work of Heintz et al. (2021).We present our main findings below: 1.For our simba simulations at z = 6, we are able to find a strong relationship between [C II] luminosity and H I gas mass: log Significantly, the relation is more tightly correlated (0.39 dex) than the [C II]-to-H 2 (0.45 dex) and [C II]-to-SFR (0.50 dex) correlations described in Vizgan et al. (2022).Furthermore, we find an anti-correlation of of β [C II] with metallicity.
2. We find that the H I gas mass is a critical baryonic matter component, with mean M H I /M = 1.4,and M H I /M bar,tot = 0.45.We conclude that in the high-redshift universe, galaxies' ISMs (excluding dust) are dominated by H I baryonic matter content.
3. We compare our work with archival [C II] observational data, finding that extrapolating H I gas masses from high-redshift [C II] sources in the ALPINE [C II] survey yields an evolution of the H I gas mass budget over stellar mass which agrees with predictions from simulations.
We ultimately conclude that [C II] is a viable proxy to infer amount of H I in galaxies at z ≈ 6. [C II] is readily available in the high-redshift universe for large surveys (e.g. the Large ALMA-ALPINE survey at z ∼ 4 − 6 (Dessauges-Zavadsky et al. 2020;Le Fèvre et al. 2020;Béthermin et al. 2020;Faisst et al. 2020, etc.); and REBELS at z ∼ 6 − 8 (e.g.; Bouwens et al. 2021;Heintz et al. 2022).Establishing a proxy for H I is particularly important as even the next-generation radio facilities such as the SKA will only be able to detect and measure H I out to z ≈ 2, and will not be able to probe the evolution of H I in the universe beyond cosmic noon.

ACKNOWLEDGEMENTS
We are grateful the anonymous referee for insights and feedback which strengthened this work.We thank Robert Thompson for developing caesar, and the yt team for development and support of yt.This research made use of the the TOPCAT data analysis software (Taylor 2005) Metallicities and H I column densities of these GRBs are taken fromBolmer et al. (2019), and the [C II] column densities are taken fromHeintz et al. (2021).
3. THE [C II]-TO-H I RELATION 3.1.Connecting L [C II] and M HI We examine the total [C II] luminosity of the z 6 simulated galaxies and its connection to the total diffuse H I gas mass in Fig. 1, color-coded as a function of SFR.In previous work, Vizgan et al. (2022) attempted to test and verify the use of [C II] as a tracer of the molecular gas based on the same set of simulated galaxies at z ≈ 6.They found a sub-linear relation between M mol and L [C II] , in contrast with the linear relation described by Zanella et al. (2018), which arose as a consequence of the Kennicutt-Schmidt Law.By performing a log-linear fit to the data, we find a strong correlation between the [C II] and H I, yielding a best-fit relation of log L [C II] = 1.02 log M H I − 1.95.

Figure 1 .
Figure 1.Top panel: Histograms of scatter around the best-fit models for the [C II]-to-H I relation (this work, crimson) and for the [C II]-H2 relation (Vizgan et al. 2022, violet); the scatter around the former relation is tighter (0.39 dex) than for the [C II]-H2 relation (0.45 dex).Bottom figure: The [C II] luminosity vs. H I gas mass relation for our z 6 simulations.We find a very strong linear correlation between these two quantities, yielding a best-fit of log L [C II] = 1.02 log MH I − 1.95.The simulations are color-coded by the star formation rate, further demonstrating a correlation between SFR and the log-linear [C II]-H I relation.When accounting only for the diffuse H I mass derived from Cloudy, the relation changes to log L [C II] = 0.84 log MH I + 0.55 with a scatter of 0.22 dex.
g. Zanella et al. 2018; Dessauges-Zavadsky et al. 2020) have investigated the use of [C II] as a molecular gas mass tracer.Vizgan et al. (2022) showed that the α [C II] derived by Zanella et al. (2018) (Z18) required further calibration, as the slope of the log-linear[C II]-M mol relation was not near unity.Dessauges-Zavadsky et al. (2020) used the Z18 α [C II] relation to derive the molecular gas budgets of their observations across redshift.

Figure 3 .
Figure3.The evolution of the H I gas mass excess with stellar mass.Our simulations are color-coded by star formation rate, and the y-axis is scaled logarithmically.The green stars represent galaxies from the ALPINE survey Dessauges-Zavadsky et al. (2020) For the ALPINE data, we derive gasphase metallicities from their M and SFRs using the massmetallicity relation inCurti et al. (2020).From there, we use Equation 2 to derive estimates of their H I gas mass content.
. This research was made possible by the National Science Foundation (NSF)-funded DAWN-IRES program and would not be possible without support from the Cosmic Dawn Center (DAWN) in Copenhagen, Denmark.The Cosmic Dawn Center (DAWN) is funded by the Danish National Research Foundation under grant No. 140.DV was funded by an Open Study/Research Award from the Fulbright U.S. Student Program in Denmark.KEH acknowledges support from the Carlsberg Foundation Reintegration Fellowship Grant CF21-0103.KPO is funded by NASA under award No 80NSSC19K1651.DN acknowledges support from the NSF via grant AST 1909153.TRG acknowledges support from the Carlsberg Foundation (grant no CF20-0534) RD acknowledges support from the Wolfson Research Merit Award program of the U.K. Royal Society.simba was run on the DiRAC@Durham facility managed by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility.The equipment was funded by BEIS capital funding