https://orcid.org/0000-0002-9593-0053
ABSTRACT
Rest-utraviolet (UV) spectroscopy can constrain properties of the stellar populations, outflows, covering fractions, and can indirectly constrain the Lyman continuum escape fraction of galaxies. Many works have studied the rest-UV spectra of more massive star-forming galaxies and low-mass galaxies selected via strong nebular line emission or via Ly |$\alpha$| emission. However, studies of rest-UV spectroscopy have yet to be done on an unbiased sample at low mass during the epoch of peak star formation (|$z\sim 2$|). We present a stacked rest-UV spectrum of a complete sample of 16 dwarf galaxies (|$\rm \langle log({\it M}^{*}/\mathrm{M}_\odot)\rangle _{median} = 8.2$|) at |$z\sim 2$|. The rest-UV Keck Low Resolution Imaging Spectrometer (Keck/LRIS) spectroscopy is complemented by rest-optical Keck/MOSFIRE spectroscopy and Hubble photometry. We find generally larger Ly |$\alpha$| equivalent widths (|$\rm EW_{Ly\alpha } = 11.2\,\,$| Å) when compared with higher mass (|$\rm \langle log({\it M}^{*}/\mathrm{M}_\odot)\rangle _{median} = 10.3$|) composites from Keck Baryonic Structure Survey (KBSS, |$\rm EW_{Ly\alpha } = -5\,\,$| Å). The average low- and high-ionization absorption line equivalent widths (EWs; |$\rm EW_{LIS}$| and |$\rm EW_{HIS}$|, respectively) are weaker (|$\rm EW_{LIS}$| = –1.18 Å, |$\rm EW_{HIS}=$| –0.99 Å) in dwarf galaxies than in higher mass galaxies (|$\rm EW_{LIS}$| = –2.04 Å, |$\rm EW_{HIS}=$| –1.42 Å). The low-ionizatioz absorption lines (LIS) are optically thick and is thus a good tracer of the neutral hydrogen covering fraction. Both higher |$\rm EW_{Ly\alpha }$| and lower |$\rm EW_{LIS}$| measurements imply that the escape fraction of ionizing radiation is larger in lower mass galaxies at |$z\sim 2$|.
1 INTRODUCTION
The evolution of galaxies over cosmic time is heavily dependent on the cycle of baryons in the interstellar medium (ISM) and circumgalactic medium (CGM). The motion and distribution of gas, dust, and metals in the ISM and CGM dictate the star formation efficiency and ionizing escape fraction of galaxies. The rest-UV spectra of galaxies can be used to constrain the motion and distribution of gas, dust, and metals. This has been well studied in high-mass (|$\rm log({\it M}^{*}/\mathrm{M}_\odot) > 9$|) galaxies at high redshift (e.g. Shapley et al. 2003; Du et al. 2018; Weldon et al. 2022). However, there is yet to be a systematic study of the rest-UV spectra of a complete sample of low-mass galaxies at high redshift.
The rest-UV spectra of galaxies contain complex and informative emission and absorption line profiles. Some of the earliest uses of rest-UV spectroscopy for high-redshift galaxies confirmed the redshifts of photometric dropout samples (e.g. Steidel et al. 1996; Lowenthal et al. 1997). More recently, properties of the stellar populations and the gas in the ISM have been inferred from the profiles and equivalent widths (EWs) of the emission and absorption lines present in the rest-UV spectra. In particular, the low- and high-ionization absorption lines (LIS and HIS, respectively) can trace the neutral and ionized components of the ISM, respectively (e.g. Hashimoto et al. 2013; Du et al. 2018, 2021; Saldana-Lopez et al. 2022). Complementary photometry can serve to correlate the measurements of the emission and absorption lines with galaxy physical properties such as UV luminosity and stellar mass to infer whether such physical properties correlate with outflow velocity or neutral gas covering fraction (e.g. Shapley et al. 2003; Du et al. 2018).
A primary use of rest-UV spectroscopy is the study of the Ly |$\alpha$| emission line. Because Ly |$\alpha$| is a resonant line transition in neutral hydrogen, its profile is affected by the existence of even small amounts of neutral hydrogen within a galaxy. However, this also makes Ly |$\alpha$| a good tracer of the covering fraction of neutral hydrogen (e.g. Matthee et al. 2021a; Snapp-Kolas et al. 2023). The escape of Ly |$\alpha$| photons is also used as a proxy of the Lyman continuum escape fraction which is relevant for the ionizing background radiation of the intergalactic medium (e.g. Matthee et al. 2021b). Moreover, several studies (Berry et al. 2012; Jones, Stark & Ellis 2012; Shibuya et al. 2014; Oyarzún et al. 2017) have shown an anticorrelation between Ly |$\alpha$| EW and LIS EW. Together this suggests greater amounts of Lyman continuum photons escaping from galaxies with higher Ly |$\alpha$| EW and lower LIS absorption EW. Because Ly |$\alpha$| emitters (LAEs) are typically less massive (e.g. Erb et al. 2014; Cullen et al. 2020; Pucha et al. 2022) this may imply greater Lyman continuum escape fractions for low-mass galaxies. Indeed, there are some studies that indicate higher Ly |$\alpha$| escape fractions (therefore, likely higher Lyman continuum escape fractions) in lower mass galaxies (e.g. Weiss et al. 2021). In fact, Flury et al. (2022a, b) have shown that the fraction of galaxies at low redshift (|$\rm z\sim 0.2{\!-\!}0.4$|) that are considered LyC emitters (LCEs in their paper) increases towards fainter absolute UV magnitudes and lower masses. The trend is particularly stark when they measure LyC by use of the UV continuum flux instead of H |$\beta$|. This helps motivate a study of fainter, low-mass galaxies at high redshift. However, there is not yet a study of a complete sample of low-mass galaxies to confirm this trend at high redshift.
Some ions in the ISM have ionization potentials lower than that of neutral hydrogen and therefore typically exist within regions of neutral hydrogen of sufficient column density to shield these ions from ionizing radiation. Because of this, these lines are often used to trace the outflows of neutral gas in the ISM (Shapley et al. 2003; Steidel et al. 2010; Jones et al. 2012; Hashimoto et al. 2013; Du et al. 2018; Sugahara et al. 2019). Generally, speaking the typical velocity offset of LIS absorption lines remains the same across galaxy properties studied in the literature and is found to be |$\sim -180\,\,\rm km \,\, s^{-1}$| (Steidel et al. 2010; Hashimoto et al. 2013; Shibuya et al. 2014; Keerthi Vasan et al. 2023). However, Erb et al. (2010) show a lower velocity offset for Q2343-BX418, which is an L* metal-poor galaxy at |$z\sim 2$|, which may suggest a connection between metallicity and velocity offset. LIS absorption equivalent width (EW) is also often correlated with Ly |$\alpha$| EW (Jones et al. 2012; Du et al. 2018) such that weaker absorption is associated with stronger Ly |$\alpha$| emission. This likely implies greater avenues of escape for Lyman continuum radiation. In fact, Saldana-Lopez et al. (2022) show an anticorrelation between LIS absorption EW and the escape fraction of Lyman continuum radiation (see their figs 7 and 12). However, some challenges to LIS tracing Lyman Continuum radiation can be seen indirectly in Le Reste et al. (2022) and Xu et al. (2022). Each of these papers show that the S iii absorption lines can be found outside of regions of neutral hydrogen, and therefore trace additional regions of the galaxy beyond neutral hydrogen. As such, direct correlations between LIS and LyC should be used with caution. Nevertheless, the indirect conclusion between LIS and LyC through Ly |$\alpha$| may still be applicable. All of these properties are well studied at higher masses (|$\rm > 10^9\,\,\mathrm{M}_\odot$|, Shapley et al. 2003; Berry et al. 2012; Jones et al. 2012; Du et al. 2018) or for samples chosen to have large Ly |$\alpha$| EWs (e.g. Hashimoto et al. 2013; Shibuya et al. 2014), but little work has been done on a complete sample at low mass to see if these trends hold for dwarf galaxies.
Beyond regions of dense neutral hydrogen the elements can be subject to more intense radiation from star-forming regions with |$\rm {\it E}_{photon}>13.6\ eV$|, producing more highly ionized ions, such as the Si iv |$\lambda \lambda$|1393,1402 and C iv |$\lambda \lambda$|1548,1550 doublets. These ions have ionization potentials well above that of neutral hydrogen and therefore will trace ionized regions of the ISM. Shapley et al. (2003) show that the HIS absorption line EW is constant in all of their non-LAE bins, but in their LAE bin the depth of the HIS EW decreases. Du et al. (2018) show similar behaviour for their |$z\sim 2$| sample with the highest Ly |$\alpha$| EW bin having weaker HIS absorption, arguably due to greater numbers of Ly |$\alpha$| emitters contributing to the stack in that bin. Both argue that there is an insignificant change in the HIS EW strength with Ly |$\alpha$| EW, but each display a sudden change in the strength of the HIS EW for LAEs. Since LAEs are less massive than Lyman break galaxies (LBGs) generally (e.g. Cullen et al. 2020; Pucha et al. 2022), it may be the case that lower mass galaxies have lower HIS EWs.
In this work, we utilize photometric and spectroscopic data to study the UV spectral properties of dwarf galaxies and compare with the better studied more massive galaxies. The remainder of the paper is organized as follows. In Section 2, we briefly review the observations and describe additional spectral energy distribution (SED) fitting, subsample selection, and describe the spectral stacking methodology. In Section 3, we present measurements of the Ly |$\alpha$|, LIS, and HIS EWs and velocity offsets. In Section 4, we compare with measurements found in the literature and discuss the implications of these comparisons. In Section 5, we summarize our findings. We adopt a |$\Lambda$|CDM cosmology with |$\Omega _m$| = 0.3, |$\Omega _{\Lambda } = 0.7$|, and |$h = 0.7$| throughout the paper and all magnitudes are in the AB system (Oke & Gunn 1983). In this work, all EWs are given in the rest frame. Emission lines are taken to have positive EWs and absorption lines are taken to have negative EWs. We use the convention of positive velocities indicating a redshift and negative velocities indicating a blueshift.
2 OBSERVATIONS, DATA REDUCTION, AND SAMPLE SELECTION
2.1 Observations and data reduction
This work is based on data discussed in Snapp-Kolas et al. (2023) and the details of the observations and reduction can be found therein. We briefly review the basics of the sample here. Our sample consists of a subset of dwarf galaxies observed with deep Hubble Space Telescope (HST) photometry and low-resolution rest-UV spectroscopy with Keck/LRIS (Oke et al. 1995). All of our galaxies are behind three lensing clusters (Abell 1689, MACS J1149, and MACS J0717) in order to observe the faintest UV continua possible with LRIS. Exposure times varied from 4500s–13000s in our 11 masks according to the conditions during observations. The typical seeing of our data is |$\sim 1\,{\rm arcsec}$|. Objects were selected to have visual magnitudes brighter than m|$_{\rm F625W}< 26.3$| and photometric redshifts in the range |$1.5< z < 3.5$|. Photometric redshifts are determined from our HST photometry (see Alavi et al. 2014, 2016 for details). Galaxies with high magnification were given priority when creating slit masks. The LRIS data were reduced and extracted using a modified version of the PypeIt v1.x reduction pipeline (Prochaska et al. 2020b), which performs flat-fielding, wavelength calibration, cosmic ray rejection, sky subtraction, and optimal extraction of 1D spectra. We correct these extracted spectra for slit-losses using Hubble photometry. The spectral coverage is 3100 Å–5600 Å and the spectral resolution is |${\it R}\sim 500$|. After removing spectra with contamination from internal reflections we have a parent sample of 127 spectra. After combining multiple images, we have a parent galaxy sample of 89 galaxies. Keck/MOSFIRE (McLean et al. 2010, 2012) rest-optical spectra were also obtained for a portion of these galaxies, which we use to confirm the redshifts and measure the H |$\alpha$| emission line of the galaxies used in this work. The details of the MOSFIRE spectra can be found in Gburek et al. (2023), but we shall summarize the spectroscopy here as well. The spectra were observed using a |$2.5\,\rm arcsec$| ABBA dither pattern in the Y, J, H, and K bands with targets selected to have typical strong nebular emission lines (i.e. [O ii] |$\lambda \lambda$|3726, 3729, H|$\beta$|, [O iii] |$\lambda \lambda$|4959, 5007, H|$\alpha$|, and [N ii] |$\lambda \lambda$|6548, 6583) in nine masks. The average exposure times for the Y, J, H, and K bands were 96, 81, 85, and 82 min with resolutions of |${\it R} =$| 3388, 3318, 3660, and 3610, respectively.1 The spectra were reduced using the MOSFIRE Data Reduction Pipeline2 (DRP). 1D spectra were then extracted from the reduced 2D spectra using bmep3 from Freeman et al. (2019). The overlap of the LRIS and MOSFIRE spectra gives a total of 45 galaxies with confirmed redshifts.
2.2 SED fit
We fit SEDs to our galaxies within the IR footprint of our Hubble photometry in Alavi et al. (2014, 2016). In that work we make use of the code fast4 (Kriek et al. 2009) and we fit Bruzual & Charlot (2003) stellar population synthesis models assuming constant star formation histories (SFHs), a Chabrier (2003) initial mass function (IMF), stellar metallicities of either |$\rm 0.2 Z_{\odot }$| or |$\rm 0.4 Z_{\odot }$|, and an SMC dust attenuation curve. Three galaxies in this sample for this work did not have SED fits, as they were not observed in all of the filters of the Alavi et al. (2014, 2016) sample. Nevertheless, the photometry was sufficient for performing SED fits. For these galaxies we made use of bagpipes5 (Carnall et al. 2018) to perform SED fitting on these galaxies. The same assumptions were used as in fast, but a Kroupa (2004) IMF is used instead as this is fixed in the bagpipes code. We note that the Chabrier (2003) and Kroupa (2004) IMF’s differ primarily at the low-mass end (|$\rm log({\it M}^{*}/\mathrm{M}_\odot) < 1$|), and differences in the two are small in terms of the number of stars of a given mass. Therefore, we argue that the two assumptions will have little difference in the estimated mass which is the primary use of the SED fits in this work.
2.3 Subsample selection
For the purposes of this study, we aim to choose a sample that is complete in terms of its star-forming properties. We place the following constraints on our sample to accomplish this goal (Snapp-Kolas et al. 2023):
Only galaxies with confirmed redshift from our rest-optical spectra are kept. These redshifts are determined from H |$\alpha$| and [O iii] |$\lambda \lambda 5007$|.
We require that H |$\alpha$| be observable within the MOSFIRE H, J, or K bands. This limits our observations to galaxies with |$z \lesssim 2.6$|.
We remove galaxies that show blending with other nearby galaxies in the HST photometry
We remove galaxies with magnification |$\mu > 30$| behind Abell 1689 and |$\mu >15$| for MACS J0717 and MACS J1149. This is to ensure the galaxies in the sample are sufficiently far away from the critical line to avoid differential magnification across a galaxy.
We remove galaxies with large slit losses (defined empirically to be a slit loss of 55 per cent or more in the LRIS and MOSFIRE spectra). Slit losses larger than this reduce confidence that the spectrum is representative of the whole galaxy, as a majority of the galaxy light lies outside of the slit.
We additionally remove any galaxies that could not have been detected at our 3 |$\sigma$| H |$\alpha$| sensitivity limit at |$\rm Log(H\alpha /UV) = 13.4$| given the magnification of each galaxy (see Snapp-Kolas et al. 2023), and could not have been detected in H |$\alpha$| below the lower end of the extrapolated star-forming main sequence of Sanders et al. (2021) given the sensitivity of our Keck/MOSFIRE spectra. This is done to remove a bias towards galaxies that have large H |$\alpha$| luminosities.
Fig. 1 shows the star formation rate (SFR) versus stellar mass of the remaining sample after the above considerations. The galaxies that have red x’s could NOT have been detected in H |$\alpha$| below the main sequence and are therefore removed from the sample. Points are colour-coded according to their magnification and the gold star represents the median SFR and Mass of the sample. The error bars on the star represent the 25th and 75th quintiles of the sample for each variable. Error bars on the individual galaxies are derived from the SED fits. These considerations leave us with a final complete sample of 16 dwarf galaxies. The sample is consistent with lying on the main sequence within 1|$\sigma$| of the Sanders et al. (2021) relation. To evaluate the effects of our selection on the sample we compare our 16 galaxy sample with the redshift confirmed parent sample of 45 galaxies. Fig. 2 shows histograms and box plots of the redshift and mass distributions of the samples. Our selection results in similar distributions in both parameters with extremes of each sample being removed. The median mass before the selection is |$\rm log({\it M}^{*}/{\rm M}_{\odot }) = 8.23$|, and after the selection it is |$\rm log(M^{*}/{\rm M}_{\odot }) = 8.25$|. This amounts to a less than 5 per cent change in the median mass. The median redshift before the selection is |$z\sim 2.4$|, and after the selection it is |$z\sim 2.3$|. This is about a 5 per cent shift in the median redshift. We also use a Mann–Whitney U-test to determine whether the new and old samples are significantly different. We set a threshold of |$p< 0.05$| to reject the null hypothesis. For the mass of our samples the test produces |$p=0.75$|, and for the redshift of our samples the test produces |$p=0.2$|. In both cases, we cannot reject the null hypothesis. Given that the median of each parameter changes very little with our selection effects, and our inability to reject the null hypothesis from our Mann–Whitney U-test, we conclude that our reduced sample is complete. The distributions show that the samples are consistent.
Galaxy main sequence for our dwarf galaxy sample. Points are colour coded according to the magnification of each galaxy (see colour bar). The main sequence extrapolated from the empirical Sanders et al. (2021) relation (equation 3 in their paper) is plotted for reference along with the 1|$\sigma$| errors shaded in grey. The errors on the individual measurements are derived from the SED fitting codes. The median SFR and mass are plotted together with a golden star. The error bars on the star represent the 25th and 75th percentiles of the sample. Galaxies excluded because they would have H |$\alpha$| luminosities below our H |$\alpha$| sensitivity limit (adjusted by redshift and magnification) are marked with red x’s.
Top Left: Histogram of the masses of our 45 galaxy parent sample and our smaller complete 16 galaxy sample. The larger sample is labelled ‘45gax’ and the smaller sample is labelled ‘16gax’ Bottom Left: box plot of the masses of the same samples showing the median, the 1st quartile, the 3rd quartile, and extensions of these by 1.5x the inner quartile range. The circle beyond the end of the boxplot represents an outlier. Top Right: Histogram of the redshifts of the 45 galaxy parent sample and our smaller 16 galaxy sample. Bottom Right: Box plot of the redshifts of the same samples.
3 RESULTS
Thanks to lensing we are able to probe down to |$\rm {\it M}_{UV}\lesssim -17$| at |$z\sim 2$|, which is two magnitudes fainter than the KBSS sample (|$\rm {\it M}_{UV}\lesssim -19$|) of Du et al. (2018). However, given the low luminosities of our sample, the S/N in the continuum is still too low to detect the LIS and HIS absorption features in individual spectra. Therefore, we choose to analyse a stack of all the galaxies in our final sample to produce a typical dwarf galaxy spectrum to compare with larger mass galaxies. We normalize the individual spectra with a power law of the form |$f_\lambda \propto \rm \lambda ^\beta$| before stacking, so that the continuum has a constant value of unity. We median stack the 16 continuum normalized spectra at each wavelength. We choose a median to reduce influence from outliers in the data. Because the sample consists of galaxies at various redshifts between 1.6 and 2.6 the spectral coverage of the stack is limited to 1200 Å to 1560 Å to ensure that all galaxies contribute to the stack at all wavelengths.
Each spectrum in the stack contains statistical uncertainty given by the error spectrum. In addition, galaxies have a wide range of properties and given the size of our sample there is inherent variance in the stack do to this variance in galaxy properties. To account for both the statistical uncertainty and the variance in galaxy properties we perturb each spectrum according to its error spectrum and randomly select with replacement from our sample. We then median stack these mock spectra. We repeat this process 1000 times and then take the standard deviation of the flux at each wavelength to be the error spectrum of our median stack. We use this error spectrum to produce the errors on our measurements of the absorption lines and the Ly |$\alpha$| emission line. The continuum normalized stack of 16 galaxies (with error spectrum) is shown in Fig. 3 along with the normalized |$\rm z\sim 2$| stack of Du et al. (2018).
The stacked spectrum of the 16 dwarf galaxies in our sample is plotted in blue. The |$z\sim 2$| stack of Du et al. (2018) is plotted in green. To compare the depths of the absorption lines we normalize the spectrum of Du et al. (2018) by the continuum, which we estimate using a running average with a width of 100 Å. The error spectrum is plotted in orange and relevant lines are labelled in the figure. Low-ionization absorption lines are labelled with dashes, high ionization lines are labelled with dot–dashes, and the NV line is labelled with a dotted line. Left: A comparison of the Ly |$\alpha$| emission line. Right: The rest-UV continuum and absorption lines of the same stacks. Generally, the Ly |$\alpha$| emission line is stronger, and both the LIS and HIS absorption lines are weaker than the Du et al. (2018) stack.
Our stacked spectrum spans the rest-frame wavelength range of 1200–1560 Å and therefore probes the absorption lines of low and high ions and common emission lines such as the Si ii fine structure emission lines, C iv emission, and N v |$\rm \lambda$|1240. We also are able to measure the Ly |$\alpha$| emission line EW and velocity offset relative to systemic to compare with Du et al. (2018).
We measure the LIS absorption lines by performing a parametric fit of the Si ii |$\rm \lambda$|1260, O i |$\rm \lambda$|1302 + Si ii |$\rm \lambda$|1304, C ii |$\rm \lambda$|1334, and Si ii |$\rm \lambda$|1527 lines. We assume Gaussian profiles and require the offset from systemic and the width of the lines to be the same for each LIS absorption line. This naturally presumes that all of the low ions occupy the same region of the galaxy. We use this model in a Markov Chain Monte Carlo procedure with PyMC3 (Salvatier, Wiecki & Fonnesbeck 2016) to fit the model to the data. We assume a normally distributed likelihood in this model fitting procedure. We make use of the Metropolis sampling method of pymc3 to sample parameter space during the fitting procedure. This method takes into account the error spectrum on the medium stack described in Section 2 and our measurement errors are taken from this fitting procedure. The HIS absorption lines are fit using a similar method but centering the Gaussian profiles on Si iv |$\rm \lambda \lambda$|1393, 1402 and C iv |$\rm \lambda \lambda$|1548, 1550 and not requiring the two to be at the same velocity shift or have the same width as in Shapley et al. (2003) and Du et al. (2018). The Si iv doublet is spectrally resolved, but the C iv doublet includes a P-Cygni profile that originates from stellar winds in massive stars. This makes it difficult to disentangle the stellar and interstellar components of the C iv profile (Du et al. 2018). Additionally, Rudie et al. (2019) observe different profiles for C iv and Si iv in their |$\rm L^{*}$| galaxies under certain conditions. The C iv profile is much wider than the Si iv profile when thermal broadening is dominant. Because of this, the C iv doublet may not be probing the same region of the galaxy as the Si iv doublet. A similar disparity between the Si iv and C iv profiles is seen in the individual galaxy Q2343-BX418 of Erb et al. (2010) supporting the separation of the two profiles in our fits. Therefore, we choose to take the HIS absorption line EW to be the average of the Si iv doublet to avoid complexities introduced by the C iv line profile.
We fit the Ly |$\alpha$| EW according to the methods of Du et al. (2018), which we briefly review here. We take the continuum to be the midpoint flux of a line passing through the flux at 1208 Å and 1240 Å. We then integrate from 1208 Å to 1240 Å to calculate the EW (see Snapp-Kolas et al. 2023, for more details). To get the velocity offset of the Ly |$\alpha$| profile, we parametrize according to a Gaussian on top of a linear continuum. The same MCMC method used for the LIS absorption lines is used for this fit. Our measured EWs and velocity offsets from systemic are listed in Table 1. Given our limited resolution in our composite spectrum we are unable to properly characterize the maximum velocity of our galaxies (Keerthi Vasan et al. 2023). We choose instead to fit a single Gaussian profile to each of our lines and use the line centre of the fit to represent the outflow velocities of our galaxies do to our low-resolution spectroscopy (|$R\sim 500$|). For the remainder of this paper ‘outflow velocity’ will refer to the velocity offset of the centroid of the Gaussian fits from the systemic redshift. This allows for direct comparison with other works in the literature (e.g. Du et al. 2018; Sugahara et al. 2019). We also measure |$\rm EW_{LIS}$| which we define as the mean EW of the Si ii |$\rm \lambda$|1260, O i |$\rm \lambda$|1302 + Si ii |$\rm \lambda$|1304, C ii |$\rm \lambda$|1334, and Si ii |$\rm \lambda$|1527 absorption lines. Other works (e.g. Prochaska, Kasen & Rubin 2011; Scarlata & Panagia 2015) have shown that blue infilling can affect the shapes of the absorption profiles of resonant absorption lines. The effect of blue infilling on each transition of a given ion will not necessarily be the same either. This effect is most prominent when fluorescent emission lines are present in the spectra. To address this we show a zoom-in of each LIS absorption line as well as an overlay of each of the lines in Figs 4 and 5. We see nearly identical velocity centroids and profiles for all of the LIS absorption lines given the resolution of our data. This suggests that taking an average of the LIS EWs is appropriate in this context. However, if there is significant blue-infilling by scattered re-emission and fluorescent lines this will result in an overestimate of the central velocity in our absorption features, and it may increase the uncertainty in the average.
Zoom in of the four low-ionization interstellar absorption lines studied in this paper (S iii |$\lambda 1260$|, O i |$\lambda 1302$| + S iii |$\lambda 1334$|, C ii |$\lambda 1334$|, and S iii |$\lambda 1527$|). These are ordered according to increasing wavelength from left to right. The location of fluorescent transitions is also shown for reference. Possible fluorescent lines are seen in O i |$\lambda 1302$| + S iii |$\lambda 1334$| and S iii |$\lambda 1527$|.
The same four absorption lines as in Fig. 4, but now overlayed on top of one another. The lines all show similar profiles. Therefore, we conclude that averaging the EWs to get |$\rm EW_{LIS}$| is acceptable in this context given the resolution of our stacked spectrum.
The emission and absorption line EWs and velocity offsets from systemic measured from the total median stack of 16 dwarf galaxies. We take the convention of positive velocity indicating a redshift and negative velocities indicating a blueshift.
| Line | EW | |$\rm EW_{err}$| | v | |$\rm v_{err}$| |
|---|---|---|---|---|
| (Å) | (Å) | (|$\rm km\,\, s^{-1}$|) | (|$\rm km\,\, s^{-1}$|) | |
| Ly |$\alpha$| | 11.2 | 1.1 | 302 | 46 |
| S iii 1260 | –1.03 | 0.26 | –125 | 40 |
| OI 1302 + S iii 1304 | –1.54 | 0.35 | –121 | 39 |
| C ii 1334 | –1.12 | 0.30 | –118 | 38 |
| S iii 1526 | –1.03 | 0.22 | –103 | 33 |
| Si iv 1393 | –1.20 | 0.37 | –71 | 67 |
| Si iv 1402 | –0.77 | 0.29 | –71 | 66 |
| C iv 1548|$^{a}$| | –0.76 | 0.31 | –449 | 60 |
| C iv 1550|$^{a}$| | –0.28 | 0.24 | –448 | 60 |
| Line | EW | |$\rm EW_{err}$| | v | |$\rm v_{err}$| |
|---|---|---|---|---|
| (Å) | (Å) | (|$\rm km\,\, s^{-1}$|) | (|$\rm km\,\, s^{-1}$|) | |
| Ly |$\alpha$| | 11.2 | 1.1 | 302 | 46 |
| S iii 1260 | –1.03 | 0.26 | –125 | 40 |
| OI 1302 + S iii 1304 | –1.54 | 0.35 | –121 | 39 |
| C ii 1334 | –1.12 | 0.30 | –118 | 38 |
| S iii 1526 | –1.03 | 0.22 | –103 | 33 |
| Si iv 1393 | –1.20 | 0.37 | –71 | 67 |
| Si iv 1402 | –0.77 | 0.29 | –71 | 66 |
| C iv 1548|$^{a}$| | –0.76 | 0.31 | –449 | 60 |
| C iv 1550|$^{a}$| | –0.28 | 0.24 | –448 | 60 |
aIt is unclear whether the absorption features in the stack are in fact interstellar C iv absorption. It is possible that there are large amounts of ‘filling in’ at low velocities from emission from the P-Cygni stellar wind profiles. However, Erb et al. (2010) show a similar velocity offset for Q2343-BX418, an L* galaxy at |$z\sim 2.3$|.
The emission and absorption line EWs and velocity offsets from systemic measured from the total median stack of 16 dwarf galaxies. We take the convention of positive velocity indicating a redshift and negative velocities indicating a blueshift.
| Line | EW | |$\rm EW_{err}$| | v | |$\rm v_{err}$| |
|---|---|---|---|---|
| (Å) | (Å) | (|$\rm km\,\, s^{-1}$|) | (|$\rm km\,\, s^{-1}$|) | |
| Ly |$\alpha$| | 11.2 | 1.1 | 302 | 46 |
| S iii 1260 | –1.03 | 0.26 | –125 | 40 |
| OI 1302 + S iii 1304 | –1.54 | 0.35 | –121 | 39 |
| C ii 1334 | –1.12 | 0.30 | –118 | 38 |
| S iii 1526 | –1.03 | 0.22 | –103 | 33 |
| Si iv 1393 | –1.20 | 0.37 | –71 | 67 |
| Si iv 1402 | –0.77 | 0.29 | –71 | 66 |
| C iv 1548|$^{a}$| | –0.76 | 0.31 | –449 | 60 |
| C iv 1550|$^{a}$| | –0.28 | 0.24 | –448 | 60 |
| Line | EW | |$\rm EW_{err}$| | v | |$\rm v_{err}$| |
|---|---|---|---|---|
| (Å) | (Å) | (|$\rm km\,\, s^{-1}$|) | (|$\rm km\,\, s^{-1}$|) | |
| Ly |$\alpha$| | 11.2 | 1.1 | 302 | 46 |
| S iii 1260 | –1.03 | 0.26 | –125 | 40 |
| OI 1302 + S iii 1304 | –1.54 | 0.35 | –121 | 39 |
| C ii 1334 | –1.12 | 0.30 | –118 | 38 |
| S iii 1526 | –1.03 | 0.22 | –103 | 33 |
| Si iv 1393 | –1.20 | 0.37 | –71 | 67 |
| Si iv 1402 | –0.77 | 0.29 | –71 | 66 |
| C iv 1548|$^{a}$| | –0.76 | 0.31 | –449 | 60 |
| C iv 1550|$^{a}$| | –0.28 | 0.24 | –448 | 60 |
aIt is unclear whether the absorption features in the stack are in fact interstellar C iv absorption. It is possible that there are large amounts of ‘filling in’ at low velocities from emission from the P-Cygni stellar wind profiles. However, Erb et al. (2010) show a similar velocity offset for Q2343-BX418, an L* galaxy at |$z\sim 2.3$|.
Nevertheless, while it may not be generally appropriate to average LIS lines (Scarlata & Panagia 2015), we define |$\rm EW_{LIS}$| this way in order to compare with the literature which typically defines |$\rm EW_{LIS}$| as such (e.g. Berry et al. 2012; Jones et al. 2012; Du et al. 2018; Saldana-Lopez et al. 2022). We measure |$\rm EW_{LIS}$| to be −1.18 |$\rm \pm 0.14$| Å and find the HIS EW to be −0.99 |$\pm 0.24$| Å for the total stack. We also find that the Ly |$\alpha$| EW is 11.2 |$\pm 1.1$|Å and the Ly |$\alpha$| velocity offset from systemic is 302 |$\pm 46$| km |$\rm s^{-1}$|.
4 DISCUSSION
To study the mass dependence of properties of dwarf galaxies at a given redshift, we compare primarily with the KBSS sample of Du et al. (2018).
4.1 Lyman alpha
Fig. 6 shows the Ly |$\alpha$| EW as a function of stellar mass. Du et al. (2018) demonstrate a relatively flat trend in |$\rm EW_{Ly\alpha }$| with mass down to |$\rm log({\it M}^{*} /\mathrm{M}_\odot) \approx 10$|. Below this mass they show an increase to |$\rm EW_{Ly\alpha }\approx 0$| Å at |$\rm log(M^{*} /\mathrm{M}_\odot) \approx 9.5$|. Our stack continues this trend demonstrating that Ly |$\alpha$| will be seen in emission, on average, below |$\rm log(M^{*} /\mathrm{M}_\odot) \approx 9$|. We see a clear increase in the Ly |$\alpha$| EW with decreasing mass. Du et al. (2018) show that for a given stellar mass |$\rm EW_{Ly\alpha }$| will increase with redshift. This is particularly stark at the lowest masses and may suggest that galaxies at the masses of our sample are Ly |$\alpha$| emitters (LAEs, |$\rm EW_{Ly\alpha }>20$| Å) on average at |$z\ge 4$|. Pahl et al. (2020) extend the work of Du et al. (2018) out to |$\rm z\sim 5$| showing a similar result in terms of mass. Their fig. 14 may even suggest a steepening of the relation with redshift, which would imply even greater Ly |$\alpha$| EWs at higher redshift for dwarf galaxies. However, the uncertainties on the measurements of Pahl et al. (2020) make such a conclusion tenuous. Nevertheless, this suggests that lower mass galaxies allow greater amounts of Ly |$\alpha$| photons to escape, and therefore suggests greater amounts of ionizing radiation are escaping from dwarf galaxies. This trend towards higher Ly |$\alpha$| EWs at lower mass is also observed in other high-redshift samples in the literature (see e.g. Oyarzún et al. 2017, |$3< z < 4.6$|).
|$\rm EW_{Ly\alpha }$| versus |$\rm log({\it M}^{*}/{\rm M}_{\odot })$| from stacked spectra at |$z\sim 2$|. Our datum is shown as a green star and the Du et al. (2018) data are shown in blue circles. The sample of Du et al. (2018) is binned according to mass and spectra are stacked in each mass bin. The errors on the KBSS sample are too small to be seen in the figure. For our dwarf galaxy sample the error bars on the Ly |$\alpha$| EW are derived from the MCMC fit to the Ly |$\alpha$| line as described in Section 3. The error bars on the mass denote the 25th and 75th percentiles of the distribution, respectively. The measured mass value is the median of the total sample. There is a clear increase in |$\rm EW_{Ly\alpha }$| with decreasing mass.
We also compare samples to determine trends in Ly |$\alpha$| EW with absolute UV magnitude. Fig. 7 is colour coded in the same manner as Fig. 6. According to Du et al. (2018), there is a flat trend for |$z\sim 2$| galaxies in |$\rm EW_{Ly\alpha }$| with |$\rm {\it M}_{UV}$| and each bin shows that Ly |$\alpha$| is observed with net absorption (|$\rm EW_{Ly\alpha } \sim (-3.5)- (-4.5)$|). In our dwarf galaxy sample, we find a positive Ly |$\alpha$| EW (|$\sim 11$| Å), showing that the typical dwarf galaxy will have net Ly |$\alpha$| emission. This is consistent with our earlier work as well (Snapp-Kolas et al. 2023). However, at higher redshift in the Du et al. (2018) sample there is a noted increase in Ly |$\alpha$| EW towards fainter absolute UV magnitudes. Additionally, we can infer from figs 6 and 9 of Saldana-Lopez et al. (2022) that the Ly |$\alpha$| EW is correlated with absolute UV magnitude in support of the conclusion that fainter galaxies have larger Ly |$\alpha$| EWs. Furthermore, with our sample added to the analysis of Du et al. (2018), we can conclude that at redshifts |$z\sim 2{\!-\!}4$| fainter galaxies produce higher Ly |$\alpha$| EWs, and generally there exists an absolute UV magnitude at which the typical galaxy shifts from being a net absorber of Ly |$\alpha$| photons, to being a net emitter of Ly |$\alpha$| photons. Pahl et al. (2020) also show a trend toward higher Ly |$\alpha$| EWs at higher redshift. At |$\rm z\sim 5$|, they show that even brighter galaxies have high Ly |$\alpha$| EWs. If the trend found in our data continues out to this redshift, then the faintest galaxies are likely to be LAEs on average. If we assume a picket fence model (e.g. Reddy et al. 2016; Vasei et al. 2016; Gazagnes et al. 2018; Steidel et al. 2018; Erb et al. 2019) of neutral hydrogen gas around galaxies, then we will expect patches of high column density neutral hydrogen to obscure Ly |$\alpha$| along lines of sight passing through these patches. This model of a patchy covering fraction is supported by the work of Saldana-Lopez et al. (2022). A larger covering fraction of neutral hydrogen will reduce the strength of the Ly |$\alpha$| emission line. Given low-ionization ions exist within regions of high column density neutral hydrogen we expect the strength of Ly |$\alpha$| to be correlated with the strength of the LIS absorption lines under this model. We also note that Saldana-Lopez et al. (2022) have shown that there is a correlation between the covering fraction of LIS absorption lines and the covering fraction of Neutral hydrogen. While the relation is not 1:1, we can conservatively confirm that there is a positive correlation between LIS covering fraction and Neutral hydrogen covering fraction (see also Reddy et al. 2016; Gazagnes et al. 2018). Fig. 8 shows the LIS EW as a function of the Ly |$\alpha$| EW. At the redshift of our sample, Du et al. (2018, blue) show a clear correlation between the LIS absorption line EW and the Ly |$\alpha$| EW. They offer that this supports a physical model of patchy optically thick clumps surrounding star-forming regions. In this scenario, the trend between the LIS EW and the Ly |$\alpha$| EW is an emergent property of the radiative transfer of Ly |$\alpha$| photons. Du et al. (2018) demonstrate that this correlation is invariant up to |$z\sim 4$|. This trend is confirmed by many others in the literature over various galaxy properties and across redshift as shown in Fig. 8.
The |$\rm EW_{Ly\alpha }$| versus |$\rm M_{UV}$| from stacked spectra at |$z\sim 2$|. The green star is the measurement from our stack and the blue dots are from Du et al. (2018). Here, Du et al. (2018) sample is binned according to absolute UV magnitude. Again the error bars on Du et al. (2018) sample are too small to be perceived in the figure and our error bars are calculated in the same manner as in Fig. 6. The error bars on the absolute UV magnitude are the 25th and 75th percentiles of the sample. There is a clear increase in the |$\rm EW_{Ly\alpha }$| at fainter UV luminosities.
The |$\rm EW_{LIS}$| versus |$\rm EW_{Ly\alpha }$| of high-redshift star-forming galaxies. The black star is measured from our total stack with the error on |$\rm EW_{LIS}$| determined from the MCMC fitting algorithm (with error spectrum taken into account) and the error on |$\rm EW_{Ly\alpha }$| is determined by propagation of error from the error spectrum. The pink diamonds are stacks on 8 galaxies each from our sample of 16 galaxies in two bins of |$\rm EW_{Ly\alpha }$| split at 6.2 Å. The errors are determined in the same manner as the total stack. We also plot values from Du et al. (2018), Jones et al. (2012), Berry et al. (2012), Shibuya et al. (2014), and Saldana-Lopez et al. (2023) in blue, orange, red, purple, and green, respectively, for comparison with our sample. Each sample bins on |$\rm EW_{Ly\alpha }$|, and measures values from stacks within the bin, except for Saldana-Lopez et al. (2023) whose values come from individual LAEs. All of the literature values show a correlation between |$\rm EW_{LIS}$| and |$\rm EW_{Ly\alpha }$| for |$\rm EW_{Ly\alpha } < 45$| Å. The measurements from our stacks lie above the trends from the literature.
We find smaller absolute values of LIS EW at a given Ly |$\alpha$| EW for our sample than those of Du et al. (2018), Berry et al. (2012), and Shibuya et al. (2014). This suggests that the trend between LIS EW and Ly |$\alpha$| EW found in Du et al. (2018) is dependent on stellar mass or UV luminosity as argued by Jones et al. (2012).
However, we have stacked on the entire sample for this comparison. In order to more closely compare with the literature we stack two subsamples chosen on Ly |$\alpha$| rest-EW as is done in these other works. We split the sample by the median Ly |$\alpha$| EW (6.2 Å). The masses of the two subsamples differ by a small amount. The lower and higher Ly |$\alpha$| EW samples have masses of |$\rm Log({\it M}^{*}/\mathrm{M}_\odot) = 8.35^{+0.32}_{-0.23}$| and |$\rm Log({\it M}^{*}/\mathrm{M}_\odot) = 8.07^{+0.32}_{-0.21}$| where the errors denote the 25th and 75th percentiles of the distributions. Each sample has 8 galaxies in the bin, they are stacked in the same manner as the full sample, and the error spectrum is found in the same manner as well. All measurements are performed the same as for the total stack. The results are plotted as pink diamonds in Fig. 8. Our data lie above the trend in the literature, suggesting the relationship between |$\rm EW_{Ly\alpha }$| and |$\rm EW_{LIS}$| may be mass dependent. However, Du et al. (2021) investigate the scatter in this trend using individual galaxy measurements to determine possible drivers of the scatter in this and other correlations. They find that for a fixed Ly |$\alpha$| EW the LIS EW will vary based on the metallicity of the galaxy, with weaker LIS absorption occurring in lower metallicity galaxies. As such, the offset of our data from the trend in the literature may be indicative of dwarf galaxies having lower metallicities (Gburek et al. 2023) on average. This is further supported by Cullen et al. (2019) who show that stellar metallicity increases monotonically from |$\rm log({\it M}^{*}/\mathrm{M}_\odot) = 8.5$| to |$\rm log({\it M}^{*}/\mathrm{M}_\odot) = 10.2$|. Moreover, Cullen et al. (2020) show that metallicity decreases for increasing |$\rm EW_{Ly\alpha }$|. Fig. 6 shows that the |$\rm EW_{Ly\alpha }$| increases significantly at lower masses. Collectively this suggests that lower mass galaxies have both lower metallicity and higher |$\rm EW_{Ly\alpha }$|, which suggests that low-mass galaxies will tend to lie above the |$\rm EW_{LIS}\,\,versus\,\,EW_{Ly\alpha }$| trend seen for higher mass galaxies. Since this relation is possibly influenced by mass and metallicity we suggest future studies with larger numbers of dwarf galaxies be conducted to solidify this relation.
4.2 LIS absorption lines and kinematics
We wish to understand the distribution of neutral hydrogen to better constrain the escape of ionizing radiation. Here we compare our results with the KBSS sample of Du et al. (2018) to find any trends in the LIS absorption lines with mass. The kinematics of ions/gas are often characterized either by the line center velocity of the absorption line or some choice of maximum velocity offset in the absorption line profile. The maximum velocity offset is often chosen to be at 90 per cent flux relative to the continuum value (e.g. Sugahara et al. 2017; Weldon et al. 2022). However, given the resolution of our spectra we choose to use the line center as described in Section 3. Fig. 9 shows the LIS absorption velocity offset from systemic as a function of mass. To compare with the literature we take the C ii 1334 velocity offset to be representative of the LIS absorption lines generally. There is a trend towards lower LIS absorption velocity offsets at lower masses relative to higher mass samples (Du et al. 2018; Sugahara et al. 2019), though the uncertainties on our measurement render this result tenuous. The L* galaxy Q2343-BX418 of Erb et al. (2010) agrees with this trend. The mass of the galaxy is |$\rm log({\it M}*/\mathrm{M}_\odot)\sim 9$| and the velocity offset of the S iii1526 line is |$v\sim -90\,\, \rm km\,\,s^{-1}$|, which if we assume the same offset from C ii as in our data set, then their |$v_{\rm LIS}\sim -105\,\,\rm km\,\,s^{-1}$|. Erb et al. (2012) also show lower velocity offsets in lower mass galaxies, but using the Mg ii and Fe ii absorption lines instead of the LIS UV absorption lines. The models from the FIRE simulations (Muratov et al. 2015) predict that the outflow velocities will be lower in lower mass galaxies. Our results are qualitatively consistent with this model.
The LIS absorption velocity offset as a function of stellar mass. The green star is from our stack and the blue dot and orange square are from Du et al. (2018) and Sugahara et al. (2019), respectively. The errors on the mass for our stack are the same as in Fig. 6 and the errors on the velocity are derived from the MCMC algorithm that fit the lines to the spectrum. The measured LIS velocity is lower than Du et al. (2018) and Sugahara et al. (2019), though the uncertainty is comparatively large. The data point from Sugahara et al. (2019) is a correction of a measurement first made in Sugahara et al. (2017).
Fig. 10 shows the LIS EW as a function of mass. Du et al. (2018) measure a single value of the LIS EW relative to mass (|$\rm EW_{LIS} \approx -2.0$| Å). According to Fig. 8 (see also Du et al. 2018, fig. 5), there is little to no dependence on the LIS absorption line EW with redshift. Therefore, there should be little variance in any relation with mass due to redshift. With this in mind we also compare with Jones et al. (2012) and Harikane et al. (2020) and observe an apparent anticorrelation. Our datum shows weaker LIS EW at lower mass and further indicates an anticorrelation between LIS EW and mass. Given this we fit an empirical relation between the LIS absorption EW and the log stellar mass of the form:
We use numpy’s polyfit algorithm to perform a least squares fit of this relation to the observed data. We find |$a_1 = -0.39\pm 0.12$| and |$a_2 = 2.12\pm 1.20$|. The best-fitting line is plotted in Fig. 10. Additionally, we observe the ratio of silicon lines to be |$\rm EW_{S\, {\small III}1260}/EW_{S\, {\small III}1526} = 1.0\pm 0.3$|, which is consistent with the LIS gas being optically thick and the absorption profiles being saturated. Seeing that saturated LIS absorption lines trace neutral hydrogen covering fractions (see Saldana-Lopez et al. 2022) we conclude that lower mass galaxies have lower covering fractions.
The |$\rm EW_{LIS}$| as a function of stellar mass. The green star is our datum, the red diamond is from Jones et al. (2012), the blue dot is from Du et al. (2018), and the orange square is from Harikane et al. (2020). The errors on the mass are as in Fig. 6 and the errors on |$\rm EW_{LIS}$| are derived from the MCMC fitting algorithm. We also plot a least-squares linear fit to the data points in purple showing that there exists an anticorrelation between |$\rm EW_{LIS}$| and |$\rm log({\it M}^{*}/\mathrm{M}_\odot)$|.
4.3 HIS absorption lines
The relative abundance of high ions and low ions is indicative of the ionization state of the ISM and of outflowing gas. A more highly ionized ISM is likely to accommodate the escape of ionizing radiation. In Fig. 11, we plot the HIS absorption EW against mass. Du et al. (2018) measure the HIS EW to be |$\sim -1.4$|Å. We find the HIS EW of our dwarf galaxies to be about 70 per cent as strong (|$\rm EW_{HIS} =-0.99\pm 0.24$|Å). At higher redshift, Jones et al. (2012) measure a comparable value (|$\rm EW_{HIS}\approx -1.5$|) to Du et al. (2018) at similar mass. This is consistent with the higher redshift samples of Du et al. (2018), which suggest the HIS absorption strength does not change with redshift. Shapley et al. (2003) show that the LAEs of their sample have weaker HIS absorption than do the LBGs of their sample. It may be the case that this difference in their sample merely reflects a difference in the mass of LAEs and LBGs.
|$\rm EW_{HIS}$| versus stellar mass. The green star is our datum, the blue dot is from Du et al. (2018), and the orange diamond is from Jones et al. (2012). The errors on our datum are determined in the same manner as Fig. 10. At |$z\sim 2$|, there is less HIS absorption at lower mass. There is no indication of a change in the depth of the HIS absorption lines with redshift for high-mass galaxies. Therefore, the depth of HIS absorption lines appear to depend primarily on mass and do not evolve with time.
We have shown that the Ly |$\alpha$| EW increases with decreasing mass in agreement with other works in the literature. As such we may expect that a sample of LAEs will have lower masses than a higher mass LBG sample. As such, the trends in |$\rm EW_{HIS}$| with |$\rm EW_{Ly\alpha }$| shown by Shapley et al. (2003) and Du et al. (2018) may suggest that |$\rm EW_{HIS}$| is mass dependent. Both of these works do show a decrease in the absolute value of |$\rm EW_{HIS}$| for their highest |$\rm EW_{Ly\alpha }$| bins, though each argues that their data is consistent with no trend. To disentangle whether our decrease in |$\rm EW_{HIS}$| is do to an increase in |$\rm EW_{Ly\alpha }$| or mass we measure |$\rm EW_{HIS}$| in our two |$\rm EW_{Ly\alpha }$| sub-stacks. The low Ly |$\alpha$| EW stack measures |$\rm EW_{HIS}=-0.86\pm 0.50$| Å and the high Ly |$\alpha$| EW stack measures |$\rm EW_{HIS}=-0.73\pm 0.20$| Å. Which are consistent with no trend in |$\rm EW_{HIS}$| with |$\rm EW_{Ly\alpha }$| in agreement with the statements of Shapley et al. (2003) and Du et al. (2018). However, our measured values in our subsamples differ from the higher mass sample of Du et al. (2018) in their fig. 5. Furthermore, our |$\rm EW_{HIS}$| is consistent with the highest |$\rm EW_{Ly\alpha }$| bin in their samples. This points to a mass dependence, rather than a |$\rm EW_{Ly\alpha }$| in our sample. Given the correlation between Ly |$\alpha$| EW and mass it is likely the case that the highest |$\rm EW_{Ly\alpha }$| samples of Shapley et al. (2003) and Du et al. (2018) are showing a mass dependent trend in |$\rm EW_{HIS}$| as well. Together, this points to |$\rm EW_{HIS}$| depending on mass, rather than the Ly |$\alpha$| EW. While the HIS EW appears to be anticorrelated with the mass of the galaxy, the HIS velocity offset is less clear.
We measure the velocity offset of our Si iv absorption lines to be |$-71\pm 67\,\,\rm km\,\, s^{-1}$| and that of our C iv absorption lines to be |$-449\pm 60\,\,\rm km\,\, s^{-1}$|. However, we caution that the velocity offset of the C iv line is complicated by possible ‘filling-in’ of the absorption feature by emission line features closer to the systemic velocity. The velocity offset of the Si iv line differs significantly from that measured in the literature (|$-220^{+150}_{-100}$|, Sugahara et al. 2019). Therefore, the outflow velocities of high-ions are lower in lower mass galaxies.
Jones et al. (2012) suggest the use of the Si iv |$\rm \lambda \lambda$|1393, 1402 doublet EWs as a means of tracing whether the HIS absorption is optically thick. If the ratio |$\rm {\it W}_{1393}/{\it W}_{1402} \sim 2$| then the gas is optically thin, but if |$\rm {\it W}_{1393}/{\it W}_{1402} \sim 1$| then the gas is optically thick. Jones et al. (2012) show a ratio of |$1.4\pm 0.4$| and argue that this means there is a significant amount of optically thick HIS gas present in their average galaxy. For our composite spectrum, we measure |$W_{1393}/W_{1402} = 1.55\pm 0.76$|, consistent with the Si iv gas being either optically thin or optically thick. Jones et al. (2012) measure the Si iv gas of their sample to be optically thick with low significance (|$1.4\pm 0.4$|). Additionally, Du et al. (2018) show that their Si iv doublet is consistent with being optically thin in their redshift 2 sample (|$2.13\pm 0.13$|). Given the low significance of the Jones et al. (2012), the results of Du et al. (2018), and the measurements of this paper the properties of the Si iv gas remain unclear. More data is needed to draw any conclusions regarding the opacity of the Si iv gas.
4.4 Oligarchs versus dwarfs
A favored model for the reionization of neutral hydrogen in the early universe has been the ‘democratic’ model (Erb 2015; Naidu et al. 2020) by large quantities of high Lyman continuum escape fraction dwarf galaxies (e.g. Livermore, Finkelstein & Lotz 2017; Endsley et al. 2023). However, it has been suggested by Naidu et al. (2020) that it is not dwarf galaxies, but the ‘oligarchs’ that are responsible for reionization. Their model shows that the low-mass objects contribute less to produce a rapid late reionization. However, our findings in this work and in Snapp-Kolas et al. (2023) have shown that dwarf galaxies will on average have larger Ly |$\alpha$| escape fractions and lower neutral hydrogen covering fractions (which likely implies larger Lyman continuum escape). Although the models of Naidu et al. (2020) focus on higher redshift galaxies, our findings in this work in comparison with Du et al. (2018) imply that galaxies with masses at and below |$10^8\,\,\rm \mathrm{M}_\odot$| at higher redshift will have greater Ly |$\alpha$| escape fractions and likely greater Lyman continuum escape fractions. These results appear to support the democratic model for reionization over the oligarchs model.
5 SUMMARY
In this paper, we have studied the UV spectroscopic properties of typical dwarf galaxies at |$z\sim 2$| via stacking. The systemic redshift of the individual galaxies is measured from our rest-optical MOSFIRE spectra. We fit the Ly |$\alpha$| emission line and the LIS and HIS absorption lines using MCMC routines to measure the velocity offsets of these lines relative to the systematic redshift. We measure the EW of Ly |$\alpha$| using the methods of Du et al. (2018), and we measure the EWs of the LIS and HIS absorption lines using the best fit model of the MCMC routines. We find the following primary results from these measurements:
We find that the typical |$\rm EW_{Ly\alpha }$| is much larger for dwarf galaxies than for the higher mass galaxy sample of Du et al. (2018). This is in agreement with our earlier work (Snapp-Kolas et al. 2023).
Lower mass galaxies have about 60 per cent of the |$\rm EW_{LIS}$| of more massive galaxies. We fit an anticorrelation and find the following best-fitting values for the linear model: |${\rm EW_{LIS}} = (-0.39\pm 0.12){\rm log(M^{*}/\mathrm{M}_\odot)} + (2.12\pm 1.20)$|.
We find that lower mass galaxies have lower |$\rm EW_{LIS}$| at fixed |$\rm EW_{Ly\alpha }$| than high-mass galaxies. This may be connected to dwarf galaxies having lower metallicities (Cullen et al. 2019; Du et al. 2021; Gburek et al. 2023).
We find the LIS gas is optically thick (|$\rm EW_{S\, {\small III}1260}/EW_{S\, {\small III}1526} = 1.0\pm 0.3$|) which implies that our measurements of |$\rm EW_{LIS}$| are still tracing the neutral hydrogen covering fraction (see Saldana-Lopez et al. 2022, for correlation).
We find velocity offsets in the LIS absorption lines for lower mass galaxies to be lower than in high-mass galaxies in agreement with the FIRE simulations (Muratov et al. 2015).
The |$\rm EW_{HIS} = -0.99\pm 0.24$|Å is smaller in absolute value than for higher mass galaxies. We find this to be true even in our |$\rm EW_{Ly\alpha }$| substacks, making it clear that this is a mass-dependent effect and not due to galaxies possessing higher |$\rm EW_{Ly\alpha }$|.
It is clear that dwarf galaxies have higher Ly |$\alpha$| EWs, weaker LIS and HIS absorption EWs, and lower LIS velocity offsets relative to more massive galaxies. Larger Ly |$\alpha$| EW’s imply higher Ly |$\alpha$| escape fractions (e.g. Yang et al. 2017) which may imply larger Lyman continuum escape fractions (Dijkstra, Gronke & Venkatesan 2016; Verhamme et al. 2017; Izotov et al. 2020; Naidu et al. 2021; Flury et al. 2022a, b). Similarly, Trainor et al. (2019) and Mainali et al. (2022) show that the Ly |$\alpha$| escape fraction is anticorrelated with |$\rm EW_{LIS}$| suggesting higher Lyman continuum escape for weaker |$\rm EW_{LIS}$| (also, see Saldana-Lopez et al. 2022, for correlation between |$\rm EW_{LIS}$| and Lyman continuum escape). While Le Reste et al. (2022) and Xu et al. (2022) may suggest a disconnect between the location of neutral hydrogen and S iii, the indirect connection between LIS and LyC through the strength of Ly |$\alpha$| is supported by our analysis in this work. Our dwarf galaxies exhibit stronger Ly |$\alpha$| and weaker LIS EWs relative to more massive samples. Additionally, our galaxies have optically thick LIS absorption lines which means that the |$\rm EW_{LIS}$| is still tracing the covering fraction and therefore there is likely greater Lyman continuum escape fractions. The cumulative evidence suggests that dwarf galaxies likely play an important role in providing the ionizing background in the early universe.
ACKNOWLEDGEMENTS
This research made use of pypeit,6 a python package for semi-automated reduction of astronomical slit-based spectroscopy (Prochaska et al. 2020a; Prochaska et al. 2020c).
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 National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.
The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain Based on observations made with the NASA/ESA HST, obtained from the Data Archive at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. These observations are associated with programmes #9289, #11710, #11802, #12201, #12931, #13389, #14209.
DATA AVAILABILITY
This paper is based on public data from the HST as well as from programmes 12201, 12931, 13389, 14209. Spectroscopic data from our survey with the Keck Observatory. These data are available upon request from Dr Christopher Snapp-Kolas or Dr Brian Siana.
