# Star formation in neutral hydrogen gas reservoirs at cosmic noon

Takhur Dharmender, Ravi Joshi, Michele Fumagalli, Pasquier Noterdaeme, Hum Chand, Luis C Ho

► To cite this version:

Takhur Dharmender, Ravi Joshi, Michele Fumagalli, Pasquier Noterdaeme, Hum Chand, et al. Star formation in neutral hydrogen gas reservoirs at cosmic noon. Astronomy & Astrophysics - A&A, 2024, 692, pp.L7. 10.1051/0004-6361/202452542. hal-05349127

HAL Id: hal-05349127

https://hal.science/hal-05349127v1

Submitted on 5 Nov 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
LETTER TO THE EDITOR

# Star formation in neutral hydrogen gas reservoirs at cosmic noon

Dharmender<fnref n="1" />,*, D, Ravi Joshi<fnref n="2" />,*, D, Michele Fumagalli<fnref n="3" />,<fnref n="4" /> D, Pasquier Noterdaeme<fnref n="5" /> D,
Hum Chand<fnref n="1" /> D, and Luis C. Ho<fnref n="6" />,<fnref n="7" /> D

Received 9 October 2024 / Accepted 15 November 2024

ABSTRACT

We aim to constrain the average star formation associated with neutral hydrogen gas reservoirs at cosmic noon. We used a unprecedented sample of 1716 high-column-density, damped Ly-α absorbers (DLAs) from the Sloan Digital Sky Survey with log(N(HI)/cm⁻<fnref n="2" />) ≥ 21. This allowed us to generate the average Ly-α emission spectrum associated to DLAs, free from any emission coming from the background quasar. We measured the Lyα emission at >5.8σ level with a luminosity of 8.95 ± 1.54 × 10⁴⁰ erg s⁻<fnref n="1" /> (corresponding to about 0.02 L* at z ~ 2–3) in systems with average log(N(HI)/cm⁻<fnref n="2" />) of ≈21.2 and at a median redshift of z ~ 2.64. The peak of the Lyα emission is apparently redshifted by ~300 km s⁻<fnref n="1" /> relative to the absorption redshift, which appears to be due to suppression of blue Ly-α photons by radiative transfer through expanding gas. We infer that DLAs form stars with an average rate of (0.08 ± 0.01)/f<sub>esc</sub> M<sub>☉</sub> yr<sup>-1</sup>; namely, ≈(0.54 ± 0.09) M<sub>☉</sub> yr<sup>-1</sup> for a typical escape fraction (f<sub>esc</sub> = 0.15) of Lyman-α emitting galaxies. DLA galaxies follow the main sequence of star-forming galaxies at high redshift, suggesting that the DLA population is dominated by the lower mass end of Lyman-α emitting galaxies.

**Key words.** galaxies: evolution – galaxies: formation – galaxies: high-redshift – galaxies: ISM – quasars: absorption lines – galaxies: star formation

**1. Introduction**

The formation and evolution of galaxies are driven by the
filamentary accretion of pristine gas from the cosmic web,
which feeds the interstellar medium (ISM) and fuels star forma-
tion (Barnes & Haehnelt 2009; Fumagalli et al. 2011; Bird et al.
2014; Faucher-Giguère & Oh 2023). As the most abundant ele-
ment in the Universe, hydrogen is a unique tracer, allowing
us to probe gas across various scales, from interstellar to cir-
cumgalactic and intergalactic medium. However, mapping H I
gas in galaxies emission is difficult even at moderate redshifts
(Bera et al. 2018). At high redshift, z ≥ 2, the Damped Lyα
(DLA) absorbers, characterized by hydrogen column densities
of log(N<sub>HI</sub>/cm<sup>-2</sup>) ≥ 20.3, offer a direct probe of the distribu-
tion of neutral gas at a mean density around one-tenth of the
star formation threshold (Cen 2012). DLAs contain a large frac-
tion of the neutral hydrogen in the Universe and are believed to
be the progenitors of normal disk galaxies (Wolfe et al. 2005;
Neeleman et al. 2020; Kaur et al. 2024). They are associated
with star-forming regions, as evidenced by their enrichment with
redshift (Rafelski et al. 2012; Neeleman et al. 2018).

To date, several thousand DLAs at *z* > 2 have been discov-
ered in the Sloan Digital Sky Survey (Prochaska & Herbert-Fort
2004; Noterdaeme et al. 2009, 2012; Chabanier et al. 2022) and

hundreds of these have been followed for high-resolution spec-
troscopy (Ho et al. 2020). Despite these advances, our under-
standing of the origin of DLAs and the physical characteris-
tics of the associated galaxies remains limited. Earlier searches
based on long-slit spectroscopic measurements yielded a low
detection rate of ~10 percent which is attributed to fac-
tors such as bright background quasars, dust attenuation, or
the possibility that only a subset of the DLA population is
directly associated with active star formation. The efforts to
map the metal-rich DLAs resulted in a higher detection rate at
~64 percent (Krogager et al. 2017), but provide limited infor-
mation on star formation rates, masses, extent of H I, and
large-scale environments (Krogager et al. 2017). Despite the
numerous efforts to search for DLA host galaxies in emission,
until recently, only ~25 DLA host galaxies have been discov-
ered so far (Christensen et al. 2014; Krogager et al. 2017).

More recently, using the large 3D field of MUSE/VLT,
Fumagalli et al. (2017) have detected a tantalizing example of
a diffuse gas environment of about 50 kpc near a *z* ~ 3.2
DLA. Mackenzie et al. (2019) have searched six DLAs using
MUSE/VLT with *z* ≥ 3 within 1000 km s⁻<fnref n="1" /> and found a high
detection rate of ~80 percent with impact parameters between
25 and 280 kpc (see also Lofthouse et al. 2023). Furthermore,
interferometers such as the ALMA have overcome the dust
bias, with the detection of a few tens of molecular gas-rich
systems using CO rotational transitions and the atomic [C II]

<footnote n="1">¹ Central University of Himachal Pradesh, Dharamshala, Kangra, India</footnote>

<footnote n="2">² Indian Institute of Astrophysics (IIA), Bengaluru, Karnataka, India</footnote>

<footnote n="3">³ Università degli Studi di Milano-Bicocca, Dip. di Fisica G. Occhialini, Piazza della Scienza 3, 20126 Milano, Italy</footnote>

<footnote n="4">⁴ INAF-Osservatorio Astronomico di Trieste, via G.B. Tiepolo 11, I-34143 Trieste, Italy</footnote>

<footnote n="5">⁵ Institut d'Astrophysique de Paris, CNRS-SU, UMR 7095, 98bis bd Arago, 75014 Paris, France</footnote>

<footnote n="6">⁶ Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, PR China</footnote>

<footnote n="7">⁷ Department of Astronomy, School of Physics, Peking University, Beijing 100871, PR China</footnote>

<footnote>* Corresponding authors; dharmender98thakur@gmail.com, rvjoshirv@gmail.com</footnote>
line (Neeleman et al. 2013, 2017, 2019; Lofthouse et al. 2023; Kaur et al. 2024). So far, these studies have focused on tracing relatively high-metallicity systems, finding the DLA host at relatively large impact parameters, ~16–45 kpc, and high molecular gas masses of $10^{10}-10^{11}$ M$_{\odot}$. These efforts have revealed that DLA host galaxies are similar to massive star-forming galaxies and are embedded in enriched neutral hydrogen gas reservoirs that extend well beyond the star-forming interstellar medium of these galaxies.

In an effort to study the average properties of DLAs, Fumagalli et al. (2014) measured the rest-frame far-ultraviolet (FUV) flux from DLAs in HST composite images using the ‘double-DLA’ technique, which uses two optically thick absorbers to eliminate the glare of the bright background quasars (see also O’Meara et al. 2006; Christensen et al. 2009). These authors excluded the presence of compact star-forming regions with SFRs as low as ~0.1 M$_{\odot}$ yr$^{-1}$ at the position of the quasar. On the other hand, the spectral stacking experiments to detect the Ly$\alpha$ emission from the DLA host galaxy have mostly set an upper limit on Ly$\alpha$ luminosity and SFR (Rahmani et al. 2010; Cai et al. 2014; Joshi et al. 2016), except for metal-rich DLAs (Joshi et al. 2016). Interestingly, Noterdaeme et al. (2014) have shown that the extremely strong DLAs resemble the Lyman-$\alpha$ emitting galaxies (LAEs) with Ly$\alpha$ luminosity of $\ge 0.7 \times 10^{42}$ erg s$^{-1}$. In this Letter, we examine DLA systems with high neutral hydrogen column densities, $log(N_{H1}/cm^{-2}) \ge 21$, which is five times lower than the threshold used by Noterdaeme et al. (2014). Using a dataset twice the size of Joshi et al. (2016), we present a clear detection of Ly$\alpha$ emission in these systems and explore the nature of the DLA host galaxies. The sample selection and analysis are provided in Sects. 2 and 3. The obtained results are given in Sect. 4, followed by a discussion and conclusion in Sect. 5. Throughout, we assume the flat Universe cosmology with $H_0 = 70$ km s$^{-1}$ Mpc$^{-1}$, $\Omega_m = 0.3$, and $\Omega_\Lambda = 0.7$.

## 2. Sample selection

Here, we utilize the SDSS-III BOSS DLA catalogue from Noterdaeme et al. (2012) updated to Data Release-12, consisting 19 535 DLA candidates with column density $log(N_{H1}/cm^{-2}) \ge 20.3$. In addition, we used the SDSS-IV Data Release-16 DLA catalogue from Chabanier et al. (2022). This catalogue has been constructed based on a convolutional neural network, comprising 30 019 DLAs with $log(N_{H1}/cm^{-2}) \ge 20.3$, and high confidence level of $\ge 0.5$. To probe the average SFR associated with DLAs at the cosmic noon, the applied selection filters were as follows: (1) the $log(N_{H1}/cm^{-2}) \ge 21$, which ensured a dark core ($\tau > 10$) of Ly$\alpha$ absorption trough spread over at least seven times the average full width at half-maximum (FWHM) of ~160 km s$^{-1}$ for the instrumental profile of the BOSS spectrograph; (2) we avoided the proximate DLAs by considering the systems with velocity offset of $\ge 5000$ km s$^{-1}$ relative to the quasar emission redshift and exclude the sightlines with broad absorption lines from quasar outflows; (3) to ensure an accurate determination of the H1 column density, we imposed a continuum to noise ratio (CNR) $\ge 4$ in the spectral region of ~20 Å blue and redder side of the DLA wing; (4) to avoid the confusion with Ly$\beta$ forest, we only considered DLAs within in Ly$\alpha$ forest region. The aforementioned selection criteria resulted in 1716 absorbers over a redshift range of $1.97 < z < 4.0$ with a median of $z = 2.637$ and a neutral hydrogen column density ranging between $21.0 \le log(N_{H1}/cm^{-2}) \le 22.3$, with median $log(N_{H1}/cm^{-2}) = 21.2$. The sample summary is given in Table 1.

<table><caption>**Table 1.** DLA sample selection.</caption><thead><tr><th>Criteria</th><th>SDSS DR12</th><th>SDSS DR16</th></tr></thead><tbody><tr><td>log(N<sub>H1</sub>/cm<sup>-2</sup>) &ge; 20.3</td><td>19 535</td><td>30 019 (Conf &gt; 0.5)</td></tr><tr><td>1.97 &le; z<sub>abs</sub> &le; 4</td><td></td><td></td></tr><tr><td>log(N<sub>H1</sub>/cm<sup>-2</sup>) &ge; 21.0</td><td>1139</td><td>1531</td></tr><tr><td>&beta; &ge; 5000 km s<sup>-1</sup></td><td></td><td></td></tr><tr><td>non-BAL</td><td></td><td></td></tr><tr><td>z<sub>abs</sub> &gt; z(Ly&beta;)</td><td></td><td></td></tr><tr><td>CNR &ge; 4</td><td>1139</td><td>930</td></tr><tr><td>Unique DLAs in DR16</td><td>-</td><td>577</td></tr><tr><td>Total Sample</td><td></td><td>1716</td></tr></tbody></table>

Finally, to avoid any uncertainty in the absorption redshift and/or H1 column density measurements, we further visually inspected the entire sample and measured the absorption redshift by cross-correlating the low-ionization metal absorption lines (e.g. CII $\lambda$1334, SiII$\lambda$1526, AlII$\lambda$1670, FeII$\lambda$1608, 2344, 2374, 2382, 2586, 2600, MgII$\lambda$2796, 2803) redward to the quasar Ly$\alpha$ emission. For the systems without a metal absorption line detection, we kept the redshift obtained from the H1 Lyman series transitions based on the CNN models (Chabanier et al. 2022). This resulted in a final sample of 1716 (excluding duplicates among DR12 and DR16) unique DLAs, of which 1515 systems have redshift determined from metal lines.

## 3. Analysis

To detect faint Ly$\alpha$ emission, we generated the stacked spectra by shifting the individual spectrum to the rest-frame of the DLA, while conserving the flux and re-binned to a common grid, keeping the same pixel size (constant in velocity space) as the original data. To remove the contribution from any possible outliers, we have used the median and $3\sigma$-clipped weighted mean statistics with $1/\sigma^2$ weighting, with $\sigma$ being the error in the flux (see also Joshi et al. 2016). Considering the wide flat, dark absorption trough of DLAs, we did not re-scale or normalize the spectrum before the co-addition. Furthermore, to test the robustness, we generated 5000 bootstrapped stacked spectra and estimated the $1\sigma$ uncertainty over each pixel as the 16th and 84th percentiles of the flux distribution of the corresponding pixel.

We note that the residual flux level within the core of the DLA absorption profile exhibits a non-zero offset, likely related to sky-subtraction errors (Rahmani et al. 2010; Joshi et al. 2016) and/or average FUV radiation from the background quasar host galaxies (Cai et al. 2014). Our stacked DLA profile also shows a positive flux with no prominent signal blue-ward of Ly$\alpha$ (see Fig. A.1). We correct this offset by subtracting the weighted mean flux in the dark trough of DLA, estimated using the pixels with $\tau > 10$, blue-ward of the line center at 1215.67 Å. Here, the IGM absorption may likely result in zero flux from DLA galaxy. This correction may potentially eliminate any continuum emission from the DLA host, but our primary interest here is on the Ly$\alpha$ emission line.

## 4. Results

In Fig. 1, we show the median and $3\sigma$-clipped weighted mean stacked spectra of Ly$\alpha$ absorption trough. We detect an asymmetric flux distribution, with enhanced flux redward of the line
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Median (left panel) and 3σ-clipped weighted mean (right panel) stacked spectrum for 1716 DLAs with median hydrogen column density of log(N<sub>H1</sub>/cm<sup>-2</sup>) = 21.2, along with 1σ error shown in grey color. The green hatched region show the dark core of absorption trough, with optical depth (τ) > 10. The red curve shows the emergent Lyα profile, after radiative transfer of Lyα photons while considering the DLAs as expanding thin-shell geometry (see text Gurung-López et al. 2022).</figcaption></figure>

center; namely, 1215.67 Å in the dark core of the absorption trough. Such Lyα emission profiles with enhanced red and suppressed blue peaks are naturally produced by the radiative transport of Lyα photons in an outflowing medium (Steidel et al. 2010; Dijkstra 2014; Galbiati et al. 2023). This has also been observed empirically (Steidel et al. 2010; Galbiati et al. 2023). To quantify the emission line flux, at first, we used the region redward of the line center and detected a strong Lyα emission profile at 5.8σ level with Lyα flux of (0.150 ± 0.026) × 10<sup>-17</sup> erg s<sup>-1</sup> cm<sup>-2</sup> in the 3σ-clipped weighted-mean stack. Similarly, for the median stack the line is detected at 4.6σ level with Lyα flux of (0.145 ± 0.032) × 10<sup>-17</sup> erg s<sup>-1</sup> cm<sup>-2</sup>. At the median redshift of our DLA sample, namely, z ~ 2.64, this corresponds to a Lyα luminosity of (8.64 ± 1.87) × 10<sup>40</sup> erg s<sup>-1</sup> in the median and (8.95 ± 1.54) × 10<sup>40</sup> erg s<sup>-1</sup> in the 3σ-clipped weighted mean stack. We get a similar luminosity of (6.45 ± 2.50) × 10<sup>40</sup> erg s<sup>-1</sup> at 2.57σ level and (6.68 ± 2.13) × 10<sup>40</sup> erg s<sup>-1</sup> at 3.1σ level for median and 3σ-clipped weighted mean stacks, respectively, if we integrate all the pixels in the entire dark trough with τ > 10.

Next, using the Lyα luminosity, we estimated the average SFR associated with DLA hosts, assuming a Lyα to Hα ratio (Case B) recombination value of 8.7 (Kennicutt 1998a). However, this provides the minimal SFR as dust obscuration and escape fraction may lower the observed Lyα emission compared to the intrinsic emission. The Hα and SFR calibration [SFR (M☉ yr⁻¹) = 7.9 × 10⁻⁴² × L<sub>Hα</sub> (erg s⁻¹)] from Kennicutt (1998a) results in an average star formation rate 〈SFR〉 ~ 0.078±0.016 M☉ yr⁻¹. We note that the above estimate is a lower limit of SFR as it does not take into account dust and consider the Lyα escape fraction (f<sub>esc</sub>) of unity. Additionally, uncertainty in the DLA redshift could contribute to the emission line broadening, potentially leading to a loss of flux near the wings. Considering a typical escape fraction of f<sub>esc</sub> = 0.15 for high-z LAEs with a typical Lyα emission line equivalent width of <20 Å (Matthee et al. 2016; Goovaerts et al. 2024), the average SFR in DLAs can be higher with 〈SFR〉 ≈ 0.9L<sub>Lyα</sub>/f<sub>esc</sub> ≲ 0.52 ± 0.11(M☉ yr⁻¹). Using the star formation rate surface density and mean gas surface density relation: Σ<sub>SFR</sub>(M☉ yr⁻¹ kpc⁻²) = (2.5 ± 0.7) × 10⁻⁴ (Σ<sub>gas</sub>/1M☉pc⁻²)<sup>1.4±0.15</sup> at the low redshift from Kennicutt (1998b, see their Eq. (4)), the lower column densities that are typical for DLAs log(N<sub>H1</sub>/cm⁻²) ≈ 21.2 cm⁻² in our sample gives an

average Σ<sub>SFR</sub> = 8.75 × 10<sup>-3</sup> (M☉ yr<sup>-1</sup> kpc<sup>-2</sup>). We note that only a small fraction, namely, ~15% of DLAs exhibit H<sub>2</sub> gas. However, the correlation between SFR and H<sub>I</sub> in low-density gas in conjunction with the large fraction of our DLAs exhibiting metals hints at some level of 'in situ' SFR (Balanhev & Noterdaeme 2018). A caveat in linking the inferred SFR with the DLA column density is that the measured H<sub>I</sub> density is not averaged over the disk, but it is a local estimate along a pencil beam. Local measurements may thus introduce more substantial scatter in the relation. A partial mitigation of this effect arises from considering the average emission in a large sample of DLAs, for which we consider a range of N(H<sub>I</sub>) values. Such an average estimate will bring us closer to the underlying values (Barbieri et al. 2005). Following Noterdaeme et al. (2014, see their Eq. (10)), using the above integrated SFR, we can obtain the DLA radius as Σ<sub>SFR</sub>πr<sub>gal</sub><sup>2</sup> = 0.078/f<sub>esc</sub> M☉ yr<sup>-1</sup>, which results in an average galaxy size of ~4 kpc and ~7 kpc for a typical f<sub>esc</sub> of 0.15 and 0.05 for LAEs and LBGs, respectively (Hayes et al. 2010; Matthee et al. 2016). We note that for the DLA galaxies of the above sizes, due to the finite SDSS(BOSS) fiber size of the radius of 1 arcsec (1.5 arcsec), which corresponds to a physical size of 8(12) kpc at the median redshift of z = 2.637, the measured fluxes suffer from the fiber losses. This is because only a part of the galaxy may lie inside the fiber (López & Chen 2012), thus, the above-measured SFR represents a lower limit on average SFR in DLAs.

We find that the Lyα emission is predominantly red-shifted relative to the systemic velocity of the DLAs with a typical line offset of 310 ± 52 km s⁻¹ in the median stack. A similar velocity offset of 323 ± 36 km s⁻¹ is found when considering the 3σ-clipped weighted mean stack. This velocity offset falls close to the typical peak shift of ~230 km s⁻¹ measured in the case of LAEs (Erb et al. 2014; Lofthouse et al. 2023) and LBGs which show a velocity offset of much less than 400 km s⁻¹ (see Noterdaeme et al. 2014; Mackenzie et al. 2019). The median (3σ-clipped weighted mean) stacked Lyα emission line FWHM in DLAs is found to be ~400 ± 137 (360 ± 94) km s⁻¹. This is slightly higher than the mean FWHM of the red peak of Lyα line in LAEs, namely, ~260 km s⁻¹, but consistent with the LBGs FWHM of 364 km s⁻¹ (Trainor et al. 2015). The excess line broadening can be reconciled with the redshift uncertainty of DLAs and the range of velocity offset and Lyα profiles from the
<figure><img src="image_3.png" /></figure>

**Fig. 2.** SFR surface densities $\Sigma_{SFR}$ of DLAs from the spectral stacks. Limits on the SFR surface densities derived from the composite images are shown as horizontal hatched blue bars (Fumagalli et al. 2015). The grey shaded region show the $\Sigma_{SFR}$ detected in the outskirts of LBGs Rafelski et al. (2011), and the blue shaded region shows the ESDLA ($N(H\alpha) > 10^{21.7}$ cm$^{-2}$) (Noterdaeme et al. 2014). The dotted black line shows where the extrapolation of the local SF law. Our results shows $\log N(H\alpha/cm^{-2}) \ge 21$ to 22.35 with range of $f_{esc}$, 0.05 and 0.15 showing dashed (red dashed) region.

DLA population, which introduces line broadening while stacking.

**5. Discussion and conclusions**

We used the largest set of 1716 high $N(H\alpha)$ DLAs to obtain direct limits on the in situ SFRs in DLAs. Several spectral stacking experiments have been performed in literature to detect the residual $Ly\alpha$ emission in the dark core of the DLA trough. Rahmani et al. (2010) studied the stacked spectra of DLAs with $\log(N_{H\alpha}/\text{cm}^{-2}) \ge 20.62$ and set a $2\sigma$ upper limit on the $Ly\alpha$ luminosity from DLA gas at $\le 2 \times 10^{41}$ erg s$^{-1}$, which corresponds to a SFR of $<0.8 M_{\odot} yr^{-1}$ at $z \sim 2.8$. In another stacking experiment, Cai et al. (2014) have used $\sim 2000$ DLA systems with $\log(N_{H\alpha}/\text{cm}^{-2}) > 20.6$ at a median absorption redshift of $\langle z \rangle = 2.6$. They did not detect any $Ly\alpha$ emission signature in the dark trough of composite spectra. Using $\sim 100$ extremely strong DLAs with $\log(N_{H\alpha}/\text{cm}^{-2}) > 21.7$, probing a small subset of DLA populations, Noterdaeme et al. (2014) detected the $Ly\alpha$ emission with luminosity of $\sim 0.6 \pm 0.2 \times 10^{42}$ erg s$^{-1}$ (corresponding to about $0.1 L^* at $z \sim 2-3$). For a DLA population of $\log(N_{H\alpha}/\text{cm}^{-2}) > 21$, Joshi et al. (2016) detected a hint of $Ly\alpha$ emission at $2.8\sigma$ level in the red part of the DLA trough with a luminosity of $<10^{41}(3\sigma)$ erg s$^{-1}$. They found that the metal-rich systems show stronger $Ly\alpha$ emission. Here, we have detected a strong signature of $Ly\alpha$ emission at $>5\sigma$ level, with an average luminosity of $(8.64 \pm 1.87) 10^{40}$ erg s$^{-1}$ and SFR of $\sim 0.078 \pm 0.016 M_{\odot} yr^{-1}$. This value is consistent with the average SFR detection limit (at $2\sigma$) of $0.09 M_{\odot} yr^{-1}$ observed over an aperture of 2 kpc in direct HST imaging of DLA host galaxies with $\log(N_{H\alpha}/\text{cm}^{-2})$ of 20.3–21.3 by Fumagalli et al. (2015).

We further explored the SFR relation with the observed neutral gas in absorption. Using our in-situ SFR measurement, we derived the star-formation surface density using a typical

<figure><img src="image_4.png" /></figure>

**Fig. 3.** Star formation main sequence of star-forming galaxies (triangle) from Genzel et al. (2010), and the direct detection of DLAs (circle) along with the best-fit MS relation (dashed black line) from Rhodin et al. (2021). The lower limit (arrow) of the stacked spectra measurements (star) is also shown.

Lyman-alpha ($Ly\alpha$) halo scale length of approximately 4.5 kpc, derived from observations of high-redshift star-forming galaxies ($3 \le z \le 6$) in the MUSE Hubble Ultra Deep Field Survey (Leclercq et al. 2017). For such scale lengths, the SDSS fiber probing a physical size of $\sim 12$ kpc likely integrates the light from the DLA host. In Fig. 2, we plot the star-formation surface density ($\Sigma_{SFR}$), assuming $f_{esc} = 0.05$ and $f_{esc} = 0.15$ for LBGs and LAEs, with H\alpha gas surface density of $\Sigma_{gas}$. It is evident that the DLAs and ESDLAs follow the KS-law for a range of H\alpha densities (see also Noterdaeme et al. 2014; Fumagalli et al. 2015).

Previous efforts to study the DLA host galaxies suggest a strong association with LAEs (Noterdaeme et al. 2014; Rubin et al. 2015; Lofthouse et al. 2023). By leveraging the average $Ly\alpha$ luminosity of DLAs and incorporating the main sequence relation, we can estimate the stellar mass of DLAs using the equation presented by Goovaerts et al. (2023). The result is $\log(M_{\star}/M_{\odot}) = (0.85 \pm 0.17) \log(L_{Ly\alpha}/\text{erg s}^{-1}) - (27.8 \pm 6.4)$, yielding an average stellar mass of $\log(M_{\star}/M_{\odot}) = 6.9 \pm 0.6$. In Fig. 3, we compare the stellar mass and average SFR in DLAs with SFGs at $z \sim 1-3$ (Genzel et al. 2010), along with a handful of known DLA host galaxies (Rhodin et al. 2021). This suggests that on an average the DLAs with $\log(N_{H\alpha}/\text{cm}^{-2}) \ge 21$ probe the lower mass end of SFG.

We also find that the $Ly\alpha$ emission shows an asymmetric emission feature with a dominant red peak and suppressed blue peak with systemic velocity offset with respect to DLA profile of $\sim 310 \pm 52$ km s$^{-1}$ (323 $\pm$ 36 km s$^{-1}$) in the median ($3\sigma$-clipped weighted mean) stack. This velocity shift implies a kinematic difference between the emitting and absorbing neutral hydrogen gas, potentially due to gas in-and-outflows or complex dynamics within these galaxies. Another possibility is that the DLA gas is rotating, with non-uniform star formation throughout (Ogura et al. 2020). To obtain further insight into the gas geometry and kinematics in DLAs, we modelled the observed $Ly\alpha$ emission profile using the thin shell model, which consists of a central $Ly\alpha$ source, surrounded by an expanding outflowing thin, spherical shell of hydrogen and dust. It successfully reproduces the diversity of line profiles such as broad absorption in some Lyman break galaxies to asymmetric
emission in LAEs (Verhamme et al. 2006). For this, we used the zELDA<fnref n="1" /> routine which uses an isothermal homogeneous spherical thin layer of neutral hydrogen gas with a constant gas temperature of $10^4$ K and a homogeneous radial bulk velocity. In addition, the dust optical depth is set to $\tau_a = (1 - A_{Lya}) \frac{Z}{E_\odot} E_\odot N_H$, where $E_\odot = 1.77 \times 10^{-21} \text{ cm}^{-2}$ is the ratio $\tau_a/N_H$ for solar metallicity, $A_{Lya} = 0.39$ is the albedo at the Ly$\alpha$ wavelength, $Z = 0.02$ (Granato et al. 2000). For this purpose, we varied the column density for $\log(N_{HI}/\text{cm}^{-2})$ between 17 and 22. The radiative transfer modelling of DLAs as an expanding shell results in an expansion velocity $V_{\text{exp}} = 30^{+55}_{-12} \text{ km s}^{-1}$, and a dust optical depth of $\log(\tau_a) = 0.20^{+0.10}_{-0.17}$. The posterior distributions of the fitted parameter are shown in Fig. A.2.

The similar velocity offset, gas kinematics, and tight SFR-MS relation between the DLAs and LAEs hint at a close association between the two populations. Considering DLAs as LAEs, for a typical characteristic luminosity of LAEs, $L^* = 5 \times 10^{42} \text{ erg s}^{-1}$ (Cassata et al. 2011), our average Ly$\alpha$ emission imply that DLAs traces the low-luminosity population. This is typically ~0.02 $L^*$, of LAEs. The long-slit spectroscopy efforts have detected the galaxy counterparts at small impact parameters of <15 kpc, suggesting a close association with the LAEs (Christensen et al. 2014; Krogager et al. 2017). Moreover, the MUSE surveys with a large 3D wide field of view have confirmed the association between DLAs and LAEs even at distances exceeding 50 kpc (Fumagalli et al. 2017; Rubin et al. 2015; Mackenzie et al. 2019). In contrast, at $z \ge 4$ DLA galaxies are generally found at impact parameters of $\approx 15-60$ kpc (Neeleman et al. 2017, 2019; Kaur et al. 2024), suggesting their origin in CGM gas. We note that the impact parameter is found to be decreasing with the increasing column density; thus, by selecting the $\log(N_{HI}/\text{cm}^{-2}) \ge 21$, we are more likely to probe the small impact parameters (see Krogager et al. 2017; Rahmati & Schaye 2014). Moreover, the environment also plays a crucial role, as observations suggest higher detections of LAEs in environments with high column density absorbers, indicating that LAEs may trace larger-scale structures that include DLAs (Lofthouse et al. 2020). The same picture is corroborated by the EAGLE cosmological simulations, which indicate that the DLAs trace neutral regions within halos with characteristic masses of $M_h \approx 10^{11}-10^{12} M_\odot$ and likely associated with the LAEs; in that case, both are influenced by the same underlying dark matter halo (Font-Ribera et al. 2012). A follow-up study to trace galaxy counterparts, at small impact parameters for a metallicity-unbiased DLA sample is crucial to uncover the faint-end population of LAEs.

*Acknowledgements.* We are thankful to the anonymous referee for constructive suggestions. LCH was supported by the National Science Foundation of China (11991052, 12233001), the National Key R&D Program of China (2022YFF0503401), and the China Manned Space Project (CMS-CSST-2021-A04, CMS-CSST-2021-A06). HC and Dharmender are grateful to IUCAA for the hospitality under IUCAA associate programme.

## References

Balashev, S., & Noterdaeme, P. 2018, MNRAS, 478, L7

Barbieri, C. V., Fraternali, F., Oosterloo, T., et al. 2005, A&A, 439, 947

Barnes, L. A., & Haehnelt, M. G. 2009, MNRAS, 397, 511

Bera, A., Kanekar, N., Weiner, B. J., Sethi, S., & Dwarakanath, K. S. 2018, ApJ, 865, 39

Bird, S., Vogelsberger, M., Haehnelt, M., et al. 2014, MNRAS, 445, 2313

Cai, Z., Fan, X., Noterdaeme, P., et al. 2014, ApJ, 793, 139

Cassata, P., Le Fèvre, O., Garilli, B., et al. 2011, A&A, 525, A143

Cen, R. 2012, ApJ, 748, 121

Chabanier, S., Etienneau, T., Le Goff, J.-M., et al. 2022, ApJS, 258, 18

Christensen, L., Noterdaeme, P., Petitjean, P., Ledoux, C., & Fynbo, J. P. U. 2009, A&A, 505, 1007

Christensen, L., Møller, P., Fynbo, J. P. U., & Zafar, T. 2014, MNRAS, 445, 225

Dijkstra, M. 2014, PASA, 31, e040

Erb, D. K., Steidel, C. C., Trainor, R. F., et al. 2014, ApJ, 795, 33

Faucher-Giguère, C.-A., & Oh, S. P. 2023, ARA&A, 61, 131

Font-Ribera, A., Miralda-Escudé, J., Arnau, E., et al. 2012, JCAP, 2012, 059

Fumagalli, M., Prochaska, J. X., Kasen, D., et al. 2011, MNRAS, 418, 1796

Fumagalli, M., O'Meara, J. M., Prochaska, J. X., Kanekar, N., & Wolfe, A. M. 2014, MNRAS, 444, 1282

Fumagalli, M., O'Meara, J. M., Prochaska, J. X., Rafelski, M., & Kanekar, N. 2015, MNRAS, 446, 3178

Fumagalli, M., Mackenzie, R., Trayford, J., et al. 2017, MNRAS, 471, 3686

Galbiati, M., Fumagalli, M., Fossati, M., et al. 2023, MNRAS, 524, 3474

Genzel, R., Tacconi, L., Gracia-Carpio, J., et al. 2010, MNRAS, 407, 2091

Goovaerts, I., Pello, R., Thai, T., et al. 2023, A&A, 678, A174

Goovaerts, I., Pello, R., Burgarella, D., et al. 2024, A&A, 683, A184

Granato, G. L., Lacey, C. G., Silva, L., et al. 2000, ApJ, 542, 710

Gurung-López, S., Gronke, M., Saito, S., Bonoli, S., & Orsi, Á. A. 2022, MNRAS, 510, 4525

Hayes, M., Östlin, G., Schaerer, D., et al. 2010, Nature, 464, 562

Ho, M.-F., Bird, S., & Garnett, R. 2020, MNRAS, 496, 5436

Joshi, R., Srianand, R., Noterdaeme, P., & Petitjean, P. 2016, MNRAS, submitted [arXiv:1610.06580]

Kaur, B., Kanekar, N., Neeleman, M., et al. 2024, ApJ, 971, L33

Kennicutt, R. C. 1998a, ARA&A, 36, 189

Kennicutt, R. C. 1998b, ApJ, 498, 541

Krogager, J.-K., Møller, P., Fynbo, J., & Noterdaeme, P. 2017, MNRAS, 469, 2959

Leclercq, F., Bacon, R., Wisotzki, L., et al. 2017, A&A, 608, A8

Lofthouse, E. K., Fumagalli, M., Fossati, M., et al. 2020, MNRAS, 491, 2057

Lofthouse, E. K., Fumagalli, M., Fossati, M., et al. 2023, MNRAS, 518, 305

López, G., & Chen, H.-W. 2012, MNRAS, 419, 3553

Mackenzie, R., Fumagalli, M., Theuns, T., et al. 2019, MNRAS, 487, 5070

Matthee, J., Sobral, D., Best, P., et al. 2016, MNRAS, 465, 3637

Neeleman, M., Wolfe, A. M., Prochaska, J. X., & Rafelski, M. 2013, ApJ, 769, 54

Neeleman, M., Kanekar, N., Prochaska, J. X., et al. 2017, Science, 355, 1285

Neeleman, M., Kanekar, N., Prochaska, J. X., et al. 2018, ApJ, 856, L12

Neeleman, M., Kanekar, N., Prochaska, J. X., Rafelski, M. A., & Carilli, C. L. 2019, ApJ, 870, L19

Neeleman, M., Prochaska, J. X., Kanekar, N., & Rafelski, M. 2020, Nature, 581, 269

Noterdaeme, P., Petitjean, P., Ledoux, C., & Srianand, R. 2009, A&A, 505, 1087

Noterdaeme, P., Laursen, P., Petitjean, P., et al. 2012, A&A, 540, A63

Noterdaeme, P., Petitjean, P., Pâris, I., et al. 2014, A&A, 566, A24

Ogura, K., Umehata, H., Taniguchi, Y., et al. 2020, PASJ, 72, 29

O'Meara, J. M., Chen, H.-W., & Kaplan, D. L. 2006, ApJ, 642, L9

Prochaska, J. X., & Herbert-Fort, S. 2004, PASP, 116, 622

Rafelski, M., Wolfe, A. M., & Chen, H.-W. 2011, ApJ, 736, 48

Rafelski, M., Wolfe, A. M., Prochaska, J. X., Neeleman, M., & Mendez, A. J. 2012, ApJ, 755, 89

Rahmani, H., Srianand, R., Noterdaeme, P., & Petitjean, P. 2010, MNRAS, 409, L59

Rahmati, A., & Schaye, J. 2014, MNRAS, 438, 529

Rhodin, N., Krogager, J., Christensen, L., et al. 2021, MNRAS, 506, 546

Rubin, K. H., Hennawi, J. F., Prochaska, J. X., et al. 2015, ApJ, 808, 38

Steidel, C. C., Erb, D. K., Shapley, A. E., et al. 2010, ApJ, 717, 289

Trainor, R. F., Steidel, C. C., Strom, A. L., & Rudie, G. C. 2015, ApJ, 809, 89

Verhamme, A., Schaerer, D., & Maselli, A. 2006, A&A, 460, 397

Wolfe, A. M., Gawiser, E., & Prochaska, J. X. 2005, ARA&A, 43, 861

<footnote n="1">¹ zELDA; https://github.com/sidgurun/Lya_zelda</footnote>
<figure><img src="image_5.png" /></figure>

**Fig. A.1.** 3σ-clipped weighted mean profile without zero-level correction. The average flux in the dark core of the DLA trough, blueward of the line center, is shown as dashed line, along with the mean error.

<figure><img src="image_6.png" /></figure>

**Fig. A.2.** Posterior distributions for free parameters from zELDA radiative transfer modeling of Lyα emission line profile in 3σ-clipped weighted mean stack, at redshift 2.635, $V_{exp} = 30_{-12}^{+55}$ km s⁻¹, $\log(N_{H\,1/cm^{-2}}) = 20.7_{-0.01}^{+0.53}$, and $\tau_{\alpha} = 0.20_{-0.17}^{+0.10}$. The grey curves indicate the 1σ and 2σ contours of the 2D distributions.

# Appendix A: Uncorrected 3σ-clipped weighted mean profile and zELDA parameter distribution for Lyα emission