# The Giant Metrewave Radio Telescope Cold-HI AT $z\approx 1$ Survey

Aditya Chowdhury  National Centre for Radio Astrophysics, Tata Institute of
Fundamental Research, Pune, India.  Nissim Kanekar  National Centre for Radio
Astrophysics, Tata Institute of Fundamental Research, Pune, India.  Jayaram N.
Chengalur  National Centre for Radio Astrophysics, Tata Institute of
Fundamental Research, Pune, India.

###### Abstract

We describe the design, data analysis, and basic results of the Giant
Metrewave Radio Telescope Cold-Hi AT $z\approx 1$ (GMRT-CAT$z1$) survey, a
$510$-hour upgraded GMRT Hi 21 cm emission survey of galaxies at $z=0.74-1.45$
in the DEEP2 survey fields. The GMRT-CAT$z1$ survey is aimed at characterising
Hi in galaxies during and just after the epoch of peak star-formation activity
in the Universe, a key epoch in galaxy evolution. We obtained high-quality Hi
21 cm spectra for 11,419 blue star-forming galaxies at $z=0.74-1.45$, in seven
pointings on the DEEP2 subfields. We detect the stacked Hi 21 cm emission
signal of the 11,419 star-forming galaxies, which have an average stellar mass
of $\textrm{M}_{*}\approx 10^{10}~{}\textrm{M}_{\odot}$, at $7.1\sigma$
statistical significance, obtaining an average Hi mass of
$\langle\rm{M_{H{\textsc{i}}}}\rangle=(13.7\pm 1.9)\times
10^{9}~{}\textrm{M}_{\odot}$. This is significantly higher than the average Hi
mass of $\langle\rm{M_{H{\textsc{i}}}}\rangle=(3.96\pm 0.17)\times
10^{9}~{}\textrm{M}_{\odot}$ in star-forming galaxies at $z\approx 0$ with an
identical stellar-mass distribution. We stack the rest-frame 1.4 GHz continuum
emission of our 11,419 galaxies to infer an average star-formation rate (SFR)
of $8.07\pm 0.82~{}\textrm{M}_{\odot}\textrm{yr}^{-1}$. Combining our average
Hi mass and average SFR estimates yields an Hi depletion timescale of $1.70\pm
0.29$ Gyr, for star-forming galaxies at $z\approx 1$, $\approx 3$ times lower
than that of local galaxies. We thus find that, although main-sequence
galaxies at $z\approx 1$ have a high Hi mass, their short Hi depletion
timescale is likely to cause quenching of their star-formation activity in the
absence of rapid gas accretion from the circumgalactic medium.

Galaxy evolution — Radio spectroscopy — Neutral hydrogen clouds

††software: CASA (McMullin et al., 2007), calR (Chowdhury, 2021), AOFLAGGER
(Offringa et al., 2012), numpy (Harris et al., 2020), astropy (Astropy
Collaboration et al., 2013, 2018), matplotlib (Hunter, 2007), scipy (Virtanen
et al., 2020), numba (Lam et al., 2015), joblib (Joblib Development Team,
2021)

##  1 Introduction

Over the past seven decades, the Hi 21 cm transition has played a fundamental
role in our understanding of galaxies and galaxy evolution. Studies of Hi 21
cm emission from galaxies in the local Universe, using both single dishes
(e.g. Zwaan et al., 2005; Haynes et al., 2018; Catinella et al., 2018) and
radio interferometers (e.g. Verheijen, 2001; Begum et al., 2008; Walter et
al., 2008; Heald et al., 2011; Hunter et al., 2012), have provided information
on the nature of dark matter halos in nearby galaxies (e.g. Bosma, 1981;
Casertano & van Gorkom, 1991; de Blok et al., 2008; Begum et al., 2008), the
mass distribution of Hi in the local Universe (the Hi mass function; e.g.
Zwaan et al., 1997, 2005; Jones et al., 2018), the connection between rotation
velocity and baryonic mass (e.g. Tully & Fisher, 1977; McGaugh et al., 2000;
Verheijen, 2001; Lelli et al., 2019), the dependence of the global Hi
properties of galaxies on their stellar properties (e.g. Saintonge &
Catinella, 2022), the relation between the Hi mass and the size of the Hi disk
(e.g. Broeils & Rhee, 1997; Wang et al., 2016), the role of Hi in regulating
star-formation in galaxies (e.g. Leroy et al., 2008; Roychowdhury et al.,
2009), the impact of environment and galaxy interactions on the Hi disks of
galaxies (e.g. Cayatte et al., 1990; Hibbard et al., 2001; Chung et al.,
2009), the cosmological mass density of neutral hydrogen (e.g. Zwaan et al.,
2005; Jones et al., 2018), and a variety of other issues.

Unfortunately, the low Einstein A-coefficient of the Hi 21 cm transition
implies that the Hi 21 cm line is very weak. This makes Hi 21 cm emission
studies of galaxies at cosmological distances challenging, even with sensitive
modern-day telescopes. Indeed, while deep searches for Hi 21 cm emission at
high redshifts have been carried out for more than thirty years (e.g.
Subrahmanyan & Anantharamaiah, 1990; Uson et al., 1991; Wieringa et al.,
1992), often with integrations of hundreds of hours (e.g. Jaffé et al., 2013;
Catinella & Cortese, 2015; Fernández et al., 2016; Gogate et al., 2020), the
highest redshift at which Hi 21 cm emission has been detected from an
individual object remains $z\approx 0.376$ (Fernández et al., 2016). Detecting
Hi 21 cm emission from galaxies at significantly higher redshifts, $z\gtrsim
1$, is one of the main goals of next-generation telescopes like the Square
Kilometre Array.

The prohibitively-large integration times required on today’s radio telescopes
to detect Hi 21 cm emission from galaxies at $z\gtrsim 1$ has meant that,
until very recently, nothing was known about the Hi masses of high-$z$
galaxies or their evolution, or relations to other galaxy properties such as
stellar masses, SFR, molecular gas mass, environment, etc. This lack of
information about Hi, the primary fuel for star-formation, in high-$z$
galaxies is in stark contrast with the spectacular progress made in measuring
their stellar properties (e.g. Madau & Dickinson, 2014), and, more recently,
their molecular gas properties (e.g. Tacconi et al., 2020).

Progress in understanding the Hi properties of high-$z$ galaxies can be made
by using the Hi 21 cm stacking approach (Zwaan, 2000; Chengalur et al., 2001).
Here, the _average_ Hi properties of a sample of galaxies can be determined by
co-adding, i.e. “stacking”, the Hi 21 cm emission signals of the individual
galaxies, as long as their positions and redshifts are accurately known.
Applying this technique to determine the average Hi mass of galaxies at
$z\gtrsim 1$ requires a large number of galaxies with spectroscopic redshifts,
located within the field of view of the telescope, and with their redshifted
Hi 21 cm line frequencies covered by a single frequency setting. Further, Hi
21 cm stacking experiments critically require accurate spectroscopic
redshifts, with redshift errors $\lesssim 100$ km s-1, to prevent the stacked
signal from being smeared in velocity (e.g. Maddox et al., 2013; Elson et al.,
2019).

In the local Universe, Hi 21 cm stacking has been used to probe the dependence
of the Hi properties of galaxies on their stellar properties and environments
(Fabello et al., 2011, 2012; Brown et al., 2015, 2017; Meyer et al., 2016), as
well as to measure the cosmological Hi mass density at $z\approx 0$ (e.g. Hu
et al., 2020). The results of these studies have been consistent with those
from direct Hi 21 cm emission surveys of individual galaxies. At low
redshifts, $z\lesssim 0.2$, successful Hi 21 cm stacking experiments have been
carried out using both single dishes (Delhaize et al., 2013) and radio
interferometers (Rhee et al., 2013). At intermediate redshifts, $z\approx
0.2-0.4$, the early Hi 21 cm stacking experiments, all using the Giant
Metrewave Radio Telescope (GMRT), obtained only tentative ($\approx
2-3~{}\sigma$) detections of the stacked Hi 21 cm emission signal (Lah et al.,
2007, 2009; Rhee et al., 2016, 2018). Recently, Bera et al. (2019) used a
175-hr upgraded GMRT111The GMRT was upgraded in 2018 with new wideband
recievers and a wideband correlator. The upgrade increased the maximum
instantaneous bandwidth from 33.3 MHz to 400 MHz. survey of the Extended Groth
Strip at $z\approx 0.2-0.4$ to obtain the first statistically-significant
detection of the stacked Hi 21 cm emission from galaxies at intermediate
redshifts. At even higher redshifts, Kanekar et al. (2016) used 60 hrs with
the GMRT to search for the stacked Hi 21 cm emission from star-forming
galaxies at $z\approx 1.3$ in the DEEP2 survey fields (Newman et al., 2013),
obtaining an upper limit on the average Hi mass of the galaxies.

Recently, Chowdhury et al. (2020) used the upgraded GMRT to carry out an Hi 21
cm emission survey of galaxies in the DEEP2 survey fields (Newman et al.,
2013), covering the redshift range $z=0.74-1.45$. Chowdhury et al. stacked the
Hi 21 cm signal from 7,653 blue star-forming galaxies at $z=0.74-1.45$ to
measure, for the first time, the average Hi mass of galaxies at $z\approx 1$.
They found that the average Hi mass of blue star-forming galaxies at $z\approx
1$, with an average stellar mass of $\textrm{M}_{*}\approx
10^{10}~{}\textrm{M}_{\odot}$, is a factor of $\approx 3$ higher than that of
galaxies at $z\approx 0$ with the same average stellar mass. However, they
also found that the Hi reservoir can sustain the high SFR in these galaxies
for only $\approx 1-2$ Gyr, in the absence of fresh gas accretion.
Subsequently, Chowdhury et al. (2021) reported results from another GMRT Hi 21
cm emission survey of the DEEP2 fields, using the original GMRT receivers and
a 33-MHz bandwidth to cover the narrow redshift range $z=1.18-1.39$. They
stacked the Hi 21 cm emission from 2,841 blue star-forming galaxies to obtain
an independent $\approx 5\sigma$ detection of the stacked Hi 21 cm signal, at
$z\approx 1.3$. Again, the Hi reservoir was found to be sufficient to sustain
the galaxy SFRs for only $\approx 2$ Gyr, in the absence of fresh gas
accretion. Chowdhury et al. (2020) suggested that the observed decline in the
star-formation activity of the Universe at $z\lesssim 1$ arises due to
insufficient gas accretion on to star-forming galaxies from the circumgalactic
medium (CGM; see also Bera et al., 2018; Chowdhury et al., 2021).

We present here the GMRT Cold-Hi AT $z\approx 1$ (GMRT-CAT$z1$) survey, a
510-hr upgraded GMRT Hi 21 cm emission survey of galaxies at $z=0.74-1.45$ in
the DEEP2 survey fields, aimed at characterising the Hi properties of galaxies
at $z\approx 1$. The survey covers a crucial epoch where the cosmic SFR
density of the Universe begins to decline after its peak at $z\approx 1-3$
(e.g. Madau & Dickinson, 2014); the GMRT-CAT$z1$ survey is thus uniquely
suited to investigate the role of Hi in the decline of the SFR density at
$z\lesssim 1$. This paper describes the survey design, the observations, and
the data analysis of the GMRT-CAT$z1$ survey, along with an accurate
measurement of the average Hi mass and the Hi depletion timescale of star-
forming galaxies at $z\approx 1$. A study of the role of Hi in the decline of
the cosmic SFR density is presented in Chowdhury et al. (2022a), while
Chowdhury et al. (2022b) compare the contributions of Hi, ${\rm H_{2}}$, and
stars to the baryonic content of star-forming galaxies at $z\gtrsim 1$. Future
papers will discuss other results from the GMRT-CAT$z1$ survey, including the
Hi scaling relations at these redshifts, a comparison between the properties
of the ionized gas and the neutral atomic gas in star-forming galaxies at
$z\approx 1$, and the cosmological Hi mass density at $z\approx 1$.

This paper is organised as follows: Section 2 provides a brief summary of the
DEEP2 Galaxy Redshift Survey, focussing on the aspects relevant for our GMRT
Hi 21 cm survey; Section 3 discusses the design of the GMRT-CAT$z1$ survey and
provides information on the upgraded GMRT observations; Section 4 presents the
analysis of the GMRT data in detail; Section 5 describes the procedures used
to stack the Hi 21 cm emission luminosities and the rest-frame 1.4 GHz
continuum luminosities; Section 6 provides detailed information on the main
sample of galaxies; Section 7 presents our measurements of the average Hi mass
as a function of spatial resolution and our final choice of the optimal
spatial resolution for all subsequent Hi 21 cm stacking; Section 8 presents
the GMRT-CAT$z1$ detection of the stacked Hi 21 cm line emission and stacked
rest-frame 1.4 GHz continuum emission from our full sample of galaxies at the
optimal spatial resolution, along with the main results of this paper
concerning the average Hi properties of star-forming galaxies at $z\approx 1$;
Section 9 provides a discussion on the average Hi properties of red galaxies
and galaxies hosting active galactic nuclei (AGNs) at $z\approx 1$; Section 10
discusses possible systematic effects, and shows that our average Hi mass
measurements are unlikely to be affected by such systematics; Section 11
presents a search for Hi 21 cm emission from the individual DEEP2 galaxies
covered by the GMRT-CAT$z1$ survey; and, finally, Section 12 summarises our
key conclusions. We refer the reader who is interested in the key science
results of this paper to Sections 8 and 12.

Throughout this paper, we use a flat “737” $\Lambda$-cold dark matter
($\Lambda$CDM) cosmology, with ($\rm H_{0}$, $\rm\Omega_{m}$,
$\rm\Omega_{\Lambda})=(70$ km s-1 Mpc-1, $0.3,0.7)$. We also assume a Chabrier
initial mass function (IMF) in all estimates of stellar masses and SFRs. SFR
estimates from the literature that assume a Salpeter IMF were converted to a
Chabrier IMF by subtracting 0.2 dex (e.g. Madau & Dickinson, 2014). All
magnitudes are in the AB system.

##  2 The DEEP2 Galaxy Redshift Survey

Figure 1: The sky area covered by the GMRT-CAT$z1$ survey in the DEEP2 survey
fields 2, 3, and 4. The three panels show the three DEEP2 fields, with the
regions covered by the DEEP2 survey marked in gray. The red circles show the
half-power point of the GMRT primary beam at $\approx 610$ MHz. The regions in
blue, orange, and green show the galaxies covered by the GMRT-CAT$z1$ survey,
with the number of blue galaxies in each pointing shown below each circle, and
the sub-field number indicated above each circle. The dashed circle shows a
slightly different pointing on DEEP2 sub-field 31 that was used in the
observations of Cycle 35.

The DEEP2 Galaxy Redshift Survey (Newman et al., 2013) used 90 nights with the
DEIMOS spectrograph on the Keck-II telescope to measure the spectroscopic
redshifts of $\approx 38,300$ galaxies in four near-contiguous regions of the
sky, with a sky area of 2.8 square degrees. The survey covered the wavelength
range $6500$ Å$-9100$ Å with a high spectral resolution (R$=6000$), allowing a
clean identification of the [Oii]$\lambda$3727Å doublet from the redshift
range $z\approx 0.7-1.45$. The limiting apparent magnitude of the survey is
R${}_{\rm AB}=24.1$ and the typical redshift accuracy, for objects with
redshift quality $\geq 3$, is $\lesssim 62$ km s-1 (Newman et al., 2013).

The DEEP2 Data Release 4 (DR4) catalogue (Newman et al., 2013) contains 27,966
galaxies with spectroscopic redshifts of quality $\geq 3$ at $z=0.7-1.45$ in
the four DEEP2 fields. 21,561 of these galaxies are located in DEEP2 fields 2,
3, and 4, which consist of seven sub-fields of size $\approx 28^{\prime}\times
52^{\prime}$. The full-width-at-half-maximum (FWHM) of the GMRT Band-4
receivers is $\approx 43^{\prime}$ at 610 MHz, implying that each of the above
seven sub-fields can be reasonably covered with a single GMRT Band-4 pointing
(see Figure 1). Further, the Hi 21 cm line from galaxies at $z=0.74-1.45$ is
redshifted to the frequency range $\approx 580-820$ MHz, i.e. into the
frequency coverage of the GMRT Band-4 receivers. DEEP2 fields 2, 3, and 4 are
thus ideal targets for a GMRT Hi 21 cm emission survey of galaxies at
$z\approx 0.74-1.45$ (e.g. Kanekar et al., 2016; Chowdhury et al., 2020,
2021). We note that although DEEP2 Field 1, the Extended Groth Strip (EGS),
has excellent multi-wavelength coverage (e.g. Davis et al., 2007), we did not
observe it as the narrowness of the EGS ($\approx 16^{\prime}$; Newman et al.,
2013) implies that a significant fraction of the GMRT Band-4 primary beam
would contain almost no galaxies with spectroscopic redshifts.

The stellar masses of the DEEP2 galaxies were estimated via a relation between
the (U$-$B) colour, the (B$-$V) colour and the ratio of the stellar mass to
the B-band luminosity (Weiner et al., 2009). This relation was calibrated at
$z\approx 1$ using the subset of DEEP2 galaxies that have direct K-band
estimates of the stellar mass. The scatter of individual stellar masses
estimated using this relation is $\approx 0.3$ dex (Weiner et al., 2009).

##  3 The Upgraded GMRT Observations

DEEP2 | Right Ascension | Declination | GMRT | On-Source | Number of | $\sigma_{\textrm{HI}}$
---|---|---|---|---|---|---
subfield | (J2000) | (J2000) | cycle | Time (hr) | Galaxies |  $\mu$Jy/Bm
21 | $16$h$47$m$59.7$s | $+34\degree 55^{\prime}40.4^{\prime\prime}$ | 37 | 32.7 | 1,547 | 201
38 | 17.9 | 1,545 | 313
22 | $16$h$51$m$28.9$s | $+34\degree 56^{\prime}58.9^{\prime\prime}$ | 37 | 22.8 | 1,623 | 274
38 | 26.9 | 1,663 | 293
31 |  $23$h$26$m$52.8$s | $+00\degree 08^{\prime}25.7^{\prime\prime}$ | 35 | 14.3 | 1,390 | 328
$23$h$27$m$26.2$s | $+00\degree 08^{\prime}22.9^{\prime\prime}$ | 37 | 12.8 | 1,405 | 338
38 | 33.9 | 1,226 | 232
32 | $23$h$29$m$49.9$s | $+00\degree 12^{\prime}12.7^{\prime\prime}$ | 35 | 14.5 | 1,403 | 304
37 | 10.7 | 1,268 | 319
38 | 26.7 | 1,431 | 288
33 | $23$h$32$m$58.7$s | $+00\degree 08^{\prime}22.7^{\prime\prime}$ | 35 | 15.3 | 1,227 | 293
37 | 14.8 | 1,140 | 338
38 | 33.9 | 1,062 | 195
41 | $02$h$28$m$24.0$s | $+00\degree 35^{\prime}27.6^{\prime\prime}$ | 35 | 7.5 | 1,878 | 355
37 | 31.4 | 1,899 | 286
38 | 31.1 | 1,903 | 268
42 | $02$h$30$m$48.0$s | $+00\degree 35^{\prime}15.0^{\prime\prime}$ | 35 | 15.0 | 1,813 | 362
37 | 17.2 | 1,780 | 308
38 | 28.0 | 1,790 | 291
Table 1: Summary of the GMRT observations and results. The columns are : (1)
the DEEP2 subfield, (2,3) the J2000 Right Ascension and Declination of the
GMRT pointing centre, (4) the observing cycle in which the observations were
carried out, (5) the on-source time, in hours, (6) the final number of
galaxies whose Hi 21 cm subcubes were stacked, and (7) the median RMS noise on
the Hi 21 cm subcubes at a velocity resolution of 30 km s-1 and a spatial
resolution of 90 kpc. See main text for discussion. Note that all observations
had the same correlator setup, covering the frequency range $530-930$ MHz,
with 8192 spectral channels.

We used the upgraded GMRT (Swarup et al., 1991; Gupta et al., 2017) Band-4
$550-850$ MHz receivers to observe DEEP2 fields 2, 3, and 4 for a total time
of $\approx$510 hours, over three GMRT cycles between October 2018 and October
2020 (proposals 35_087, 37_063 and 38_033; PI: Aditya Chowdhury). The total
time was divided approximately equally between seven pointings in the three
DEEP2 fields. This was motivated by (a) minimizing the effect of cosmic
variance on our measurements, by increasing the sky area, and (b) reducing the
risk of the root-mean-square (RMS) noise on the spectra of individual galaxies
not decreasing $\propto 1/\sqrt{\Delta t}$ on a single field, due to
systematic effects such as dynamic range issues.

The DEEP2 sky area of $\approx 2$ sq. degrees covered by the GMRT-CAT$z1$
survey (sky volume of $\approx 10^{7}$ comoving Mpc3) is sufficient to ensure
that the effects of cosmic variance are negligible (Newman & Davis, 2002;
Newman et al., 2013). Driver & Robotham (2010) find that these effects would
be $\lesssim 10\%$ for a single contiguous survey volume of $\gtrsim 10^{7}$
cMpc3. The total survey volume of $\approx 10^{7}$ cMpc3 of the GMRT-CAT$z1$
survey consists of three separate contiguous regions (DEEP2 fields 2, 3, and
4); the effects of cosmic variance are hence expected to be even lower than
$\approx 10\%$, by a factor of $\approx\sqrt{3}$ (Driver & Robotham, 2010).

The initial 90 hours of observations were carried out between October 2018 and
March 2019 (GMRT Cycle 35), with five pointings222The allocated time for the
project in Cycle 35 was 100 hrs; we lost an entire 10 hour run on DEEP2 field
41 due to severe radio frequency interference. on DEEP2 fields 3 and 4; the
analysis of these data was presented in Chowdhury et al. (2020). Between
October 2019 and March 2020 (GMRT Cycle 37), we used 170 hours of observations
to observe all three DEEP2 fields with seven pointings. The remaining 250
hours were obtained between May 2020 and October 2020 (GMRT Cycle 38), again
with seven pointings on the three DEEP2 fields. The total on-source observing
time for each of the seven DEEP2 subfields was $\approx 50-60$ hours. We note
that the pointing centre on DEEP2 subfield 31 was shifted by $\approx
8^{\prime}$ between our observations of Cycle 35 and those of Cycles 37 and
38; this was done to reduce the deconvolution errors from bright radio-
continuum sources at the edge of the pointing. Table 1 provides a summary of
the 510 hours of observations, while Figure 1 shows the different pointings on
the three DEEP2 fields.

We used the GMRT Wideband Backend (Reddy et al., 2017) as the correlator,
covering the frequency range $530-930$ MHz with a total bandwidth of 400 MHz,
divided into 8,192 spectral channels. In each observing run, we used
observations of one or more of the standard calibrators 3C48, 3C147, or 3C286
to calibrate the flux density scale, and observations of the nearby compact
sources 0022+002, 0204+152, or 1609+266 to calibrate the antenna complex gains
and antenna bandpass shapes.

##  4 Data Analysis, Sample Selection, and Statistical Tests

###  4.1 The Data Analysis

All data were analyzed in the Common Astronomy Software Applications package
(casa Version 5; McMullin et al., 2007) following standard procedures. The
same procedures, described in detail below, were used for the data from all
observing cycles. We note that the analysis of the initial 90 hours of data
from Cycle 35 was presented by Chowdhury et al. (2020). The new analysis
described here contains a few minor improvements over that of Chowdhury et al.
(2020).

The GMRT consists of 30 antennas, with 14 of these in a central 1 sq. km.
region (the “central square”) and the remaining 16 arranged along three arms,
forming a “Y”-shape and providing baselines out to $\approx 25$ km.
Terrestrial radio frequency interference (RFI) is typically stronger on the
shorter central-square baselines, and decorrelates on the longer baselines. To
reduce the effects of RFI, we entirely excluded the 91 baselines between pairs
of central square antennas, and restricted our analysis to the remaining 344
baselines. The 91 central square baselines that were excluded have UV
distances of $\approx 0.08-3.8$ k$\lambda$ at an observing frequency of
$\approx 650$ MHz; these correspond to angular scales of $\approx
0.9^{\prime}-43^{\prime}$, far larger than the angular scales of interest in
this work.

The data for each DEEP2 sub-field from the three GMRT observing cycles were
analysed independently. The result of the analysis is thus either two or three
independent spectral cubes for each DEEP2 sub-field, one each for the data of
each cycle. This was done to prevent systematic errors, such as those due to
low-level RFI, imperfect deconvolution, etc, in the data of one GMRT cycle on
a given field from affecting the overall data quality for that field. The
independent spectral cubes allow us to separately examine the quality of the
spectra from all DEEP2 galaxies from each GMRT cycle. For example, if the
spectrum of a particular DEEP2 galaxy from Cycle 37 is affected by RFI, our
approach ensures that the spectra of the galaxy from Cycles 35 and 38 can be
used, if these are “clean”.Conversely, if the data from all three cycles were
combined to generate a single spectral cube for the pointing, we would have
had to entirely exclude the DEEP2 galaxy in question from our sample.

For each observing run, after initially removing data from non-working
antennas, the aoflagger (Offringa et al., 2012) package was used to excise
data affected by RFI. The antenna gains and bandpass shapes were determined
using the data on the calibrator sources, and these solutions were applied to
the target source visibilities. All antenna-based gain and bandpass
calibration, as well as self-calibration, was performed using the calR333The
package is publicly available at https://github.com/chowdhuryaditya/calR
(Chowdhury, 2021) package (Chowdhury et al., 2020), a collection of robust
calibration routines within the CASA framework. Following this, all visibility
data on each pointing from each cycle were combined together to produce a
single multi-channel data set for each pointing. A standard iterative self-
calibration procedure, along with further excision of data affected by low-
level RFI, was then separately performed on the data of each pointing, again
for each observing cycle. For each subfield, the data of the first observing
cycle were calibrated using $3-4$ rounds of imaging and phase-only self-
calibration, followed by $2-3$ rounds of imaging and amplitude-and-phase self-
calibration. For observations of the same subfield in later cycles, the
continuum image obtained from the first observing cycle was used as the
initial self-calibration model (solving for both amplitude and phase),
followed by at least 2 rounds of imaging and amplitude-and-phase self-
calibration. The imaging was done with the casa task tclean, with w-projection
(Cornwell et al., 2008), multi-frequency synthesis (2nd-order expansion; Rau &
Cornwell, 2011), and Briggs weighting (Briggs, 1995), with a robust parameter
of $-0.5$. For each field, the self-calibration procedure was continued until
no improvement was seen in either the image or in the residuals after
subtracting the image from the calibrated visibilities. At the end of the
self-calibration procedure, the calibrated visibilities of each DEEP2 subfield
of each cycle were separately imaged with the task tclean, again using
w-projection, multi-frequency synthesis (2nd-order expansion), and Briggs
weighting with a robust parameter of $0.0$.

We next used the final continuum images of each target field to subtract out
all detected continuum emission from the self-calibrated spectral-line
visibilities. For each field, the continuum subtraction was performed
separately for the data in each observing cycle, using the continuum image of
that cycle. We then used aoflagger (Offringa et al., 2012) to perform one
final round of RFI excision on the continuum-subtracted spectral-line
visibilities.

Figure 2: The fraction of data excised across the observing band due to time-
variable issues (see main text for details), shown separately for the data
obtained in each of the three GMRT cycles.

The fraction of data on each target field that was lost due to time-variable
issues such as RFI, temporary problems with antennas, etc., but not including
antennas that were not available throughout the observing run and the 91
baselines amongst the central-square antennas that were excised at the outset
of the analysis, was $\approx 26\%$, $\approx 32\%$, and $\approx 19\%$ for
Cycles 35, 37, and 38, respectively. Figure 2 shows, separately for each
observing cycle, the fraction of data excised due to such time-dependent
issues as a function of observing frequency.

The casa task tclean was then used to make spectral cubes from the continuum-
subtracted visibilities of each target field, and from each cycle; this
yielded a total of 19 spectral cubes. The cubes were made in the barycentric
frame, with w-projection and Briggs weighting with a robust parameter of $+1$.
We experimented with various values of the robust parameter, and found Briggs
weighting with a robust parameter of $+1$ to be the optimal choice; this
results in reducing the effect of deconvolution errors around bright radio
continuum sources, without causing a significant increase in the spectral RMS
noise of the cubes. Each cube covers a sky area of $0.8^{\circ}\times
0.8^{\circ}$, larger than the FWHM of the GMRT primary beam at the lowest
observing frequency of the band; this allowed us to obtain Hi 21 cm spectra
for all DEEP2 galaxies within the FWHM of the GMRT primary beam at the
redshifted Hi 21 cm line frequency of each galaxy. The channel width of the
spectral cubes is 48.8 kHz, corresponding to a velocity resolution of $18-25$
km s-1 across the frequency band. The synthesized beams of the cubes have
FWHMs of $4.0^{\prime\prime}-7.5^{\prime\prime}$, corresponding to spatial
resolutions of $29-63$ kpc for the redshift range $z=0.74-1.45$.

###  4.2 Radio continuum Images

Figure 3: The GMRT 655 MHz continuum images of the seven DEEP2 sub-fields. The blue dashed-dotted and dotted circles in each panel show, respectively, the FWHM of the GMRT primary beam at $580$ MHz and $816$ MHz. DEEP2 subfield | Synthesized Beam | $F_{\textrm{max}}$ | $\sigma_{\textrm{cont}}$
---|---|---|---
|  | mJy Beam-1 |  $\mu$Jy Beam-1
21 | $3.9^{\prime\prime}\times 3.1^{\prime\prime}$ | 152.3 | 4.5
22 | $3.3^{\prime\prime}\times 2.6^{\prime\prime}$ | 158.5 | 8.0
31 | $4.1^{\prime\prime}\times 3.3^{\prime\prime}$ | 82.4 | 6.2
32 | $4.1^{\prime\prime}\times 3.3^{\prime\prime}$ | 29.7 | 5.0
33 | $4.1^{\prime\prime}\times 3.3^{\prime\prime}$ | 34.4 | 4.6
41 | $3.7^{\prime\prime}\times 2.9^{\prime\prime}$ | 284.0 | 10.3
42 | $4.1^{\prime\prime}\times 3.2^{\prime\prime}$ | 75.6 | 5.9
Table 2: Properties of the GMRT 655 MHz continuum images of each DEEP2
subfield. The columns are (1) the DEEP2 subfield, (2) the FWHM of the
synthesized beam, (3) the peak flux density of the brightest source in the
field, uncorrected for the primary beam response, and (4) the RMS noise on the
image, obtained by taking the median of the local RMS noise computed on
regions of size $\approx 84^{\prime\prime}\times 84^{\prime\prime}$. Note that
the continuum image of DEEP2 subfield 31 uses data from Cycles 37 and 38 only
(see main text for details).

The final 655 MHz radio continuum images of each DEEP2 subfield were made
after combining all available data on each pointing. For each pointing, we
first combined the calibrated visibilities from all cycles into a single data
set, and then performed a few iterations of self-calibration on the combined
data set. The self-calibrated visibilities of each subfield were then imaged,
with w-projection, multi-frquency synthesis (2nd order expansion), and Briggs
weighting with a robust parameter of $0.0$. For each pointing, we imaged a
region of $\approx 1.5\degree\times 1.5\degree$ around the pointing centre,
extending well beyond the null of the GMRT primary beam at these frequencies.
The median of the RMS noise values in each continuum image is $\approx
5-10~{}\mu$Jy Beam-1, while the FWHMs of the synthesized beams are $\approx
3^{\prime\prime}-4^{\prime\prime}$. Table 2 lists the FWHMs of the synthesized
beams and the RMS noise values of these final radio continuum images. The RMS
noise values listed in the table were obtained by taking the median of the
local RMS noise computed on regions of size $\approx 84^{\prime\prime}\times
84^{\prime\prime}$, without primary beam correction. The final continuum
images of the seven DEEP2 subfields are shown in Figure 3. We note that the
GMRT pointing on subfield 31 in Cycle 35 was slightly different from the
pointing used in Cycles 37 and 38 (see Figure 1). The final radio continuum
image of subfield 31 in Fig. 3 is from the data obtained in Cycles 37 and 38.

###  4.3 Sample Selection

Figure 4: The rest-frame (U$-$B) vs rest-frame M${}_{\textrm{B}}$ colour-
magnitude diagram for the 16,250 DEEP2 galaxies covered by our observations.
The blue points show the location of each DEEP2 galaxy in the diagram. The
dashed line divides the sample into the red and blue galaxy populations
(Willmer et al., 2006).

Our upgraded GMRT observations cover the redshifted Hi 21 cm line for 16,250
DEEP2 galaxies with accurate redshifts (redshift quality, Q$\geq$3 in the
DEEP2 DR4 catalogue; Newman et al., 2013) at $z=0.74-1.45$, lying within the
FWHM of the GMRT primary beam at the redshifted Hi 21 cm frequency of the
galaxy. The FWHM of the GMRT primary beam is $\approx 43^{\prime}$ at 610 MHz,
and scales with frequency ($\nu$) as FWHM $\propto 1/\nu$. The Hi 21 cm lines
of the 16,250 galaxies at $z=0.74-1.45$ are redshifted to frequencies $\approx
580-820$ MHz, where the Band-4 receivers have their highest sensitivity.

The DEEP2 survey is magnitude-limited in the R-band (R $<24.1$) and this
preferentially picks out blue objects at $z>0.7$ (Willmer et al., 2006; Newman
et al., 2013). Indeed, only 2,222 out of the 16,250 DEEP2 objects covered by
our observations are part of the “red cloud” in the color-magnitude diagram
(Willmer et al., 2006). Figure 4 shows the distribution of 16,250 DEEP2
galaxies in the rest-frame (U$-$B) vs rest-frame M${}_{\textrm{B}}$ colour-
magnitude diagram. We ensure the homogeneity of our sample by restricting our
study to the 14,028 blue objects at $z=0.74-1.45$ that are covered by our
observations. These 14,028 galaxies lie below the green valley in the rest-
frame (U$-$B) vs rest-frame M${}_{\textrm{B}}$ colour-magnitude diagram (see
Figure 4), and were selected using the criterion C$\leq 0$, where the colour
${\rm C=U-B}+0.032\times({\rm M_{B}}+21.63)-1.014$ (Willmer et al., 2006).

Some of the above 14,028 blue DEEP2 galaxies may host AGNs, which could affect
the gas properties of the galaxy. We hence used our radio-continuum images of
the DEEP2 subfields to exclude all detected radio AGNs from our sample. Radio-
continuum studies show a bimodality in the distribution of rest-frame 1.4-GHz
radio luminosity (L${}_{1.4\ \textrm{GHz}}$), with objects having L${}_{1.4\
\textrm{GHz}}>2\times 10^{23}$ W Hz-1 being predominantly radio-bright AGNs,
and objects with L${}_{1.4\ \textrm{GHz}}<2\times 10^{23}$ W Hz-1 being
predominantly star-forming galaxies (Condon et al., 2002). We use this
criterion to exclude the 882 DEEP2 objects which are detected at $\geq
4\sigma$ statistical significance in our radio-continuum images, with
L${}_{1.4\ \textrm{GHz}}>2\times 10^{23}$ W Hz-1. After excluding these 882
radio-bright AGNs, our sample contains 13,146 blue star-forming galaxies at
$z=0.74-1.45$.

Finally, we excluded from the sample the 487 galaxies that have stellar masses
$\textrm{M}_{*}<10^{9}\ \textrm{M}_{\odot}$. This was done in order to ensure
that our results can be directly compared with results for the xGASS survey
(Catinella et al., 2018), which has measured the Hi properties of galaxies at
$z\approx 0$ with $\textrm{M}_{*}>10^{9}\ \textrm{M}_{\odot}$. We note that
only $\approx 4\%$ of our galaxies have $\textrm{M}_{*}<10^{9}\
\textrm{M}_{\odot}$ and their exclusion from the sample does not affect the
results presented in this work (within the statistical uncertainties). After
excluding the 487 galaxies with $\textrm{M}_{*}<10^{9}\ \textrm{M}_{\odot}$,
our sample contains 12,659 blue star-forming galaxies at $z=0.74-1.45$.

###  4.4 Hi 21 cm spectral subcubes

We obtain multiple Hi 21 cm spectra, with uncorrelated statistical noise, for
nearly every blue star-forming DEEP2 galaxy in our sample444Henceforth, for
brevity, we will refer to Hi 21 cm spectra with uncorrelated statistical noise
as “independent” Hi 21 cm spectra.. Specifically, for each DEEP2 galaxy, we
obtain 2 or 3 independent Hi 21 cm spectra from the observations in the
different GMRT cycles. We also obtain additional independent Hi 21 cm spectra
for the galaxies that lie in the overlap regions of our pointings on the DEEP2
subfields. A total of 33,640 independent Hi 21 cm spectra were obtained for
the 12,659 galaxies in our sample, with up to six independent Hi 21 cm spectra
per DEEP2 galaxy.

For each DEEP2 galaxy, we extracted an Hi 21 cm subcube centred on the galaxy
from each spectral cube that covered its Hi 21 cm line. Each subcube covers an
angular extent of $\pm 76.8^{\prime\prime}$ around the galaxy location, and a
velocity range of $\pm 1500$ km s-1 around its redshifted Hi 21 cm line
frequency. We convolved each of the 33,640 independent Hi 21 cm subcubes with
Gaussian beams such that the FWHMs of the final beams of each convolved
subcube are identical.

Next, the spatial extent of the Hi 21 cm emission from galaxies at these
redshifts is not known. We hence initially convolved each subcube to a range
of spatial resolutions, 60 kpc, 70 kpc, 80 kpc, 90 kpc, 100 kpc, 110 kpc, 120
kpc, 150 kpc, and 200 kpc. The analysis of the subcubes was carried out at
each of the above resolutions. Our final choice of the spatial resolution is
described in Section 7 below.

During the process of convolution, care was taken to normalize the convolved
subcubes such that the peak of the convolved point-spread function (using the
same kernel) is unity (Chowdhury et al., 2020). Any spectral channel where the
intrinsic beam has a FWHM $>60$ kpc was excised at this stage. Next, we
regridded each subcube to a uniform spatial and spectral grid, with $10$ kpc
spatial pixels covering $\pm 500$ kpc around the position of the DEEP2 galaxy,
and $30$ km s-1 velocity channels covering $\pm 1500$ km s-1 around its
redshifted Hi 21 cm line frequency. Finally, we fitted a second-order
polynomial to the spectrum at each spatial pixel of the subcubes, and
subtracted this out. This was done to remove any residual spectral baselines
due to deconvolution errors from bright radio-continuum sources.

###  4.5 Statistical tests for systematic effects in the spectral cubes

We carried out a series of tests on the subcubes, aiming to remove any
subcubes affected by non-Gaussian systematic effects. This was done to ensure
that the noise properties of the stacked Hi 21 cm subcubes are not limited by
such systematics. Initially, we discarded any Hi 21 cm subcube which has
$>15\%$ of its spectral channels excised due to RFI; this resulted in the
excision of 3,721 Hi 21 cm subcubes, i.e. $\approx 11$% of the full sample.

Next, we tested whether the noise properties of the Hi 21 cm subcubes are
consistent with their arising from a Gaussian distribution. The tests were
carried out on the subcubes with a spatial resolution of 60 kpc; performing
these tests at coarser spatial resolutions yielded similar results. We
excluded spectra based on the following criteria :

  1. 1.

Any Hi 21 cm subcube having a spectral feature of $\geq 6.0\sigma$
significance, at either the native velocity resolution ($30$ km s-1), or after
smoothing to resolutions of $60$ km s-1 and $120$ km s-1, was rejected.

  2. 2.

Each Hi 21 cm subcube was tested for the presence of correlations between
neighboring spectral channels (e.g., due to a residual spectral baseline) by
examining the decrease in the RMS noise after smoothing to coarser velocity
resolutions. Specifically, each Hi 21 cm subcube was smoothed by a factor of
10 to a spectral resolution of 300 km s-1; any subcube whose RMS noise was
found to decrease by a factor $>0.47$ after the smoothing was excluded from
the sample.

These tests resulted in our excluding 926 Hi 21 cm subcubes, i.e. $\approx
3\%$ of the remaining 29,919 Hi 21 cm subcubes. Our final sample, after
excising 4,647 subcubes in all, contains a total of 28,993 independent Hi 21
cm subcubes for 11,419 blue star-forming galaxies at $z=0.74-1.45$. Table 1
lists the final number of galaxies (i.e. Hi 21 cm subcubes) obtained from the
observations of each subfield in each GMRT cycle. We emphasize that the
results of this paper are not sensitive to the exact choice of the thresholds
used in the above tests.

###  4.6 The RMS noise on the individual Hi 21 cm

The presence of systematic effects in the data, such as deconvolution errors,
residual low-level RFI, etc., can limit the final spectral RMS noise obtained
on the Hi 21 cm spectra. To test for such effects, we computed the RMS noise
on our final sample of 28,993 independent Hi 21 cm subcubes, at a spatial
resolution of 90 kpc, and compared this to the spectral RMS noise expected for
upgraded GMRT observations. For a given observation of a DEEP2 subfield, we
compute the expected spectral RMS noise taking into account (1) the
sensitivity of the upgraded GMRT Band-4 receivers (as measured by the
observatory), (2) the total on-source time obtained on the DEEP2 subfield in
that GMRT cycle, (3) the fraction of data excised due to RFI, non-working
antennas, power failures, etc., (4) the effect of spectral smoothing to obtain
a velocity resolution of 30 km s-1, and (5) the effect of spatial smoothing to
obtain a resolution of 90 kpc.

Figures 16, 17, and 18 in Appendix A compare the spectral RMS noise obtained
on the Hi 21 cm subcubes of the DEEP2 galaxies with the expected RMS noise for
each observation. We find that the actual RMS noise obtained on our Hi 21 cm
subcubes is within $\approx 10\%$ of the RMS noise predicted using the GMRT
sensitivity curve for the Band-4 receivers. We note that the GMRT sensitivity
curve is itself only accurate to $\approx 10\%$, while the typical flux-scale
uncertainty for upgraded GMRT observations (such as the ones presented here)
is also $\approx 10\%$. We thus find no evidence for systematic effects that
might affect the spectral RMS noise on our sample of 28,993 independent Hi 21
cm subcubes. We also repeated the above analysis at other spatial resolutions
($>60$ kpc) and find similar results. Overall, we find no evidence suggesting
that the final RMS noise obtained on our Hi 21 cm subcubes might have been
limited by systematic effects.

##  5 The Stacking Analysis

###  5.1 Stacking the Hi 21 cm Emission

For each Hi 21 cm subcube, we first corrected the measured flux density to
take into account the position of the DEEP2 galaxy in the GMRT primary beam,
and then converted the flux density to the corresponding Hi 21 cm line
luminosity density, ${\rm L_{H\textsc{i}}}$ (in units of Jy Mpc2), using the
relation ${\rm L_{H\textsc{i}}}=4\pi\ {\rm S_{H\textsc{i}}}\ {\rm
D_{L}}^{2}/(1+z)$, where $\rm S_{H\textsc{i}}$ is the Hi 21 cm line flux
density (in units of Jy), and ${\rm D_{L}}$ is the luminosity distance of the
galaxy (in units of Mpc). The stacked Hi 21 cm spectral cube for the DEEP2
galaxies was obtained by taking an average, across all Hi 21 cm subcubes of
the final sample, of the Hi 21 cm line luminosity densities in the
corresponding spatial pixels and velocity channels of the individual subcubes.
We then fitted a second-order spectral baseline to the spectrum of each
spatial pixel of the stacked cube, excluding the central $\pm 250$ km s-1
velocity range, and subtracted out this baseline from each spatial pixel to
obtain the final stacked Hi 21 cm spectral cube.

We determined the RMS noise on the stacked cube by using Monte Carlo
simulations in which we shifted the central velocity of each DEEP2 galaxy in
the range $\pm 1500$ km s-1, and then stacked the velocity-shifted Hi 21 cm
subcubes. Spectral channels that were shifted outside the $\pm 1500$ km s-1
velocity range were wrapped around to the other side of the spectrum, before
the stacking. We repeated the above procedure to obtain 104 realizations of
the stacked Hi 21 cm subcube. For each spatial and velocity pixel of the
stacked Hi 21 cm subcube, we computed the RMS of the Hi 21 cm luminosities
across the $10^{4}$ realizations to obtain an estimate of the RMS noise on the
pixel.

Finally, we used a boxcar kernel to smooth the stacked Hi 21 cm subcubes,
including those derived via the Monte Carlo simulations, to a velocity
resolution of 90 km s-1. This was done in order to increase the signal-to-
noise ratio (SNR) per channel, to clearly identify the velocity range with Hi
21 cm emission. We used these subcubes to estimate the average Hi mass of the
DEEP2 galaxies, and the error on the average Hi mass. We note that our results
are not sensitive to the exact choice of the final velocity resolution of the
stacked Hi 21 cm cubes. The average Hi mass derived from the stacked Hi 21 cm
spectra at other resolutions (e.g. 60 km s-1, 120 km s-1, etc) are consistent
with those reported in this paper, for a velocity resolution of $90$ km s-1.

We also computed the errors on the stacked Hi 21 cm subcube via two other
methods: (i) bootstrap resampling with replacement, and (ii) computation of
the RMS noise from the image plane of the stacked subcube. The errors derived
via these methods are very similar to those derived via our Monte Carlo
approach.

The average Hi mass of our sample of DEEP2 galaxies was obtained as follows:
(i) the central velocity channels of the final stacked cube were integrated to
produce an image of the Hi 21 cm emission, (ii) the stacked Hi 21 cm spectrum
was obtained by taking a cut through the location of the peak luminosity
density in this Hi 21 cm image, (iii) a contiguous range of central velocity
channels in the stacked Hi 21 cm spectrum, each containing emission at $\geq
1.5\sigma$ statistical significance, was selected, (iv) the signal in these
channels was integrated to obtain the average velocity-integrated Hi 21 cm
line luminosity density ($\int{\rm L_{H\textsc{i}}\ dV}$), in units of ${\rm
Jy~{}Mpc^{2}}$ km s-1, and (v) the average Hi mass of the sample was obtained
via the expression $\rm{M_{H\textsc{i}}}=[1.86\times 10^{4}\times\int{\rm
L_{H\textsc{i}}\ dV}]~{}\textrm{M}_{\odot}$.

We note that the average Hi masses obtained by integrating the stacked Hi 21
cm spectra over a wide velocity range of $\pm 250$ km s-1 are consistent with
those obtained from the above approach, integrating over a contiguous range of
central velocity channels with emission at $\geq 1.5\sigma$ statistical
significance.

###  5.2 Stacking the rest-frame 1.4 GHz continuum emission

Measurements of the rest-frame 1.4 GHz radio luminosity of a star-forming
galaxy can be used to infer its SFR via the known correlation between the
radio and the far-infrared (FIR) luminosities (Condon, 1992; Yun et al.,
2001). We use our radio-continuum images of the DEEP2 subfields, along with
the FIR-radio correlation, to estimate the average SFR of our galaxies (e.g.
White et al., 2007; Bera et al., 2018; Leslie et al., 2020).

The synthesized beams of our radio-continuum images correspond to a physical
scale of $\approx 24-35$ kpc over the redshift range $z=0.74-1.45$. We
extracted $\approx 84^{\prime\prime}\times 84^{\prime\prime}$ sub-images
around each DEEP2 galaxy of our sample and convolved each sub-image with a
Gaussian kernel such that the final synthesized beam has an FWHM of 40 kpc
(again normalizing the sub-images such that the peak of the convolved point-
spread function is unity; Chowdhury et al., 2020). We then regridded the sub-
images to a uniform grid with 5.2 kpc pixels and extending over $\pm 260$ kpc.
Next, for each DEEP2 galaxy, we converted the observed flux density in each
pixel to the rest-frame 1.4 GHz luminosity at the galaxy redshift, assuming a
spectral index of $\alpha=-0.8$ (Condon, 1992), with
$S_{\nu}\propto\nu^{\alpha}$. We note that the central frequency of our radio-
continuum images corresponds to rest-frame frequencies of $\approx 1.14-1.61$
GHz for the galaxies of our sample, quite close to 1.4 GHz; our results are
hence insensitive to the exact choice of $\alpha$. A median stacking approach
was then used to estimate the average rest-frame 1.4 GHz luminosity of our
sample (White et al., 2007). In this approach, we compute the median of the
1.4 GHz luminosities of each spatial pixel, across the sample of galaxies. The
median rest-frame 1.4 GHz luminosity is then converted to a median SFR using
the relation SFR $(\textrm{M}_{\odot}/\textrm{yr})=(3.7\pm 1.1)\times
10^{-22}\times{\rm L_{1.4GHz}\ (W/Hz)}$ (Yun et al., 2001, after scaling to a
Chabrier IMF).

In order to test for systematic effects and to compute the RMS noise on our
stacked continuum image, we repeated the above procedure for sub-images at
locations offset by 100′′ from the DEEP2 galaxies. The stack at the offset
locations show that the mean of the distribution of luminosity-density values
is slightly shifted to negative values; in flux-density units, the offset is
$\approx-0.4\ \mu$Jy, more than an order of magnitude lower than the RMS noise
on each of our radio-continuum images. This weak bias in the mean of the
distribution is likely to be due to negative sidelobes of very faint sources
in our continuum maps, i.e. those with flux densities comparable to or lower
than our cleaning thresholds. For the rest-frame 1.4 GHz continuum stack of a
given subsample of galaxies, we correct for this effect by (i) computing the
mean luminosity density of the stack at locations offset by 100′′ from the
target galaxies, and (ii) subtracting this mean luminosity density from all
pixels of the stacks at both the galaxy locations and the offset locations.
Effectively, this amounts to a small zero-point correction in our continuum
stacked images; the correction is at the level of $\approx 4-5\%$ of the
detected 1.4 GHz luminosity in the stacked radio-continuum images.

We note that uncertainties in the flux density scale of our radio-continuum
images would affect our radio-derived SFR estimates. These systematic
uncertainties are typically $\lesssim 10\%$ for the GMRT, for our calibration
procedure. We have very conservatively treated this as a $1\sigma$ error on
the flux density estimates. Thus, the errors on our SFR values include both a
$10\%$ systematic uncertainty and the $1\sigma$ statistical uncertainty.

In passing, we note that we are unlikely to miss any radio-continuum emission
from the star-forming regions of the galaxies of our sample because the 40-kpc
beam of the stacked radio-continuum images is much larger than the observed
sizes of star-forming regions in galaxies at these redshifts (Trujillo et al.,
2004). Indeed, the FWHM of the R-band emission is less than 10 kpc for
$\approx 98\%$ of the 11,419 DEEP2 galaxies in our sample (Coil et al., 2004).

##  6 The Sample of 11,419 Blue, Star-forming Galaxies

Our main sample consists of 11,419 blue star-forming galaxies at $z=0.74-1.45$
in the seven uGMRT pointings on DEEP2 fields 2, 3 and 4, after excluding AGNs,
red galaxies, galaxies with stellar masses $\textrm{M}_{*}<10^{9}\
\textrm{M}_{\odot}$ (see Section 4.3), and galaxies whose Hi 21 cm subcubes
were affected by discernible systematic effects (see Section 4.5). Our
upgraded GMRT observations provide up to six independent measurements of the
Hi 21 cm spectrum of each galaxy of our sample (see Section 4.4).
Approximately $57\%$ of the galaxies have $\geq 3$ independent measurements of
their Hi 21 cm spectra, with at least one from each GMRT cycle. In all the
analysis presented in this paper, we have treated the independent Hi 21 cm
spectra as arising from separate “objects”. This effectively implies that, in
computing the average quantities of the sample, each of the 11,419 sample
galaxies has a weight proportional to the number of independent measurements
of its Hi 21 cm spectrum.

###  6.1 Redshifts and Stellar Masses

Figure 5: [A] The redshift distribution of our main sample of 11,419 galaxies.
The histogram shows the number of independent Hi 21 cm spectra as a function
of redshift. [B] The stellar-mass distribution of the sample. The histogram
shows the number of independent Hi 21 cm spectra in each logarithmic stellar-
mass bin. The dashed orange lines in Panel [A] and Panel [B] show,
respectively, the average redshift and the average stellar mass of the sample.

The redshift distribution of the 11,419 galaxies of our sample, after
accounting for the number of independent Hi 21 cm spectra per galaxy, is shown
in Figure 5[A]. The sample spans the redshift range $z=0.74-1.45$, with a mean
redshift $\langle z\rangle=1.04$.

Our sample of 11,419 galaxies has stellar masses in the range
$\textrm{M}_{*}=10^{9}-10^{11.4}\textrm{M}_{\odot}$. The stellar mass
distribution of the 11,419 galaxies, after factoring in the number of
independent Hi 21 cm spectra per galaxy, is shown in Figure 5[B]. The mean
stellar mass of the sample is $\langle\textrm{M}_{*}\rangle=9.9\times
10^{9}~{}\textrm{M}_{\odot}$.

Finally, we note that both the redshift and the stellar-mass distributions of
the 28,993 Hi 21 cm subcubes (shown in Figure 5), are similar to those of the
11,419 galaxies.

###  6.2 The star-forming main-sequence

An important question is whether our sample is dominated by main-sequence
galaxies, or whether it contains a significant population of starburst
systems. To test this, we binned the sample of galaxies into multiple stellar-
mass subsamples, and measured the average SFR in each of the stellar-mass bins
to test whether the average SFR and average stellar mass are consistent with
the star-forming main sequence at these redshifts. Further, the star-forming
main sequence has been shown to evolve within our redshift range,
$z=0.74-1.45$ (e.g. Whitaker et al., 2014; Leslie et al., 2020). We hence
divided our sample into two redshift ranges, $z=0.74-1.00$ and $z=1.00-1.45$,
and, in each redshift bin, we measured the average SFR of galaxies in stellar-
mass subsamples of width 0.5 dex. This was done by separately stacking the
rest-frame 1.4 GHz luminosities of the galaxies in each stellar-mass subsample
to determine their average SFR, using the procedure described in Section 5.2.
The stacking was performed using weights such that the redshift distributions
of the stacked sub-images in the stellar-mass subsamples are identical.
Finally, for each redshift bin, we compared our measurements of the average
stellar mass and the average SFR with the star-forming main-sequence relation
of Whitaker et al. (2014). We note there were fewer than 35 galaxies with
$\textrm{M}_{*}>10^{11}\ \textrm{M}_{\odot}$ in both redshift intervals; the
average SFRs of these highest-stellar mass subsamples may thus be affected by
small number statistics and are hence not used for this comparison.

Figure 6: The average stellar-mass and average SFR of the DEEP2 galaxies of
our sample. The filled circles show the average SFRs of galaxies in four
stellar-mass subsamples at $z=0.74-1.00$ (green) and $z=1.00-1.45$ (red),
obtained via stacking their rest-frame 1.4 GHz continuum emission. The
vertical error bars show the $1\sigma$ error on each measurement, obtained by
adding in quadrature the $1\sigma$ statistical uncertainty and the $10\%$
flux-scale uncertainty. The horizontal error bars show the range of stellar
masses in each subsample. The dashed blue and orange curves (“W14”) show the
star-forming main-sequence relation obtained for a stellar-mass-complete
sample of star-forming galaxies in each redshift range (Whitaker et al.,
2014). The average SFRs and average stellar masses of our galaxies are seen to
be consistent with the star-forming main-sequence relation in both redshift
intervals.

Figure 6 shows our measurements of the average SFR of galaxies in the four
stellar-mass subsamples, for the two redshift bins, $z=0.74-1.00$ and
$z=1.00-1.45$. For comparison, we also plot the star-forming main-sequence
relations obtained for a stellar-mass-complete sample of star-forming galaxies
at similar redshifts (Whitaker et al., 2014). These authors provide the star-
forming main-sequence relation for the redshift ranges $z=0.5-1.0$ and
$z=1.0-1.5$; we have interpolated between these measurements to infer the
main-sequence relations at $z=0.74-1.00$ and $z=1.00-1.45$. Figure 6 shows
that our average SFR values in each of the four stellar-mass bins are
consistent with the star-forming main-sequence relations in the two redshift
intervals.

##  7 The average Hi mass and the optimum spatial resolution

Figure 7: The stacked Hi 21 cm emission spectra of the DEEP2 galaxies, obtained at different spatial resolutions, from 60 kpc to 200 kpc. Each panel shows (in red) the stacked Hi 21 cm spectrum at a particular resolution, listed at the top right, with the black dashed curves indicating the $\pm 1\sigma$ error on each 90 km s-1 channel. For comparison, the stacked Hi 21 cm spectrum at a resolution of 90 kpc, the optimal spatial resolution, is shown in blue in all panels. Spatial Resolution | $\langle\rm{M_{H\textsc{i}}}\rangle$ | SNR
---|---|---
(kpc) | ($\times 10^{9}~{}\textrm{M}_{\odot}$) |
60 | 10.0 $\pm$ 1.5 | 6.7
70 | 11.7 $\pm$ 1.6 | 7.3
80 | 12.9 $\pm$ 1.8 | 7.4
90 | 13.7 $\pm$ 1.9 | 7.1
100 | 14.2 $\pm$ 2.1 | 6.8
110 | 14.6 $\pm$ 2.3 | 6.4
120 | 14.8 $\pm$ 2.4 | 6.2
150 | 15.2 $\pm$ 2.8 | 5.4
200 | 15.4 $\pm$ 3.7 | 4.2
Table 3: The average Hi mass of the DEEP2 galaxies of our sample at different
spatial resolutions, from 60 kpc to 200 kpc. The average Hi 21 cm emission
within the central beam was obtained from the stacked Hi 21 cm spectra of
Figure 7. The last column lists the SNR of the detection of the stacked Hi 21
cm emission signal. Figure 8: The average Hi mass of the DEEP2 galaxies of our
sample, plotted as a function of spatial resolution. The dashed line shows the
average Hi mass at a spatial resolution of 200 kpc.

We used the procedure described in Section 5.1 to stack the 28,993 Hi 21 cm
subcubes of the 11,419 blue star-forming galaxies of our sample, at the nine
different spatial resolutions (60 kpc, 70 kpc, 80 kpc, 90 kpc, 100 kpc, 110
kpc, 120 kpc, 150 kpc, and 200 kpc) at which we obtained Hi 21 cm subcubes of
the DEEP2 galaxies. For each resolution, the Hi 21 cm stacking was carried out
with identical weights assigned to each Hi 21 cm subcube. Figure 7 shows the
stacked Hi 21 cm spectra of the 11,419 galaxies at the nine different spatial
resolutions. We clearly detect the average Hi 21 cm emission signal at all
spatial resolutions, with $\approx 4.2\sigma-7.4\sigma$ significance.

We integrated the detected Hi 21 cm emission signals of Figure 7 over the
velocity range [$-150$ km s-1, +210 km s-1] to infer the average Hi mass of
the DEEP2 galaxies, within the central spatial beam; these measurements are
listed in Table 3. Figure 7 shows the average Hi mass of the galaxies as a
function of spatial resolution. The average Hi mass is seen to increase from
$(10.0\pm 1.5)\times 10^{9}\ \textrm{M}_{\odot}$ at a resolution of 60 kpc to
$(15.4\pm 3.7)\times 10^{9}\ \textrm{M}_{\odot}$ at 200 kpc. Further, the
increase in the average Hi mass shows clear evidence of flattening at coarser
resolutions (see Fig. 8). Increasing the size of the spatial beam of the Hi 21
cm subcubes comes at the cost of down-weighting the longer GMRT baselines, and
consequently raising the RMS noise on the stacked spectrum. We find that the
RMS error on the stacked Hi 21 cm cube increases approximately linearly with
spatial resolution over $60-200$ kpc, with the SNR of the detections peaking
at a resolution of $\approx 80$ kpc (see Table 3).

###  7.1 The Optimal Spatial Resolution

The choice of spatial resolution is important in terms of both accurately
measuring the average Hi mass of the DEEP2 galaxies and maximizing the SNR of
the final Hi 21 cm spectrum. As can be seen from Table 3 and Figure 8, using
too narrow a spatial resolution resolves out some of the Hi 21 cm emission
signal, and results in under-estimating the average Hi mass. Conversely, using
too coarse a spatial resolution would include all the Hi 21 cm emission but at
the cost of increasing the RMS noise on the signal. Ideally, the spatial
resolution would be matched to the spatial extent of the Hi 21 cm emission.
However, the spatial extent of the Hi 21 cm emission from galaxies at
$z\approx 1$ is not a priori known. We hence aimed to identify the optimal
spatial resolution by measuring the average Hi mass at different resolutions,
and finding the resolution above which the measured average Hi mass does not
continue to increase.

An important subtlety in measuring the average Hi mass at different spatial
resolutions arises from the fact that the mass measurements are correlated, as
a subset of the interferometer visibilities is common to the measurements.
Thus, one cannot assume independent errors when taking the difference between
the values of the average Hi mass measured at different spatial resolutions.
We hence measured the difference between the average Hi masses at each pair of
spatial resolutions by stacking the difference of the Hi 21 cm spectra at the
location of each galaxy at the two resolutions. For example, to estimate the
excess Hi mass at 80-kpc resolution relative to 60-kpc resolution, we first
subtracted the Hi 21 cm spectrum of each individual subcube at 60-kpc
resolution from that of the same subcube at 80-kpc resolution to obtain a
difference spectrum for the subcube. We then stacked these difference spectra
to measure the excess Hi 21 cm emission signal. The error on the stacked
difference spectrum for each pair of resolutions was obtained via the Monte
Carlo approach described in Section 5.1. The above procedure was carried out
for every pair of the spatial resolutions at which we obtained the Hi 21 cm
subcubes, i.e. every pair of 60 kpc, 70 kpc, 80 kpc, 90 kpc, 100 kpc, 110 kpc,
120 kpc, 150 kpc, and 200 kpc.

We find evidence at $\gtrsim 2.5\sigma$ statistical significance for an
increase in the average Hi mass of our sample of 11,419 galaxies out to a
resolution of 90 kpc. However, the difference between the average Hi mass
measured at a spatial resolution of 90 kpc and at any coarser resolution has
$<2\sigma$ significance. In other words, the average Hi mass of our galaxies,
measured at a resolution of $90$ kpc is consistent, within statistical
uncertainties, with that measured at coarser resolutions. We thus identify 90
kpc as the optimal spatial resolution for the Hi 21 cm stacking.

Unless otherwise mentioned, all subsequent results of the Hi 21 cm emission
stacking of this survey are at a spatial resolution of 90 kpc.

##  8 The Average Hi properties of Star-Forming Galaxies at $z\approx 1$

In this section, we present the main results of this study, from stacking the
Hi 21 cm line emission and the rest-frame 1.4 GHz continuum emission signals
of the full sample of 11,419 blue star-forming galaxies. Possible systematic
effects are considered in Section 10; we note here, in passing, that we find
no evidence in Section 10 for systematic effects that might affect our
results.

Number of Galaxies | $11,419$
---|---
Number of Hi 21 cm subcubes | $28,993$
Redshift range | $0.74-1.45$
Mean redshift, $\langle z\rangle$ | $1.04$
Stellar mass range | $1.0\times 10^{9}\ \textrm{M}_{\odot}\ -2.4\times 10^{11}\ \textrm{M}_{\odot}$
Mean stellar mass, $\langle\textrm{M}_{*}\rangle$ | $9.9\times 10^{9}\ \textrm{M}_{\odot}$
Mean Radio-derived SFR | $8.07\pm 0.82\ \textrm{M}_{\odot}/\textrm{yr}$
Mean Hi mass, $\langle\rm{M_{H\textsc{i}}}\rangle$ | $(13.7\pm 1.9)\times 10^{9}~{}\textrm{M}_{\odot}$
Hi depletion timescale, $\langle{\rm t_{dep,H{\textsc{i}}}}\rangle$ |  $(1.70\pm 0.29)$ Gyr
Table 4:  Details of the sample. The rows are (1) the number of galaxies, (2)
the number of independent Hi 21 cm subcubes, (3) the redshift range of the
galaxies, (4) their average redshift, $\langle z\rangle$, (5) the stellar mass
range of the galaxies, (5) their average stellar mass,
$\langle\textrm{M}_{*}\rangle$, (6) the SFR derived from the rest-frame
average 1.4 GHz radio luminosity density, (7) the average Hi mass,
$\langle\rm{M_{H\textsc{i}}}\rangle$, and (8) the characteristic Hi depletion
timescale, $\langle{\rm
t_{dep,H{\textsc{i}}}}\rangle\equiv\langle\rm{M_{H\textsc{i}}}\rangle/\langle\textrm{SFR}\rangle$.
See main text for discussion.

###  8.1 The average Hi Mass and the average SFR of the Sample

Figure 9: The average Hi 21 cm emission signal from blue star-forming galaxies
at $z\approx 1$. [A] The average Hi 21 cm emission image of the 11,419 blue
star-forming galaxies at $z=0.74-1.45$, obtained by integrating the emission
over the central velocity channels. The circle on the bottom left of the panel
shows the 90-kpc spatial resolution of the image. The contour levels are at
$-3.0\sigma$ (dashed), $+3.0\sigma$, $+4.0\sigma$, $+5.0\sigma$, $+6.0\sigma$,
and $+7.0\sigma$ statistical significance. The average Hi 21 cm emission
signal is clearly detected in the central region of the image. The effect of
the synthesized beam on the noise properties of this stacked image is
discussed in Section 10.1 and Figure 13. [B] The average Hi 21 cm emission
spectrum of the 11,419 blue star-forming galaxies at $z=0.74-1.45$, obtained
by taking a spectral cut through the location of the peak luminosity density
of the left panel. The channel width of the spectrum is 90 km s-1. The dashed
horizontal curves show the $\pm 1\sigma$ error on the spectrum. A clear
detection of the average Hi 21 cm emission signal can be seen in the central
velocity channels of the spectrum.  Figure 10: The median-stacked rest-frame
1.4 GHz continuum emission from [A] the DEEP2 galaxies, and [B] positions
offset from the DEEP2 galaxies by $100\arcsec$. A clear ($\approx 67\sigma$
significance) detection is visible at the location of the stacked DEEP2
galaxies in the left panel, while the stack at offset positions in the right
panel shows no evidence for either continuum emission or any systematic
patterns. The contour levels are at $5\sigma,\ 10\sigma,\ 20\sigma,\ {\rm
and}\ 40\sigma$ statistical significance. The circle in the bottom left corner
represents the $40$ kpc beam to which all continuum images were convolved
before the stacking.

The stacked Hi 21 cm emission image and the stacked Hi 21 cm spectrum of the
11,419 blue star-forming galaxies, obtained by stacking the 28,993 independent
Hi 21 cm subcubes at a spatial resolution of 90 kpc, are shown in Fig. 9. A
clear detection of the stacked Hi 21 cm emission signal can be seen in both
the stacked spectrum and the stacked Hi 21 cm emission image. The velocity-
integrated average Hi 21 cm signal has $7.1\sigma$ statistical significance.
Integrating the stacked Hi 21 cm spectrum over the velocity range [$-150$ km
s-1, $+210$ km s-1], we find that the average velocity-integrated Hi 21 cm
line luminosity of the 11,419 galaxies at $\langle z\rangle=1.04$ is $(7.33\pm
1.03)\times 10^{5}$ Jy Mpc2 km s-1. This yields an average Hi mass of
$\langle\rm{M_{H\textsc{i}}}\rangle=(1.37\pm 0.19)\times 10^{10}\
\textrm{M}_{\odot}$ for blue star-forming galaxies at $\langle z\rangle=1.04$.
This is consistent with the earlier measurement of
$\langle\rm{M_{H\textsc{i}}}\rangle=(1.19\pm 0.26)\times 10^{10}\
\textrm{M}_{\odot}$ at $\langle z\rangle\approx 1.0$ by Chowdhury et al.
(2020), from the 90-hours of observations in GMRT Cycle 35.

The average SFR of the 11,419 galaxies of our sample was determined from their
stacked rest-frame 1.4 GHz continuum luminosities, following the procedures of
Section 5.2. Fig. 10[A] shows the image obtained by stacking the rest-frame
1.4 GHz luminosities of the 11,419 galaxies, while Fig. 10[B] shows the stack
at positions offset from the DEEP2 galaxies: a clear detection of the stacked
1.4 GHz continuum emission, at $\approx 67\sigma$ significance, is visible in
the left panel, while no systematic effects can be seen in the right panel.
Using the SFR calibration of Yun et al. (2001), adjusted to a Chabrier IMF,
the detection yields an average SFR of $(8.07\pm 0.82)$ $\textrm{M}_{\odot}\
\textrm{yr}^{-1}$ for the sample. The average properties of the blue, star-
forming galaxies of our sample are summarised in Table 4.

The Hi mass of blue galaxies in the local Universe, with NUV$-$r$<4$ and with
a stellar mass distribution identical to the 11,419 galaxies at $z\approx 1$,
is $(3.96\pm 0.17)\times 10^{9}~{}\textrm{M}_{\odot}$ (Catinella et al.,
2018)555The errors on the average Hi mass of the xGASS galaxies from Catinella
et al. (2018) were computed using bootstrap resampling with replacement. We
emphasize that the average Hi mass of the blue galaxies in the xGASS sample
was computed with weights such that their effective stellar mass distribution
is identical to that of the 11,419 blue star-forming galaxies at
$z=0.74-1.45$. As can be seen in Fig. 11[A], we find clear evidence, at
$5.1\sigma$ significance, for redshift evolution in the average Hi mass of
blue galaxies beteween $z\approx 1$ and $z\approx 0$. Specifically, we find
that blue star-forming galaxies at $z\approx 1$, i.e. at the end of the epoch
of peak cosmic SFR density, have Hi reservoirs that are larger by a factor of
($3.5\pm 0.5$) than those of blue galaxies with an identical stellar-mass
distribution in the local Universe.

###  8.2 The Hi depletion timescale

Figure 11: Redshift evolution of [A] the average Hi mass,
$\langle\rm{M_{H\textsc{i}}}\rangle$, and [B] the characteristic Hi depletion
timescale, $\langle\rm{M_{H\textsc{i}}}\rangle/\langle\textrm{SFR}\rangle$,
for blue star-forming galaxies, having identical stellar mass distributions,
with $\langle\textrm{M}_{*}\rangle\approx 10^{10}~{}\textrm{M}_{\odot}$. In
both panels, the blue circle shows the result from the xGASS survey of local
Universe galaxies (Catinella et al., 2018), while the red square shows the
measurement at $z\approx 1$ from the current work.

The availability of neutral gas, the fuel for star-formation, determines the
time for which a galaxy can sustain its current SFR. The gas depletion
timescale, defined as the ratio of the gas mass (Hi or ${\rm H_{2}}$) to the
SFR, is an important metric to understand how long a galaxy can sustain its
current SFR. We define the “characteristic” Hi and ${\rm H_{2}}$ depletion
timescales of the galaxies of a given sample as, respectively, $\langle{\rm
t_{dep,H{\textsc{i}}}}\rangle\equiv\langle\rm{M_{H\textsc{i}}}\rangle/\langle\textrm{SFR}\rangle$
and $\langle{\rm t_{\rm dep,H_{2}}}\rangle\equiv\langle\rm{M}_{\rm
H_{2}}\rangle/\langle\textrm{SFR}\rangle$. In the local Universe, blue
galaxies with the same stellar mass distribution as the 11,419 galaxies in our
sample have $\langle{\rm t_{dep,H{\textsc{i}}}}\rangle=(4.5\pm 0.2)$ Gyr
(Catinella et al., 2018) and $\langle{\rm t_{\rm dep,H_{2}}}\rangle=(0.45\pm
0.04)$ Gyr (Saintonge et al., 2017)666We have divided the molecular gas masses
of Saintonge et al. (2017) by a factor of 1.36 to obtain the ${\rm H_{2}}$
masses of their galaxies. Further, we note that the average gas depletion
timescales in this paper are all calculated consistently by taking the ratio
of the weighted-average gas mass to the weighted-average SFR of the sample,
with weights such that the stellar mass distribution of the sample is
identical to that of Figure 5[B].. The Hi depletion timescale of galaxies with
$\textrm{M}_{*}\approx 10^{10}~{}\textrm{M}_{\odot}$ in the local Universe is
thus much longer than the ${\rm H_{2}}$ depletion timescale. Local Universe
galaxies can thus sustain their current SFR for a long timescale, $\langle{\rm
t_{dep,H{\textsc{i}}}}\rangle\approx 4.5$ Gyr, even without the accretion of
fresh gas from the CGM or via mergers. In other words, the availability of Hi
is not a bottleneck in the star-formation process in local Universe galaxies.

For the DEEP2 galaxies, we combine the average Hi mass of
$\langle\rm{M_{H\textsc{i}}}\rangle=(13.7\pm 1.9)\times 10^{9}\
\textrm{M}_{\odot}$ with the average SFR of $(8.07\pm 0.82)\
\textrm{M}_{\odot}\ \textrm{yr}^{-1}$ to obtain a characteristic Hi depletion
timescale of $\langle{\rm t_{dep,H{\textsc{i}}}}\rangle=(1.70\pm 0.29)$ Gyr,
for blue star-forming galaxies with $\langle\textrm{M}_{*}\rangle\approx
10^{10}~{}\textrm{M}_{\odot}$ at $\langle z\rangle=1.04$. Our measurement of
$\langle{\rm t_{dep,H{\textsc{i}}}}\rangle$ of blue galaxies at $z\approx 1$
is three times smaller than the characteristic Hi depletion timescale of
$\langle{\rm t_{dep,H{\textsc{i}}}}\rangle\approx 4.5\pm 0.2$ Gyr of blue
galaxies with an identical stellar mass distribution in the local Universe
(see Figure 11[B]). Further, the Hi depletion timescale at $z\approx 1$ is
only a factor of $\approx 3$ higher than the ${\rm H_{2}}$ depletion timescale
of $\approx 0.5$ Gyr777We note that this is the ${\rm H_{2}}$ depletion
timescale, after dividing the molecular gas depletion timescale by a factor of
1.36. in main-sequence galaxies at similar redshifts (Tacconi et al., 2013).
Our results thus clearly establish, consistent with the findings of Chowdhury
et al. (2020), that blue star-forming galaxies at the end of the epoch of peak
cosmic SFR density can sustain their SFR for a short timescale,, only $\approx
1.5$ Gyr, in the absence of gas accretion from the CGM. This supports the
hypothesis that accretion of gas from the CGM may have been insufficient to
sustain the high SFR of galaxies at $z\approx 1$, causing the observed decline
in the star-formation activity of the Universe at lower redshifts (Bera et
al., 2018; Chowdhury et al., 2020, 2021). Further, using Hi 21 cm data from
the present GMRT-CAT$z$1 survey, Chowdhury et al. (2022a) find direct evidence
that the average Hi mass of star-forming galaxies at $z\approx 1$ is a factor
of $\approx 3.2$ lower than that of galaxies with the same stellar-mass
distribution at $z\approx 1.3$, indicating that accretion was insufficient to
replenish the gas reservoirs of massive galaxies.

In passing, we note that there are a number of possible causes for the decline
in the gas accretion on to massive galaxies at $z\lesssim 1$, including (1) a
transition in the mode of accretion from cold mode at high redshifts to hot
mode at $z\lesssim 1$, which would slow down the accretion process (e.g. Kereš
et al., 2005; Dekel et al., 2009), (2) AGN or stellar feedback, especially in
massive galaxies (e.g. Weiner et al., 2009; Steidel et al., 2010; Kakkad et
al., 2020; Valentino et al., 2021), and (3) heating of the gas reservoir in
the CGM (e.g. Schawinski et al., 2014). The current Hi 21 cm (and ancillary)
data on the DEEP2 fields do not allow us to distinguish between these (and
other) possibilities. Further, it is also possible that environmental effects
(e.g. Tal et al., 2014) might contribute to the decline in the star-formation
activity at $z\lesssim 1$. Deeper Hi 21 cm data should allow us to separate
the galaxies into isolated systems and groups, and enable us to study such
environmental effects.

##  9 The Average Hi Mass of Red Galaxies and AGNs at $z\approx 1$

###  9.1 Red Galaxies

Figure 12: [A] The stacked Hi 21 cm spectrum from the 1,738 red galaxies at
$z=0.74-1.45$, obtained by stacking the Hi 21 cm spectra obtained at the
location of the galaxies. The channel width of the spectrum is 90 km s-1. The
dashed horizontal curves show the $\pm 1\sigma$ error on the spectrum. A
tentative ($2.9\sigma$ significance) detection of the average Hi 21 cm
emission signal can be seen in the central velocity channels of the spectrum.
[B] The median-stacked rest-frame 1.4 GHz continuum emission from the red
galaxies of the left panel. A clear ($\approx 25\sigma$ significance)
detection of the stacked continuum emission is visible at the centre of the
image, i.e. at the location of the stacked DEEP2 galaxies. The contour levels
are at $5\sigma,\ 10\sigma,\ {\rm and}\ 20\sigma$ statistical significance.
The circle in the bottom left corner represents the $40$ kpc beam to which all
continuum images were convolved before the stacking.

The DEEP2 survey targetted galaxies down to a limiting magnitude of
R${}_{\textrm{AB}}=24.1$; this results in a bias against red galaxies at
$z>0.7$, with the bias becoming stronger at higher redshifts (see Section 6;
Willmer et al., 2006; Newman et al., 2013). Indeed, only $\approx 14\%$ of the
DEEP2 galaxies at $z=0.74-1.45$ that lie within our uGMRT pointings are part
of the “red cloud” (see Section 6) and only $\approx 26\%$ of these are at
$z>1$. In order to ensure the homogeneity of our sample, we had excluded the
red DEEP2 galaxies from our main sample of blue star-forming galaxies. Here,
we examine the average Hi mass and the average SFR of the red DEEP2 galaxies
at $z=0.74-1.45$, lying within our uGMRT pointings, and compare their average
properties to those of the blue DEEP2 galaxies of our main sample.

Our GMRT observations cover the redshifted Hi 21 cm line for 2,222 red
galaxies at $z=0.74-1.45$. After excluding galaxies hosting radio-bright AGNs
(see Section 4.3) and galaxies whose Hi 21 cm subcubes were affected by
systematic effects (identified using the procedures of Section 4.5), our
sample contains 4,346 independent Hi 21 cm subcubes of 1,738 red galaxies at
$z=0.74-1.45$.

We stacked the 4,346 Hi 21 cm subcubes of the 1,738 red galaxies at
$z=0.74-1.45$, following the procedures of Section 5.1. Figure 12[A] shows the
stacked Hi 21 cm emission signal of the 1,738 red galaxies. We obtain a
tentative detection, at $2.9\sigma$ statistical significance, of the average
Hi 21 cm emission from the 1,738 red galaxies at $\langle z\rangle=0.94$.
Integrating the average Hi 21 cm emission signal over the velocity range [-150
km s-1,+210 km s-1] yields an average Hi mass of
$\langle\rm{M_{H\textsc{i}}}\rangle=(12.4\pm 4.2)\times
10^{9}~{}\textrm{M}_{\odot}$. The average Hi mass of the red galaxies is thus
consistent with $\langle\rm{M_{H\textsc{i}}}\rangle=(13.7\pm 1.9)\times
10^{9}\ \textrm{M}_{\odot}$, the average Hi mass of the 11,419 blue star-
forming galaxies of our main sample (Section 8). However, we note that the
average stellar mass of the 1,738 red galaxies is
$\langle\textrm{M}_{*}\rangle\approx 6\times 10^{10}~{}\textrm{M}_{\odot}$,
far higher than the average stellar mass of the blue galaxies,
$\langle\textrm{M}_{*}\rangle\approx 10^{10}~{}\textrm{M}_{\odot}$. The ratio
of the average Hi mass to the average stellar mass,
$\langle\rm{M_{H\textsc{i}}}\rangle/\langle\textrm{M}_{*}\rangle=0.21\pm
0.07$, for the red galaxies is thus far lower than the same ratio,
$\langle\rm{M_{H\textsc{i}}}\rangle/\langle\textrm{M}_{*}\rangle=1.38\pm
0.19$, for the blue star-forming galaxies.

However, we note that both the stellar-mass and the redshift distributions of
the samples of blue galaxies and red galaxies are different, with the red
sample having both higher stellar masses and lower redshifts. Chowdhury et al.
(2022a) find that the average Hi properties of blue galaxies depends on both
their average redshift and their average stellar mass; these dependences would
affect the above comparisons between the red and blue galaxies. The
differences in the redshift and the stellar-mass distributions of the two
galaxy samples should be taken into account by using appropriate weights in
future comparisons.

We estimate the average SFR of the 1,738 red galaxies by median-stacking their
rest-frame 1.4 GHz continuum luminosities, following the procedures of Section
5.2. Figure 12[B] shows the stacked rest-frame 1.4 GHz continuum emission of
the red galaxies. We clearly detect the stacked 1.4 GHz continuum emission
from the sample of red galaxies, at $\approx 25\sigma$ significance, obtaining
an average SFR of $6.05\pm 0.65~{}\textrm{M}_{\odot}\textrm{yr}^{-1}$. As
noted above, the sample of red galaxies has a high average stellar mass,
$\langle\textrm{M}_{*}\rangle\approx 6\times 10^{10}~{}\textrm{M}_{\odot}$;
the average SFR of $6.05\pm 0.65~{}\textrm{M}_{\odot}\textrm{yr}^{-1}$ for
these galaxies is $\approx 4.5$ times lower than that of main-sequence
galaxies with $\langle\textrm{M}_{*}\rangle\approx 6\times
10^{10}~{}\textrm{M}_{\odot}$ at similar redshifts (Whitaker et al., 2014).
Combining the average Hi mass and the average SFR yields a characteristic Hi
depletion timescale of $\langle{\rm t_{dep,H{\textsc{i}}}}\rangle=(2.03\pm
0.73)$ Gyr for the red galaxies at $\langle z\rangle=0.94$.

Overall, we find that the red galaxies in the DEEP2 survey are massive, but
have an average SFR far lower than that of blue galaxies with similar stellar
masses; this suggests that most of the red objects are not dusty star-forming
galaxies. The red galaxies also have a lower ratio of the average Hi mass to
the average stellar mass than the 11,419 blue galaxies of our main sample, but
also have a significantly higher stellar mass than the above blue galaxies.

###  9.2 Galaxies hosting AGNs

The GMRT-CAT$z1$ survey covers the redshifted Hi 21 cm line for 882 blue DEEP2
galaxies that were found to host an AGN with ${\rm L}_{\rm 1.4GHz}>2\times
10^{23}$ W/Hz (see Section 4.3). We investigated the 2,368 Hi 21 cm subcubes
of these 882 AGN-hosting galaxies for systematic issues, following the
procedures described in Section 4.5. After excluding the Hi 21 cm subcubes
affected by discernible systematic effects, we stacked the 2,087 Hi 21 cm
subcubes of the remaining 823 AGN-hosting galaxies. We do not detect the
average Hi 21 cm emission signal from this sample, obtaining a $3\sigma$ upper
limit of $\langle\rm{M_{H\textsc{i}}}\rangle<24\times
10^{9}~{}\textrm{M}_{\odot}$ on the average Hi mass of the AGN-hosting
galaxies, assuming an Hi 21 cm line FWHM of $360$ km s-1. The upper limit on
the Hi mass of the AGN-hosting galaxies is consistent with the average Hi mass
of $\langle\rm{M_{H\textsc{i}}}\rangle=(13.7\pm 1.9)\times 10^{9}\
\textrm{M}_{\odot}$ for our main sample of 11,419 blue star-forming galaxies
with no AGNs.

Overall, we find no evidence for a high average Hi mass in the galaxies of our
sample that host AGNs. However, the number of such objects is more than an
order of magnitude lower than the number of blue galaxies in our main sample,
implying that we do not obtain tight constraints on the average Hi mass of the
AGN sample. Probing the influence of AGNs on the average Hi properties of
galaxies at $z\approx 1$ will require a larger AGN sample or significantly
deeper observations.

##  10 Tests for Systematic Issues in the Hi 21 cm stacking

###  10.1 The Effect of the Dirty Beam

Figure 13: Subtraction of the dirty beam from the stacked Hi 21 cm emission
image of the 11,419 blue star-forming galaxies at $z=0.74-1.45$. The four
panels show (clockwise, from top left): the stacked dirty beam, the stacked
“raw” Hi 21 cm emission image, the restored Hi 21 cm emission image, and the
residual image after subtracting out the scaled stacked dirty beam. The
residual image was obtained by (a) scaling the stacked dirty beam by the peak
luminosity density of the stacked image, and (b) subtracting out the scaled
dirty beam from the stacked image. The contour levels on all stacked Hi 21 cm
images are at $-3.0\sigma$ (dashed), $+3.0\sigma$, $+4.0\sigma$, $+5.0\sigma$,
$+6.0\sigma$, and $+7.0\sigma$ statistical significance.

The stacked Hi 21 cm emission image of Fig. 9[A] is the average of the
observed Hi 21 cm emission images of the individual 11,419 galaxies. Further,
the observed Hi 21 cm emission image of each galaxy is a convolution of the
“true” Hi 21 cm emission image with the point spread function (the “dirty
beam”) of the GMRT observations of the galaxy. The stacked Hi 21 cm emission
image of Fig. 9[A] thus contains the combined effect of the point spread
functions of the different observations. For normal Hi images (i.e. without
stacking), in the absence of deconvolution, the point spread function would
affect the noise properties of the image (yielding structures similar to those
of the dirty beam). The fact that we are stacking Hi 21 cm emission from
different regions of the sky, with different dirty beams, implies that it is
not straightforward to deconvolve the dirty beam from the stacked Hi 21 cm
emission image. However, the pattern of the average dirty beam is clearly
visible on inspecting the stacked Hi 21 cm emission image. To correct for
this, we subtracted out the stacked dirty beam from the stacked Hi 21 cm
emission image; a similar deconvolution strategy was also used by Chen et al.
(2021) in an Hi 21 cm emission stacking experiment targetting galaxies at
$z\approx 0$. We emphasise that the deconvolution of the dirty beam carried
out here is an approximation, which is exact only for the case of identical Hi
masses of all the galaxies of the sample.

We obtain the stacked dirty beam by taking the average of the dirty beams of
the independent Hi 21 cm subcubes in the sample. Next, we scale the average
dirty beam to the peak luminosity density of the stacked Hi 21 cm emission
image, and subtract out this scaled dirty beam from the stacked emission image
to obtain the residual image. We then obtain the final restored Hi 21 cm
emission image by adding to the residual image a symmetric Gausssian having an
FWHM of 90 kpc and the peak luminosity density of the original Hi 21 cm
emission image. Figure 13 shows the stacked dirty beam, the original Hi 21 cm
emission image (the “dirty image”), the residual Hi 21 cm image, and the
restored, stacked Hi 21 cm emission image. A comparison between the original
and restored Hi 21 cmemission images in Figure 13 shows clearly that the
subtraction of the stacked dirty beam from the stacked Hi 21 cm image improves
the noise properties of the image. Further, the residual map in Figure 13
shows no evidence for any extended emission at the location of the DEEP2
galaxies, consistent with the findings of Section 7 that the average Hi 21 cm
emission signal is unresolved at a spatial resolution of 90 kpc.

###  10.2 The RMS noise of the stacked spectra

Figure 14: The RMS noise on the stacked Hi 21 cm spectra as a function of the
number of the Hi 21 cm spectra that were stacked together. The blue points
show the RMS noise, in units of Hi mass (assuming a velocity width of 360 km
s-1), obtained on stacking N Hi 21 cm spectra, randomly selected from the full
sample. The red star shows the RMS noise on the stacked Hi 21 cm spectrum
using all the 28,993 Hi 21 cm spectra in our sample. The dotted line shows the
relation $\textrm{RMS}\propto\textrm{N}^{-0.5}$, expected if the noise
properties of the individual Hi 21 cm spectra are uncorrelated, with no
underlying systematic effects. It is clear that the RMS noise obtained on the
stacked spectra is consistent with the relation ${\rm
RMS}\propto\textrm{N}^{-0.5}$. We thus find no evidence for systematic issues
affecting the 28,993 Hi 21 cm spectra of our sample.

The sensitivity of the stacking procedure critically depends on the noise
properties of the individual Hi 21 cm spectra that are stacked together. The
spectral RMS noise on the stacked Hi 21 cm spectrum is expected to decrease
with the number (N) of individual Hi 21 cm spectra as RMS
$\propto\textrm{N}^{-0.5}$, for independent noise on the individual spectra.
However, systematic issues in the data could introduce correlations between
the individual spectra that may limit the sensitivity of the stacked spectrum.
We tested for such issues in our sample of 28,993 Hi 21 cm spectra by
measuring the dependence of the RMS noise on the stacked spectrum on the
number of spectra that were stacked together.

This was done by randomly selecting N spectra from our full sample of 28,993
Hi 21 cm spectra, where N$=$100, 200, 400, 800, 1600, 3,200, 6,400, 12,800,
and 25,600. For each N, we stacked the randomly-selected Hi 21 cm spectra to
obtain a stacked spectrum, and then followed the Monte Carlo approach
described earlier to estimate the RMS noise on the stacked spectrum.

Figure 14 shows the RMS noise obtained on the stacked Hi 21 cm spectrum as a
function of the number of stacked galaxies, N. It is clear from the figure
that the RMS noise measurements are consistent with the relation RMS
$\propto\textrm{N}^{-0.5}$. We thus find no evidence for systematic issues
that might limit the sensitivity of our stacked Hi 21 cm spectrum.

###  10.3 The Effect of Source Confusion

The stacked Hi 21 cm emission signal can include, in addition to the Hi 21 cm
emission from our target galaxies, Hi 21 cm emission from companion galaxies
lying within the interferometer beam with Hi 21 cm emission at the same
velocities as the target galaxy. Chowdhury et al. (2020) used the S3-SAX-Sky
(Obreschkow et al., 2009) simulations to find that the effect of such “source
confusion”, due to companion galaxies lying within their 60 kpc spatial
resolution, on the stacked Hi 21 cm emission of galaxies at $z\approx 1$ is
small. We repeat the procedure of Chowdhury et al. (2020), but with a spatial
resolution of 90 kpc, to find that the effect of source confusion on our
measurement of the average Hi mass is also expected to be small, with
companion galaxies contributing $\lesssim 5\%$ to the observed average Hi 21
cm emission signal.

We further probe the effect of source confusion on the measurement of the
average Hi mass of our sample galaxies, by identifying target galaxies that
have spectroscopically-identified companion galaxies in the DEEP2 DR4
catalogue (Newman et al., 2013), such that the companion galaxies might
contribute to our measurement of the Hi 21 cm emission from the target galaxy.
Our measurement of the average Hi 21 cm emission is at a spatial resolution of
90 kpc, with the detected average Hi 21 cm emission spanning $\approx\pm 180$
km s-1 around the systemic velocity. We find that only 276 galaxies of the
11,419 galaxies in our main sample ($\approx 3\%$ of the sample) have
spectroscopic companions in the DEEP2 DR4 catalogue that lie within $\pm 45$
kpc and whose redshifts are within $\pm 200$ km s-1 of the target galaxy; the
Hi 21 cm emission from these galaxies might be included in our measurement of
the average Hi 21 cm emission of the target galaxies. We exclude these 276
galaxies and stack the Hi 21 cm subcubes of the remaining 11,143 galaxies.
This yields an average Hi mass for the 11,143 galaxies of
$\langle\rm{M_{H\textsc{i}}}\rangle=(1.40\pm 0.20)\times 10^{10}\
\textrm{M}_{\odot}$. This is entirely consistent with the measured Hi mass of
the full sample, $\langle\rm{M_{H\textsc{i}}}\rangle=(1.37\pm 0.19)\times
10^{10}\ \textrm{M}_{\odot}$. We thus find no evidence that source confusion
due to companion galaxies, identified in the DEEP2 spectroscopic catalogue,
might affect our measurement of the average Hi mass of galaxies at $z\approx
1$.

The spectroscopic completeness of the DEEP2 survey is $\approx 50\%$ (Conroy
et al., 2007). The analysis presented above would thus not account for any
companion galaxies for which the DEEP2 survey failed to obtain a redshift
measurement. We estimate here the effect of such companion galaxies, not
included in the DEEP2 spectroscopic catalogue, on our measurement of the
average Hi mass. We find that 1,928 of the 11,419 galaxies in our sample have
at least one object in the DEEP2 photometric catalogue (Coil et al., 2004)
that lies within $\pm 45$ kpc of the target galaxy and that meets the DEEP2
colour and magnitude selection criteria for spectroscopic targets in Fields 2,
3, and 4 (Newman et al., 2013). Note that the redshift of the “companion”
galaxies thus identified could be completely different from the redshift of
the target galaxy. We exclude these 1,928 galaxies and stack the Hi 21 cm
subcubes of the remaining 9,491 galaxies of our sample to obtain an average Hi
mass of $\langle\rm{M_{H\textsc{i}}}\rangle=(1.48\pm 0.21)\times 10^{10}\
\textrm{M}_{\odot}$. This is again consistent with the measured Hi mass of the
full sample, $\langle\rm{M_{H\textsc{i}}}\rangle=(1.37\pm 0.19)\times 10^{10}\
\textrm{M}_{\odot}$. We thus find no evidence that source confusion due to
companion galaxies, even those for which the DEEP2 survey failed to obtain a
spectroscopic redshift, might affect our measurement of the average Hi mass of
star-forming galaxies at $z\approx 1$.

Overall, we conclude that our measurement of the average Hi mass of galaxies
at $z=0.74-1.45$ is not significantly affected by source confusion.

##  11 Upper limits on the Hi Mass of Individual Galaxies

Figure 15: The 5$\sigma$ upper limits obtained on [A] the Hi mass and [B] the
Hi fraction ($\rm{M_{H\textsc{i}}}/\textrm{M}_{*}$) of each of the 13,596
DEEP2 galaxies covered by the GMRT-CAT$z1$ survey. The upper limits, shown as
blue points, assume an Hi 21 cm line FWHM of 300 km s-1. The red curve in
panel [A] shows, as a function of redshift, the median of the $5\sigma$ upper
limits on the Hi mass of the individual galaxies. The dotted horizontal line
in panel [B] shows the ratio of the average Hi mass to the average stellar
mass for our main sample of 11,419 blue star-forming galaxies.

We also carried out a search for Hi 21 cm emission from the individual DEEP2
galaxies covered by the GMRT-CAT$z1$ survey at their spatial locations and
redshifted Hi 21 cm emission line frequencies. The search was carried out on
all DEEP2 galaxies covered in our GMRT survey, including the 2,222 red
galaxies, the 882 galaxies hosting radio AGNs, and the 487 galaxies with
$\textrm{M}_{*}<10^{9}~{}\textrm{M}_{\odot}$ (see Section 4.3). Further, we
also retained the Hi 21 cm subcubes of galaxies that were removed from our
main sample due to the presence of a $\gtrsim 6\sigma$ feature in one of their
subcubes (see Section 4.5); this ensures that we do not exclude any real Hi 21
cm emission signals. Overall, we searched for the Hi 21 cm emission signal
from 13,596 DEEP2 galaxies at $z=0.74-1.45$.

For each DEEP2 galaxy, we first combined all available Hi 21 cm subcubes,
weighting by the inverse-variance of each cube, to obtain a single Hi 21 cm
subcube for the galaxy. The Hi 21 cm subcubes used for the search had a
spatial resolution of 90 kpc, the optimal resolution for the average Hi 21 cm
emission signal (see Section 7). The search for Hi 21 cm emission was carried
out after smoothing the subcubes, using a boxcar kernel, to ten different
velocity resolutions ranging from $30$ km s-1 to $300$ km s-1, in steps of
$30$ km s-1. The search was done at a range of velocity resolutions in order
to maximize the sensitivity to Hi 21 cm emission from galaxies at a range of
inclinations. We searched for Hi 21 cm emission, at $\geq 5\sigma$ statistical
significance, at the location of each DEEP2 galaxy and in the central $\pm
250$ km s-1 around its redshifted Hi 21 cm emission frequency. We did not
detect any emission feature with $\geq 5\sigma$ significance in the spectra of
any of the 13,596 DEEP2 galaxies, at any of the ten velocity resolutions.

The $5\sigma$ upper limits on the Hi masses of the 13,596 galaxies, for an
assumed “typical” Hi 21 cm line FWHM of $300$ km s-1, are shown in Figure
15[A]. We obtain a median $5\sigma$ upper limit of $\approx 5\times 10^{11}\
\textrm{M}_{\odot}$ for galaxies at $z\approx 0.74-1.0$, and
$\approx(5-12)\times 10^{11}~{}\textrm{M}_{\odot}$ for galaxies at $z\approx
1.0-1.45$. The corresponding upper limits on the Hi fraction
($\rm{M_{H\textsc{i}}}/\textrm{M}_{*}$) for each of the 13,596 galaxies are
shown in Figure 15[B]. Except a few very massive galaxies, the upper limits on
the Hi fraction of the 13,596 galaxies are far higher than our measurement of
the ratio of the average Hi mass to the average stellar mass,
$\langle\rm{M_{H\textsc{i}}}\rangle/\langle\textrm{M}_{*}\rangle=1.38\pm
0.19$, of the sample. Assuming that the galaxies are viewed close to face-on,
with an Hi 21 cm line FWHM of $60$ km s-1, yields a median $5\sigma$ upper-
limit of $\approx 2.5\times 10^{11}~{}\textrm{M}_{\odot}$ for galaxies at
$z\approx 0.74-1.0$, and $\approx(2.5-5)\times 10^{11}~{}\textrm{M}_{\odot}$
for galaxies at $z\approx 1.0-1.45$. These $5\sigma$ upper limits on the Hi
mass of the 13,596 galaxies are $\approx 10-100$ times higher than our
measurement of the average Hi mass of blue galaxies at $z\approx 1$ (see
Section 8). This allows us to rule out the presence of extremely large Hi
reservoirs, with $\rm{M_{H\textsc{i}}}\gtrsim(3-25)\times
10^{11}~{}\textrm{M}_{\odot}$, in any of the 13,596 DEEP2 galaxies at
$z=0.74-1.45$.

##  12 Summary

In this paper, we present the GMRT-CAT$z1$ survey, a 510-hour GMRT Hi 21 cm
emission survey of galaxies at $z=0.74-1.45$ in seven sub-fields of the DEEP2
Galaxy Redshift Survey (Newman et al., 2013). We describe the GMRT
observations, the data analysis, and the main results obtained from stacking
the Hi 21 cm emission signals of our full sample of blue star-forming
galaxies. Additional key results of the survey, including the role of Hi in
the decline of star-formation activity of the Universe at $z\lesssim 1$, the
contribution of Hi to the baryonic mass of galaxies at $z\approx 1$, the
dependence of the Hi properties of star-forming galaxies at $z\approx 1$ on
their stellar properties, and estimates of the cosmological Hi mass density of
the Universe at $z\approx 1$, will be described in separate papers (e.g.
Chowdhury et al., 2022a, b). To summarise:

  * •

The GMRT observations cover the redshifted Hi 21 cm line for 16,250 DEEP2
galaxies at $z=0.74-1.45$, lying within the half-power point of our GMRT
pointings. We excluded red galaxies, radio AGNs, galaxies with
$\textrm{M}_{*}<10^{9}\ \textrm{M}_{\odot}$, and any Hi 21 cm subcubes
affected by discernible systematic issues to obtain our main sample of 11,419
blue star-forming galaxies with $\textrm{M}_{*}\geq
10^{9}~{}\textrm{M}_{\odot}$ at $z=0.74-1.45$. The observations provide up to
6 independent Hi 21 cm subcubes spectra for each galaxy in the sample,
yielding a total of 28,993 independent Hi 21 cm subcubes for the 11,419
galaxies.

  * •

To identify the optimal spatial resolution for the stacking, we stacked the Hi
21 cm spectra of the 11,419 blue star-forming galaxies at nine different
spatial resolutions, 60 kpc, 70 kpc, 80 kpc, 90 kpc, 100 kpc, 110 kpc, 120
kpc, 150 kpc and 200 kpc. We obtained clear detections of the average Hi 21 cm
signal at all nine resolutions, at $4.2-7.4\sigma$ statistical significance.
We find that the average Hi mass of the sample at a resolution of 90 kpc is
consistent with that at all coarser spatial resolutions. This implies that 90
kpc is the optimal spatial resolution for the Hi 21 cm stacking for our galaxy
sample.

  * •

We stacked the Hi 21 cm subcubes of the sample at a resolution of 90 kpc to
obtain a clear detection, with $\approx 7.1\sigma$ statistical significance,
of the stacked Hi 21 cm emission signal. The detection yields an average Hi
mass of $\langle\rm{M_{H\textsc{i}}}\rangle=(13.7\pm 1.9)\times 10^{9}\
\textrm{M}_{\odot}$ for blue star-forming galaxies with
$\langle\textrm{M}_{*}\rangle\approx 10^{10}~{}\textrm{M}_{\odot}$ at $\langle
z\rangle=1.04$.

  * •

We stacked subsamples of galaxies to find that the RMS noise on the stacked Hi
21 cm spectrum decreases with the number, N, of stacked spectra as
$1/\sqrt{\rm N}$, as expected if the spectra have uncorrelated Gaussian noise.
We thus find no evidence for any systematic effects that might affect our
final stacked Hi 21 cm spectrum.

  * •

We investigated the effect of source confusion on our estimate of the average
Hi mass of the sample, by excluding all 1,928 target galaxies with either
spectroscopic or photometric companions, with magnitudes and colours that meet
the DEEP2 selection criteria, and that lie within $\pm 45$ kpc of a target
galaxy. We stacked the Hi 21 cm spectra of the remaining 9,491 galaxies,
obtaining an average Hi mass consistent with that of the average Hi mass of
the full sample of 11,419 galaxies. We thus find no evidence that the average
Hi mass estimate might be contaminated by source confusion. We further used
the S3-SAX-Sky simulations (Obreschkow et al., 2009) to find that the effect
of source confusion on our stacked Hi 21 cm spectrum is expected to be
$\lesssim 5\%$ at our spatial resolution of 90 kpc.

  * •

We estimated the average SFR of the galaxies of the sample from their average
rest-frame 1.4 GHz luminosity, by carrying out a median stack of the rest-
frame 1.4 GHz continuum emission. This yielded an average SFR of $(8.07\pm
0.82)$ $\textrm{M}_{\odot}\textrm{yr}^{-1}$. We also stacked the rest-frame
1.4 GHz continuum emission in galaxy subsamples based on stellar mass and
redshift, to find that the average stellar masses and the average SFRs of the
galaxies in each subsample are consistent with their lying on the main
sequence at their respective redshifts.

  * •

We find that the average Hi mass of blue galaxies in the local Universe, with
stellar-mass distribution identical to that of our full sample of 11,419 blue
star-forming DEEP2 galaxies, is $(3.96\pm 0.17)\times
10^{9}~{}\textrm{M}_{\odot}$. We thus find clear evidence, at $\approx
5.1\sigma$ significance, that the average Hi mass of blue galaxies has
declined, by a factor of $(3.5\pm 0.4)$, from $z\approx 1$ to $z\approx 0$.

  * •

We combine our measurements of the average Hi mass and the average SFR of the
11,419 blue star-forming galaxies at $z\approx 1$ to infer a characteristic Hi
depletion timescale of $\langle{\rm
t_{dep,H{\textsc{i}}}}\rangle\equiv\langle\rm{M_{H\textsc{i}}}\rangle/\langle\textrm{SFR}\rangle=(1.70\pm
0.29)$ Gyr. This is significantly shorter than the characteristic Hi depletion
timescale of $4.5\pm 0.2$ Gyr in blue galaxies with an identical stellar-mass
distribution in the local Universe. We thus confirm, at a high statistical
significance, the result that the Hi reservoir of star-forming galaxies at
$z\approx 1$ can sustain their current SFRs for a short period of $\approx
1.7$ Gyr, in the absence of accretion of fresh atomic gas from the CGM or via
minor mergers (Bera et al., 2018; Chowdhury et al., 2020, 2021).

  * •

We stacked the Hi 21 cm spectra of the 1,738 red galaxies at $z=0.74-1.45$ to
obtain a tentative ($2.9\sigma$ significance) detection of their average Hi 21
cm emission signal. We obtain an average Hi mass of
$\langle\rm{M_{H\textsc{i}}}\rangle=(12.4\pm 4.2)\times
10^{9}~{}\textrm{M}_{\odot}$, consistent with the value of
$\langle\rm{M_{H\textsc{i}}}\rangle=(13.7\pm 1.9)\times 10^{9}\
\textrm{M}_{\odot}$ for the blue star-forming galaxies. However, the red
galaxies have an average stellar mass of $6\times
10^{10}~{}\textrm{M}_{\odot}$, far higher than the average stellar mass of
$10^{10}~{}\textrm{M}_{\odot}$ of the blue galaxies. The ratio of the average
Hi mass to average stellar mass of the red galaxies is
$\langle\rm{M_{H\textsc{i}}}\rangle/\langle\textrm{M}_{*}\rangle=0.21\pm
0.07$, far lower than the value
$\langle\rm{M_{H\textsc{i}}}\rangle/\langle\textrm{M}_{*}\rangle=1.38\pm 0.19$
of the blue galaxies. We also stacked the rest-frame 1.4 GHz luminosities of
the 1,738 red galaxies to estimate an average SFR of $6.05\pm
0.65~{}\textrm{M}_{\odot}\textrm{yr}^{-1}$, $\approx 4.5$ times lower than
that of main-sequence galaxies at $z\approx 1$ with $\textrm{M}_{*}\approx
6\times 10^{10}~{}\textrm{M}_{\odot}$. The low average SFR indicate that most
of the red objects are unlikely to be dusty star-forming galaxies.

  * •

We stacked the Hi 21 cm spectra of 823 galaxies hosting radio-bright AGNs at
$z=0.74-1.45$, but did not obtain a detection of the average Hi 21 cm emission
signal. This yielded the $3\sigma$ upper limit of $24\times
10^{9}~{}\textrm{M}_{\odot}$ on the average Hi mass of the 823 galaxies,
consistent with that of the main sample of blue galaxies without AGNs at
$z\approx 1$.

  * •

Finally, we searched the spectra of all 13,596 DEEP2 galaxies (including red
galaxies, objects containing AGNs, and low-stellar mass galaxies) of the
sample for Hi 21 cm emission at the expected redshifted Hi 21 cm line
frequency, at a spatial resolution of 90 kpc and velocity resolutions of
$30-300$ km s-1. We find no evidence for individual redshifted Hi 21 cm
emission from any of the DEEP2 galaxies, obtaining $5\sigma$ upper limits of
$\approx(3-25)\times 10^{11}~{}\textrm{M}_{\odot}$ on the Hi masses of
individual galaxies.

We thank the staff of the GMRT who have made these observations possible. The
GMRT is run by the National Centre for Radio Astrophysics of the Tata
Institute of Fundamental Research. NK acknowledges support from the Department
of Science and Technology via a Swarnajayanti Fellowship
(DST/SJF/PSA-01/2012-13). All authors acknowledge the Department of Atomic
Energy for funding support, under project 12-R&D-TFR-5.02-0700.

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##  Appendix A The RMS noise on the individual Hi 21 cm spectra

Figure 16: The spectral RMS noise on the Hi 21 cm subcubes of galaxies in
DEEP2 subfields 21 and 22. Observations in different GMRT cycles (35, 37, and
38) are shown in separate panels, with the red dots indicating the spectral
RMS noise per 30 km s-1 channel for each galaxy as a function of observing
frequency. The blue curve in each panel shows the theoretical RMS noise for
the amount of on-source time, taking into account the data that were excised,
and also considering the spatial resolution of 90 kpc at which the Hi 21 cm
spectra were extracted. The panels list the on-source time for each DEEP2
subfield in each cycle. Note that the scatter by a factor of $\approx 2$ in
the measured RMS noise values at any frequency is due to the location of the
galaxies in the primary beam. The spectral RMS noise values obtained on the Hi
21 cm spectra are consistent with the theoretical RMS noise, within the
typical 10$\%$ uncertainty in the GMRT flux density scale. Figure 17: The
spectral RMS noise on the Hi 21 cm spectra of galaxies in DEEP2 subfields 31,
32, and 33. See the caption of Fig. 16 for details. Figure 18: The spectral
RMS noise on the Hi 21 cm spectra of galaxies in DEEP2 subfields 41 and 42.
See the caption of Fig. 16 for details.