# Cold Gas Reservoirs of Low- and High-mass Central Galaxies Differ in
Response to Active Galactic Nucleus Feedback

Hong Guo Corresponding Author  Shanghai Astronomical Observatory, Chinese
Academy of Sciences, Shanghai 200030, China<EMAIL_ADDRESS>Michael G.
Jones Corresponding Author  Steward Observatory, University of Arizona, 933
North Cherry Avenue, Rm. N204, Tucson, AZ 85721-0065, USA<EMAIL_ADDRESS>Jing Wang Corresponding Author  Kavli Institute for Astronomy and
Astrophysics, Peking University, Beijing 100871, China<EMAIL_ADDRESS>
###### Abstract

The growth of supermassive black holes, especially the associated state of
active galactic nuclei (AGNs), is generally believed to be the key step in
regulating star formation in massive galaxies. As the fuel of star formation,
the cold gas reservoir is a direct probe of the effect of AGN feedback on
their host galaxies. However, in observation, no clear connection has been
found between AGN activity and the cold gas mass. In this paper, we find
observational signals of significant depletion of the total neutral hydrogen
gas reservoir in optically-selected type-2 AGN host central galaxies of
stellar mass $10^{9}$–$10^{10}M_{\odot}$. The effect of AGN feedback on the
cold gas reservoir is stronger for higher star formation rates and higher AGN
luminosity. But it becomes much weaker above this mass range, consistent with
previous findings focusing on massive galaxies. Our result suggests that low-
mass and gas-rich AGN host central galaxies would first form dense cores
before AGN feedback is triggered, removing their neutral hydrogen gas. More
massive central galaxies may undergo a significantly different formation
scenario by gradually building up dense cores with less effective and
recurrent AGN feedback.

##  1 Introduction

In current galaxy formation theories, feedback from an active galactic nucleus
(AGN) is regarded as one of the most effective channels of shutting down star
formation, through the depletion and heating of cold gas within and
surrounding a galaxy (see e.g., Heckman & Best, 2014; Förster Schreiber &
Wuyts, 2020, for reviews). While AGN-driven outflows and winds have been known
for decades (e.g., Fabian, 2012), it is still controversial whether these can
sufficiently reduce the overall gas reservoir to trigger quenching of star
formation (Harrison, 2017).

Since the quenching of satellite galaxies is found to be mostly driven by the
halo environmental effect of cold gas depletion (e.g., Wetzel et al., 2013;
Tal et al., 2014; Jaffé et al., 2015; Brown et al., 2017; Stevens et al.,
2019), we only focus on central galaxies in this study. In our previous work
(Guo et al., 2021, hereafter G21), we find that the star formation activity of
central galaxies in the local universe is directly regulated by the available
atomic neutral hydrogen (H i) reservoir . It is therefore essential to
quantify the effect of AGN feedback on the H i gas mass in order to understand
its role in the quenching of star formation.

However, previous observational efforts to measure the cold gas mass in AGN
host galaxies revealed no strong dependence on AGN luminosity for both H i
mass (Fabello et al., 2011; Geréb et al., 2015; Ellison et al., 2019) and
molecular gas mass (e.g., Shangguan et al., 2020), challenging current galaxy
formation models.

To better understand the controversy, here we apply an established H i spectra
stacking technique (G21) to a large statistical sample of 11240 star-forming
galaxies (SFGs) and 6368 type-2 AGN host galaxies from Sloan Digital Sky
Survey (SDSS; Abazajian et al., 2009) DR7. Different to previous studies, we
compare their H i reservoir at the same stellar mass ($M_{\ast}$) and star
formation rate (SFR) bins, i.e. $M_{\rm HI}({\rm SFR}|M_{\ast})$, rather than
comparing $M_{\rm HI}(M_{\ast})$ for AGN hosts and non-AGN control galaxies as
in Ellison et al. (2019). As will be shown below, such a division is essential
to isolate the influence of AGN hosts from their compound dependence on both
$M_{\ast}$ and SFR. We further extend the work of Ellison et al. (2019) by
including the effect of central stellar surface density within 1 kpc (denoted
as $\Sigma_{1}$), which is found to be tightly correlated with $M_{\rm HI}$ in
G21.

The structure of this paper is as follows. We describe the galaxy samples and
stacking method in §2. We present the results in §3. We summarize and discuss
the results in §4. Throughout the paper, the halo mass is in units of
$h^{-1}M_{\sun}$, while the stellar and H i masses are in units of $M_{\sun}$.

Figure 1: Sample definition. The SFGs and AGN hosts (represented by dots of
different colors) are classified with the demarcation line (Kauffmann et al.,
2003) (dotted line). The AGNs are divided into subsamples using the Eddington
parameter (ratio between [Oiii] luminosity $L_{\rm[O{\sc III}]}$ and black
hole mass $M_{\rm BH}$, left panel) and $L_{\rm[O{\sc III}]}$ (right panel).
The characteristic value of $\log(L_{\rm[O{\sc III}]}/M_{\rm BH})\sim-0.2$
roughly corresponds to 1% of the Eddington ratio (Kauffmann & Heckman, 2009),
separating the AGNs into radiative and jet modes (Heckman & Best, 2014).

##  2 Data and Method

The galaxy sample in this work is the same as in G21. The galaxies used for
the H i spectra stacking are selected from the overlap regions between the
optical data of SDSS DR7 and H i 21 cm data of the Arecibo Fast Legacy ALFA
Survey (ALFALFA; Giovanelli et al., 2005; Haynes et al., 2018) 100% complete
catalog in the redshift range of $0.0025<z<0.06$. The central galaxies are
identified with a galaxy group catalog based on SDSS (Lim et al., 2017).

We adopt the galaxy stellar mass and SFR measurements from the GSWLC-2 catalog
(Salim et al., 2018), where the UV/optical spectral energy distribution
fitting was applied to have reliable SFRs for both SFGs and AGN hosts (Salim
et al., 2016). We also use the measurements of $\Sigma_{1}$ (in units of
$M_{\odot}/\rm{kpc}^{2}$) as in G21, which is obtained from the product of the
total light within 1 kpc and the $i$-band mass-to-light ratio.

The SDSS galaxy emission line fluxes and stellar velocity dispersion
measurements are obtained from the MPA-JHU DR7 release111https://wwwmpa.mpa-
garching.mpg.de/SDSS/DR7/. Based on the BPT diagram (Baldwin et al., 1981;
Veilleux & Osterbrock, 1987), we select type-2 AGNs from galaxies with S/N$>3$
in all four emission lines of [Oiii]$\lambda$5007, [Nii]$\lambda$6583,
H$\alpha$ and H$\beta$, following the demarcation line (Kauffmann et al.,
2003), $\log([{\rm OIII}]/{\rm H}\beta)>0.61/[\log([{\rm NII}]/{\rm
H}\alpha])-0.05]+1.3$.

Taking advantage of the large statistical sample, we are able to separate the
AGN hosts into different $M_{\ast}$ and SFR bins. As shown in Figure 1, the
subsamples are further divided according to the [Oiii] luminosity
($L_{\rm[O{\sc III}]}$, in units of $\rm{erg/s}$, right panel) and the
Eddington parameter ($L_{\rm[O{\sc III}]}/M_{\rm BH}$, a proxy of Eddington
ratio suggested in Heckman et al. 2004, left panel). The [Oiii] luminosity has
been corrected for dust extinction using the Balmer decrement by assuming a
dust attenuation law of $\tau_{\lambda}\propto\lambda^{-0.7}$ (Charlot & Fall,
2000). The black hole mass $M_{\rm BH}$ is estimated using the stellar
velocity dispersion–black hole mass relation (Tremaine et al., 2002). The
characteristic value of $\log(L_{\rm[O{\sc III}]}/M_{\rm BH})\sim-0.2$ roughly
corresponds to 1% of the Eddington ratio (Kauffmann & Heckman, 2009),
separating the AGNs into radiative and jet modes (Heckman & Best, 2014).

For the H i mass measurements, we follow our previous H i spectra stacking
technique (G21), an improvement of the methods of previous ALFALFA-based
stacking works (Fabello et al., 2011; Guo et al., 2020). Adaptive aperture
sizes were applied for galaxies with different stellar masses, as
$\log(D_{\mathrm{aper}}/\mathrm{kpc})=0.130\log(M_{\ast}/\mathrm{M_{\odot}})+0.635$,
with a lower limit of $4^{\prime}$ to account for the resolution of Arecibo
telescope at 21 cm. With the adaptive aperture sizes, the effect of confusion
caused by the Arecibo beam size is minimized. We estimate that the typical
correction of the stacked H i mass is found to be only around 0.05 dex, which
would not significantly affect our results. The measurement errors of the
stacked H i masses were estimated from the statistical uncertainties in the
stacked spectra, which provides a comparable estimate to the bootstrapping
method. These are typically quite small with a large number of stacked
spectra. We refer the readers to G21 for more details.

After the sample selection, our galaxy catalog consists of 8118 AGN hosts and
13672 SFGs. The galaxy H i spectra with excessive noise are discarded to
achieve the best S/N, since most of the noise is caused by the radio frequency
interference (RFI) that is not related to the H i signal (Guo et al., 2020).
Finally, there are 6368 AGN hosts and 11240 SFGs used in the direct spectra
stacking. Moreover, only 1607 (25%) AGN hosts and 5455 (49%) SFGs in the
stacked galaxies have available individual H i mass measurements from ALFALFA.
The H i detection rate for the AGN hosts increases from 14% in
$10^{9.5}$–$10^{10}M_{\sun}$ to 27% in $10^{10.5}$–$10^{11}M_{\sun}$, while
that for SFGs is roughly constant around 48%, which is indicative of the
decreased H i reservoir in AGN hosts compared to the star-forming counterparts
at the low-mass end. It also makes the H i stacking method important for the
quantitative studies of the cold gas reservoir.

Figure 2: Stacked H i measurements in $M_{\ast}$ and SFR bins. The stacked H i
masses are measured for galaxies in three stellar mass bins from
$10^{9.5}M_{\odot}$ to $10^{11}M_{\odot}$ and 7 SFR bins from
$10^{-2}M_{\odot}/\mathrm{yr}$ to $10^{1.5}M_{\odot}/\mathrm{yr}$. The
measurements for AGNs are shown for the divisions in Eddington parameter
(upper panels) and [Oiii] luminosity (lower panels), respectively. The symbol
colors are the same as in Fig. 1. The SFR measurements shown are the median
values in each bin. The vertical lines are the locations of the star formation
main sequence in each mass bin (Equation 2 of G21), and the horizontal lines
represent the corresponding H i main sequence ($\log M_{\rm HIMS}=0.42\log
M_{\ast}+5.35$) for star-forming galaxies (G21). Some of the error bars for
the H i masses are invisible due to their typically small values (less than
$0.05$) using stacked measurements.

##  3 Results

As shown in Fig. 2, we split the galaxy sample into three $M_{\ast}$ bins of
$10^{9.5}$–$10^{10}M_{\odot}$, $10^{10}$–$10^{10.5}M_{\odot}$ and
$10^{10.5}$–$10^{11}M_{\odot}$ and measure the stacked H i masses for SFGs and
AGN hosts in the same SFR bins, which ensures that the comparison is not
affected by the different SFR distributions of the two populations (Ellison et
al., 2019). The star-formation main sequence (SFMS, G21) and the corresponding
H i main sequence (HIMS, defined for star-forming galaxies in G21, $\log
M_{\rm HIMS}=0.42\log M_{\ast}+5.35$) are represented by the vertical and
horizontal dotted lines, respectively.

There is a clear trend that lower-mass AGN hosts have significantly depleted H
i reservoirs compared to their star-forming counterparts (left panel). This
effect is even stronger for higher SFRs, more luminous AGNs and also those
with higher accretion rates (i.e. larger $L_{\rm[O{\sc III}]}/M_{\rm BH}$). In
the lowest mass sample, the H i masses of AGN hosts are smaller than their
star-forming counterparts by up to $\sim$0.5 dex. This offset is not affected
by the bin size in $M_{\ast}$ (0.5 dex), as AGN hosts are typically 0.1 dex
more massive than the SFGs in each mass bin. That means the difference between
AGN hosts and SFGs is even larger in terms of the H i gas fraction ($f_{\rm
HI}\equiv M_{\rm HI}/M_{\ast}$). It is also not caused by the bin size of SFR
(0.5 dex), as the SFR values shown in each bin are the median measurements. We
show in G21 that for galaxies at a given $M_{\ast}$, the average relation
between SFR and $M_{\rm HI}$ is around SFR$\propto M_{\rm HI}^{2.75}$, i.e. to
account for the 0.5 dex decrease in $M_{\rm HI}$, the SFR needs to be
decreased by 1.38 dex, much larger than the bin size effect.

However, for massive galaxies with $\log(M_{\ast}/M_{\odot})>10.5$, the AGN
hosts and SFGs have very similar H i masses, consistent with previous studies
(Fabello et al., 2011; Geréb et al., 2015; Ellison et al., 2019). This shows
that the global star formation law between SFR and $M_{\rm HI}$ for the most
massive galaxies is not affected by the AGN activity, regardless of the
Eddington parameter or [Oiii] luminosity.

Since both the measurements of AGN activity and H i masses are instantaneous,
as opposed to the time-averaged SFR, these thus provide observational
signature of cold gas depletion in low-mass galaxies hosting optical type-2
AGNs. As quenched galaxies at $z\sim 0$ on average have H i masses $\sim$0.6
dex lower than the SFGs at all stellar masses (G21), the negative AGN feedback
would thus act as the dominant mechanism of star-formation quenching in the
stellar mass range $10^{9.5}$–$10^{10}M_{\odot}$, while its contribution seems
to gradually decrease as stellar mass increases.

Previously, no significant difference was found in H i fractions of AGN and
non-AGN control galaxies for the mass range probed in this work (Ellison et
al., 2019). This discrepancy is partially caused by the fact that here we
exclude those galaxies with low S/N in the four emission lines of the BPT
diagram, which could otherwise lead to galaxies being mis-classified. These
galaxies with weak emission lines were included in the non-AGN control samples
in the previous works (Fabello et al., 2011; Ellison et al., 2019). Another
important difference is that the comparisons between AGN hosts and non-AGNs in
the previous works were made with the stacked signals of $f_{\rm
HI}(M_{\ast})$, unlike in our case of $M_{\rm HI}({\rm SFR}|M_{\ast})$. The
essential dependence of $M_{\rm HI}$ on SFR is marginalized in $f_{\rm
HI}(M_{\ast})$. Although in each mass bin, the AGN population is dominated by
those galaxies with lower SFRs compared to the SFGs, the effect of AGN
feedback is, however, stronger at higher SFRs. Therefore, constructing the
non-AGN control samples by matching both the stellar mass and SFR of AGN hosts
(as in the previous work) would significantly weaken the signal of gas
depletion, as the apparent differences shown in $M_{\rm HI}({\rm
SFR}|M_{\ast})$ at the high SFRs will be largely down-weighted by the SFR
distribution peaked at the low SFRs in the integrated $M_{\rm HI}(M_{\ast})$.
This is further elaborated in the Appendix A.

Figure 3: Relation between H i mass and $\Sigma_{1}$ parameter. Both the H i
and $\Sigma_{1}$ measurements are scaled by their corresponding values from
galaxies in the SFMS. The $\Sigma_{1}$ measurements shown are the median
values in each $M_{\ast}$ and SFR bin. The symbols are the same as in Fig. 2,
with the symbol sizes representing the values of SFRs, with larger sizes for
higher SFRs. The measurements of all galaxies including those unclassified
galaxies in different $M_{\ast}$ and SFR bins from G21 are shown as the gray
bands, with thicker lines indicating higher SFRs. The positions of AGN hosts
in the mass range of $10^{9.5}$–$10^{10}M_{\odot}$ are well separated from the
SFGs, with much higher $\Sigma_{1}$ and significantly decreased $M_{\rm HI}$.
In more massive galaxies, they are approaching each other to form a tight
$M_{\rm HI}$–$\Sigma_{1}$ relation.

The H i mass of a galaxy has been found to be tightly correlated with the
central stellar surface density within 1 kpc ($\Sigma_{1}$) in the quenching
phase (G21), with $M_{\rm HI}\propto\Sigma_{1}^{-2}$. To further investigate
the effect of AGN on the quenching process, we show in Fig. 3 the relation
between $M_{\rm HI}$ and $\Sigma_{1}$ for the SFGs and AGN hosts in different
$M_{\ast}$ and SFR bins, where $M_{\rm HI}$ and $\Sigma_{1}$ are normalized by
the main sequence values of $M_{\rm HIMS}$ and $\Sigma_{\rm 1,MS}$
($\log\Sigma_{\rm 1,MS}=0.81\log M_{\ast}+0.607$ as in G21), respectively. The
measurements of all galaxies (including unclassified galaxies) from G21 in
each bin are also shown (gray bands).

In the mass range of $10^{9.5}$–$10^{10}M_{\odot}$, the overall relation is
dominated by the SFGs due to their larger sample size. It is remarkable that
all AGN hosts, irrespective of the Eddington parameter or [Oiii] luminosity,
have $\Sigma_{1}$ measurements well above $\Sigma_{\rm 1,MS}$ by at least 0.25
dex, even for AGN hosts with high SFRs. As the SFR values are indicated by the
symbol sizes, we find that the concentrated distribution of the AGN hosts in
the figure is not caused by the selection effects of their SFRs. In fact,
these AGN hosts have on average 0.4 dex higher $\Sigma_{1}$ than the
corresponding SFGs in the same SFR bins. The AGN activity is therefore
associated with the increase of $\Sigma_{1}$ and decrease of $M_{\rm HI}$.

As the correlation between $M_{\rm HI}$ and $\Sigma_{1}$ becomes much weaker
for the AGN hosts at various SFRs, it may indicate that AGN luminosity is the
main driving force of cold gas depletion in these low-mass galaxies after they
form the dense cores through the compaction processes (Dekel & Burkert, 2014;
Zolotov et al., 2015). Their SFRs will soon decrease due to the loss of the H
i gas, leading to a quenched state before the next episode of star formation
(likely indicated by the lowest blue dot shown in the left panel of Fig. 3).

We further emphasize that $\Sigma_{1}$ is not equivalent to the global
morphology of galaxies. As demonstrated in G21, the $M_{\rm HI}$-SFR relation
does not depend on the galaxy morphology. The reduced $M_{\rm HI}$ in AGN
hosts is then not due to their morphology changes with respect to the SFGs, as
we also compare the gas reservoir at the same SFR bins. In fact, as discussed
in Chen et al. (2020), $\Sigma_{1}$ is increasing with $M_{\rm BH}$. The
dependence of $M_{\rm HI}$ on $\Sigma_{1}$ thus reflects the gas stripping
caused by the black hole growth, which will be explored in our upcoming work.

For more massive galaxies above $10^{10}M_{\odot}$, the distribution of AGN
hosts in the diagram moves closer to the SFGs and shows a strong dependence of
$M_{\rm HI}$ on $\Sigma_{1}$. They are almost indistinguishable from each
other for $M_{\ast}>10^{10.5}M_{\odot}$ and form a tight $M_{\rm
HI}$–$\Sigma_{1}$ relation, consistent with the case in Fig. 2 for the $M_{\rm
HI}$–SFR relation. Such a similarity in the H i content of AGN hosts and SFGs
does not necessarily mean that AGN feedback is not effective in these massive
galaxies. It has been proposed that the instantaneous mass accretion rate
traced by the AGN luminosity could vary significantly during a typical star
formation episode (Novak et al., 2011; Hickox et al., 2014; Harrison, 2017),
making the difference between SFGs and AGN-dominated galaxies less apparent in
the global H i reservoir. One other possibility is that the AGN-driven
outflows and jets only directly affect the inner regions of the host galaxies
within a few kpc (Karouzos et al., 2016; Ellison et al., 2021; Shi et al.,
2021), while the global cold gas reservoir roughly remains the same.

It is important to note that the typical H i disc diameter scales with stellar
mass as $D_{\rm HI}\propto M_{\ast}^{0.5}$. (Wang et al., 2016) For example,
$D_{\rm HI}$ will decrease from about 60 kpc to 30 kpc when $M_{\ast}$
decreases from $10^{10}M_{\odot}$ to $10^{9.5}M_{\odot}$. It potentially makes
the effect of AGN luminosity on the H i gas more significant for lower-mass
galaxies, given that there is only weak dependence of $L_{\rm[O{\sc III}]}$ on
stellar mass (Kauffmann et al., 2003), with the average $L_{\rm[O{\sc III}]}$
remaining roughly constant at $\sim 10^{38.3}\,{\rm erg/s}$ for
$M_{\ast}<10^{10.5}M_{\sun}$.

The higher gas fractions of low-mass galaxies supply more fuel for the central
supermassive black holes to reach the high-accretion state, while the
shallower gravitational potential wells mean that gas is more loosely bound to
the galaxies. Combined with the fact that in massive galaxies the AGNs are
transitioning to the jet mode (or maintenance mode), the cumulative energy
release by the recurrent low-luminosity radio-AGN activity will prevent the
hot halo gas from further cooling and allow for an efficient self-regulating
AGN cycle, which keeps the global H i reservoir at a similar level to the SFGs
(Heckman & Best, 2014).

##  4 Conclusions and Discussions

In this paper, we compare the stacked H i masses for SFGs and type-2 AGN hosts
at the same $M_{\ast}$ and SFR intervals in the redshift range
$0.0025<z<0.06$. We find that AGN hosts have systematically smaller H i
reservoir than their star-forming counterparts (by a maximal amount of $\sim
0.5$ dex) with the same $M_{\ast}$ and SFR in the stellar mass range
$10^{9.5}$–$10^{10}M_{\odot}$. This effect is even stronger for AGN hosts with
higher SFRs, [Oiii] luminosity and Eddington ratios, providing observational
support for the effect of AGN luminosity on the gas depletion. For more
massive galaxies, the difference in $M_{\rm HI}$ is, however, significantly
smaller, consistent with previous literature probing the same mass ranges.

Our detection of reduced H i reservoir in low-mass AGN hosts suggests that the
instantaneous AGN feedback is likely more effective in gas-rich host galaxies.
These AGN hosts first grow dense cores, represented by their higher
$\Sigma_{1}$ values than SFGs of the same mass. This is the so-called “blue-
nugget” phase (Dekel & Burkert, 2014). As proposed by theoretical models
(Barro et al., 2013; Cui et al., 2021), the dissipative gas inflow would then
lead to rapid central black hole growth, thus triggering AGN feedback and
depleting the surrounding cold gas (Chen et al., 2020). The prerequisite for
such an effect to be observable is that the AGN feedback is so violent that
the global cold gas content, especially those distributed in the outer parts
of galaxies, can be significantly depleted within the timescale of an AGN
activity cycle (typically much less than 100 Myr). This probably requires the
AGN hosts to be small. Therefore, the different behaviors of $M_{\rm HI}$–SFR
as the masses of AGN hosts increase, may reflect the change from instantaneous
to integrated AGN feedback effects, along with the changes in AGN modes.

For an order-of-magnitude estimation, the gravitational potential energy of
$10^{9}M_{\odot}$ H i gas (with $D_{\rm HI}\sim 30\,$kpc) exerted by all the
stars in a $10^{9.5}M_{\odot}$ galaxy is roughly $10^{55}$ erg, which is
similar to the energy required to fully ionize the gas. The gravitational
potential energy from the dark matter is ignored, as the depleted gas does not
necessarily leave the host halo. If we take the lower threshold of the AGN
luminosity $L_{\rm[O{\sc III}]}=10^{39}\,{\rm erg/s}$, along with a factor of
600 for the bolometric correction (Kauffmann & Heckman, 2009), and 10% of
energy release to the surrounding gas, the cumulative energy released within 5
Myrs also reaches $10^{55}$ erg. Although such an estimation is quite
uncertain without detailed models and it is not really required to expel all
the gas, it at least suggests that the feedback from AGNs to drive the gas
depletion is quantitatively feasible, as implemented in the modern
hydrodynamical simulations (Weinberger et al., 2018).

We emphasize that the causal link between H i depletion and AGN luminosity
cannot be directly inferred from our current measurements. But compared to
other mechanisms, the AGN feedback is still the most likely cause. The stellar
feedback is generally found to be dominant for galaxies with
$M_{\ast}<10^{9}M_{\sun}$ and the energy injected by stellar winds is
typically proportional to SFR (Weinberger et al., 2018). Our comparisons of
$M_{\rm HI}({\rm SFR}|M_{\ast})$ are thus made for galaxies with similar
levels of stellar feedback, further highlighting the influence of AGN
luminosity.

The AGN luminosity might also be effective in even lower mass galaxies, below
$10^{9.5}M_{\odot}$, as inferred from a possible deficit gas fraction in AGN
hosts at these masses (Bradford et al., 2018; Ellison et al., 2019). Due to
the low AGN fraction, when extending our sample to the range of
$10^{9}$–$10^{9.5}M_{\odot}$, we can only obtain H i measurements for AGN
hosts in two $\log({\rm SFR}/{\rm yr}^{-1}M_{\odot})$ bins of $[-1.5,-1]$ and
$[-1,-0.5]$, which are just around the SFMS at this mass range. The
corresponding $\log(M_{\rm HI}/M_{\odot})$ measurements are $7.63\pm 0.49$
($8.99\pm 0.03$) and $8.10\pm 0.20$ ($9.31\pm 0.02$) for all AGNs (SFGs),
respectively. In terms of the $\log(\Sigma_{1}/\Sigma_{\rm 1,MS})$
measurements, they are 0.36 (-0.01) and 0.44 (-0.06) for AGNs (SFGs),
respectively. These measurements are in line with the sample of
$10^{9.5}$–$10^{10}M_{\odot}$, and significant enough to confirm that the AGN
feedback triggered in galaxies with dense cores is driving the cold gas
depletion in the whole mass range of $10^{9}$–$10^{10}M_{\odot}$. Future
resolved 21 cm and molecular gas surveys targeting low-mass AGN hosts would be
a promising way to fully understand the underlying physics of AGN-driven
quenching in this mass regime.

We thank the anonymous reviewer for the helpful comments that improve the
presentation of this paper. This work is supported by the National SKA Program
of China (grant No. 2020SKA0110100), National Key R&D Program of China (grant
No. 2018YFA0404503), National Science Foundation of China (Nos. 11922305,
11833005, 12073002, 11721303, 12011530159) and the science research grants
from the China Manned Space Project with NO. CMS-CSST-2021-A02. We acknowledge
the use of the High Performance Computing Resource in the Core Facility for
Advanced Research Computing at the Shanghai Astronomical Observatory. Arecibo,
Sloan

##  Appendix A Comparison to Literature

Our analysis based on $M_{\rm HI}({\rm SFR}|M_{\ast})$ reveals strong
differences between the SFGs and AGN hosts in the low-mass systems. Some
previous works that found no significant differences in the H i content of AGN
hosts and non-AGN galaxies selected only galaxies more massive than
$10^{10}M_{\odot}$ (Fabello et al., 2011; Geréb et al., 2015), consistent with
our findings for these massive galaxies. The non-AGN control galaxies used in
previous works (Fabello et al., 2011; Ellison et al., 2019) include both the
SFGs and those galaxies with weak emission lines (low S/N for any of the four
emission lines in the BPT diagram). The construction of the control sample and
how it is matched to the target sample has the potential to affect the final
results. Our sample classification can be more robust without including these
low S/N sources in either target or control sample.

The previous literature focus on the comparisons of $f_{\rm HI}(M_{\ast})$, or
equivalently $\langle M_{\rm HI}(M_{\ast})\rangle$ at the same mass bin, which
can be in principle obtained from our measurements of $M_{\rm HI}({\rm
SFR}|M_{\ast})$ as,

$\langle M_{\rm HI}(M_{\ast})\rangle=\frac{\Sigma N({\rm SFR}|M_{\ast})M_{\rm
HI}({\rm SFR}|M_{\ast})}{\Sigma N({\rm SFR|M_{\ast}})},$ (A1)

where $N({\rm SFR|M_{\ast}})$ is the number of galaxies in the SFR bin at the
given $M_{\ast}$ range and the summations are over all the SFR bins.
Constructing non-AGN control samples by matching both $M_{\ast}$ and SFR of
the AGN hosts as in the previous work (Ellison et al., 2019) is essentially
replacing $N({\rm SFR|M_{\ast}})$ of the non-AGNs in Eq. (A1) with that of the
AGNs.

In order to compare more directly with these previous works, we apply the H
i-stacking and measure $M_{\rm HI}({\rm SFR}|M_{\ast})$ for the non-AGNs by
including the SFGs and weak emission line galaxies. Then the stacked $\langle
M_{\rm HI}(M_{\ast})\rangle$ can be obtained with Eq. (A1). We show in Table 1
the resulting $\langle M_{\rm HI}(M_{\ast})\rangle$ for the AGN, SFG, non-AGN,
SFG control and non-AGN control samples, where the control samples are using
$N({\rm SFR|M_{\ast}})$ of the AGN hosts in each $M_{\ast}$ bin. For galaxies
in the mass range $10^{9.5}$–$10^{10}M_{\odot}$, after matching the SFR
distributions of the AGN hosts, the non-AGNs have only $0.1$ dex larger
$\langle M_{\rm HI}\rangle$ than that of AGNs, despite the large differences
between the $M_{\rm HI}({\rm SFR}|M_{\ast})$ measurements of SFGs and AGNs.
This is due to the fact that the SFR distribution of AGNs peaks at the lower
end where the differences between $M_{\rm HI}({\rm SFR}|M_{\ast})$ of SFGs and
AGNs are much smaller. The effect of including weak emission line galaxies in
the non-AGNs is minor for these low-mass galaxies.

The contributions of weak emission line galaxies and the SFR-matching scheme
for the more massive samples are slightly different. But the overall effect is
the much smaller difference between $\langle M_{\rm HI}(M_{\ast})\rangle$ for
the AGNs and non-AGN control samples. Our integrated measurements of $\langle
M_{\rm HI}(M_{\ast})\rangle$ are also consistent with previous work (Ellison
et al., 2019). Our experiment here demonstrates that $M_{\rm HI}({\rm
SFR}|M_{\ast})$ is a much better indicator when comparing the H i masses for
different samples than $M_{\rm HI}(M_{\ast})$, which would be affected by the
distribution of $N({\rm SFR|M_{\ast}})$.

Table 1: $M_{\rm HI}(M_{\ast})$ estimates for the different samples

$\log M_{\ast}$ | $[9.5,10]$ | $[10,10.5]$ | $[10.5,11]$
---|---|---|---
$\log M_{\rm HI,SFG}$ | $9.53\pm 0.02$ | $9.68\pm 0.02$ | $9.90\pm 0.04$
$\log M_{\rm HI,non-AGN}$ | $9.49\pm 0.02$ | $9.55\pm 0.02$ | $9.66\pm 0.04$
$\log M_{\rm HI,SFG,control}$ | $9.28\pm 0.03$ | $9.49\pm 0.05$ | $9.64\pm 0.06$
$\log M_{\rm HI,non-AGN,control}$ | $9.21\pm 0.04$ | $9.43\pm 0.05$ | $9.67\pm 0.06$
$\log M_{\rm HI,AGN}$ | $9.11\pm 0.08$ | $9.35\pm 0.04$ | $9.66\pm 0.03$

The displayed $M_{\rm HI}(M_{\ast})$ are obtained through Eq. A1 with the
stacked measurements of $M_{\rm HI}({\rm SFR}|M_{\ast})$ for different
samples. The control samples mean that their SFRs are matched to the
corresponding AGNs at the same mass bins. All masses are in units of
$M_{\odot}$.

##  Appendix B Robustness of Measurements

As extensively discussed in previous works (Schawinski et al., 2010; Trump et
al., 2015), the star formation dilution by the H ii regions will cause the AGN
hosts selected through the BPT diagram systematically biased against low-mass,
star-forming and disk-dominated galaxies. The observed low-mass AGN hosts
would then be biased towards both higher luminosity and Eddington ratio. As we
show in Fig. 2, the AGN hosts with larger $L_{\rm[O{\sc III}]}$ and higher
Eddington ratios have consistently lower $M_{\rm HI}$ for
$M_{\ast}<10^{10.5}M_{\odot}$. If we would be able to correct for the
selection bias by removing the AGN hosts with low luminosities and Eddington
ratios from the observed SFG population, the resulting $M_{\rm HI}$ for the
“pure” star-forming galaxies would be even higher. It would then lead to
larger differences between $M_{\rm HI}$ of the SFGs and high-luminosity AGN
hosts for these low-mass galaxies, further supporting our conclusion. We thus
emphasize that our conclusion is still robust in light of this potential bias,
but the exact $M_{\rm HI}$ offsets between the SFGs and AGN hosts would depend
on the appropriate corrections of the selection effect. For more massive
galaxies, our results would remain the same, since the AGN selection bias is
less severe and there is no trend of $M_{\rm HI}$ with AGN luminosity.

Since the SDSS fiber aperture size of $3\arcsec$ would cover around 3.7 kpc at
the maximum redshift of $z=0.06$, the amount of star formation dilution may be
more severe by the relative larger coverage for lower-mass galaxies. We test
this effect by limiting our samples to a reduced maximum redshift of $z=0.04$
and find very similar results as in Fig. 2. It demonstrates that the aperture
effect is not important in this study.

Figure 4: Comparisons of the SED-based total SFRs and those from within the
SDSS fibers ($\rm SFR_{fib}$). The comparisons are shown for the SFGs and AGN
hosts of different [Oiii] luminosities as in Fig. 2, with the same color
coding. We show the median values with the 1$\sigma$ errors in each panel.
There is no obvious bias for the $\rm SFR_{fib}$–SFR relations between the
SFGs and AGN hosts of $M_{\ast}<10^{10.5}M_{\odot}$. For more massive
galaxies, the $\rm SFR_{fib}$ estimates for AGN hosts of low SFRs are reaching
the lower limit of $\log({\rm SFR_{fib}}/M_{\ast})=-11.5$, where the
measurements are not reliable.

Another potential bias for our analysis is that the SFR estimates of the AGN
hosts from the GSWLC-2 catalog may suffer from the potential AGN contamination
of the emission lines. Although accurate corrections for the contamination is
very difficult and uncertain, we can still estimate its influence on our
results. For each galaxy in our sample, we further retrieve the SFR estimates
within the SDSS fibers (denoted as $\rm SFR_{fib}$) from the MPA-JHU catalog
(Brinchmann et al., 2004), which is to check the effect of different SFR
estimates, as well as differences between the fiber-based central SFRs and
SED-based integrated SFRs. While the $\rm SFR_{fib}$ estimates for the SFGs
are based on the emission line fluxes, those for AGN hosts are derived from
the D4000 index.

As the contamination from type-2 AGNs is not important for the D4000-based
SFRs, we can use $\rm SFR_{fib}$ of AGNs to check whether there is any
systematic bias between SFRs of AGNs and SFGs, despite the large scatters of
D4000-based SFRs. If the differences of $M_{\rm HI}$ between SFGs and AGN
hosts were caused by the fact that SFRs of AGN hosts are biased high, we would
expect to see systematic offsets in the relations between SFR and $\rm
SFR_{fib}$ for SFGs and AGN hosts, as well as the systematic trend with the
[Oiii] luminosity. Since the scatter of the $\rm SFR_{fib}$ does not depend on
the [Oiii] luminosity (Rosario et al., 2016), it will not introduce any
further bias.

We show in Figure 4 comparisons between SFR and $\rm SFR_{fib}$ for SFGs and
AGN hosts of different [Oiii] luminosities. As for all the bins with ${\rm
SFR_{fib}}/M_{\ast}>10^{-11.5}{\rm yr}^{-1}$ (where reliable estimates of
${\rm SFR_{fib}}$ can be obtained), there is not any obvious bias for the $\rm
SFR_{fib}$–SFR relations between the SFGs and AGN hosts at different stellar
masses, as well as no trend with the [Oiii] luminosity. We also test that the
results are very similar if we limit the redshift range of $0.0025<z<0.04$. We
further note that the scatters of $\rm SFR_{fib}$ are very similar for SFGs
and AGN hosts, indicating that the D4000-based SFRs for AGNs in our redshift
range do not cause any further significant errors with respect to the more
accurate $\rm SFR_{fib}$ for SFGs.

It demonstrates that there is no strong systematic bias in the integral SFRs
for the AGN hosts in our current sample. The differences between central SFRs
and integral SFRs also do not show any systematic bias towards AGN hosts. Our
SFR bins of 0.5 dex are already wide enough to take into account the residual
uncertainties of the SFR estimates. Therefore, we conclude that our results of
the $M_{\rm HI}$ trend with the AGN luminosity is not likely caused by the
systematic bias of SFR estimates for the AGN hosts.

## References

  * Abazajian et al. (2009) Abazajian, K. N., Adelman-McCarthy, J. K., Agüeros, M. A., et al. 2009, ApJS, 182, 543, doi: 10.1088/0067-0049/182/2/543
  * Baldwin et al. (1981) Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, PASP, 93, 5, doi: 10.1086/130766
  * Barro et al. (2013) Barro, G., Faber, S. M., Pérez-González, P. G., et al. 2013, ApJ, 765, 104, doi: 10.1088/0004-637X/765/2/104
  * Bradford et al. (2018) Bradford, J. D., Geha, M. C., Greene, J. E., Reines, A. E., & Dickey, C. M. 2018, ApJ, 861, 50, doi: 10.3847/1538-4357/aac88d
  * Brinchmann et al. (2004) Brinchmann, J., Charlot, S., White, S. D. M., et al. 2004, MNRAS, 351, 1151, doi: 10.1111/j.1365-2966.2004.07881.x
  * Brown et al. (2017) Brown, T., Catinella, B., Cortese, L., et al. 2017, MNRAS, 466, 1275, doi: 10.1093/mnras/stw2991
  * Charlot & Fall (2000) Charlot, S., & Fall, S. M. 2000, ApJ, 539, 718, doi: 10.1086/309250
  * Chen et al. (2020) Chen, Z., Faber, S. M., Koo, D. C., et al. 2020, ApJ, 897, 102, doi: 10.3847/1538-4357/ab9633
  * Cui et al. (2021) Cui, W., Davé, R., Peacock, J. A., Anglés-Alcázar, D., & Yang, X. 2021, Nature Astronomy, 5, 1078, doi: 10.1038/s41550-021-01456-3
  * Dekel & Burkert (2014) Dekel, A., & Burkert, A. 2014, MNRAS, 438, 1870, doi: 10.1093/mnras/stt2331
  * Ellison et al. (2019) Ellison, S. L., Brown, T., Catinella, B., & Cortese, L. 2019, MNRAS, 482, 5694, doi: 10.1093/mnras/sty3139
  * Ellison et al. (2021) Ellison, S. L., Wong, T., Sánchez, S. F., et al. 2021, MNRAS, 505, L46, doi: 10.1093/mnrasl/slab047
  * Fabello et al. (2011) Fabello, S., Kauffmann, G., Catinella, B., et al. 2011, MNRAS, 416, 1739, doi: 10.1111/j.1365-2966.2011.18825.x
  * Fabian (2012) Fabian, A. C. 2012, ARA&A, 50, 455, doi: 10.1146/annurev-astro-081811-125521
  * Förster Schreiber & Wuyts (2020) Förster Schreiber, N. M., & Wuyts, S. 2020, ARA&A, 58, 661, doi: 10.1146/annurev-astro-032620-021910
  * Geréb et al. (2015) Geréb, K., Morganti, R., Oosterloo, T. A., Hoppmann, L., & Staveley-Smith, L. 2015, A&A, 580, A43, doi: 10.1051/0004-6361/201424810
  * Giovanelli et al. (2005) Giovanelli, R., Haynes, M. P., Kent, B. R., et al. 2005, AJ, 130, 2598, doi: 10.1086/497431
  * Guo et al. (2020) Guo, H., Jones, M. G., Haynes, M. P., & Fu, J. 2020, ApJ, 894, 92, doi: 10.3847/1538-4357/ab886f
  * Guo et al. (2021) Guo, H., Jones, M. G., Wang, J., & Lin, L. 2021, ApJ, 918, 53, doi: 10.3847/1538-4357/ac062e
  * Harrison (2017) Harrison, C. M. 2017, Nature Astronomy, 1, 0165, doi: 10.1038/s41550-017-0165
  * Haynes et al. (2018) Haynes, M. P., Giovanelli, R., Kent, B. R., et al. 2018, ApJ, 861, 49, doi: 10.3847/1538-4357/aac956
  * Heckman & Best (2014) Heckman, T. M., & Best, P. N. 2014, ARA&A, 52, 589, doi: 10.1146/annurev-astro-081913-035722
  * Heckman et al. (2004) Heckman, T. M., Kauffmann, G., Brinchmann, J., et al. 2004, ApJ, 613, 109, doi: 10.1086/422872
  * Hickox et al. (2014) Hickox, R. C., Mullaney, J. R., Alexander, D. M., et al. 2014, ApJ, 782, 9, doi: 10.1088/0004-637X/782/1/9
  * Jaffé et al. (2015) Jaffé, Y. L., Smith, R., Candlish, G. N., et al. 2015, MNRAS, 448, 1715, doi: 10.1093/mnras/stv100
  * Karouzos et al. (2016) Karouzos, M., Woo, J.-H., & Bae, H.-J. 2016, ApJ, 819, 148, doi: 10.3847/0004-637X/819/2/148
  * Kauffmann & Heckman (2009) Kauffmann, G., & Heckman, T. M. 2009, MNRAS, 397, 135, doi: 10.1111/j.1365-2966.2009.14960.x
  * Kauffmann et al. (2003) Kauffmann, G., Heckman, T. M., Tremonti, C., et al. 2003, MNRAS, 346, 1055, doi: 10.1111/j.1365-2966.2003.07154.x
  * Lim et al. (2017) Lim, S. H., Mo, H. J., Lu, Y., Wang, H., & Yang, X. 2017, MNRAS, 470, 2982, doi: 10.1093/mnras/stx1462
  * Novak et al. (2011) Novak, G. S., Ostriker, J. P., & Ciotti, L. 2011, ApJ, 737, 26, doi: 10.1088/0004-637X/737/1/26
  * Rosario et al. (2016) Rosario, D. J., Mendel, J. T., Ellison, S. L., Lutz, D., & Trump, J. R. 2016, MNRAS, 457, 2703, doi: 10.1093/mnras/stw096
  * Salim et al. (2018) Salim, S., Boquien, M., & Lee, J. C. 2018, ApJ, 859, 11, doi: 10.3847/1538-4357/aabf3c
  * Salim et al. (2016) Salim, S., Lee, J. C., Janowiecki, S., et al. 2016, ApJS, 227, 2, doi: 10.3847/0067-0049/227/1/2
  * Schawinski et al. (2010) Schawinski, K., Urry, C. M., Virani, S., et al. 2010, ApJ, 711, 284, doi: 10.1088/0004-637X/711/1/284
  * Shangguan et al. (2020) Shangguan, J., Ho, L. C., Bauer, F. E., Wang, R., & Treister, E. 2020, ApJ, 899, 112, doi: 10.3847/1538-4357/aba8a1
  * Shi et al. (2021) Shi, F., Li, Z., Yuan, F., & Zhu, B. 2021, Nature Astronomy, 5, 928, doi: 10.1038/s41550-021-01394-0
  * Stevens et al. (2019) Stevens, A. R. H., Diemer, B., Lagos, C. d. P., et al. 2019, MNRAS, 483, 5334, doi: 10.1093/mnras/sty3451
  * Tal et al. (2014) Tal, T., Dekel, A., Oesch, P., et al. 2014, ApJ, 789, 164, doi: 10.1088/0004-637X/789/2/164
  * Tremaine et al. (2002) Tremaine, S., Gebhardt, K., Bender, R., et al. 2002, ApJ, 574, 740, doi: 10.1086/341002
  * Trump et al. (2015) Trump, J. R., Sun, M., Zeimann, G. R., et al. 2015, ApJ, 811, 26, doi: 10.1088/0004-637X/811/1/26
  * Veilleux & Osterbrock (1987) Veilleux, S., & Osterbrock, D. E. 1987, ApJS, 63, 295, doi: 10.1086/191166
  * Wang et al. (2016) Wang, J., Koribalski, B. S., Serra, P., et al. 2016, MNRAS, 460, 2143, doi: 10.1093/mnras/stw1099
  * Weinberger et al. (2018) Weinberger, R., Springel, V., Pakmor, R., et al. 2018, MNRAS, 479, 4056, doi: 10.1093/mnras/sty1733
  * Wetzel et al. (2013) Wetzel, A. R., Tinker, J. L., Conroy, C., & van den Bosch, F. C. 2013, MNRAS, 432, 336, doi: 10.1093/mnras/stt469
  * Zolotov et al. (2015) Zolotov, A., Dekel, A., Mandelker, N., et al. 2015, MNRAS, 450, 2327, doi: 10.1093/mnras/stv740