# What determines the H I gas content in galaxies?: morphological dependence
of the H I gas fraction across $M_{*}$-SFR plane

Shgieru V. Namiki The Graduate University for Advanced Studies, SOKENDAI,
2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan  Subaru Telescope, National
Astronomical Observatory of Japan, National Institutes of Natural Sciences,
650 North A’ohoku Place, Hilo, HI 96720, USA  Yusei Koyama  The Graduate
University for Advanced Studies, SOKENDAI, 2-21-1 Osawa, Mitaka, Tokyo,
181-8588, Japan  Subaru Telescope, National Astronomical Observatory of Japan,
National Institutes of Natural Sciences, 650 North A’ohoku Place, Hilo, HI
96720, USA  Shuhei, Koyama  Institute of Astronomy, Graduate School of
Science, University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-0015, Japan
Takuji Yamashita  National Astronomical Observatory of Japan, National
Institutes of Natural Sciences, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
Masao Hayashi  National Astronomical Observatory of Japan, National Institutes
of Natural Sciences, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Martha P.
Haynes  Cornell Center for Astrophysics and Planetary Science, Space Sciences
Building, Cornell University, Ithaca, NY 14853 USA  Rhythm Shimakawa  Subaru
Telescope, National Astronomical Observatory of Japan, National Institutes of
Natural Sciences, 650 North A’ohoku Place, Hilo, HI 96720, USA  Masato Onodera
The Graduate University for Advanced Studies, SOKENDAI, 2-21-1 Osawa, Mitaka,
Tokyo, 181-8588, Japan  Subaru Telescope, National Astronomical Observatory of
Japan, National Institutes of Natural Sciences, 650 North A’ohoku Place, Hilo,
HI 96720, USA

###### Abstract

We perform a stacking analysis of the H I spectra from the Arecibo Legacy Fast
ALFA (ALFALFA) survey for optically-selected local galaxies from the Sloan
Digital Sky Survey (SDSS) to study the average gas fraction of galaxies at
fixed stellar mass ($M_{*}$) and star formation rate (SFR). We first confirm
that the average gas fraction strongly depends on the stellar mass and SFR of
host galaxies; massive galaxies tend to have a lower gas fraction, and
actively star-forming galaxies show higher gas fraction, which is consistent
with many previous studies. Then we investigate the morphological dependence
of the H I gas mass fraction at fixed $M_{*}$ and SFR to minimize the effects
of these parameters. We use three morphological classifications based on
parametric indicator (Sérsic index), non-parametric indicator (C-index), and
visual inspection (smoothness from the Galaxy Zoo 2 project) on the optical
image. We find that there is no significant morphological dependence of the H
I gas mass fraction at fixed $M_{*}$ and SFR when we use C-index. In
comparison, there exists a hint of diminishment in the H I gas mass fraction
for “smooth” galaxies compared with “non-smooth” galaxies. We find that the
visual smoothness is sensitive to the existence of small-scale structures in a
galaxy. Our result suggests that even at fixed $M_{*}$ and SFR, the presence
of such small-scale structures (seen in the optical image) is linked to their
total H I gas content.

galaxies: evolution, galaxies: halos, galaxies: structure

††journal: ApJ

##  1 Introduction

Morphologies of galaxies are known to be strongly correlated with their star
formation activity. Late-type galaxies are actively star-forming in general,
while star formation in early-type galaxies tends to be much less active.
Historically, the most common approach to classify galaxy morphologies was the
visual inspection by human eyes (see Kennicutt 1998). With the advent of the
large and digitalized format of astronomical datasets over the last decades
(and accordingly the significant increase of the galaxy sample size), it has
become much more common to use analytical (or automated) classification, such
as Sérsic index ($n$, Sérsic 1963), concentration parameter ($C$, often
defined as the ratio between half light radius and 90% radius), stellar mass
surface density, bulge-to-total ratio (e.g., Strateva et al. 2001; Catinella
et al. 2010; Wuyts et al. 2011; Fang et al. 2013; Cook et al. 2019, 2020). A
strong correlation between the morphologies and the H I gas content of
galaxies has also been well established—i.e., late-type galaxies are gas-rich,
while early-type galaxies tend to be gas-poor. Indeed, in the past studies,
the galaxy morphologies along the Hubble sequence were used to estimate their
H I gas mass (see Roberts & Haynes 1994), which is often used to quantify the
“deficiency” of atomic hydrogen in galaxies residing in dense environments (H
I deficiency; Gavazzi et al. 2008, Boselli et al. 2010, Hughes et al. 2013).

With the recent large, H I 21 cm line survey in the local universe, such as
the GALEX Arecibo SDSS Survey (GASS; Catinella et al. 2013) and the Arecibo
Legacy Fast ALFA (ALFALFA) survey (Haynes et al. 2018), it has become possible
to investigate the morphological dependence of the H I gas fraction of local
galaxies in a more statistical way. By using the data from the GASS survey and
various morphological classifications from the visual classification to the
automated methods, Calette et al. (2018) reported that late-type galaxies tend
to have higher H I gas fraction than early-type galaxies at a given stellar
mass. While Calette et al. (2018) divided their sample into stellar mass bins,
they did not split the sample by star formation rates (SFR). Because late-type
galaxies tend to have higher SFRs than early-type galaxies in general and are
expected to have a large gas reservoir, the morphological dependence reported
in Calette et al. (2018) might be produced by the different SFR between the
early- and late-type galaxy samples. Moreover, some outliers do not follow the
general trend between the average star formation activity and gas content or
galaxy morphology, such as the H I-excess systems (early-type galaxies with
large H I reservoirs and negligible star-formation; Geréb et al. 2016, 2018)
or passive spirals (e.g., George 2017; Guo et al. 2020 but see also Cortese
2012).

A more recent study by Cook et al. (2019) used extended GALEX Arecibo SDSS
Survey (xGASS; Catinella et al. 2010, 2018) to investigate the relation
between H I gas mass and the bulge-to-total ratio (measured with the 2-D
Bayesian light profile fitting code (ProFit); Robotham et al. 2017) for local
galaxies. They showed that the H I gas mass of star-forming galaxies do not
depend on the bulge-to-total mass ratio, suggesting that the presence of bulge
has little impact on their H I gas content. However, we should note that Cook
et al. (2019) selected star-forming galaxies by simply excluding the quiescent
galaxy population based on the distance from the star formation main sequence
(Catinella et al., 2018; Janowiecki et al., 2019). Also, their morphological
classification is different from that of Calette et al. (2018). In these ways,
the sample definition and/or the morphological classifications vary from study
to study, making it difficult to interpret the impact of galaxy morphologies
on their H I gas content.

In our study, we carry out a comprehensive analysis by using the multiple
morphological indicators (Sérsic index, C-index, and visual smoothness) and by
dividing our sample by their stellar mass and SFR. We stack the radio spectra
of galaxies from the ALFALFA survey to calculate the average gas fraction.
Then we can compare the average H I gas content of galaxies with different
morphologies at the same stellar mass and star formation rate.

The structure of this paper is as follows. In Sec. 2, we show our sample
selection and summarize the galaxy information. The procedure to stack the
radio spectra and the stacking result for our “star-forming” galaxy sample are
summarized in this section. We then investigate the morphological dependence
of H I gas mass at fixed stellar mass and SFR in Sec. 3, and interpret our
results in Sec. 4. Finally, we summarize our results in Sec. 5. Throughout
this paper, we adopt a flat $\Lambda$CDM cosmology with $\Omega_{m}=0.3$,
$\Omega_{\lambda}=0.7$, and $H_{0}=67.8\ {\rm km\ s^{-1}\ Mpc^{-1}}$ and
Chabrier initial mass function (Chabrier, 2003).

##  2 Data and H I spectral stacking

To investigate the morphology dependence of H I contents in local galaxies, we
need not only H I information but also various parameters of host galaxies. A
combination of the large data sets from GALEX-WISE-SDSS Legacy Catalog 2
(GSWLC2, Salim et al. 2018) and ALFALFA survey enables us to study the H I gas
properties of galaxies statistically.

Our sample is drawn from the GSWLC2, which contains the stellar mass and the
star formation rate of $\sim 700,000$ galaxies derived from the fitting of
Spectral Energy Distribution for the multiwavelength dataset. We then cross-
matched the GSWLC2 catalog with the MPA-JHU catalog (Abazajian et al., 2009)
of SDSS DR7 to obtain the spectroscopic redshift of each target. We then
select 32,717 galaxies (with $0.01<z<0.05$) located within the ALFALFA H I 21
cm line survey footprint. Here we note that 14,252 galaxies having companions
within the cut-out region of radio spectra (4 arcmin; see Sec.2.1) are
excluded to avoid overestimating H I gas mass and the effect of galaxy-galaxy
interaction. To identify companions, we do not apply any criteria for stellar
mass, color, or redshift. This method increases the number of discarded
galaxies that are potentially not accompanied. However, in this study, we
conservatively discard all galaxies having any companion within the cut-out
region of H I emission line. In the following analysis, we restrict the sample
to 18,465 galaxies with $M_{*}$ and SFR range of $9.0<\log_{10}M_{*}<12.0$ and
$-2.0<\log_{10}SFR<2.0$. In addition, considering the possible effect of
active galactic nuclei (AGN) in our analysis, we exclude 7,573 AGN host
candidates from our sample using the BPT diagram (Kauffmann et al., 2003).
Here we used the [O III], [N II], H$\alpha$ and H$\beta$ emission line fluxes
of individual galaxies from the MPA-JHU catalog, while we exclude 5 galaxies
for which any of the emission line fluxes are not properly measured in the
MPA-JHU catalog. In this study, we use the remaining 10,887 galaxies as our
parent ‘star-forming’ galaxy sample.

###  2.1 H I spectral stacking

The H I gas mass, $M_{{\rm H_{I}}}$, is derived from the 21 cm line flux
(Roberts, 1963) in this paper. Although the H I-detected source catalog from
the ALFALFA survey is already public (Haynes et al. 2018), directly using the
H I-detected source catalog may cause a potential bias towards the H I-rich
galaxies due to the detection limit. The H I gas mass, $M_{{\rm H_{I}}}$, is
derived from the flux of 21 cm line ($S$) following the equation 1 (Roberts
1963),

$\displaystyle\frac{M_{{\rm H_{I}}}}{M_{\odot}}=\frac{2.356\times
10^{5}}{1+z}\left[\frac{D_{L}(z)^{2}}{{\rm Mpc}}\right]\left(\frac{S}{{\rm Jy\
km\ s^{-1}}}\right),$ (1)

where $D_{L}(z)$ is the luminosity distance to the object. The lower limit of
detectable H I gas mass depends on the distance to the object. More distant
galaxies with less H I gas, therefore, might not be detected through the
pipeline of ALFALFA survey.

To avoid this potential bias, we apply the H I stacking analysis following the
previous studies (e.g., Fabello et al. 2011, Brown et al. 2015). The radio
spectra around H I 21 cm line of our sample ($8^{\prime}\times 8^{\prime}$
square) are extracted from the full volume ALFALFA data cubes using R.A., Dec,
and $cz$ in the MPA-JHU catalog regardless of the detection of H I 21 cm line.
A spectrum of one galaxy has two polarizations and contains velocity, flux,
and quality weight $w$ for each velocity bin. The quality weight $w$ evaluates
the effect of radiofrequency interference and/or hardware issues, ranging from
0 (unusable data) to 1 (good data). We discard velocity bins with $w<0.5$ and
take the average of two polarizations. If more than 40% of velocity bins have
$w$ less than 0.5 in a spectrum, we exclude such spectrum from our stacking
analysis. Forty galaxies are removed through this procedure. After that, the
spectrum is rest-frame shifted using the redshift from optical spectroscopy so
that the center of H I 21 cm line should be set to $0$ km/s. Also the noise
level of each spectrum is evaluated using $rms$ of the spectrum outside of H I
emission from the target galaxy ($-1000<v\ [{\rm km\ s^{-1}}]<-500$ and
$500<v\ [{\rm km\ s^{-1}}]<1000$, see Sec. 2.2). Because we eliminate the
sources having one or more close companions, our sample can be free from the
effect of the beam confusion (Jones et al., 2016).

By considering the possible correlations between H I gas properties, stellar
mass, and the SFR, we aim to study the morphological dependence of H I gas
properties at fixed stellar mass and SFRs. In the stacking process, we give a
weight for each spectrum as $(1+z)^{2}/D_{L}(z)^{2}M_{*}$ (see Sec. 3.3 in
Fabello et al. 2011). If we stack the radio spectra without any weight,
massive and/or nearby galaxies will significantly contribute to the resulting
H I gas fraction ($F_{\rm H_{I}}$). In equation 1, $1+z$ is not squared
because it assumes that H I 21 cm line flux $S$ is rest-frame shifted
correctly. However, because our calculation starts from the observed H I 21 cm
line flux $S_{obs}$, we have to weight $1+z$ in the rest-frame shifting. We
solve this problem by changing the stacking weight from $(1+z)/D_{L}M_{*}$ to
$(1+z)^{2}/D_{L}M_{*}$. We also note that we perform stacking analysis only
for the bins with a sample size of $\geq$10.

Figure 1: An example of the stacked H I spectra obtained in Sec. 2.2. The
light-blue region shows the error in each velocity bin derived from the $rms$
of individual spectra. Vertical dashed lines are shown at $\pm 350$ km/s,
between which the flux is summed up to calculate the gas fraction ($F_{\rm
H_{I}}$, see Sec. 2.1).

After subtracting the baseline of a stacked spectrum by linear fitting, we
calculate the average gas fraction in each bin by summing up the flux in the
velocity range of $-350<v\ [{\rm km\ s^{-1}}]<350$ (dashed lines in Figure 1).
This velocity range is determined to cover the widest emission line after the
stacking process to be performed in Sec. 2.2. Adopting a fixed velocity range
may lead to an increase in the error of $F_{{\rm H_{I}}}$ measurements.
However, we decided to adopt this fixed velocity range for all the stacked
spectra to estimate the errors and upper limits for H I undetected sources in
a consistent manner. The flux error of each velocity component in a stacked
spectrum is derived by propagating the $rms$ from individual spectra before
stacking (the light-blue region in Figure 1). On the other hand, we adopt the
Bootstrap resampling approach when calculating the average gas fractions to
consider the sampling errors. In the following analyses, we use the average of
gas fraction $F_{\rm H_{I}}$ and its standard deviation from 1000 times
Bootstrap resampling as the average gas fraction and its $1\sigma$ error. Here
we note that the sampling error dominates the total error budget in our
analyses.

###  2.2 Average H I gas fraction across the star-forming main sequence

Firstly, we simply divide our sample by the stellar mass and SFR ($\Delta
M_{*}=\Delta\mathit{SFR}=0.5$ dex), and carry out the stacking process as
explained above. Figure 2 summarizes the number of galaxies included in each
bin. The sample size tends to be small at high $M_{*}$ and/or low SFR ends,
and we do not perform H I stacking analyses for the bins with the sample size
of $N<10$. We note that the results presented in this paper mainly focus on
galaxies on the star-forming main sequence.

Figure 2: The $M_{*}$-SFR diagram to show the distribution of all our sample
(grey contours) and the number of galaxies used for H I stacking at each
($M_{*}$, SFR) bin. The grid size indicates $\Delta M_{*}=\Delta SFR=0.5$ dex
(see Sec. 2.2 for details). Orange shaded bins are used for the stacking
(N$\geq$10).

In the left panel of Figure 3, the color-coding indicates the average gas
fraction of galaxies at each stellar mass and SFR. Here we include the
marginal detection down to $S/N=3$. It can be seen that the average gas
fraction gradually changes with the stellar mass and the SFR. The increasing
gas fraction with increasing SFR at fixed stellar mass seen in this diagram is
consistent with a picture that the rich gas reservoir supports an active star-
formation (Tumlinson et al., 2017).

In the right panel of Figure 3, we show the relation between the gas fraction
and stellar mass, with the color-coding based on the median SFR in each bin.
The upper limits represented by the triangles and arrows are the $3\sigma$
value. It is clear from the right panel of Figure 3 that there is a strong
correlation between H I gas fraction and stellar mass, consistent with
previous studies. The black squares connected by the solid line in Figure 3
(right) show the H I gas scaling relation derived by Brown et al. (2015). Our
results are in good agreement with the black lines at
$M_{*}<10^{10.2}M_{\odot}$, while at the massive end, our results tend to show
higher values than the average scaling relation determined by Brown et al.
(2015). The distinction of $F_{gas}$ in the massive side is not surprising
because we performed the H I stacking analyses only for the bins with the
sample size of $N\geq 10$, and most of the bins below the star-formation main
sequence are not used in this study. Brown et al. (2015) suggested that star-
forming galaxies tend to host more H I gas than quenched galaxies, which can
explain the difference between Brown et al. (2015) and our results at
$M_{*}>10^{10.2}M_{\odot}$. We emphasize that our stacking analysis shows an
excellent agreement with Brown et al. (2015) when we perform the H I stacking
using all SDSS galaxies at each stellar mass bin without considering the SFR
binning (see magenta stars in Figure 3 right).

Figure 3: Left: The average gas fraction (see color bar) at each position on
the stellar mass vs. SFR plane from our ALFALFA stacking analysis. We include
the marginal detection ($S/N<3$) in this panel. The gas fraction depends both
on the stellar mass and SFR. The black contours show the distribution of the
parent ‘star-forming’ galaxies. Right: The gas fraction plotted against
stellar mass. The color-coding of this plot shows the median SFR of each bin.
Circles are the points with $S/N>3$, and inverted triangles mean the $3\sigma$
upper limit. The magenta stars show the stacking result for all local galaxies
by simply dividing our sample into five stellar mass bins (without considering
SFR difference). Here, we include the galaxies having the potential companion
within four arcmins to set the same selection criteria to Brown et al. (2015).
The gray error bars are derived from the Bootstrap method (Sec. 2.1). We show
the $M_{*}$–$F_{{\rm H_{I}}}$ scaling relation derived by Brown et al. (2015)
as the black squares connected by the black solid line.

##  3 Morphological dependence of H I gas fraction at fixed $M_{*}$ and SFR

The primary goal of this study is to investigate the morphological dependence
of the H I gas fraction of our sample at fixed stellar mass and SFR. Here we
use three morphological indicators of galaxies; Sérsic $n$, concentration
index (C-index), and visual smoothness from the Galaxy Zoo 2 project (GZ2,
Lintott et al. 2008; Willett et al. 2013; Hart et al. 2016).

The Sérsic profile can reproduce the classical surface brightness distribution
of early-type galaxies (the de Vaucouleurs profile) when $n\sim 4$, and the
exponential disk profile of late-type galaxies when $n=1$. The C-index is
often defined as the ratio of the half-light radii $R_{50}$ and $R_{90}$,
where $R_{x}$ means the radius in which $x$ % of the total flux is enclosed.
It is shown that the C-index has a strong correlation with the dominance of
the bulge component in galaxies (e.g., Shimasaku et al. 2001). We also
introduce the “visual smoothness” from GZ2 as a proxy for the traditional
visual classifications made by human eyes (see Sec. 3.3 for more details).

We cross-matched our sample constructed in Sec.2.2 with the New York
University Value-Added Catalog (NYU-VAGC; Blanton et al. 2005) and the full
GZ2 catalog (Hart et al., 2016). This new catalog contains 7712 objects, all
of which have measurements of $M_{*}$, SFR, redshift, ALFALFA radio spectra,
Sérsic $n$, C-index, and visual smoothness. We discuss the morphological
impacts on the $M_{*}$–$F_{{\rm H_{I}}}$ relation with this new sample in the
following subsections.

###  3.1 Sérsic index

We use the Sérsic index $n$ measured in the $r$-band of individual galaxies
published in NYU-VAGC. In this study, we select 498 early-type and 2856 late-
type galaxies by applying $n>3.5$ and $n<1.5$, respectively. Red and blue
contours in Figure 4 show the distribution of early-type and late-type
galaxies on the $M_{*}$-SFR diagram. Here we normalize the contours based on
the total number of each population. Because we mainly focus on the galaxies
on the star-formation main sequence, the number of late-type galaxies is
larger than that of early-type galaxies.

We then conducted the stacking analysis to the early/late-type subsamples in
the same way as described in Sec.2.2. Here we use the same bin size for
stacking as that in Sec.2.2 ($\Delta M_{*}=\Delta\mathit{SFR}=0.5$ dex). The
number of early/late-type galaxies in each bin is shown in Figure 4.

Figure 4: Same figure as Figure 2 but for late-type (blue) and early-type
(red) galaxies divided by the Sérsic $n$. Blue and red contours show the
distribution of late-type and early-type galaxies on this plane, respectively.
Here we normalize the contours based on the total number of each population.
The width of the grid is $\Delta M_{*}=\Delta SFR=0.5$ dex. Here we show the
region of $9.0<\log_{10}M_{*}<11.0$ and $-2.0<\log_{10}SFR<1.0$ because all
other bins have sample sizes of $N<10$. Orange shaded bins are used for the
comparison of $F_{\rm HI}$ in panel (c) of Figure 5 ($N\geq 10$ for both
populations).

The left column in Figure 5 show the result. Panel (a) and (b) in Figure 5
show the relationship between the median stellar mass and the average H I gas
fraction when we divide our sample into late-type and early-type by the Sérsic
$n$. As we did in Figure 3, we use the bins with $N\geq 10$ for each
morphological type. The general trend does not change from Figure 3; the H I
gas fraction is anticorrelated with the stellar mass and correlated with the
SFR.

Figure 5: The result of our stacking analysis when we divide our sample by
Sérsic $n$ (left), C-index (middle), and visual smoothness (right). The top
panels (a)/(d)/(g) show the relation between the stellar mass and the average
H I gas fraction of late-type/disk/non-smooth populations, respectively. The
second row (b)/(e)/(h) is the same as the upper panels but for early-
type/bulge/smooth galaxies. The meanings of the large circles and inverted
triangles in the top and second row are the same as the right panel of Figure
3. The panels (c)/(f)/(i) show the difference in the amount of H I gas between
the above two populations as a function of their stellar mass. The meaning of
each symbol is summarized in Sec. 3.1. Colors indicate the median SFR of each
subsample. The gray error bars are also derived by the Bootstrap method (see
Sec.2.1). The black squares connected by the solid line show the scaling
relation from Brown et al. (2015) (same as Figure 3).

We compute the difference of H I gas mass between early-type and late-type
galaxies with the same stellar mass and SFR, and they are plotted in Figure 5
(c) as a function of stellar mass. This comparison is performed for the bins
in which both populations have more than nine galaxies in Figure 4. Here we
note that there are two classes of bin types in terms of the H I detection.

  1. 1.

Both populations have $S/N>3$ ($\circ$ in Figure 5).

  2. 2.

The $F_{{\rm H_{I}}}$ of late-type/disk/non-smooth galaxies show $S/N>3$, but
early-type/bulge/smooth galaxies show $S/N<3$ ($\triangle$ in Figure 5).

There are no bins with properties opposite to those of class 2 for all
morphological indicators. In Figure 5 (c), we use large circles and normal
triangles for the class 1 and 2, respectively. The number of bins in each
class is summarized in Table 1.

Unfortunately, there are only two bins in class 1, and the remaining bins are
class 2 or non-detection ($S/N<3$). The $F_{gas}$ differences in these two
class 1 bins are $-0.09$ and $0.07$, suggesting that there is no significant
difference in the H I gas mass between late-type and early-type galaxies at
fixed $M_{*}$ and SFR in those bins. Outside of these two bins
($\log_{10}M_{*}<10.0$ or $\log_{10}M_{*}>10.5$), we could not detect H I in
the stacked spectra due to the poor statistics, especially for early-type
galaxies.

We also conduct the same analysis with the different Sérsic $n$ criteria. Here
early/late-type galaxies are defined as those sitting in the top/bottom
20%-ile profile in the distribution of Sérsic $n$; i.e. $n<1.25$ for late-
types and $n>2.30$ for early-types. This method enables us to match the total
size of subsamples and increase the number of bins in class 1. In the range of
$9.5<\log_{10}M_{*}<10.5$ and $-0.5<\log_{10}SFR<0.5$, we find that there is
no significant difference in the H I gas mass between early- and late-type
galaxies. Using this method, however, early-type subsample can include
contaminants from “intermediate” morphology ($n\sim 2-3$). It is, therefore,
difficult to conclude there is no difference in HI gas mass fraction between
early-type and late-type galaxies at fixed stellar mass and SFR with this
percentile approach.

Table 1: The number of bins for class 1 and 2 according to the S/N of the
stacked H I flux

.  class 1 class 2 $S/N_{\rm pop.1}(F_{{\rm H_{I}}})$ $>3$ $>3$ $S/N_{\rm
pop.2}(F_{{\rm H_{I}}})$ $>3$ $<3$ Sérsic $n$ 2 5 C-index 9 3 Visual
smoothness 7 1

Note. — The “class 1” means that H I is detected at $S/N>3$ for both of the
populations in that bin. The “class 2” indicates the case where the first
population shows $S/N(F_{{\rm H_{I}}})>3$, while the second population has
$S/N(F_{{\rm H_{I}}})<3$. There are no bins with the properties opposite to
those of class 2. In the lower row, we show the number of bins for each class
and each morphological index. The class 1 and 2 are shown as circles and
triangles in the bottom panels of Figure 5, respectively.

###  3.2 Concentration index

We also retrieve the r-band Petrosian half-light radii $R_{50}$ and $R_{90}$
from the NYU-VAGC catalog, and calculate C-index as a ratio of these two
values ($R_{90}/R_{50}$). While the criteria of C-index used for the
morphological classification are different from study to study (e.g., Deng
2013; Koyama et al. 2019), we adopt $C>2.8$ and $C<2.5$ for bulge-dominated
and disk-dominated galaxies, respectively. We obtain 660 bulge and 5020 disk
galaxies in total. Figure 6 shows the $M_{*}$-SFR diagram for bulge/disk
galaxies. Binning width is the same as that in Sec. 3.1 ($\Delta
M_{*}=\Delta\mathit{SFR}=0.5$ dex), and the number of galaxies in each bin is
also summarized in Figure 6.

Figure 6: Same figure as Figure 4 but for disk (blue) and bulge (red) galaxies
divided by the C-index.

The middle column of Figure 5 shows the results of our H I stacking analysis
when we use C-index for morphological classification. The panels (d) and (e)
in Figure 5 show the scaling relation for disk- and bulge-dominated galaxies.
In the panel (f), we show the difference between the disk and bulge samples by
computing $M_{{\rm H_{I},Disk}}$/$M_{{\rm H_{I},Bulge}}$ at each stellar mass
and SFR. The meanings of the symbols are the same as those in panel (c). The
weighted average of $\log_{10}(M_{{\rm H_{I},Disk}}/M_{{\rm H_{I},Bulge}})$ of
the “class 1” bins ($S/N(F_{{\rm H_{I}}})>3$ for both bulge and disk
populations) is $0.09\pm 0.10$, suggesting that disk galaxies and bulge
galaxies at fixed stellar mass and SFR have similar amount of H I gas on the
star-formation main sequence ($9.0<\log_{10}M_{*}<11.0$). We verify that our
results are unchanged even if we instead use the upper/lower 20 percentile in
the distribution of C-index to select bulge and disk populations ($C>2.59$ and
$C<2.07$). Again, we note that the intermediate population can contaminate the
morphological selection with this percentile approach.

###  3.3 Visual classification with GZ2

Galaxy Zoo project (Lintott et al., 2008) provides visual classifications of
morphologies given by citizen scientists for a large number of galaxies
observed in SDSS. In the Galaxy Zoo project, citizen scientists are asked to
inspect galaxies’ images and choose their morphological class (e.g.,
elliptical, clock-wise spiral). Following Galaxy Zoo, Galaxy Zoo 2 project
(GZ2, Willett et al. 2013) aims to describe more detailed morphological
properties using a similar method to that of Galaxy Zoo. We here focus on the
first question of GZ2: “Is the galaxy simply smooth and rounded, with no sign
of a disk?”. All participants of the GZ2 project are asked to choose one
answer from “Smooth and rounded”, “Features or disk”, or “Star or artifact”.
Then, GZ2 calculates the “vote fraction” for each answer. Willett et al.
(2013) mentioned that, for most of clean spirals in Galaxy Zoo, the vote
fraction for “Features or disk” in GZ2 is similar to that for spiral galaxies
in Galaxy Zoo.

Hart et al. (2016) revised the vote fraction with the idea that the actual
distribution of the vote fraction should be independent of the redshift in the
local universe. They remove the effect of size, luminosity, and redshift of
galaxies and introduce the debiased vote fraction. Following the
recommendation by the GZ2 project, we use this debiased vote fraction from
Hart et al. (2016) in this paper, rather than directly using the original vote
fraction provided by Willett et al. (2013).

We define “smooth” galaxies as those having the debiased vote fraction of
$>0.8$ for “Smooth and rounded” in GZ2. On the other hand, we define “non-
smooth” galaxies as those with the debiased vote fraction of $>0.8$ for
“Features or disk”. Here we follow the recommendation by Willett et al. (2013)
to use the criteria of the debiased vote fraction $>0.8$ when performing any
morphological classification with GZ2. The bin size for our H I stacking
analyses is the same as that in Sec 3.1 ($\Delta M_{*}=\Delta\mathit{SFR}=0.5$
dex), and Figure 7 shows the number of galaxies in each bin.

Figure 7: Same figure as Figure 4 but for non-smooth (blue) and smooth (red)
galaxies divided by the visual smoothness.

The result is shown in the right column of Figure 5. As we performed for
Sérsic index and C-index in the previous subsections, we show in panels (g)
and (h) the scaling relation for non-smooth and smooth galaxies, respectively.
Panel (i) shows the difference between these two populations at fixed $M_{*}$
and SFR. Interestingly, smooth galaxies tend to have significantly lower gas
fraction than non-smooth galaxies, and we find that there are six bins where
both non-smooth and smooth galaxies are detected at $S/N(F_{{\rm H_{I}}})>3$
(class 1). The weighted average of $\log_{10}(M_{{\rm H_{I},Non-
smooth}}/M_{{\rm H_{I},Smooth}})$ is $0.71\pm 0.11$, suggesting a significant
difference in H I gas fraction between the smooth and non-smooth galaxies at
fixed stellar mass and SFR in the range of $9.0<\log_{10}M_{*}<10.5$. This is
the main result of our paper. We find no bin where H I is detected only for
smooth galaxies. This result is also unchanged even if we use the percentile
approach to define smooth and non-smooth galaxies as we did in Sec.3.1 and
Sec.3.2.

##  4 Discussion

The morphological dependence of the H I gas mass in local galaxies has been
discussed for decades (e.g., Roberts & Haynes 1994). The H I gas mass is known
to depend on the stellar mass and the SFR of host galaxies (e.g., Brown et al.
2015). On the other hand, the morphology of galaxies is also related to the
stellar mass and the SFR (e.g., Kauffmann et al. 2003). These relationships
between multiple parameters make it difficult to understand the real impact of
galaxy morphologies on their H I gas mass content.

In our study, we divide our sample into small bins on the $M_{*}$-SFR plane
($\Delta M_{*}=\Delta SFR=0.5$ dex). The galaxies in each bin are further
divided by their morphology with three morphological indicators; Sérsic $n$,
C-index, and the visual smoothness. Our study revealed that visually smooth
galaxies have lower gas fraction than non-smooth galaxies at fixed stellar
mass and SFR. Such a morphological trend is not observed when we use C-index
(Figure 5). Below, we will discuss the potential candidates which may affect
the H I gas content of galaxies and why we see morphological dependence only
when we use visual smoothness.

###  4.1 Stellar mass, SFR, and environment

When investigating the effect of galaxy morphology on the H I gas mass, it is
crucial to exclude the impact of other properties of galaxies. Many previous
papers show that H I gas mass strongly depends on the stellar mass of host
galaxies ($M_{*}$-$M_{HI}$ scaling relation, e.g., Fabello et al. 2011; Brown
et al. 2015; Healy et al. 2019). A simple approach to remove the stellar mass
dependence is to check the H I scaling relations of each subsample. Calette et
al. (2018) compared the H I scaling relation of late-type galaxies and early-
type galaxies and concluded that late-type galaxies have higher H I gas
fraction than early-type galaxies at all stellar mass range. However, the
stellar mass is not the only parameter that determines the H I gas mass of the
host galaxies, and other parameters can also affect the scaling relation
(Cortese et al., 2011; Brown et al., 2015; Cook et al., 2019). For example,
Cook et al. (2019) studied the impact of the bulge-to-total mass ratio on the
H I scaling relation and found no significant effect of the morphology when
they limited their sample to the star-forming galaxies. They argue that the
morphological dependence of H I scaling relation reported in previous studies
originates from the correlation between the star-formation activity and galaxy
morphology at fixed stellar mass. On the other hand, the amount of molecular
hydrogen in the star-forming galaxy is shown to be approximately fixed in a
wide range of bulge-to-total mass ratio, whereas that of H I can change by a
factor of 100 (see Figure 10 in Catinella et al. 2018). This is also supported
by Koyama et al. (2019), who showed similar molecular gas mass fractions for
green-valley galaxies with different morphologies (classified by C-index) at
fixed stellar mass and SFR.

Because all the analyses presented in this work are performed at fixed stellar
mass and SFR, our results should not be affected by different stellar masses
or SFRs. It is true that there remains a possibility that there is a small
difference in the distribution of stellar mass and/or SFR within the small
($M_{*}$, SFR) bin. We calculate the median $M_{*}$ and SFR for smooth and
non-smooth galaxies in each bin ($\delta M_{*}$ and $\delta SFR$), and confirm
that the difference is very small for all the bins used in Figure 5 (i)
($\delta M_{*}\leq 0.08$, and $\delta SFR\leq 0.11$). By recalling Figure 3,
the small difference existing in each bin cannot explain the large difference
(0.71 dex) in the gas fraction between smooth and non-smooth galaxies.

Although we consider that the stellar mass and the star-formation activity are
the primary parameters that determine the H I gas content of galaxies, their
surrounding environments may also affect the H I scaling relation.
Observations revealed that late-type galaxies in dense environments tend to
have less H I gas than those in the general field (e.g., Haynes & Giovanelli
1984; Solanes et al. 2001), likely due to environmental processes such as
galaxy-galaxy interactions or ram pressure stripping (Moore et al., 1998; Gunn
& Gott, 1972; Cortese et al., 2021). It is also true that early-type galaxies
in the traditional Hubble sequence (ellipticals/S0s) tend to be located in
cluster environments in the local universe (e.g., Dressler 1980, Bamford et
al. 2009).

To check the environment of smooth and non-smooth galaxies, we investigate the
halo mass of smooth and non-smooth galaxies. By cross-matching our sample with
the SDSS DR7 group catalog from Yang et al. (2008), we obtain the halo mass of
galaxies. We then divide these galaxies into small bins of stellar mass and
SFR as used for our stacking analysis ($\Delta M_{*}=\Delta\mathit{SFR}=0.5$
dex), and carry out the Kolmogorov–Smirnov (KS) test on the halo mass
distribution of two populations. We find that $p$-values are $>$0.05 for most
of the bins, suggesting that we cannot rule out the null hypothesis that the
two populations are drawn from the same parent population. Therefore, it is
unlikely that our results shown in Figure 5 are affected by the dense
environment.

We note again that the morphological difference in the H I gas fraction is
visible only when we use visual smoothness for the morphological
classification. We do not see the difference when we use C-index (Figure 5
(f)), consistent with the conclusion of Cook et al. (2019). A question here
is—what is the visual smoothness? We will discuss this in Sec. 4.2, and
attempt to identify reasons responsible for the different behavior when we use
smoothness as a morphological indicator.

###  4.2 Visual smoothness

We introduce the visual smoothness as a parameter describing the appearance of
galaxies. In our analysis, smooth and non-smooth galaxies are determined by
the debiased vote fraction of each answer to the first question in GZ2
(Willett et al., 2013), “Is the galaxy simply smooth and rounded, with no sign
of a disk?” This unique classification distinguishes between H I-rich and H
I-poor population at fixed $M_{*}$ and SFR, but what determines the visual
smoothness of galaxies? To interpret the visual smoothness, we investigate how
the visual smoothness correlates with the other two morphological parameters
used in this study (Sérsic $n$ and C-index; see Figure 8).

Figure 8: Number distribution of non-smooth and smooth galaxies for Sérsic $n$
(upper) and C-index (lower). We normalized the number distribution by the
total number of each population.

From Figure 8, we realize that both smooth and non-smooth galaxies are
distributed over a wide range in Sérsic $n$ and C-index. The distribution of
smooth galaxies has a peak around $n\sim 1$, corresponding to a pure
exponential disk, and there are non-smooth galaxies at $n\sim 4$, which
corresponds to the de Vaucouleurs profile. For C-index, smooth galaxies and
non-smooth galaxies have a different distribution in the bottom panel of
Figure 8, but the distribution of the smooth galaxies is peaked at $C\sim
2.5$, which is actually used to select “disk” galaxies in Sec.3.2. Figure 8
suggests that the visual smoothness judged by the citizen scientists is not
simply identifying early/late-type or bulge/disk-like morphologies. We show
examples of the optical images of our non-smooth and smooth galaxies from SDSS
DR12 in Figure 9. The stellar mass, SFR, Sérsic $n$, and C-index of these
galaxies are fixed at $10.0<\log_{10}M_{*}<10.5$, $0.0<\log_{10}SFR<0.5$,
$1.0<n<1.5$, and $2.0<C<2.5$. In other words, only visual smoothness is
different between the six galaxies in the top and bottom panels of Figure 9.

By visually inspecting the optical images in Figure 9, we realize that many of
the smooth galaxies show prominent bulge and disk structure. It is likely that
the citizen scientists’ critical features to identify non-smoothness would be
the small structures like spiral arms and/or prominent bar structure within
the galaxies. Indeed, non-smooth galaxies in Figure 9 seem to have spiral arms
or prominent bar structure (upper six panels), while smooth galaxies do not
have such a small-scale structure (lower six panels). Although the Sérsic $n$
and C-index are the morphological indicators commonly used to describe the
overall light profile from the core to the outskirts of galaxies, it would not
be possible to identify such small-scale structures by those automated
parameters.

Our results suggest that galaxy morphologies defined by Sérsic $n$ and C-index
are not identical to the classification made by human eyes. We note that we
are not discussing which is the best indicator of galaxy morphologies. We
suggest that the visual smoothness can better distinguish gas-rich and gas-
poor populations at fixed stellar mass and SFR. We should also note that our
sample is limited to the local universe ($0.01<z<0.05$), so that the physical
resolution is high (typically 0.94 kpc at $z=0.033$). This might help citizen
scientists to identify small structures in the galaxies.

Figure 9: Examples of optical images of non-smooth (upper 6 panels) and smooth
galaxies (lower 6 panels) from SDSS DR12. We note that all these galaxies
listed here have fixed stellar mass, SFR, Sérsic $n$, and C-index
($10.0<\log_{10}M_{*}<10.5$, $0.0<\log_{10}SFR<0.5$, $1.0<n<1.5$,
$2.0<C<2.5$).

It would also be important to understand the effect (or bias) produced by the
redshift of galaxies on the visual classification of the citizen scientists in
GZ2. As shown in Figure 4 of Willett et al. (2013), the fraction of smooth
galaxies increases with redshift, while the non-smooth population decreases.
This trend is not surprising because the physical resolution becomes poorer
for more distant galaxies, and thus it becomes more difficult to identify
small-scale structures within more distant galaxies. Hart et al. (2016)
corrected the vote fraction by removing the bias produced by the different
redshifts. Because we use the debiased vote fraction derived by Hart et al.
(2016), our results would not be affected by the redshift effects. Figure 10
shows the redshift distributions of our smooth and non-smooth galaxies in each
($M_{*}$, SFR) bin. This plot suggests that smooth galaxies tend to have
higher redshifts than non-smooth galaxies below the star-formation main
sequence, while this trend is often reversed for galaxies located above the
main sequence. The H I mass discrepancy between smooth and non-smooth galaxies
reported in Figure 5 (i) is seen regardless of the stellar mass or SFR of
galaxies, and therefore it is unlikely that the different redshift
distribution within each ($M_{*}$, SFR) bin has significant impacts on the
elevated H I mass excess in non-smooth galaxy population.

Figure 10: The cumulative redshift distribution of our non-smooth (blue) and
smooth (red) galaxies for each stellar mass and SFR bin. The median value of
the redshift in each bin is plotted as dashed vertical lines. The stellar mass
range, SFR range (log scale), and the p-value from the KS test are shown in
each panel. We note that we require a minimum sample size of 10 for both
smooth and non-smooth galaxy subsamples to compute the p-value.

Our results suggest that the existence of small-scale structures in the
galaxies (e.g., spiral arms) would be the key to determining the H I gas
fraction. These small-scale structures might be missed by the C-index and
Sèrsic $n$ because they are roughly tracing the overall light profile. In
contrast, human eyes are more sensitive to such internal structures, and this
would be the main cause of the different morphological dependence of H I gas
mass when we use C-index or visual smoothness for the morphological
classification. Considering the fact that the amount of molecular hydrogen is
almost constant (Catinella et al., 2018; Koyama et al., 2019), our result
suggests that non-smooth galaxies have a larger amount of H I that is not
involved in the star-formation than smooth galaxies, even at the same stellar
mass and SFR. More detailed theoretical approaches and/or observations of
atomic gas kinematics within the galaxies are necessary to understand the
missing link between the small structures likely caused by the local
instability (e.g., Toomre 1977) and the global properties of H I gas in
galaxies. It is expected that simulations will allow one to trace the motion
of gaseous and stellar components within galaxies. However, in most
simulations, visual smoothness is not carefully examined because it requires
cooperation from many citizen scientists to determine galaxies’ visual
smoothness. As suggested by Dickinson et al. (2018), even the most recent
cosmological simulations cannot perfectly reproduce morphological properties
of present-day galaxies, including the visual smoothness.

##  5 Summary

In this work, we performed H I spectral stacking analysis for local star-
forming galaxies with a wide range in stellar mass, SFR, and morphological
types. Following the same stacking method presented by Fabello et al. (2011)
and Brown et al. (2015), we show the scaling relation between the stellar mass
and the H I gas fraction (Figure 3). Figure 3 also suggests that the H I gas
mass depends not only on the stellar mass but also on the star-formation
activity of the host galaxies. This result is consistent with Brown et al.
(2015), who concluded that the star-formation activity is a primary driver of
the H I gas content in a galaxy.

We then divide our sample by their morphologies using three morphological
parameters; Sérsic $n$, C-index, and visual smoothness. We separate each
subsample into small bins on the SFR–$M_{*}$ diagram ($\Delta M_{*}=\Delta
SFR=0.5$ dex), and performed the stacking analysis of the radio spectra. Our
study revealed that, at fixed stellar mass and SFR, H I gas mass fraction
($F_{{\rm H_{I}}}$) does not significantly depend on their morphologies when
we use C-index for morphological classification, while we do find a
significant morphological difference ($\sim$0.7 dex) when we use visual
smoothness as a morphological indicator (Figure 5). Unfortunately, we could
not obtain any clear trend from our analysis with Sèrsic index due to the
small number of early-type galaxies. Because we fixed the stellar mass and the
SFR of two morphological populations when comparing the H I gas mass, our
result is free from any bias by the stellar mass and the SFR. We also
investigate the environmental impact on our results. We performed the K-S test
and found $p$-values of $>$0.05 for most of the bins. We, therefore, conclude
that our results are not affected by galaxies in dense environments like
galaxy clusters.

Finally, we study how the visual smoothness correlates with the other two
morphological indicators. By comparing the distributions of Sérsic $n$ and
C-index for non-smooth and smooth galaxies, we find that the visual smoothness
judged by the citizen scientists is different from the traditional automated
distinction between early/late-type or bulge/disk morphologies at least in the
local universe (Figure 8). We also compare the optical images of non-smooth
and smooth galaxies in Figure 9. We notice that only non-smooth galaxies have
small-scale structures within the galaxies. Therefore we consider that the
existence of small-scale structures would be the key to determine the $F_{{\rm
H_{I}}}$ of local galaxies. Because Sérsic $n$ and C-index are the indicators
that describe the overall light profile from the center of the galaxies to the
outskirts, the small-scale structure would be missed by those parameters. The
potential link between the small-scale structure and the global $F_{{\rm
H_{I}}}$ should be revealed with future spatially-resolved observations and
theoretical approaches.

We thank the referee for reviewing our paper and providing us with useful
comments that improved the paper. ALFALFA surveys, on which this work is
based, were conducted at the Arecibo Observatory. The Arecibo Observatory is
operated by SRI International under a cooperative agreement with the National
Science Foundation (AST-1100968), and in alliance with Ana G. Méndez-
Universidad Metropolitana, and the Universities Space Research Association.
Funding for the Sloan Digital Sky Survey (SDSS) and SDSS-II has been provided
by the Alfred P. Sloan Foundation, the Participating Institutions, the
National Science Foundation, the U.S. Department of Energy, the National
Aeronautics and Space Administration, the Japanese Monbukagakusho, and the Max
Planck Society, and the Higher Education Funding Council for England. The SDSS
Web site is http://www.sdss.org/. The SDSS is managed by the Astrophysical
Research Consortium (ARC) for the Participating Institutions. The
Participating Institutions are the American Museum of Natural History,
Astrophysical Institute Potsdam, University of Basel, University of Cambridge,
Case Western Reserve University, The University of Chicago, Drexel University,
Fermilab, the Institute for Advanced Study, the Japan Participation Group, The
Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the
Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist
Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National
Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-
Institute for Astrophysics (MPA), New Mexico State University, Ohio State
University, University of Pittsburgh, University of Portsmouth, Princeton
University, the United States Naval Observatory, and the University of
Washington. This work was financially supported in part by Grants-in-Aid for
Scientific Research (No. 18K13588) by the Japanese Ministry of Education,
Culture, Sports and Science.

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