# Beyond Ultra-diffuse Galaxies. II. Environmental Quenching of Mass–Size
Outliers among the Satellites of Milky Way Analogs

Jiaxuan Li (李嘉轩) Department of Astrophysical Sciences, 4 Ivy Lane, Princeton
University, Princeton, NJ 08544, USA<EMAIL_ADDRESS>Jenny E. Greene
Department of Astrophysical Sciences, 4 Ivy Lane, Princeton University,
Princeton, NJ 08544, USA  Johnny Greco Department of Astrophysical Sciences, 4
Ivy Lane, Princeton University, Princeton, NJ 08544, USA  Center for Cosmology
and AstroParticle Physics (CCAPP), The Ohio State University, Columbus, OH
43210, USA  Rachael Beaton Department of Astrophysical Sciences, 4 Ivy Lane,
Princeton University, Princeton, NJ 08544, USA  Shany Danieli NASA Hubble
Fellow  Department of Astrophysical Sciences, 4 Ivy Lane, Princeton
University, Princeton, NJ 08544, USA  Andy Goulding Department of
Astrophysical Sciences, 4 Ivy Lane, Princeton University, Princeton, NJ 08544,
USA  Song Huang (黄崧) Department of Astrophysical Sciences, 4 Ivy Lane,
Princeton University, Princeton, NJ 08544, USA  Department of Astronomy and
Tsinghua Center for Astrophysics, Tsinghua University, Beijing 100084, China
Erin Kado-Fong Department of Astrophysical Sciences, 4 Ivy Lane, Princeton
University, Princeton, NJ 08544, USA  Physics Department, Yale Center for
Astronomy & Astrophysics, PO Box 208120, New Haven, CT 06520, USA

###### Abstract

Recent observations have reignited interest in a population of dwarf galaxies
that are large and diffuse for their mass, often called ultra-diffuse
galaxies. However, the origin and evolution of these mass–size outliers and
the role of the environment are still unclear. Using the exquisitely deep and
wide Hyper Suprime-Cam Strategic Survey images, we search for ultra-puffy
galaxies, defined as being $1.5\sigma$ larger than the average size for their
mass, around Milky Way-like galaxies. We present the sizes and radial
distributions of mass–size outliers and derive their quenched fraction to
explore the impact of the environment. Surprisingly, despite being outliers in
size, the ultra-puffy galaxies have a similar quenched fraction as normal-
sized satellites of Milky Way analogs in both observations and simulations,
suggesting that quenching is not tied to being a mass–size outlier. The
quenched fraction is higher for the ultra-puffy galaxies associated with
redder hosts, as well as those that are closer to the host in projection. In
contrast, the ultra-diffuse galaxies are overall redder and more quiescent
compared with normal satellites. We show that the classic definition of ultra-
diffuse galaxies is heavily weighted toward quenched galaxies and thus cannot
be used for a study of quenching of mass–size outliers.

Low surface brightness galaxies (940), Dwarf galaxies (416), Galaxy properties
(615), Galaxy quenching (2040)

††software: NumPy (Harris et al., 2020), Astropy (Astropy Collaboration et
al., 2013), SciPy (Jones et al., 2001), Matplotlib (Hunter, 2007), statmorph
(Rodriguez-Gomez et al., 2019), Halotools (Hearin et al., 2017), Colossus
(Diemer, 2018), scarlet (Melchior et al., 2018), unagi.

##  1 Introduction

Dwarf galaxies, given their overwhelming abundance, shallow gravitational
potential wells, diverse evolutionary histories, and high dark matter content,
are ideal probes for testing the $\Lambda$CDM paradigm and understanding dark
matter (Bullock & Boylan-Kolchin, 2017) and baryonic processes (Sales et al.,
2022). In particular, dwarf galaxies and their star formation history are
sensitive to the environments where they reside. Nearly all isolated dwarf
galaxies in the field are star-forming (Geha et al., 2012), but satellite
dwarf galaxies in the Local Group and Local Volume hosted by Milky Way
(MW)-mass galaxies are much more quiescent in star formation, with near-unity
quenched fraction at $M_{\star}\lesssim 10^{8}\ M_{\odot}$ (e.g., Grcevich &
Putman, 2009; Spekkens et al., 2014; Wetzel et al., 2015b; Baxter et al.,
2021; Mao et al., 2021; Putman et al., 2021; Carlsten et al., 2022a; Greene et
al., 2023; Karunakaran et al., 2022b). Such a contrast indicates that
environment plays an important role in regulating star formation in dwarf
galaxies.

Several physical processes are believed to be responsible for the cessation of
star formation (also known as “quenching”) in dwarf galaxies. Isolated dwarf
galaxies can be quenched by bursty stellar feedback (e.g., El-Badry et al.,
2018), reionization (for ultra-faint dwarfs; Bullock et al. 2000; Benson et
al. 2002; Somerville 2002; Tollerud & Peek 2018; Applebaum et al. 2021), or
previously passing a more massive halo, as in the case of so-called backsplash
galaxies (Simpson et al., 2018; Benavides et al., 2021). For the satellite
galaxy of an MW analog (a galaxy having a similar stellar or halo mass as the
MW), the ram pressure experienced by the satellite as it moves through the hot
circumgalactic medium (CGM) of the host galaxy could remove the gas and cause
the cessation of star formation (e.g., Gunn & Gott, 1972; McCarthy et al.,
2008; Grcevich & Putman, 2009; Emerick et al., 2016; Simpson et al., 2018;
Tremmel et al., 2020; Samuel et al., 2022). It has been shown that ram
pressure stripping can efficiently quench galaxies at $M_{\star}<10^{8}\
M_{\odot}$ (Fillingham et al., 2016; Simpson et al., 2018; Buck et al., 2019).
Starvation, where cold gas supplies are halted following infall to a more
massive hot halo, is believed to be dominant for higher-mass satellites
(Fillingham et al., 2016). Tidal stripping can also remove the gas from the
satellite and cause quenching (Simpson et al., 2018), but strong tidal
interactions are needed because the dark matter needs to be stripped before a
significant gas loss happens. A satellite dwarf galaxy might also be
preprocessed in a lower-mass group prior to falling into the current host
galaxy, and such preprocessing would increase the quenched fraction (Wetzel et
al., 2015a; Jahn et al., 2022; Samuel et al., 2022). Extensive studies have
been done on the quenching of satellites in MW analogs using simulations
(e.g., Simpson et al., 2018; Buck et al., 2019; Garrison-Kimmel et al., 2019;
Simons et al., 2020; Akins et al., 2021; Joshi et al., 2021; Karunakaran et
al., 2021; Font et al., 2022; Pan et al., 2023; Samuel et al., 2022), and many
of them are able to reproduce the observed quenched fraction in the Local
Group and Local Volume. It is now time to understand the relative importance
of these mechanisms as a function of satellite and host properties.

Interestingly, several of these physical processes might be able to puff up
satellite galaxies and turn them into outliers with respect to the average
mass–size relation. An example class of mass–size outlier is the ultra-diffuse
galaxies (UDGs, van Dokkum et al. 2015), which have a large size ($r_{e}>1.5$
kpc) and low surface brightness ($\mu_{0}(g)>24\ \mathrm{mag\ arcsec}^{-2}$).
It is therefore valuable to ask if the same mechanism that dominates quenching
also produces the observed population of mass–size outliers. This will provide
a unique angle to peek into the formation and evolution of satellite galaxies
in MW analogs and help us understand whether the mass–size outliers are a
distinct class of satellite galaxies or just the large-size tail of the
satellite population.

Large samples of mass–size outliers already exist in galaxy cluster
environments, but lower-density environments such as groups are relatively
unexplored (e.g., Karunakaran & Zaritsky, 2023). In Li et al. (2022a,
hereafter L22), we presented a sample of dwarf galaxies that are mass–size
outliers among the satellites of MW analogs at $0.01<z<0.04$. As a follow-up
study, in this paper, we ask whether the mass–size outliers are more quiescent
compared to the “normal” satellite population of MW analogs. We take the
mass–size outliers from L22 (described in §2) and present their
characteristics, including their size and radial distributions, in §3. We then
derive the quenched fractions as a function of satellite stellar mass, host
color, and projected distance to the host (§4). We compare the quenched
fractions of mass–size outliers with the bulk of the satellite population of
nearby MW analogs and simulations. In §5, we discuss the implications of these
results on the formation and quenching of mass–size outliers. We adopt a flat
$\Lambda$CDM cosmology from Planck Collaboration et al. (2016) with
$\Omega_{\rm m}=0.307$ and $H_{0}=67.7\ $km s-1 Mpc-1. We use the AB system
(Oke & Gunn, 1983) for magnitudes. The stellar masses used in this work are
based on the Chabrier (2003) initial mass function.

##  2 Data and Sample Selection

In this section, we briefly summarize the data and the mass–size outlier
samples presented in L22. We refer interested readers to L22 for a detailed
description of the samples and the search algorithms.

###  2.1 mass–size outlier sample

In L22, we performed a systematic search for low surface brightness galaxies
(LSBGs) in Subaru’s Hyper Suprime-Cam Strategic Survey Program (HSC-SSP,
Aihara et al. 2018; hereafter the HSC survey). The HSC survey is an imaging
survey using the 8.2-m Subaru telescope and the Hyper Suprime-Camera (Miyazaki
et al., 2012, 2018), covering $\sim 1000\ \rm{deg}^{2}$ in five broad bands
($grizy$) and reaching a depth of $g=26.6$ mag, $r=26.2$ mag and $i=26.2$ mag
($5\sigma$ point source detection). In L22, we used the data release PDR2,
which covers $\sim 300\ \rm{deg}^{2}$ and has a global sky subtraction to
preserve low surface brightness features (Aihara et al., 2018; Li et al.,
2022b).

We search for LSBGs following the method in Greco et al. (2018) with several
modifications to suit PDR2 and improve the completeness and purity. Briefly,
we run SExtractor (Bertin & Arnouts, 1996) on the coadd images after removing
bright extended sources and associated diffuse light. After applying an
initial size and color cut to the output catalog, we model each source by
running scarlet (Melchior et al., 2018) and extract a series of structural and
morphological parameters from the nonparametric model. We design a metric
based on the color, size ($r_{e}$, circularized half-light radius), surface
brightness ($\overline{\mu}_{\mathrm{eff}}(g)$, average surface brightness
within $r_{e}$ in the $g$ band), and morphology and use it to remove false
positives that are not likely to be real LSBGs. For the remaining objects, we
fit a parametric model to estimate their sizes, magnitudes, and surface
brightnesses. The completeness of the search is characterized by injecting
mock galaxies into coadd images and recovering them with our algorithm. In the
size range of $3\arcsec<r_{e}<14\arcsec$, our search is $>70\%$ complete to
$\overline{\mu}_{\mathrm{eff}}(g)<26.5\ \mathrm{mag\ arcsec}^{-2}$ and $>50\%$
complete to $\overline{\mu}_{\mathrm{eff}}(g)\leqslant 27.0\ \mathrm{mag\
arcsec}^{-2}$. For comparison, Zaritsky et al. (2021) searched for LSBGs in
the Dark Energy Camera Legacy Survey and reached $\sim 25\%$ completeness at
$\mu_{0}(g)\approx 25.5\ \mathrm{mag\ arcsec}^{-2}$. Tanoglidis et al. (2021)
reported the LSBG search using Dark Energy Survey data and showed a
completeness $\sim 30\%$ at $\overline{\mu}_{\mathrm{eff}}(g)\approx 26\
\mathrm{mag\ arcsec}^{-2}$. Therefore, our completeness is high compared with
other LSBG searches, which ensures high fidelity in the scientific results. We
remove LSBGs with a completeness of less than 10% for cleaner statistics.

Then we cross-match our LSBG sample with MW analogs selected from the NASA-
Sloan Atlas111http://nsatlas.org (Blanton et al., 2005, 2011) catalog by
requiring $0.01<z<0.04$, $10.2<\log\ M_{\star}/M_{\odot}<11.2$, and being in
the HSC PDR2 footprint. In this way, we select 922 MW analogs. For context, we
compare our selection with two surveys that also search satellites of MW
analogs. The Satellites Around Galactic Analogs (SAGA; Geha et al., 2017; Mao
et al., 2021) survey is an ongoing spectroscopic survey of classical
satellites of 100 MW analogs at $20$ Mpc $<D<40$ Mpc. Their MW analogs are in
a stellar mass range of $10.2<\log\ M_{\star}/M_{\odot}<11.0$. The Exploration
of Local VolumE Satellites (ELVES; Carlsten et al., 2020, 2021, 2022b, 2022a)
survey maps the satellites of 30 host galaxies with $M_{\star}>10^{9.9}\
M_{\odot}$ and $D<12$ Mpc. Most of the satellites have direct distances from
either the tip of the red giant branch or surface brightness fluctuations,
with the latter dominating for the faint satellites. The ELVES sample already
includes MW and M31 satellites. To sum up, our MW analog selection is similar
to that of SAGA. Because of the volume-limited criterion, ELVES includes
several groups more massive than the SAGA hosts and ours.

We calculate the virial mass of MW analogs based on the stellar-to-halo mass
relation in Behroozi et al. (2010) using halotools (Hearin et al., 2017). Then
we convert virial mass to virial radius $R_{\rm vir}$ assuming a flat
$\Lambda$CDM cosmology where the virial overdensity only depends on
cosmological parameters and redshift (Bryan & Norman, 1998). For a given MW
analog, we associate any LSBG that falls inside its projected virial radius
with the MW analog as the host galaxy. If one LSBG is matched to more than one
host, we assign it to the nearest host based on the angular separation
normalized by the host virial radius. In total, we surveyed the 922 MW
analogs, and we found 2510 LSBG candidates associated with 689 MW analogs. We
assume that the LSBGs are at the same redshifts as their hosts.

After cross-matching, we select two mass–size outlier samples, namely UDGs and
ultra-puffy galaxies (UPGs). The UDGs are defined to have
$r_{e}+\sigma(r_{e})>1.5\ \mathrm{kpc}$ and
$\overline{\mu}_{\mathrm{eff}}(g)+\sigma(\overline{\mu}_{\mathrm{eff}}(g))>25\
\mathrm{mag\ arcsec}^{-2}$, which takes the $1\sigma$ measurement error into
account. This definition is consistent with the original definition in van
Dokkum et al. (2015) for galaxies with Sérsic indices $n\sim 1$. There are 412
LSBG candidates that satisfy the UDG definition, and they are defined as our
UDG sample. As we argued in L22, the UDG definition does not consider the
dependence of galaxy size on galaxy mass. A UDG with $r_{e}=1.5$ kpc is an
outlier in size if its stellar mass is $10^{7}\ M_{\odot}$, but it will be
normal-sized if its stellar mass is $10^{8.5}\ M_{\odot}$. Therefore, UDGs are
not necessarily mass–size outliers. We propose the concept of ultra-puffy
galaxies, which are defined to lie $1.5\sigma$ above the average mass–size
relation of the satellite galaxies. Because we are interested in mass–size
outliers associated with MW analogs, we take the mass–size relation and its
scatter from Carlsten et al. (2021), which is derived from the satellites of
MW analogs in the Local Volume. The mass–size relation in Carlsten et al.
(2021) is measured for $10^{5.5}<M_{\star}/M_{\odot}<10^{8.5}$, and we
linearly extrapolate this relation to $M_{\star}\sim 10^{9}\ M_{\odot}$ to
select UPGs in this work. Among our LSBG candidates, we have 337 galaxies as
our sample of UPGs that fall $1.5\sigma$ above the average mass–size relation.
The UPGs are associated with 239 MW analogs.

###  2.2 Contamination correction

We note that the LSBGs are associated with the MW-like hosts only in
projection, so a certain fraction of them will be foreground or background
galaxies that happen to be close to the MW analogs in the sky. Therefore, we
apply a statistical interloper correction as follows. We randomly select a
continuous patch of the sky of 24 deg2 in HSC PDR2 regardless of whether it
contains MW analogs. Then we repeat the LSBG search in this area and apply the
same cuts as we described above to remove false positives. There are 480 LSBG
candidates in this area that represent possible contaminants for the UDG and
UPG samples. Because distances are needed to define the UDG and UPG classes,
we randomly match these 480 LSBGs with the 922 MW analogs that we have
surveyed. With such “artificial” associations, we calculate the corresponding
physical sizes and stellar masses and select UDGs and UPGs accordingly. Such
matching was repeated 200 times, and we obtain 7625 artificial UDGs and 8267
artificial UPGs. These UDGs and UPGs are “artificial” only in the sense of
being associated with random MW-like hosts. Therefore, the number densities of
artificial UDGs and UPGs are $S_{\rm UDG}=1.60\pm 0.25\ \mathrm{deg}^{-2}$ and
$S_{\rm UPG}=1.72\pm 0.23\ \mathrm{deg}^{-2}$, respectively. Equivalently, the
contamination fractions for both samples are $f_{\rm contam}^{\rm UDG}\approx
35\%\pm 5\%$ and $f_{\rm contam}^{\rm UPG}\approx 45\%\pm 6\%$. We have
checked that these fractions are not sensitive to the specific sky regions
used to construct the artificial UDG and UPG samples (L22). We will use these
values to correct the contribution from the foreground and background
interlopers when deriving the size and radial distributions in §3.1 and §3.2.

Furthermore, the contaminants might not be homogeneous in color and could bias
the color distribution, thereby changing the quenched fraction of the
mass–size outliers. If the artificial UDGs (UPGs) have different properties
from the real ones, we can use this information to derive a probability that
an object is a real UDG (UPG) at the proposed distance. Indeed, we find that
the $g-i$ color distribution of the “artificial” UDG (UPG) sample is bluer
than that of the observed UDG (UPG) sample. Specifically, the 25th, 50th, and
75th quantiles of the $g-i$ color are (0.50, 0.71, 0.82) for the real UPG
sample and are (0.42, 0.54, 0.72) for the artificial UPG sample. The color
distribution of the observed UDGs (UPGs) will thus be biased to be bluer
probably because interlopers such as field dwarfs and spiral LSBGs tend to be
blue. This motivates us to assign importance weights based on the $g-i$ color
distribution and the contamination fraction $f_{\rm contam}$.

Taking UDGs as an example, we first compute the normalized histograms of $g-i$
colors for both observed UDG and artificial UDG samples (denoted as
$\lambda_{k}^{\rm obs}$ and $\lambda_{k}^{\rm artificial}$, at the $(g-i)_{k}$
bin, where $\sum_{k}\lambda_{k}=1$). The weight assigned to UDGs in color bin
$(g-i)_{k}$ is then estimated to be $w_{k}=\max\,(1-f_{\rm contam}^{\rm
UDG}\lambda_{k}^{\rm artificial}/\lambda_{k}^{\rm obs},0)$. This weight stands
for the possibility of not being a contaminant. The weights of UPGs are
assigned following the same procedure. Such weights are applied when we
calculate the quenched fraction in §4. We test this method by generating a
population of mock UDGs (UPGs), adding a bluer population of contaminants, and
recovering the underlying UDG (UPG) color distribution and quenched fraction.
Such a mock test verifies that this color-based contamination subtraction is
sufficient for this work, and our main results are robust against
contamination subtraction.

##  3 Sample Characteristics

In this section, we present statistical analyses of the mass–size outliers to
gain a comprehensive understanding of the sample. We derive the size (§3.1)
and radial (§3.2) distributions, paving the way for the discussion of
quenching and environmental effects.

Figure 1: Size distribution of UDGs (left) and UPGs (right) hosted by MW
analogs. The contribution from the foreground and background contaminants
(gray dots) is subtracted, and the completeness effect has been corrected. We
fit a power law to the size distribution of UDGs and get a power law
$\mathrm{d}n/\mathrm{d}\log r_{e}\propto r_{e}^{-1.45\pm 0.20}$. By comparing
with the size distributions of UDGs in van der Burg et al. (2016, 2017), we
find that the power law becomes steeper as the average halo mass increases. It
is possible that denser environments provide stronger tidal forces and thus
produce more small UDGs. The UPG size distribution is suppressed at the
smaller-size end because small galaxies are not $1.5\sigma$ above the
mass–size relation and thereby not included as UPGs.

###  3.1 Size distribution

The size distribution of UDGs is an important topic, since it has been used to
test the formation scenarios of UDGs (e.g., Amorisco & Loeb, 2016; van der
Burg et al., 2017). In this section, we calculate the size distributions of
our UDG and UPG samples and compare them with the literature. We bin the sizes
on a logarithmic scale ($\log\,r_{e}$) and calculate the size distribution
$\mathrm{d}n/\mathrm{d}\log r_{e}$ as follows. First of all, we take the
artificial UDGs in the random fields (described in §2) and calculate their
size distribution per square degree as a proxy for contamination. For each
host, we calculate the size distribution of the associated UDGs, and we
multiply the contaminant size distribution by the virial area of the host and
subtract it from the UDG size distribution. We combine the UDG size
distributions for all hosts by taking the average size distribution, shown as
green pentagons in Figure 1. For reference, we plot the contaminant size
distribution in an average virial area as gray dots. The completeness is
calculated for each size bin, and the correction is applied. The final size
distribution is shown as red squares. Although the number of mass–size
outliers scales with stellar mass, we do not weight each host according to
stellar mass because the stellar masses of the hosts in our sample are quite
similar. The error shown in Figure 1 takes both the Poisson error and the
measurement error in size into account.

We find that the UDG size distribution roughly follows a power law. We then
fit a power law to our UDG size distribution and get
$\mathrm{d}n/\mathrm{d}\log r_{e}\propto r_{e}^{-1.45\pm 0.20}$. This is
shallower than the power laws presented in van der Burg et al. (2016,
$\mathrm{d}n/\mathrm{d}\log r_{e}\propto r_{e}^{-3.40\pm 0.19}$) and van der
Burg et al. (2017, $\mathrm{d}n/\mathrm{d}\log r_{e}\propto r_{e}^{-2.71\pm
0.33}$, shown as gray dashed-dotted lines in Figure 1), where they also
corrected for background contribution and completeness. Among others, van der
Burg et al. (2016) focused on large galaxy clusters and find a quite steep
power law; van der Burg et al. (2017) included less-massive groups and the
resulting power law is less steep. Combined with our findings, it might be
possible that a denser environment produces more small UDGs, probably due to
stronger tidal interactions.

The distribution of $\log\,r_{e}$ for UPGs is shown in the right panel of
Figure 1. The size distribution is no longer monotonic because the UPG sample
is constructed not by cutting at a certain size but by cutting along the
mass–size relation. Consequently, for a given mass, many small UDGs are not in
the UPG sample, since their sizes are not extreme on the mass–size plane. The
size distribution of the UPG sample is thus suppressed at the smaller size
end. We also split the UDG and UPG samples based on their host stellar masses
and distance to hosts. For UDGs, we consistently find shallow power laws with
indices of $\sim-1.5$, not depending on host stellar mass. Interestingly, we
do not find a significant change in the size distribution as UDGs (UPGs) get
closer to their hosts.

###  3.2 Radial distribution

Figure 2: Radial distributions of UDGs (left) and UPGs (right). We show the
radial distributions after subtracting the foreground and background
contamination (shown in teal) and correcting for completeness in each radial
distance bin (shown in red). After excluding $R<0.2\,R_{\rm vir}$ (shown in
lighter colors), we fit projected NFW and Einasto profiles to the radial
distributions and find good fits for both profiles. The radial distributions
of UDGs and UPGs are similar in shape. The best-fit NFW concentration is
consistent with an MW-mass halo, whereas the best-fit Einasto profiles have a
smaller concentration than MW-mass halos.

The spatial distribution of satellite galaxies around their host is proposed
as a good tracer of the host dark matter halo profile and thus is a probe of
environmental effects. Many studies have found that the radial distribution of
satellites can be well fit by a Navarro-Frenk-White (NFW; Navarro et al.,
1997) profile, although the radial distribution of satellites is a function of
host mass, satellite mass, and satellite color (e.g., van den Bosch et al.,
2005; Sales et al., 2007; Budzynski et al., 2012; Tal et al., 2012; Wang et
al., 2014; Carlsten et al., 2020; McDonough & Brainerd, 2022). On the other
hand, the radial distribution of satellites is a sensitive probe of many
physical processes, including reionization (Kravtsov et al., 2004) and tidal
disruption (Samuel et al., 2020). Subhalos can also be artificially disrupted
due to numerical issues in simulations (van den Bosch et al., 2018; Carlsten
et al., 2020), thus changing the radial distribution of satellites.
Furthermore, it is unclear whether the mass–size outliers follow the same
radial distribution as normal satellites (e.g., Tremmel et al., 2020). In
cluster environments, the number of UDGs is found to be depleted near the
centers of clusters, indicating that they are more likely to be disrupted near
the cluster center (e.g., van Dokkum et al., 2015; van der Burg et al., 2016;
Mancera Piña et al., 2018). The radial distribution of mass–size outliers in
groups is not as well explored. In this subsection, we derive the radial
distributions of the mass–size outliers, compare them with literature results,
and discuss possible implications.

We calculate the radial distribution as follows. For each host, we count the
number of UDGs (UPGs) in each radial bin scaled by $R_{\rm vir}$ and calculate
the number density of UDGs (UPGs) within each radial annulus. Since foreground
and background contaminants are distributed quite homogeneously in the sky,
their contribution to the observed radial distribution can be subtracted based
on the average contaminant density and the angular area occupied by the host.
Then we average over all hosts and correct for completeness. The final radial
distributions are shown in Figure 2. Red squares are the number of UDGs (UPGs)
per radial bin, and the error includes the Poisson, contamination subtraction,
and completeness errors. The radial distributions of both UDGs and UPGs turn
over at $R<0.2\,R_{\rm vir}$ (shown in lighter colors). Completeness may well
drop with proximity to the host due to the blending between the UDG and the
host galaxy or due to sky subtraction issues. Although we have corrected each
object for completeness based on size and surface brightness, it is still
possible that we have not fully corrected for radial incompleteness within a
halo. As we mentioned above, it is also possible that UDGs and UPGs are
depleted because of tidal disruption.

We fit the radial distributions of UDGs (UPGs) with the projected NFW and
Einasto (Einasto, 1965) profiles for $R>0.2R_{\rm vir}$ using colossus
(Diemer, 2018). The Einasto profile introduces an extra “shape” parameter
$\alpha_{\rm Ein}$ and has been argued to be a better description of dark
matter halo profiles in simulations (e.g., Navarro et al., 2004; Gao et al.,
2008; Navarro et al., 2010; Dutton & Macciò, 2014). The Einasto profile also
makes concentration estimates less sensitive to the radial range fitted. The
best-fit parameters are obtained using the least-squares method, and the
parameter uncertainty is from the estimated covariance matrix of the
parameters. The best-fit NFW (blue) and Einasto (red) profiles are shown in
Figure 2 as solid lines. The best-fit Einasto profile from van der Burg et al.
(2016) is shown as the dashed gray line.

Compared with van der Burg et al. (2016), there are more UDGs at smaller
radial distances in our sample; thus, the UDG radial distribution is more
concentrated, even though we exclude $R<0.2\ R_{\rm vir}$. van der Burg et al.
(2016) found that the radial distribution of UDGs cannot be well described by
an NFW profile, but an Einasto profile does provide a good fit to the data.
Unlike van der Burg et al. (2016), we find that both the NFW and Einasto
profiles describe the radial distribution of UDGs (UPGs) quite well. The
concentration of the best-fit NFW profile is $c_{\rm
NFW,UDG}=10.0^{+4.5}_{-3.3}$ for UDGs and $c_{\rm NFW,UPG}=8.5^{+5.2}_{-3.2}$
for UPGs. The best-fit Einasto profile has $\alpha_{\rm
Ein,UDG}=0.33^{+0.35}_{-0.17},\ c_{\rm Ein,UDG}=4.02^{+3.98}_{-2.00}$ for UDGs
and $\alpha_{\rm Ein,UPG}=0.34^{+0.55}_{-0.20},\ c_{\rm
Ein,UPG}=3.70^{+4.77}_{-2.08}$ for UPGs. The radial distribution profiles of
UDGs and UPGs are found to be very similar in shape. Our best-fit Einasto
profiles have lower $\alpha$ and higher concentration compared with van der
Burg et al. (2016), where they have $\alpha_{\rm
Ein,UDG}=0.92^{+0.08}_{-0.18},\ c_{\rm Ein,UDG}=1.83^{+0.13}_{-0.12}$.

According to the concentration–mass relation of dark matter halos, the
concentration of an MW-like halo is $c_{\rm NFW}\sim 10$ (e.g., Bullock et
al., 2001; Duffy et al., 2008; Dutton & Macciò, 2014; Diemer & Joyce, 2019).
The Einasto shape parameter for an MW-like halo is $\alpha_{\rm Ein}\sim 0.15$
at $z=0$ and its concentration is $c_{\rm Ein}\sim 8-10$ (Gao et al., 2008;
Dutton & Macciò, 2014). From Figure 2, the best-fit NFW profiles for the
radial distributions agree with the MW-like halo in terms of concentration,
but the best-fit Einasto profiles have lower concentration compared with MW-
like halos. This agrees with the fact that the concentration of the satellite
radial distribution is lower than that of the halo (e.g., McDonough &
Brainerd, 2022). We notice that the errors of the best-fit parameters are
large due to the sample size and also the fact that concentration is most
sensitive to data at smaller radial distances, which are excluded from the
analysis. A larger, cleaner, and more complete sample is needed to better
constrain the radial distributions.

Figure 3: Distribution of UDGs (left) and UPGs (right) on the mass–size plane.
We classify galaxies into quiescent and star-forming based on a mass-dependent
color cut. The average mass–size relation and $1.5\sigma$ above it are shown
in green. The solid lines are constant surface brightness cuts at
$\overline{\mu}_{\mathrm{eff}}(g)=25\ \mathrm{mag\ arcsec}^{-2}$ for two
different colors $g-i=0.4$ (blue) and $g-i=0.8$ (red). The UDG sample includes
a significant number of galaxies that are not mass–size outliers (falling
below the $1.5\sigma$ line) that are red in color because the surface
brightness cuts are different on the mass–size plane for blue and red
galaxies.

##  4 Quenching

As argued in §1, the star-forming properties of mass–size outliers are an
interesting subject given their diffuse stellar components and unknown
formation history. In this section, we first discuss how to define “quenching”
for our sample and present the distribution of mass–size outliers on the
mass–size plane (§4.1). Then we study the quiescent fractions for UDGs and
UPGs as a function of stellar mass and host properties and compare them with
other observations and simulations (§4.2). We discuss how these results would
imply the formation and quenching of mass–size outliers in §5.

###  4.1 Quenching criteria

In principle, direct estimates of the current star formation rate (SFR) from
UV or H$\alpha$ or estimates for the H I gas are needed to define whether a
satellite is quenched. For example, the SAGA survey (Geha et al., 2017; Mao et
al., 2021) measures the H$\alpha$ equivalent width (EW) from spectra to define
quenched satellites. There are also many studies trying to probe H I for star-
forming satellites in the Local Group (e.g., Grcevich & Putman, 2009; Spekkens
et al., 2014; Putman et al., 2021; Karunakaran et al., 2022b; Zhu & Putman,
2023) and derive the quiescent fraction. However, due to the low surface
brightness and low luminosity nature of our mass–size outliers, obtaining such
measurements is extremely expensive over the full footprint of our sample.
Therefore, we seek other indicators for SFR, including the broadband colors
and morphology.

The ELVES survey (Carlsten et al., 2022a) searches for satellite galaxies of
30 MW-like hosts in the Local Volume ($D<12$ Mpc). Carlsten et al. (2022a)
visually inspected all satellites in the ELVES survey and classified them into
early-type (red and smooth) and late-type (blue, asymmetric, clumpy). Using
this sample, they found that a mass-dependent color cut $(g-i)_{Q}=-0.067\cdot
M_{V}-0.23$ could divide the sample into two subsets that are nearly identical
to the early and late types based on morphology. Carlsten et al. (2022a)
derived the quenched fraction of the ELVES satellites using such a color cut
and showed that the resulting quenched fractions are very similar to the
morphology-based quenched fractions. Furthermore, Font et al. (2022) showed
that this color cut effectively separates star-forming galaxies from quiescent
ones in simulations that are not fine-tuned to match the observed properties
of ELVES galaxies. Therefore, we use this color cut to define quenched
galaxies among our mass–size outliers: galaxies that are redder than
$(g-i)_{Q}$ are defined as quenched, whereas bluer galaxies are defined as
star-forming. To apply the color cut, we derive the $V$-band apparent
magnitude following $V=g-0.5784\cdot(g-r)-0.0038$ 222This relation was derived
for SDSS filters. We neglect the small difference between SDSS and HSC filter
systems.
http://classic.sdss.org/dr4/algorithms/sdssUBVRITransform.html#Lupton2005 and
convert it to absolute magnitude $M_{V}$. For comparison with ELVES and SAGA
(Figures 4, 5, 6), we use the same color cut to maintain consistency.

Before calculating the quenched fraction, we first look at the distributions
of mass–size outliers on the mass–size plane, as shown in Figure 3. This
figure is similar to Fig. 5 in L22 but here we highlight the quiescent
galaxies in red and star-forming galaxies in blue to emphasize how the star
formation properties differ between the two samples. The average mass–size
relation from Carlsten et al. (2021) and the $1.5\sigma$ line above it are
shown in green. The blue and red solid lines show the constant surface
brightness line ($\overline{\mu}_{\mathrm{eff}}(g)=25\ \mathrm{mag\
arcsec}^{-2}$) for galaxies with $g-i=0.4$ and $0.8$ respectively. The two
colors are chosen as examples to highlight the dependence of surface
brightness cut on galaxy color; for a given stellar mass, a bluer galaxy must
have a larger size to be considered as a UDG. Compared with the UPG sample, we
find that the UDG sample includes many galaxies that are below the $1.5\sigma$
line and quiescent. Red galaxies dominate the region below the $1.5\sigma$
line because blue galaxies do not satisfy the surface brightness cut in the
UDG definition. In contrast, the UPG sample is comprised of many star-forming
galaxies at the high-mass end.

###  4.2 Quenched fractions

In this section, we study the quenched fraction as a function of satellite
stellar mass. We divide the stellar mass range
$6.4<\log\,M_{\star}/M_{\odot}<9.0$ into eight bins and calculate the fraction
of quiescent galaxies for each bin. Both the denominator and numerator are
weighted by the importance weight $w_{k}$ which represents the likelihood of
not being a contaminant (see §2.2). We also apply completeness corrections to
the denominator and numerator. Not applying the importance weights will make
the quenched fraction lower, since the background contaminants are bluer, on
average, than UDGs and UPGs.

Figure 4: Quenched fractions of UDGs (gray) and UPGs (green) as a function of
their stellar masses. The results from ELVES (Carlsten et al., 2022a) and SAGA
(Mao et al., 2021) are also shown for comparison, where quenched fractions are
all defined based on the mass-dependent color cut and are corrected for
incompleteness following Mao et al. (2021). We find that UDGs have a high
quenched fraction that changes little over a wide range of stellar mass. On
the contrary, the quenched fraction of UPGs is lower and decreases with
increasing satellite stellar mass. Given their large sizes, UPGs have a
similar quenched fraction to the normal satellites of MW analogs in ELVES.

Figure 5: Same as Figure 4, but the samples are divided into subsets based on
the projected distance to the host $R/R_{\rm vir}$ (top panels) and host $g-i$
color (bottom panels), shown as dashed red and blue lines. The quenched
fraction is larger for those associated with redder hosts and those that are
closer to the host.

We plot the quenched fractions $f_{q}$ of the full UDG (gray) and UPG (green)
samples in Figure 4. The error bars correspond to the $1\sigma$ Bernoulli
standard error. We plot the UPG quenched fraction above $M_{\star}>10^{8.5}\
M_{\odot}$ with lighter colors to emphasize where we extrapolate the mass–size
relation in Carlsten et al. (2021) to define UPGs. The quenched fraction of
UDGs is high ($f_{q}\sim 0.8$) and weakly depends on the stellar mass. Goto et
al. (2023) also find a high quenched fraction for UDGs among the satellites of
MW analogs in the SMUDGes survey. On the contrary, for UPGs, the quenched
fraction is lower than that of UDGs and decreases more rapidly with increasing
stellar mass. Lower-mass UPGs ($M_{\star}\sim 10^{7}\ M_{\odot}$) are mostly
quiescent, roughly half of the intermediate-mass UPGs ($M_{\star}\approx
10^{8}\ M_{\odot}$) are quenched, and higher-mass UPGs ($M_{\star}>10^{8.5}\
M_{\odot}$) are mostly star-forming. Such distinctions in quenched fractions
highlight that UDGs and UPGs select different subsets of the satellite
population. In §5.1, we argue that the high quenched fraction of UDGs is
merely an artifact of the UDG definition.

We compare the quenched fractions of mass–size outliers (UDGs and UPGs) with
those of the satellites of MW analogs in the Local Volume (ELVES; orange line)
and the nearby Universe (SAGA; gray squares). Following Carlsten et al.
(2022a), the quenched fractions of ELVES and SAGA are calculated based on the
same color cut as we use for mass–size outliers333We note that some galaxies
in ELVES and SAGA data only have $g-r$ color because certain surveys might not
have $i$-band data. Carlsten et al. (2022a) converted $g-r$ color to $g-i$
following their Eqn. (1) in Carlsten et al. (2021) that is derived from simple
stellar population models. Thus, the quenched fraction of SAGA in Figure 4 is
slightly lower than the values in Fig. 11 of Mao et al. (2021), where their
quenched fraction is defined based on the detection of H$\alpha$. The quenched
fractions of SAGA and ELVES are all corrected for incompleteness. We note that
the error bars of the SAGA quenched fraction in Figure 4 are smaller than the
ones in Mao et al. (2021). The tip of the light green error bar in Fig. 11 of
Mao et al. (2021) is derived assuming that all potential satellites without a
redshift detection are real quenched satellites. In our case, we adopt the
satellite probability for each redshift failure from Mao et al. (2021) and
then apply a color cut to both spectroscopically confirmed and nonconfirmed
dwarfs, resulting in a smaller upper bound of the quenched fraction. Overall,
the SAGA quenched fraction is lower than that of ELVES and the MW and M31. As
suggested by Carlsten et al. (2022a), the difference in both luminosity
function and quenching could be naturally explained if the SAGA sample is
preferentially missing $\sim 1-1.5$ satellites per host, and quiescent
galaxies are fainter than star-forming ones at a fixed stellar mass (see also
Font et al., 2022; Greene et al., 2023).

From Figure 4, the quenched fraction of UDGs is higher than that of normal
satellites in ELVES and SAGA, especially at the high-mass end ($M_{\star}\sim
10^{8}\ M_{\odot}$). However, the quenched fraction of UPGs agrees with ELVES
reasonably well at $7<\log\,M_{\star}/M_{\odot}<8.2$. At the higher-mass end
($\log\,M_{\star}/M_{\odot}>8.4$), the UPG quenched fraction agrees with SAGA
but is lower than ELVES, with a caveat that the mass–size relation we use
might not be valid in this mass range. Overall, it is surprising that UPGs,
being mass–size outliers, have a similar quenched fraction as the normal-sized
satellites of MW analogs.

We further divide the sample based on the projected radial distance to the
host $R/R_{\rm vir}$ and the host $g-i$ color. As shown in the top panels of
Figure 5, we find that UDGs (UPGs) that are closer to their hosts have higher
quenched fractions. The average difference in quenched fractions between the
two radial bins is $\sim 0.1$ for UDGs and $\sim 0.2$ for UPGs. This trend
agrees with the findings in Greene et al. (2023) and Karunakaran & Zaritsky
(2023) for normal satellites in the ELVES survey. From the bottom panels of
Figure 5, we find that UDGs (UPGs) hosted by redder hosts also have a higher
quenched fraction. The difference in quenched fractions between the two host
color bins is $\sim 0.2$ for UDGs. But the host color has a smaller impact
than the distance to the host on the quenched fraction of UPGs. Additionally,
we divide the samples based on the host stellar mass and redshift but do not
find a significant difference in quenched fractions.

Figure 6: Left: quenched fractions of UPGs in this work and in the ELVES
survey. We select UPGs from the ELVES sample and calculate the quenched
fraction, shown as the brown line. The quenched fraction of UPGs in this work
is highlighted in green, while the quenched fraction of the whole ELVES sample
is shown in orange. We do not find a significant dependence of the quenched
fraction on the size of satellites by comparing UPGs with the bulk of the
satellites. Right: comparisons with simulations of satellites in MW analogs.
The purple line and pink line show the quenched fractions produced in the
ARTEMIS (Font et al., 2022) and FIRE-2 (Samuel et al., 2022) simulations,
respectively. The quenched fraction of UPGs agrees quite well with that of
normal-sized satellites in simulations.

As a sanity check, we select UPGs in the ELVES sample and calculate the
quenched fraction, shown as the brown line in the left panel of Figure 6. Out
of the 313 ELVES satellites that have secure distances around hosts that are
mapped out to $R>200$ kpc, there are 27 UPGs (see Greene et al., 2023).
Despite the number of UPGs in ELVES being small, the quenched fraction of
ELVES UPGs agrees with that of our UPG sample (green line) quite well. We also
do not find a significant difference between the quenched fraction of the
whole ELVES sample from that of ELVES UPGs.

We compare the quenched fraction of UPGs with the simulation results from
ARTEMIS (purple lines in Figure 6; Font et al., 2022) and FIRE-2 (pink lines
in Figure 6; Samuel et al., 2022), which focus on studying normal-sized
satellites of MW analogs. The quenched galaxies in these simulations are
defined as those with no instantaneous (for ARTEMIS) or recent ($<200$ Myr for
FIRE-2) star formation.444Font et al. (2022) found a similar quenched fraction
for ARTEMIS when using the same color cut as we do. We select ARTEMIS and
FIRE-2 among other simulations because they roughly cover the highest and
lowest quenched fraction for MW satellites produced in simulations (see Fig.
13 in Samuel et al. 2022 for a compilation). Since none of these data sets are
designed to study mass–size outliers, their quenched fractions are presumably
dominated by normal-sized satellites. As shown in the right panel of Figure 6,
our UPG quenched fraction agrees best with ARTEMIS but is also consistent with
the FIRE-2 result. We discuss the implications of these results in §5.2.

##  5 Discussion

###  5.1 The High Quenched Fraction of UDGs Is an Artifact

In L22, we propose the concept of ultra-puffy galaxies (UPGs) as a means to
robustly study mass–size outliers. Compared with the UDG selection, UPGs are
not selected via a constant cut in half-light radius. The UPG selection
considered the fact that the average sizes of satellite galaxies increase with
stellar mass following a mass–size relation. There are many UDGs that are not
outliers with respect to the mass–size relation. Thus, the UPGs better
represent the tail of the satellite size distribution. Moreover, for a given
stellar mass and size, blue galaxies have brighter surface brightness than red
galaxies because red galaxies have a higher mass-to-light ratio. As a
consequence, blue galaxies will be preferentially excluded if one applies a
hard cut on surface brightness, as in the definition of UDG. As seen in Figure
3, the UDG sample includes a number of galaxies below the $1.5\sigma$ line,
and these galaxies are mostly red and quenched, therefore giving rise to a
high quenched fraction in Figure 4. This high quenched fraction of UDGs
compared to normal-sized dwarfs is just an artifact of the UDG definition. The
hard size cut and surface brightness cut make it difficult to directly compare
the red and blue galaxy populations and hamper the study of diffuse galaxies.
The cut at $1.5\sigma$ above the average mass–size relation does not
discriminate blue or red galaxies but just selects size outliers at a given
stellar mass. The UPGs are physically motivated and naturally represent the
large-size tail of satellite galaxies in MW analogs.

We note that Lim et al. (2020) defined UDGs in the Virgo cluster as the
outliers of the scaling relations of Virgo satellites. However, in clusters,
the difference between such a definition and the fiducial UDG definition in
van Dokkum et al. (2015) becomes minor because nearly all UDGs are red and
quenched. Nevertheless, we advocate studying outliers of scaling relations,
including UPGs, which provide an unbiased perspective on the formation and
evolution of diffuse dwarf galaxies.

###  5.2 Formation and Quenching of mass–size Outliers

In this paper, we study the mass–size outliers associated with MW analogs in
the nearby Universe. We calculate the quenched fraction of UPGs in L22 and
compare it with the ELVES survey, the SAGA survey, and numerical simulations.
One key finding is that UPGs have a similar quenched fraction as those normal-
sized satellites of MW analogs in the Local Volume (ELVES; Figure 4) and
numerical simulations (ARTEMIS and FIRE-2; Figure 6). We also check the
quenched fraction of UPGs among ELVES satellites and find similar results
(Figure 6). In addition, the radial distribution of mass–size outliers can be
well described by an NFW (or Einasto) profile at $R>0.2\ R_{\rm vir}$. Thus,
it is intriguing that despite being selected as outliers in size, UPGs are
acting like “normal” satellites in terms of quenched fraction and radial
distribution. Furthermore, Carlsten et al. (2021) found that the mass–size
relation of satellites in MW analogs does not depend on the morphology or
color of the satellites. All of these pieces of evidence suggest that, for
satellites in MW analogs, quenching is not tied to being a mass–size outlier.
Quenching and morphological transformation might involve very mild size
evolution.

We are left with the question of what physical processes are responsible for
puffing up satellites and quenching them such that quenching and size growth
happen separately. If the mass–size outliers were normal-sized before falling
into the group, then tidal interactions are believed to puff them up. Jiang et
al. (2019) found that in simulations, the UDGs in groups are accreted as
either UDGs from the field or normal dwarfs but tidally heated near the
orbital pericenter. Tremmel et al. (2020) studied simulated UDGs in the
cluster environment and found that UDGs with higher mass ($M_{\star}>10^{8}\
M_{\odot}$) are puffed up suddenly due to tidal heating at the pericenter, but
UDGs with lower mass ($M_{\star}\sim 10^{7.5}\ M_{\odot}$) are gradually
puffed up due to adiabatic expansion as a response to the mass loss from tidal
and ram pressure stripping. In this scenario, normal-sized star-forming dwarf
galaxies are accreted from the field, then consequently puffed up by strong
tidal interactions. If so, we would expect a higher quenched fraction for
mass–size outliers, since they must have undergone violent ram pressure
stripping near the pericenter or lost gas due to tidal stripping. This
contradicts our results in Figure 4.

On the other hand, the mass–size outliers can be puffed up when they are still
in the field. For example, bursty stellar feedback can cause the stellar
component of the dwarf galaxy to expand (e.g., Di Cintio et al., 2017; Chan et
al., 2018; Carleton et al., 2019; Jiang et al., 2019; Martin et al., 2019).
Analytical models also support a scenario where UDGs originate from a
population of dwarf galaxies residing in halos with higher spin (Dalcanton et
al., 1997; Amorisco & Loeb, 2016; Rong et al., 2017; Liao et al., 2019).
Wright et al. (2021) showed that field UDGs can also be formed from major
mergers that cause star formation to migrate outward. If mass–size outliers
are already puffed up prior to infall, in order to achieve a similar quenched
fraction as normal satellites, they must remain star-forming after being
puffed up such that they can be quenched together with normal satellites.
Wright et al. (2021) showed that an early merger does not significantly change
the total SFR. Samuel et al. (2022) showed that preprocessing can boost the
quenched fraction by 20% at $M_{\star}\approx 10^{8}\ M_{\odot}$ and merely
change the quenched fraction for lower-mass satellites. Although it is not
clear whether the high halo spin is the cause or the consequence of UPG
formation, it is probable that a higher halo spin does not quench a UPG. If
any of these mechanisms can only increase the size to make UPGs but not quench
them when they are still in the field, it provides a plausible way to produce
the observed trend in Figures 4 and 6.

Mass–size outliers and normal satellites might be quenched together after
falling into the group. It is not obviously clear whether they are quenched
mainly by tidal or ram pressure stripping. In the tidal stripping scenario,
the dark matter needs to be removed before a significant fraction of stars
and/or gas can be stripped by tidal forces, indicating a longer quenching
timescale. Jiang et al. (2019) argued that if tidal stripping dominates the
quenching of UDGs, the satellites closer to the host will have a smaller
stellar mass and effective radius, since stars are also stripped. They found
no such trend in simulations of group environments. In §3.1, we split the
UDG/UPG samples into two radial distance bins but do not find a significant
change in size or stellar mass distribution as the mass–size outliers get
closer to the host. This suggests that tidal stripping does not dominate the
quenching of UDGs and UPGs in MW analogs.

Many studies support the idea that ram pressure stripping is the dominant
quenching mechanism for normal-sized satellites with $M_{\star}<10^{8.0}\
M_{\odot}$ (e.g., Tonnesen & Bryan, 2009; Jaffé et al., 2015; Simpson et al.,
2018; Akins et al., 2021; Wang et al., 2021; Samuel et al., 2022). In the
Auriga simulations, for instance, Simpson et al. (2018) showed that the
quenched fraction of satellites $M_{\star}<10^{8}\ M_{\odot}$ have a strong
dependence on the distance to the hosts, and they considered ram pressure
stripping as the main quenching mechanism. Using the FIRE-2 simulation, Samuel
et al. (2022) also showed that the quenched fraction increases as the distance
to the host decreases, and hosts with higher CGM mass have more quenched
satellites. Such trends are also found in observations (e.g., Greene et al.,
2023; Karunakaran et al., 2022a). In Figure 4, by comparing UDGs and UPGs at
two radial bins, we find a very similar trend that satellites that are closer
to the host are more quiescent. Although we are not able to derive a quenching
timescale to better compare with simulations, we consider our results to be
consistent with the ram pressure stripping scenario.

In Figure 5, we also find that UDGs and UPGs associated with redder hosts are
more quiescent than those in bluer hosts, although the trend is less
significant for UPGs. This trend agrees with “galaxy conformity,” which refers
to the excess of early-type satellites in the vicinity of early-type central
galaxies compared to satellites around late-type centrals (Weinmann et al.,
2006). Wang & White (2012) argued that galaxy conformity arises because
quiescent centrals occupy more massive halos than star-forming centrals. More
massive halos have more hot gas and stronger tidal fields, leading to more
efficient quenching. If quiescent centrals are in older halos, their
satellites tend to be accreted earlier and thus have more time to be quenched.
Based on such models, the galaxy conformity signals from UDGs and UPGs make
sense if they are puffed up before the infall and quenched together with
normal satellites due to ram pressure stripping.

The efficiency of ram pressure stripping also depends on the stellar mass
density, which provides the restoring force and the gas mass density. The
diffuse stellar component might make mass–size outliers more vulnerable to ram
pressure and tidal stripping. However, Kado-Fong et al. (2022) found in
observations that although UDGs have a more diffuse stellar component, they
harbor the same amount of H I gas as normal dwarfs with similar stellar sizes.
Equivalently, for a given stellar mass, UDGs (UPGs) have higher H I mass than
normal dwarfs. Thus, even if UDGs and UPGs are more vulnerable to ram pressure
stripping, they have more gas to be stripped. It is probable that the net
effect of low stellar mass density and high H I mass is that UPGs have a
similar quenched fraction as normal satellites. Of course, the origin and
evolution of the mass–size outliers in MW analogs could also be a mixture of
many scenarios. Using our observations, it is hard to sort out the detailed
mechanisms for quenching and size growth. More detailed observations and
simulations are needed to solve this intriguing puzzle.

##  6 Summary

In this work, we present a statistical analysis of mass–size outliers among
the satellite galaxies of MW analogs at $0.01<z<0.04$ based on the sample from
L22. Besides the ultra-diffuse galaxies (UDGs), we study “ultra-puffy
galaxies” (UPGs), which are defined to lie $1.5\sigma$ above the average
mass–size relation and better represent the large-size tail of the dwarf
galaxy population. We derive the size distribution (§3.1), radial distribution
(§3.2), and quenched fractions (§4) of mass–size outliers (UDGs and UPGs) and
discuss implications on their formation and evolution (§5). We summarize our
main findings and prospects as follows.

  1. 1.

The size distribution of UDGs follows a power law $\mathrm{d}n/\mathrm{d}\log
r_{e}\propto r_{e}^{-1.45\pm 0.20}$ which is shallower than the UDG size
distribution in larger groups and clusters (e.g., van der Burg et al., 2016,
2017). Since the UPG sample includes fewer small satellites, its size
distribution is suppressed at the smaller-size end (Figure 1). We do not find
significant dependence of size distribution on the host stellar mass or the
distance to the host.

  2. 2.

The radial distributions of UDGs and UPGs can be described by projected NFW
and Einasto profiles (Figure 2). UDGs and UPGs follow similar radial
distributions. We find that the best-fit NFW profiles have concentrations
similar to that of an MW-mass halo. The best-fit Einasto profiles are less
concentrated than MW-mass halos.

  3. 3.

The UDGs have a very high quenched fraction ($\sim 70\%$) that remains roughly
constant over 1 dex in satellite stellar mass (Figure 4). However, for UPGs,
the quenched fraction shows a strong dependence on satellite stellar mass; 80%
of UPGs are quiescent at the lower-mass end $M_{\star}=10^{6.8}\ M_{\odot}$,
but the fraction drops to 20% at $M_{\star}=10^{8.5}\ M_{\odot}$. Almost half
of UPGs are quenched at $M_{\star}\approx 10^{8}\ M_{\odot}$. The quenched
fractions of both UDGs and UPGs increase as satellites get closer to the
hosts, agreeing with the trends of normal-sized satellites (Greene et al.,
2023; Karunakaran et al., 2022a). Redder hosts also harbor more quenched
mass–size outliers, showing evidence for “galaxy conformity.”

  4. 4.

Surprisingly, although UPGs have a much larger size than “normal” satellites
of similar stellar mass, they show a similar quenched fraction as the normal-
sized satellites in MW analogs (Figure 6). The UPG quenched fraction is
consistent with the results from both observations (ELVES) and simulations
(ARTEMIS, FIRE-2) for normal-sized satellites. Such a null trend of the
quenched fraction on the size of satellites indicates that the quenching and
size evolution of mass–size outliers happen separately in MW-like
environments. It is plausible that these mass–size outliers are puffed up in
the field before accretion and quenched together with normal satellites
(§5.2).

  5. 5.

We argue that the high and constant quenched fraction for UDGs is merely an
artifact of the UDG definition, where the constant surface brightness cut
preferentially selects more red galaxies (Figure 3). We demonstrate that the
more physically motivated UPG selection does not introduce artifacts in the
mass–size distribution and better represents the large-size tail of the dwarf
galaxy population.

## Acknowledgment

We thank the anonymous reviewer for useful comments that make the manuscript
much clearer. J.L. is grateful for the discussions with Meng Gu, Frank van den
Bosch, and Sihao Cheng. J.L. also thanks David Tao and his Soul Power live
album. J.E.G gratefully acknowledges support from NSF grant AST-1007052. S.D.
is supported by NASA through Hubble Fellowship grant HST-HF2-51454.001-A
awarded by the Space Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy, Incorporated, under
NASA contract NAS5-26555.

The Hyper Suprime-Cam (HSC) collaboration includes the astronomical
communities of Japan and Taiwan and Princeton University. The HSC
instrumentation and software were developed by the National Astronomical
Observatory of Japan (NAOJ), Kavli Institute for the Physics and Mathematics
of the Universe (Kavli IPMU), University of Tokyo, High Energy Accelerator
Research Organization (KEK), Academia Sinica Institute for Astronomy and
Astrophysics in Taiwan (ASIAA), and Princeton University. Funding was
contributed by the FIRST program from the Japanese Cabinet Office, Ministry of
Education, Culture, Sports, Science and Technology (MEXT), Japan Society for
the Promotion of Science (JSPS), Japan Science and Technology Agency (JST),
Toray Science Foundation, NAOJ, Kavli IPMU, KEK, ASIAA, and Princeton
University. The authors are pleased to acknowledge that the work reported on
in this paper was substantially performed using the Princeton Research
Computing resources at Princeton University, which is a consortium of groups
led by the Princeton Institute for Computational Science and Engineering
(PICSciE) and the Office of Information Technology’s Research Computing.

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