# The morphological mix of dwarf galaxies in the nearby Universe

I. Lazar1, S. Kaviraj1, A. E. Watkins1, G. Martin2,3,4, B. Bichang’a1 and R.
A. Jackson5
1Centre for Astrophysics Research, University of Hertfordshire, College Lane,
Hatfield AL10 9AB, UK
2School of Physics and Astronomy, University of Nottingham, University Park,
Nottingham NG7 2RD, UK
3Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu,
Daejeon 34055, Korea
4Steward Observatory, University of Arizona, 933 N. Cherry Ave, Tucson, AZ
85719, USA
5Department of Physics and Astronomy, University of Victoria, Victoria, BC,
Canada V8P 5C2
E-mail<EMAIL_ADDRESS>
###### Abstract

We use a complete, unbiased sample of 257 dwarf (108 M⊙ < M⋆ < 109.5 M⊙)
galaxies at $z<0.08$, in the COSMOS field, to study the morphological mix of
the dwarf population in low-density environments. Visual inspection of
extremely deep optical images and their unsharp-masked counterparts reveals
three principal dwarf morphological classes. 43 and 45 per cent of dwarfs
exhibit the traditional ‘early-type’ (elliptical/S0) and ‘late-type’ (spiral)
morphologies respectively. However, 10 per cent populate a ‘featureless’
class, that lacks both the central light concentration seen in early-types and
any spiral structure - this class is missing in the massive-galaxy regime. 14,
27 and 19 per cent of early-type, late-type and featureless dwarfs
respectively show evidence for interactions, which drive around 20 per cent of
the overall star formation activity in the dwarf population. Compared to their
massive counterparts, dwarf early-types show a much lower incidence of
interactions, are significantly less concentrated and share similar rest-frame
colours as dwarf late-types. This suggests that the formation histories of
dwarf and massive early-types are different, with dwarf early-types being
shaped less by interactions and more by secular processes. The lack of large
groups or clusters in COSMOS at $z<0.08$, and the fact that our dwarf
morphological classes show similar local density, suggests that featureless
dwarfs in low-density environments are created via internal baryonic feedback,
rather than by environmental processes. Finally, while interacting dwarfs can
be identified using the asymmetry parameter, it is challenging to cleanly
separate early and late-type dwarfs using traditional morphological
parameters, such as ‘CAS’, M20 and the Gini coefficient (unlike in the
massive-galaxy regime).

###### keywords:

galaxies: formation – galaxies: evolution – galaxies: dwarf – galaxies:
structure

††pubyear: 2024††pagerange: The morphological mix of dwarf galaxies in the
nearby Universe–A

##  1 Introduction

Morphology is a fundamental parameter in observational astrophysics, which is
strongly correlated with the evolution of galaxies. In the massive-galaxy (M⋆
> 109.5 M⊙) regime, the principal morphological classes are well described by
the classical ‘Hubble sequence’ (Hubble, 1936): ‘early-type’ galaxies (ETGs),
which include S0 and elliptical systems, and ‘late-type’ galaxies (LTGs),
which include different types of disc (spiral) galaxies. Many studies have
shown that, in massive galaxies, these morphological types differ not only in
their structural characteristics but also in their physical properties, such
as colour, star formation rate (SFR) and stellar mass (e.g. Conselice et al.,
2014; Martin et al., 2018; Sampaio et al., 2022). ETGs, which are more
pressure-supported than LTGs, typically exhibit low SFRs, red colours and high
stellar masses (e.g. Bernardi et al., 2003; Kaviraj et al., 2007; Cappellari
et al., 2013). LTGs, which are largely supported by rotation (and exhibit
spiral arms as a result), typically exhibit higher SFRs, blue colours and
lower stellar masses.

Morphology encodes key information about the dominant physical processes that
have shaped the formation of galaxies. The general consensus, in the massive-
galaxy regime, is that LTGs largely form via secular cold gas accretion (White
& Rees, 1978; Fall & Efstathiou, 1980) and experience either a relatively
quiet history (e.g. Jackson et al., 2022) or a larger fraction of gas-rich
(and mainly prograde) mergers that helps maintain their discy morphologies and
relatively high SFRs over their lifetimes (e.g. Martin et al., 2018). ETGs, on
the other hand, are thought to be the end products of multiple minor or major
mergers (e.g. Martin et al., 2018) and, in high density environments, also
experience processes that promote gas depletion, such as tidal interactions
(Moore et al., 1998; Jackson et al., 2021) and ram pressure stripping (Walker
et al., 1996; Martin et al., 2019; Jackson et al., 2021).

A wide array of methods have traditionally been used to determine the
morphology of galaxies (where some notable innovative studies include the work
done in e.g. de Vaucouleurs, 1959; Sandage, 1961; Buta & Combes, 1996). Direct
visual inspection of galaxy images, whilst the most time-consuming, produces
accurate classifications (e.g. Lintott et al., 2011; Kaviraj, 2014), against
which automated methods are often calibrated. The classification of galaxies
in large surveys typically requires automation, which is often achieved using
both parametric and non-parametric methods. A commonly used parametric method
for distinguishing between early and late-type galaxies is fitting Sérsic
indices (Sérsic, 1963) using galaxy surface brightness profiles (e.g. Bottrell
et al., 2019). In massive galaxies, the steeper profiles of ETGs results in
them having larger values of the Sérsic index ($n$ > 2.5), while LTGs
typically exhibit indices lower than this value (e.g. Shen et al., 2003).

While parametric techniques require the assumption of a fitting function (such
as a Sérsic profile), many non-parametric methods have been successfully used
to measure morphology from survey data. The pioneering studies of Conselice
(2003, C03 hereafter), Abraham et al. (2003) and Lotz et al. (2004, L04
hereafter) introduced five such morphological parameters which have been
widely used in galaxy morphological classification in the literature:
concentration, asymmetry and clumpiness (known collectively as the ‘CAS’
system), M20 and the Gini coefficient (e.g. Pearson et al., 2021). Many
studies that probe optical and near-infrared images, particularly in the
nearby Universe where galaxies are well resolved, show that massive ETGs
exhibit higher concentration, lower asymmetry and lower clumpiness than their
LTG counterparts (e.g. Conselice, 2003; Holwerda et al., 2014; Cheng et al.,
2021).

Mergers and tidally-disturbed systems typically show the highest values of
asymmetry, while galaxies undergoing starbursts typically show the highest
values of clumpiness (e.g. Conselice, 2003). The Gini – M20 space in the
optical wavelengths offers a reliable discriminant, at least in the massive-
galaxy regime, both between early and late type galaxies and between
interacting systems and their non-interacting counterparts (e.g. Lotz et al.,
2004, 2008). Similar results have been found in the near-infrared (Holwerda et
al., 2014), which is less sensitive to dust obscuration (and therefore a more
reliable indicator of the underlying structure of the system), using galaxies
from the local Universe in the Spitzer Survey of Stellar Structure in Galaxies
(S4G) (Sheth et al., 2010). Forthcoming ‘Big Data’ surveys, from instruments
like the Rubin Observatory’s LSST (Ivezić et al., 2019) and Euclid (Laureijs
et al., 2010), will present unique challenges for morphological classification
work due to their unprecedented data volumes. Machine learning techniques
(e.g. Hocking et al., 2018; Martin et al., 2020; Walmsley et al., 2022;
Pearson et al., 2022; Domínguez Sánchez et al., 2023), used in conjunction
with visual inspection and morphological parameters, are therefore likely to
become important for the next generation of surveys.

While a rich literature already exists on galaxy morphology in the massive-
galaxy regime (e.g. Bílek et al., 2020; Fraser-McKelvie & Cortese, 2022;
Nersesian et al., 2023), much less is known about the dwarf regime (M⋆ < 109.5
M⊙) outside the very local Universe. For example, are the principal visual
morphological classes and their formation histories in dwarf galaxies similar
to what is seen in their massive counterparts? How frequent are morphological
details like bars and interactions? How do commonly-used morphological
parameters perform in the dwarf regime in separating morphological classes and
identifying interacting systems?

The current lack of statistical knowledge about dwarf morphology is partly
driven by the fact that, while dwarfs can be studied in detail in the very
local Universe, up to distances of $\sim$50 Mpc (e.g. Mateo, 1998; Tolstoy et
al., 2009; Besla et al., 2016)), typical dwarfs are too faint to be detected,
at cosmological distances, in past wide-area surveys like the SDSS (e.g.
Jackson et al., 2021; Davis et al., 2022). This is because, while these
surveys provide large sky areas, they have relatively shallow detection
limits. The dwarfs that are visible in large shallow surveys of the past tend
to be those which have relatively high SFRs. The high star formation boosts
the luminosity of the dwarfs above the detection thresholds of shallow
surveys, making them detectable (e.g. Jackson et al., 2021). However, this
also biases these dwarf samples towards systems that are blue and therefore
more likely to have late-type morphology (Kaviraj et al. in prep). Unbiased
morphological studies in the dwarf regime have so far been possible, either in
our local neighbourhood (e.g. Tolstoy et al., 2009), in nearby groups and
clusters (e.g. Boselli et al., 2008; Venhola et al., 2017; Eigenthaler et al.,
2018) or around nearby massive galaxies (e.g. Duc et al., 2015; Geha et al.,
2017; Carlsten et al., 2021; Mao et al., 2021; Trujillo et al., 2021; Holwerda
et al., 2023), regions where relatively complete dwarf samples can be
assembled. Exploring the morphological mix of dwarfs in the general Universe,
in low-density environments, requires surveys which are both deep and wide,
like the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP; Aihara et al.,
2018), in which dwarf galaxy populations are likely to be complete, down to M⋆
$\sim$ 108 M⊙ out to at least $z\sim 0.3$.

It is worth noting here that recent work has shown that typical morphological
classes, such as ETGs and LTGs, behave differently in the dwarf regime
compared to the massive-galaxy regime. For example, Lazar et al. (2023) use
ultra-deep HSC-SSP imaging, which has a point source depth of $\sim$28
magnitudes111The $i$-band 3$\sigma$ limiting surface-brightness (measured in a
10$\times$10 pixel patch) is around 31 mag arcsec-2. (more than 5 magnitudes
deeper than standard-depth SDSS imaging) of over 100 blue dwarf ellipticals to
show that less than 3 per cent of these systems show signs of tidal
interactions, lower than the interaction fraction seen in the general galaxy
population at similar stellar masses. This is in contrast to the massive-
galaxy regime, in which more than 70 per cent of ellipticals show tidal
features in deep images (e.g. van Dokkum, 2005).

The past literature shows that, in the high mass regime, ETGs typically
exhibit Sérsic indices ($n$) around 4, while $n\sim 1$ corresponds to LTGs (de
Vaucouleurs, 1959, 1977; De Propris et al., 2016). However, some studies
indicates that these trends may not be preserved in the dwarf regime. For
example, Conselice (2003), who study galaxy morphology in the local Universe
(out to $\sim$50 Mpc) using optical data, show that concentration cannot be
used to separate the ETG and LTG populations in the dwarf regime. Such results
suggest that, rather than being strongly shaped by interactions, which would
increase the central concentration and result in tidal features, ETGs in the
dwarf regime may evolve preferentially via secular processes like gas
accretion. More broadly, the evolutionary histories of traditional
morphological types (e.g. ETGs and LTGs) in the dwarf regime could potentially
be different from those in the massive-galaxy regime.

A detailed census of the morphological mix of dwarf galaxies in the general
Universe, outside the local neighbourhood and in low-density environments, is
largely missing and clearly desirable for establishing the morphological
trends in the dwarf population. Such a census, which requires an exploration
using surveys that are both deep and wide, is the purpose of this study. This
paper is organized as follows. In Section 2, we describe the datasets used in
this paper and the selection of a sample of nearby dwarf galaxies that
underpins this study. In Section 3, we explore the morphological mix of our
dwarfs via visual inspection of their HSC $gri$ composite images and their
unsharp-masked counterparts, identify the principal morphological classes in
the dwarf regime, explore the role of morphological details like bars and
interactions and study their recent star formation histories via their rest-
frame colours. We also compare our findings in the dwarf regime to what is
known in massive galaxies. In Section 4, we explore dwarf morphology using
commonly-used morphological parameters, such as the Sérsic index,
concentration, asymmetry and clumpiness (CAS), M20 and the Gini coefficient,
and compare the distributions of these parameters in dwarfs to those in their
massive counterparts in the nearby Universe. In Section 5, we bring our
results together and discuss the implications of our findings for the
evolution of different dwarf morphological classes. We summarise our findings
in Section 6.

##  2 Data

Our study is underpinned by the Classic version of the COSMOS2020 catalogue
(Weaver et al., 2022), which provides physical parameters, such as photometric
redshifts, stellar masses and SFRs for $\sim$1.7 million sources in the
$\sim$2 deg2 COSMOS field (Scoville et al., 2007). These parameters are
calculated using deep photometry from 40 broadband filters, across the UV
through to the mid-infrared, from the following instruments: GALEX (Zamojski
et al., 2007), MegaCam/CFHT (Sawicki et al., 2019), ACS/HST (Leauthaud et al.,
2007), Hyper Suprime-Cam (Aihara et al., 2019), Subaru/Suprime-Cam (Taniguchi
et al., 2007, 2015), VIRCAM/VISTA (McCracken et al., 2012) and IRAC/Spitzer
(Ashby et al., 2013; Steinhardt et al., 2014; Ashby et al., 2015, 2018). The
optical and infrared aperture photometry is extracted using the SExtractor and
IRACLEAN codes respectively and physical parameters are calculated using the
LePhare SED-fitting algorithm (Arnouts et al., 2002; Ilbert et al., 2006). The
40-filter photometry results in accurate parameters, with photometric redshift
accuracies better than $\sim$1 and $\sim$4 per cent for bright ($i<22.5$ mag)
and faint ($25<i<27$ mag) galaxies respectively. Our visual inspection uses
optical $gri$ colour composite images from the HSC-SSP Ultra-deep layer, which
have a 5$\sigma$ point source depth of $\sim$28 magnitudes. This is around 5
magnitudes deeper than standard depth SDSS imaging and almost 10 magnitudes
deeper than the detection limit of the SDSS spectroscopic main galaxy sample.
The median seeing of the HSC images is $\sim$0.6 arcseconds (around a factor
of 2 better than the SDSS).

###  2.1 A complete sample of nearby dwarf galaxies

To construct our dwarf galaxy sample, we first select objects which are
classified as galaxies by LePhare (‘type’ = 0 in the COSMOS2020 catalogue). We
then restrict our study to galaxies which have stellar masses in the range 108
M⊙ < M⋆ < 109.5 M⊙ and redshifts in the range $z<0.08$ and which lie within
the HSC-SSP footprint and outside the HSC-SSP bright-star masks defined by
Coupon et al. (2018). We restrict ourselves to $z<0.08$ because visual
inspection of these dwarfs via their HSC images suggests that morphological
classification becomes more difficult beyond this redshift. The sample
obtained after applying these constraints is comprised of 283 dwarf galaxies.

We then further exclude 26 objects that either have an ‘extendedness’ of 0 in
the HSC $griz$ filters (i.e. are classified as stars via this parameter, even
though they are classified as galaxies by LePhare222These objects clearly look
like stars when visually inspected (see Figure 5).) or, after visual
inspection, either appear to have low signal to noise or are objects where a
large foreground or background galaxy is contaminating the photometry of the
object in question. The final sample we use for our analysis contains 257
dwarf galaxies. The median redshift and stellar mass errors in our dwarf
sample are 0.02 and 0.08 dex, respectively. Note that $z\sim 0.08$ is much
lower than the redshift out to which COSMOS2020 is expected to be complete
($z\sim 0.3$), for galaxies that have stellar masses of M⋆ > 108 M⊙ (see e.g.
Figure 1 in Jackson et al., 2021). The sample of dwarfs used here therefore
offers an unbiased statistical sample of galaxies which can be used to study
the morphological properties of the general dwarf population in the nearby
Universe.

It is instructive to consider the types of large-scale structures that are
actually present in the COSMOS2020 footprint at the redshifts probed in this
study. Using the X-ray group catalogues compiled by Finoguenov et al. (2007),
George et al. (2011) and Gozaliasl et al. (2019), which incorporate HST-ACS
data from Leauthaud et al. (2007) and photometric redshifts from Ilbert et al.
(2009), we check the M200 values of groups that reside within the COSMOS2020
footprint at $z<0.1$. The virial masses of the three groups that fit this
description lie in the range 1012.9 M⊙ < M200 < 1013.2 M⊙. In comparison, a
small cluster like Fornax has a virial mass of $\sim$1013.9 M⊙ (Drinkwater et
al., 2001), while larger clusters like Virgo and Coma have virial masses of
$\sim$1015 M⊙ (e.g. Fouqué et al., 2001; Gavazzi et al., 2009). The COSMOS2020
galaxy population, in our redshift range of interest, therefore resides
preferentially in low-density environments.

##  3 Morphological classifications via visual inspection

We use visual inspection of HSC $gri$ colour composite images to classify our
dwarf galaxies into their principal morphological classes. In order to
generate the red-green-blue composite images we make use of the Python
function make_lupton_rgb (described in Lupton et al., 2004) from the python
library astropy. Unlike massive galaxies, dwarfs are intrinsically faint and
their internal structures (disks, bars, tidal features etc.) may have low
contrast in our images. Therefore, for each galaxy, we also create and
visually inspect an ‘unsharp masked’ version of each colour composite image.
In unsharp masking (e.g. Malin, 1977), a blurred image is created by
convolving the original with a kernel. The blurred version is subtracted from
the original and the difference image is then multiplied by a factor which
represents the strength of the sharpening. The kernel size and sharpening
strength are the free parameters in this process. The technique has the effect
of sharpening the edges of structures in a galaxy. Given that the sizes of
structures may vary in different galaxies, and since our dwarfs span a range
(albeit small) in redshift, we explore multiple values for both the blurring
kernel and the sharpening strength in each galaxy333We use the interactive
unsharp mask filter in the GIMP software package to interactively vary the
kernel and the strength in individual dwarf galaxy images..

Unsharp masking has previously been used in astronomy to detect faint, low-
contrast features like shells and tidal features inside and around nearby
massive galaxies (e.g. Malin & Carter, 1983). Since they are intrinsically
bright, the internal constituents of massive galaxies (spiral arms, bars etc.)
are readily visible in contemporary surveys without unsharp masking. However,
the same may not be true for dwarfs, which are relatively fainter and unsharp
masking could increase the efficacy of our morphological classifications. The
visual classifications were performed by one expert classifier (SK). The
images were randomised, both the original and unsharp-masked images of each
galaxy were classified at the same time and physical parameters (e.g. stellar
mass and redshift) were kept hidden during the classification process to avoid
introducing any biases. Our visual inspection records the following
information about each galaxy: its morphological class, evidence of an ongoing
or recent interaction (tidal features, visible large-scale asymmetry in the
main body of the galaxy, shells and dust features) and the presence of a bar.

###  3.1 Principal morphological classes in dwarf galaxies

We begin by presenting, in Figures 1, 2 and 3, the three principal
morphological classes yielded by our visual inspection: ETGs, i.e. ellipticals
and S0s (Figure 1), LTGs (Figure 2) and featureless dwarfs (Figure 3). ETGs
and LTGs in the dwarf regime are similar to the classical morphological types
known from studies of massive galaxies. While we do not attempt to divide our
LTGs into more granular subclasses, our dwarf LTGs are typically akin to the
‘Sc’ or ‘Sd’ morphologies seen in the massive-galaxy population. The
featureless dwarfs, on the other hand, have flat, smooth profiles that lack
either the central light concentration that typifies ETGs or any disk
structure that is found in LTGs. A very small number of objects (less than 2
per cent) have a mostly irregular morphology that does not fit into these
classes. Examples of these objects are shown in Figure 4. Given their small
contribution to the overall number of dwarfs, these galaxies are omitted from
the analysis below for clarity.

Finally, in Figure 5, we show examples of the 26 objects that are excluded
from our analysis (as described in Section 2.1), either because they are
classified as stars by the HSC extendedness parameter (even though they are
classified as galaxies by LePhare) or because they are contaminated by nearby
massive galaxies or are low signal to noise objects. Table 1 summarises both
the number fractions of dwarfs in these different morphological classes (upper
sub-table) and the fractions of galaxies in each morphological class which
show evidence for ongoing or recent interactions (lower sub-table). The first
column (presented in bold) indicates fractions for the entire dwarf sample,
while the second and third columns show values for the lower and upper halves
of our stellar mass range respectively. Throughout this paper uncertainties
are calculated following Cameron (2011).

We note that the featureless class strongly resembles what in the nearby
Universe are commonly referred to as dwarf spheroidals (dSph). Indeed, similar
galaxies were discovered near the Milky Way as early as the 1930s (Shapley,
1938), and in the Virgo Cluster as early as the 1950s (Reaves, 1956; van den
Bergh, 1959). Reaves (1956) referred to those in Virgo as IC 3475-type
objects, and described them as having "no trace of any small central nucleus
or arm structure", with "relatively slight concentration of light to the
center, if any", which is extremely similar to our description of the
featureless galaxies found in this study. These featureless dwarfs thus may be
dSph-type galaxies.

In this context, it is also instructive to explore the connection between the
featureless class and the population of ‘ultra-diffuse galaxies’ (UDGs, e.g.
van Dokkum et al., 2015; Koda et al., 2015), which are a subset of the dSph
population (Conselice, 2018) and have been prominent in the recent literature.
Typical UDGs have effective surface brightnesses ($\mu_{\rm eff}$) fainter
than $\sim$25 mag arcsec-2 and effective radii ($R_{\rm eff}$) larger than 1.5
kpc (e.g. Conselice, 2018). However, while 19 out of 24 galaxies in our
featureless class have $R_{\rm eff}$ larger than 1.5 kpc, virtually all of
these galaxies have $\mu_{\rm e}$ brighter than 25 mag arcsec-2. Only two of
our featureless galaxies are consistent with the definition of a UDG (if
either $r$ or $i$ band images are considered). Thus, while the featureless
objects are likely related to dSPhs, and could be brighter versions of UDG-
like systems, we choose to call them featureless for now, until we can conduct
more detailed comparisons of their structural properties with dSph galaxies
using larger datasets.

Figure 1: Examples of ETGs in our dwarf sample. For each galaxy the left-hand
panel shows the HSC colour image, while the right-hand panel shows its
unsharp-masked counterpart. ETG1 is an example of a system which shows an
internal asymmetry. ETG2 shows a faint tidal feature to the north east of the
galaxy. ETG7 is the only dwarf ETG in our sample that exhibits a dust lane,
while ETG8 shows an interacting system with two noticeable tidal tails. As the
images suggest, blue cores and regions are common in dwarf ETGs whether they
are interacting or not. Figure 2: Examples of LTGs in our dwarf sample. For
each galaxy the left-hand panel shows the HSC colour image, while the right-
hand panel shows its unsharp-masked counterpart. LTG3 shows an example of a
system which shows an internal asymmetry, while LTG6 shows an example of a
system with a tidal feature. Figure 3: Examples of dwarf galaxies classified
as featureless. For each galaxy the left-hand panel shows the HSC colour
image, while the right-hand panel shows its unsharp-masked counterpart. Figure
4: Examples of dwarf galaxies which have largely irregular morphology and are
difficult to put into the ETG, LTG and featureless categories above. The
fraction of such objects in our sample is negligible (less than 2 per cent).
Figure 5: Examples of objects that are misclassified and removed from our
analysis. These include stars (M1 - 5) which have HSC extendedness values of
0, i.e. are classified as stars by the HSC pipeline even though they are
classified as galaxies by LEPHARE. Note that these objects clearly look like
stars in the images. M6 and M7 are likely to be contaminated by the light from
an overlapping massive galaxy. M8 appears to be an object embedded within the
outskirts of a massive galaxy. M9 is a very low S/N object, while M10 is
likely to be a high-redshift background galaxy residing behind a broad tidal
feature from a nearby galaxy. Number fractions in different morphological
classes
---
| 108 M⊙ < M⋆ < 109.5 M⊙ | 108 M⊙ < M⋆ < 108.75 M⊙ | 108.75 M⊙ < M⋆ < 109.5 M⊙
dETG | 0.43${}^{\textbf{0.03}}$ | 0.450.03 | 0.370.06
dLTG | 0.45${}^{\textbf{0.03}}$ | 0.400.03 | 0.630.06
dF | 0.10${}^{\textbf{0.02}}$ | 0.120.02 | -
dIrr | 0.02${}^{\textbf{0.01}}$ | 0.030.01 | -
Interaction fractions in different morphological classes
| 108 M⊙ < M⋆ < 109.5 M⊙ | 108 M⊙ < M⋆ < 108.75 M⊙ | 108.75 M⊙ < M⋆ < 109.5 M⊙
dETG | 0.14${}^{\textbf{0.03}}$ | 0.150.04 | 0.100.06
dLTG | 0.28${}^{\textbf{0.04}}$ | 0.240.04 | 0.350.07
dF | 0.20${}^{\textbf{0.07}}$ | 0.200.07 | -
dIrr | 0.40${}^{\textbf{0.16}}$ | 0.400.16 | -
Table 1: Upper sub-table: Number fractions of dwarf galaxies in each
morphological class (dETG = dwarf early-type galaxies, dLTG = dwarf late-type
galaxies,  dF = dwarf featureless galaxies, dIrr = dwarf irregular galaxies),
in three mass ranges. The left-hand column shows the number fractions for the
full mass range in our sample (108 M⊙ < M⋆ < 109.5 M⊙). In the middle and
right-hand columns we split the mass range into its lower and upper halves
respectively. Errors, which are shown as superscripts, are calculated
following Cameron (2011). Lower sub-table: The fraction of galaxies in a given
morphological class which shows evidence of interactions (see text in Section
3 for details).  The dashes indicate instances where there are no galaxies
corresponding to a specific morphological type.

The number fractions of ETGs and LTGs in dwarfs in the general Universe are
reasonably similar, although there is an excess of late-types at higher
stellar masses. This is different from the situation in high-density
environments, reported in other work, where the fraction of dwarf ETGs tends
to be higher. For example, the dwarf ETG fraction measured in the MATLAS
survey, which samples dwarf satellites around nearby massive galaxies, is
$\sim$ 70 per cent (Poulain et al., 2021). Similar results have been obtained
by Carlsten et al. (2021), who performed a comparative study of ETGs and LTGs
in the ELVES (Carlsten et al., 2022), NGVS (Ferrarese et al., 2012) and NGFS
(e.g. Muñoz et al., 2015) surveys, which probe dwarfs in the local volume,
Virgo and Fornax respectively. These trends suggest that the likelihood of
dwarfs having early-type morphology increases in regions of higher density,
akin to the morphology-density relation seen in the massive-galaxy regime
(e.g. Oemler, 1974; Dressler, 1980; Sazonova et al., 2020).

To compare the visual morphological mix of dwarfs to what is known in the
massive-galaxy regime, we compare the results of our visual classification to
those from Kaviraj (2010), who performed morphological classification, via
visual inspection, of $\sim$1000 massive galaxies in the SDSS Stripe 82. The
galaxies in this sample have upper redshift and lower mass limits of $z\sim
0.05$ and M⋆ $\sim$ 1010 M⊙ respectively. Around 60 per cent of the Kaviraj
(2010) sample is composed of LTGs, slightly higher than the late-type fraction
in the dwarf regime.

However, the largest difference, in terms of major morphological classes,
between dwarfs and massive galaxies is the existence of the featureless
galaxies, which do not have an equivalent in the massive-galaxy regime. It is
worth noting that all featureless galaxies reside in the lower half of our
stellar mass range (see Table 1). In other words, the fraction of featureless
dwarfs increases towards lower stellar masses, which suggests that their
formation becomes easier as the gravitational potential well becomes
shallower. This, in turn, indicates that their formation likely depends on
processes like baryonic feedback or tidal perturbations, whose effect will
become stronger as the potential well becomes shallower (e.g. Jackson et al.,
2021).

###  3.2 Local densities of different dwarf morphological classes

We quantify the relative local densities of the various dwarf morphological
classes by calculating projected distances of individual dwarfs from the first
to the tenth nearest massive (M⋆ > 1010 M⊙) neighbours, using a redshift
tolerance of 0.02. While the distance to the first nearest neighbour provides
a measure of very local density, distances to progressively farther neighbours
provide estimates of the ambient densities averaged over larger distances
(e.g. Dressler, 1980). Recall that the galaxy population in COSMOS, at the
redshifts we are considering here ($z<0.08$), reside in low-density
environments (Section 2.1). Our aim here is to understand if there are any
strong trends in relative density between the different dwarf morphological
classes. In Figure 6, we show the distances to the nearest, third nearest and
tenth nearest massive neighbour. We find no significant differences between
the different dwarf morphological classes in terms of their local density,
with the median values overlapping within the statistical errors. The same
general trends are present in all other distances (not shown for brevity). It
is worth noting, however, that there are more featureless dwarfs at distances
less than 250 kpc from the nearest massive galaxies than in other
morphological classes (top panel of Figure 6), although this trend has to be
confirmed using larger samples of dwarfs in future work.

Figure 6: Distributions of projected distances to the first (top panel), third
(middle panel) and tenth (bottom panel) nearest massive (M⋆ > 1010 M⊙)
neighbour, within a redshift tolerance of 0.02. The histograms are normalized
by their areas.

###  3.3 The role of interactions

The interaction fraction in dwarf LTGs ($\sim$28 per cent, Table 1) is around
a factor of 2 higher than that found in massive LTGs, which exhibit
interaction fractions between 11 and 16 per cent, depending on the exact
morphological subclass (Kaviraj, 2014). Recall that our interaction flag
includes galaxies that have both tidal features and show large-scale internal
asymmetries. The higher interaction fraction in dwarf LTGs, compared to their
massive counterparts, is likely to reflect the fact that inducing
morphological disturbances in dwarfs is easier (e.g. via mergers, flybys
around massive galaxies or internal stellar feedback) due to their shallower
potential wells (e.g. Agertz & Kravtsov, 2016; Martin et al., 2021).

Some interesting differences between dwarfs and massive galaxies arise when
considering the interaction fraction in dwarf ETGs. Dust lanes in massive ETGs
are signposts of merger activity with lower mass companions (e.g. Kaviraj et
al., 2012; Davis et al., 2015), with around 7 per cent of massive ETGs showing
these large-scale dust features (Kaviraj, 2010). However, only 1 dwarf ETG
(out of 110) shows a dust lane (see Figure 1). The incidence of dust lanes
therefore appears to be markedly lower in dwarf ETGs than in their massive
counterparts. In a similar vein, the incidence of interactions in massive ETGs
tends to be higher (by around a factor of $\sim$1.5) than in massive LTGs,
particularly when compared to the interaction fractions in massive Sc and Sd
type systems that are morphologically similar to our dwarf LTGs (see Table 1
in Kaviraj (2014) and Kaviraj (2010)). However, the dwarf regime does not
appear to preserve this trend, with dwarf LTGs showing higher interaction
fractions, by around a factor of 2, than their ETG counterparts.

Finally, the interaction fractions in dwarf ETGs are significantly lower than
that found in the massive ETGs. For example, while the interaction fraction in
dwarf ETGs is $\sim$14 per cent (Table 1), it is $\sim$70 per cent (i.e. a
factor of 5 higher) in massive red ETGs (van Dokkum, 2005) in images that are
around 2 magnitudes shallower than the HSC images used in this study. The
interaction fraction in massive galaxies could, therefore, be expected to be
even higher in images that have similar depth to the ones used in this study.
This suggests that the origin of dwarf ETGs may have less to do with
interactions than their massive counterparts, in line with the findings of
recent observational work that suggests that secular accretion from the cosmic
web is the dominant evolutionary channel for these systems (Lazar et al.,
2023). We explore this point in more detail in Section 5.1.

When large statistical samples are available, the interaction fraction in a
population can be combined with the enhancement of the specific SFR (sSFR) in
interacting galaxies to estimate the fraction of the star formation activity
which is being driven by interactions (Eq. 2 in Kaviraj, 2014). Large samples
likely span the range of properties (e.g. the mass ratio and coalescence
timescale of interacting systems) that may influence the interaction-driven
sSFR of the system (e.g. Lotz et al., 2010a, b). Following Kaviraj (2014), we
calculate the enhancement of the sSFR in different dwarf morphological classes
by calculating the ratio of the median sSFR in interacting systems to the
median sSFR in non-interacting systems. Combining these with the interaction
fractions in Table 1 suggests that around 27, 19 and 14 per cent of the star
formation activity in our dwarf LTG, featureless and ETG populations are
driven by interactions respectively. Combining these values, weighted by the
number fractions in the different dwarf morphological classes, suggests that
around 20 per cent of the overall star formation activity in dwarfs is
triggered by interactions. It is interesting to note that the fraction of star
formation activity in massive nearby LTGs that is likely triggered by
interactions is higher (around 40 per cent, see Kaviraj, 2014). Together with
the low frequency of tidal features seen in the dwarf ETGs, this further
suggests that, in general, the evolution of dwarf galaxies may have had less
to do with interactions than their massive counterparts and that their
evolution is likely to be influenced more by secular accretion and internal
processes.

Figure 7: Top: Rest-frame $(g-i)$ colours vs stellar mass of COSMOS2020
galaxies at $z<0.2$, shown as a heatmap. The dashed lines show simple stellar
populations (SSPs) which form at various look-back times (10, 4, and 2 Gyrs).
We use the median metallicity as a function of stellar mass Gallazzi et al.
(2005) to construct the rest-frame colour for all SSPs. The three principal
dwarf morphological classes are shown overplotted in different colours (see
legend). Bottom: Same as the top panel but for interacting galaxies only. The
horizontal dashed line at rest-frame $(g-i)=0.7$ separates red and blue
galaxies.

###  3.4 Rest-frame colours

In Figure 7, we explore the rest-frame colours of the different dwarf
morphological classes. The top panel shows the rest-frame $(g-i)$ colour vs
stellar mass of the COSMOS2020 population at $z<0.2$ as a heatmap. Galaxies in
our dwarf morphological classes are shown overplotted using different colours
(see legend). The bottom panel shows the same heatmap as the top panel but
this time with only interacting dwarfs overplotted. In the dwarf regime, this
heatmap is bimodal around $(g-i)\sim 0.7$ (indicated using the black dashed
line), with well-defined red and blue peaks. In both panels we also overlay
rest-frame $(g-i)$ colours of simple stellar populations (SSPs) which form at
look-back times of 2, 4 and 10 Gyrs (taken from the Bruzual & Charlot (2003)
population synthesis models). Since galaxies show a relationship between
stellar mass and metallicity (e.g. Gallazzi et al., 2005), these SSPs use the
median stellar metallicity of galaxies at the stellar mass in question. While
real galaxies do not have star formation histories that correspond exactly to
SSPs, these SSP-based colours serve as a useful guide to understanding the
broad features of the star-formation histories of galaxies in this colour-mass
diagram. For example, they indicate that a very small fraction of dwarfs (less
than 8 per cent in any morphological class) are consistent with purely old
stellar populations (i.e. a ‘monolithic’ formation scenario). In a similar
vein, dwarfs which reside in the rest-frame $(g-i)$ blue cloud lie blueward of
the 4 Gyr SSP, suggesting that they are likely to have had some star formation
within the last 4 Gyrs.

Table 2 summarises the results in Figure 7. The upper sub-table shows the red
fractions in each morphological class i.e. the fraction of galaxies that have
$(g-i)>0.7$, while the lower sub-table shows the same for interacting galaxies
only. Together with Figure 7, we find that the red fractions in interacting
dwarfs are lower across all morphological classes, indicating that
interactions generally enhance star formation in dwarfs, as is the case in
massive galaxies (e.g. Kaviraj, 2014). The featureless dwarfs are not all red,
which indicates that star formation in at least some of these objects is not
completely quenched (or has quenched very recently). Around 60 per cent of
dwarf ETGs are blue, and comparison to the 4 Gyr-old SSP suggests that these
dwarf ETGs are likely to have had some star formation in the last 4 Gyrs.

In Figure 8, we compare the colours of our dwarf morphological classes with
their counterparts in the massive (M⋆ > 1010 M⊙) galaxy regime from Kaviraj
(2010). While the majority of dwarf ETGs live in the blue cloud, this is
qualitatively different from the massive-galaxy regime, where ETGs tend to be
preferentially red. This suggests differences between the formation channels
of ETGs in the massive and dwarf regimes, a point we study further in Section
5.1. Nevertheless, the dwarf ETGs do contain the highest fraction of red
objects compared to the other morphological classes.

In it instructive to compare our red fractions to past work which has probed
red/quenched fractions in dwarf galaxies. Some studies, based on the SDSS,
have suggested that, at $M_{\star}<10^{9}$ M⊙, the quenched fraction in nearby
($z<0.055$) dwarfs that reside in low-density environments may be close to
zero (e.g. Geha et al., 2012). This is, however, likely to be affected by the
selection biases (described in the introduction) whereby red dwarfs
preferentially fall out of the selection in shallow surveys outside the local
neighbourhood. Indeed, when a similar analysis is performed, using the SDSS,
at very low redshift ($z<0.02$), which mitigates some of this bias, the dwarf
population shows a pronounced red sequence, which suggests a much higher
red/quenched fraction (e.g. Barazza et al., 2006). This agrees with recent
work on nearby low-surface-brightness galaxies (which are dominated by dwarfs)
using the Dark Energy Survey (Abbott et al., 2018). The red fraction using the
$(g-i)$ colour is around 30 per cent (Tanoglidis et al. (2021), see also
Thuruthipilly et al. (2023)), in reasonable agreement with the values we find
in this study.

Figure 8: Comparison between the rest-frame $(g-i)$ colours of our dwarf
morphological classes with their counterparts in the massive-galaxy regime
from Kaviraj (2010). Red fractions
---
dETG | 0.410.04
dLTG | 0.230.03
dF | 0.520.09
Red fractions in interacting galaxies
dETG | 0.250.09
dLTG | 0.130.05
dF | 0.200.14
Table 2: Upper sub-table: Red fractions of dwarf galaxies in different dwarf
morphological classes. A galaxy is defined as red if its rest-frame $(g-i)$
colour is greater than 0.7 (see text for details). dETG = dwarf early-types,
dLTG = dwarf late-types, dF = dwarf featureless. Errors, which are shown as
superscripts, are calculated following Cameron (2011). Lower sub-table: Red
fractions of interacting galaxies in different dwarf morphological classes.
Figure 9: Examples of galaxies with bars in our dwarf sample. For each galaxy
the left-hand panel shows the HSC colour image, while the right-hand panel
shows its unsharp-masked counterpart.

###  3.5 Bars

We complete our visual exploration of dwarf morphologies by considering the
incidence of bars in our dwarf galaxy sample. Figure 9 shows examples of four
barred galaxies in our dwarfs. The bar fraction in face-on late-type dwarfs is
$\sim$11 $\pm$ 3 per cent (9 out of 82 face-on late type galaxies). These are
likely to be strong bars (e.g. Nair & Abraham, 2010) given that we are using
ground-based images of relatively small galaxies. The bar therefore has to
extend along a significant fraction of the galaxy to be visible (e.g. Géron et
al., 2023).

The bar fractions at the upper end of the mass range traced by our dwarf
galaxies are similar to values reported by recent work (e.g. Géron et al.,
2021). In comparison, the strong bar fraction in massive galaxies (e.g.
Masters et al., 2011; Cheung et al., 2013; Géron et al., 2021) is around 20
per cent. The frequency of strong bars therefore decreases as we move from the
massive-galaxy to the dwarf regime.

Figure 10 shows the rest-frame colours of the barred dwarfs compared to their
unbarred counterparts. Barred dwarfs in our sample have a similar colour
distribution as unbarred dwarfs with similar median values (which overlap
within their uncertainties). A KS test between the two distributions returns a
K-S value of 0.22 and p-value of 0.6 indicating that the two distributions are
similar. The trends found here appear to be somewhat in contrast to what is
found in massive galaxies (e.g. Géron et al., 2021) where strongly-barred
galaxies tend to be redder.

Figure 10: Rest-frame $(g-i)$ colours of barred and unbarred dwarfs in our
sample.

##  4 Morphological parameters

We proceed by investigating the differences between dwarf and massive galaxies
from the perspective of commonly-used morphological parameters that dominate
the recent literature: concentration (C), asymmetry (A), clumpiness (S)
(collectively know as the ‘CAS’ system), M20, the Gini coefficient and the
Sérsic index. We compare our results to previous studies that have used
optical data in the dwarf and massive-galaxy regimes, both in the very local
Universe (within 50 Mpc) and in the general Universe at low redshift
($z<0.1$).

Prior to the calculation of morphological parameters for our dwarf sample we
mask any interloper sources, foreground stars and background and foreground
galaxies that may interfere with the measurement of the surface brightness
profile or morphology of the object in question. In order to obtain accurate
unbiased estimates for the morphological parameters studied in this work, we
estimate the masked flux using the interpolation algorithm described in
Watkins et al. (2022), which uses the Fourier transform of the azimuthal
surface brightness profiles in concentric radial bins to reconstruct the
missing flux.  The missing flux is reconstructed concentrically until the edge
of the image is reached (i.e. where the semi-major axis of the interpolation
ellipse reaches the edge of the image) leaving the area outside the
interpolation ellipse unchanged. Any masked regions outside the interpolation
area are filled with Gaussian noise 1$\sigma$ away from the RMS of the image.
We use the modified interpolated images from the algorithm to calculate
effective radii, effective surface brightnesses and central concentrations.
The asymmetry, clumpiness, M20, Gini coefficient and Sérsic index are
estimated by employing the Python statmorph package (Rodriguez-Gomez et al.,
2019) on the same interpolated images, using Petrosian radii estimated by
statmorph as described below. We calculate the morphological parameters and
physical properties mentioned above in five HSC bands (grizy) for 247 dwarfs
from our initial sample of 257. The dwarfs for which parameters cannot be
calculated either have relatively low signal to noise, suffer from some light
contamination from a nearby bright galaxy or are relatively compact sources.

###  4.1 Concentration

We calculate the concentration parameter (C82), described in Eq. 1, as defined
by Kent (1985), Bershady et al. (2000) and C03.

$\rm\mathit{C}_{82}=5\times
log_{10}\left(\frac{\mathit{R}_{80}}{\mathit{R}_{20}}\right)$ (1)

where R80 and R20 correspond to the radii enclosing 80% and 20% of the total
light of the galaxy.

We calculate R80 and R20 from the curve of growth, without making any
assumptions about the shapes of the light profiles. As opposed to other
studies in which set apertures are used, we estimate the total luminosity of
galaxies by extrapolating their total luminosities to infinity, where the
slope of the curve of growth tends to zero (Muñoz-Mateos et al., 2015).

###  4.2 Asymmetry

The asymmetry parameter as defined by Abraham et al. (1996); Conselice et al.
(2000b); Rodriguez-Gomez et al. (2019) is described in Eq. 2 below.

$\rm\mathit{A}=\frac{\sum_{\mathit{i},\mathit{j}}\mid\mathit{I}_{ij}-\mathit{I}_{ij}^{180}\mid}{\sum_{\mathit{i},\mathit{j}}\mid\mathit{I}_{ij}\mid}-\mathit{A}_{bgr}$
(2)

where Ii,j and I$\rm{}_{i,j}^{180}$ are the pixel values of the original and
the rotated images, respectively. We calculate asymmetry within a circular
aperture of either 1 or 1.5 $\times$ Rpetro depending on the dataset that we
are comparing our sample with. In Sections 4.7 and 4.9 all pixels within a
circular aperture of radius 1.5 $\times$ Rpetro are taken into account for the
calculation of asymmetry. However, in Section 4.8 the aperture changes to 1
$\times$ Rpetro.  Abgr is the asymmetry of the background (Lotz et al., 2004).
This quantity is calculated as in Eq. 3 where Ibgr;i,j and
I$\rm{}_{bgr;i,j}^{180}$ are the pixel values of the original and the rotated
images respectively, corresponding to the region outside the circular
aperture, which we define as the background.

$\rm\mathit{A_{\rm
bgr}}=\frac{\sum_{\mathit{i},\mathit{j}}\mid\mathit{I}_{bgr;ij}-\mathit{I}_{bgr;ij}^{180}\mid}{\sum_{\mathit{i},\mathit{j}}\mid\mathit{I}_{bgr;ij}\mid}$
(3)

###  4.3 Clumpiness

The clumpiness (sometimes also referred to as the smoothness index), as
defined in L04 and Rodriguez-Gomez et al. (2019), is described in Eq. 4 below.

$\rm\mathit{S}=\frac{\sum_{\mathit{i},\mathit{j}}\mathit{I}_{ij}-\mathit{I}_{ij}^{S}}{\sum_{\mathit{i},\mathit{j}}\mathit{I}_{ij}}-\mathit{S}_{bgr}$
(4)

where Ii,j and I$\rm{}_{i,j}^{S}$ are the pixel values of the original image
and its smoothed version, respectively,  within circular apertures of 1 or 1.5
$\times$ Rpetro, depending on which dataset we are comparing our sample with.
The smoothed image is obtained using a boxcar filter of width $\sigma$, which
is set to 0.25 $\times$ Rpetro, as in Lotz et al. (2004, L04 hereafter). The
calculation is performed only for the pixels corresponding to radii between
$\sigma$ and 1.5 $\times$ Rpetro (or 1 $\times$ Rpetro for the comparison with
DES data in Section 4.8), since the central region is avoided due to most
galaxies showing significant central concentration. The pixels with a negative
numerator value in Eq. 4 are excluded from the summation. Sbgr is the
background clumpiness, calculated using the background pixels residing outside
the segmentation map (Eq. 5).

$\rm\mathit{S\rm_{bgr}}=\frac{\sum_{\mathit{i},\mathit{j}}\mathit{I}_{bgr,ij}-\mathit{I}_{bgr,ij}^{S}}{\sum_{\mathit{i},\mathit{j}}\mathit{I}_{bgr,ij}}$
(5)

where Ibgr;i,j and I$\rm{}_{bgr;i,j}^{S}$ are the pixel values of the original
image and its smoothed version, respectively, corresponding to the region
outside the circular aperture, which we define as the background.

###  4.4 Gini coefficient

We calculate the Gini coefficient (Abraham et al., 2003; Lotz et al., 2004;
Rodriguez-Gomez et al., 2019) as described in Eq. 6.

$\rm\mathit{G}=\frac{1}{\mid\mathit{\overline{X}}\mid\mathit{n}(\mathit{n}-1)}\sum_{\mathit{i}=1}^{\mathit{n}}(2\mathit{i}-\mathit{n}-1)\mid\mathit{X}_{i}\mid$
(6)

where n is the number of pixels in the image, $\overline{X}$ is the mean of
the pixel values and Xi corresponds to the value of each pixel. Following Lotz
et al. (2004) we use a segmentation map for the calculation of the Gini
coefficient. The segmentation map is constructed by convolving the image with
a Gaussian kernel of $\sigma$ = Rpetro/5. We then select pixels from the
original image that are above the mean surface brightness of the convolved
image at Rpetro.

Figure 11: Combinations of CAS parameters for various morphological classes in
our dwarf and the C03 samples. Distributions of parameters and median values
(together with their associated uncertainties) are shown on the sides of all
panels. ‘m’ and ‘d’ correspond to the massive (M⋆ > 1010 M⊙) and dwarf (108 M⊙
< M⋆ < 109.5 M⊙) regimes, respectively. ETG = early-type galaxy, LTG = late-
type galaxy, F = featureless galaxy.

###  4.5 M20

The M20 index (L04) is the second order moment of the brightest 20 per cent of
the galaxy’s flux, divided by the total second order central moment
($\rm\textit{M}_{tot}$; see Eq. 7). The formula for calculating this statistic
is given in Eq. 8.

$\rm\mathit{M}_{tot}=\sum_{\mathit{i}}^{\mathit{n}}\mathit{M}_{i}=\sum_{\mathit{i}}^{\mathit{n}}\mathit{f}_{i}((\mathit{x}_{i}-\mathit{x}_{c})^{2}+(\mathit{y}_{i}-\mathit{y}_{c})^{2})$
(7)

where fi is the flux of each pixel, xi and yi represent the positions of each
pixel, xc and yc correspond to the locations of the galaxy’s centre, which are
estimated by minimizing Mtot.

$\rm\mathit{M}_{20}=log_{10}\left(\frac{\sum_{i,BRG}\mathit{M}_{i}}{\mathit{M}_{tot}}\right)$
(8)

where $\rm\sum_{i,BRG}$ Mi represents the summation over the brightest pixels
of the image corresponding to 20 per cent of the galaxy’s total flux. The
pixels which are taken into account for the calculation of this statistic are
selected using the Gini segmentation map described in Section 4.4.  We note
that the segmentation maps (i.e. the collections of pixels taken into account)
used to calculate concentration, asymmetry and clumpiness are different,
because they are either defined based on set apertures using Rpetro or by
extrapolating the total galaxy luminosity to infinity (in the case of
concentration).

###  4.6 Sérsic index

The details of the Sérsic fitting procedure in this study can be found in
Rodriguez-Gomez et al. (2019) as we use the statmorph package to perform the
fitting. We fit 2D single component Sérsic profiles using the Python astropy
modelling package within statmorph.

In the following sections we compare the morphological parameters derived for
our dwarf galaxies first to dwarfs and massive galaxies in the very local
Universe (within 50 Mpc) and then to massive galaxies in the general Universe
at low redshift ($z<0.1$). We then consider whether combinations of parameters
exist which can separate interacting dwarfs from their non-interacting
counterparts. We perform these comparisons via parameters calculated using HSC
r band images, which is closest to the filters used in previous studies.

###  4.7 Comparison to dwarf and massive galaxies in the very local Universe
(within 50 Mpc)

In Figures 11 and 12 we compare our results to C03 and L04 who have used the
CAS system, M20 and the Gini coefficient to study galaxy morphology in the
optical wavelengths in the very local Universe (within 50 Mpc), in galaxies
that span all Hubble types from Frei et al. (1996). It is worth noting that
the numbers of galaxies in these studies is relatively small, which may affect
the reliability of the comparisons. However, the proximity of the galaxies
studied by C03 and L04 means that the dwarf samples are relatively unbiased in
terms of morphological type, stellar mass and colour distribution, although
there is still a bias because the dwarfs from these studies reside in a
relatively dense environment. Nevertheless, such a comparison can provide a
useful sanity check of the parameter values we have found in our dwarf
population.  In order to perform this comparison consistently with these
previous studies, we consider asymmetry and clumpiness for our dwarfs
calculted using pixels that reside within 1.5 $\times$ Rpetro, as in C03 and
L04. We also restrict dwarfs from C03 and L04 to the stellar mass range
spanned by our HSC dwarfs.

It is instructive to note the physical scales that are being traced in the
images used to calculate morphological parameters in the different datasets.
Given the upper redshift limit of our dwarf sample ($z\sim 0.08$) and a median
HSC seeing of 0.6 arcseconds, the physical scales resolved in these galaxies
is $\sim$0.9 kpc or better. Given a median seeing of around 2 arcseconds on
the Palomar P60 telescope, the Frei et al. images are able to resolve physical
scales of $\sim$0.4 kpc or better in these galaxies (within a factor of 2 of
our HSC dwarf sample).

Figure 12: M20 vs Gini coefficient for various morphological classes in our
dwarf and the L04 samples. Distributions of parameters and median values
(together with their associated uncertainties) are shown on the sides of all
panels. ‘m’ and ‘d’ correspond to the massive (M⋆ > 1010 M⊙) and dwarf (108 M⊙
< M⋆ < 109.5 M⊙) regimes, respectively. ETG = early-type galaxy, LTG = late-
type galaxy, F = featureless galaxy.

The top panel of Figure 11 presents the clumpiness vs asymmetry plane for both
our dwarfs and the C03 galaxies. The distributions of parameters and median
values (together with their associated uncertainties) are shown on the sides
of all panels. It is worth noting first that, while the different
morphological classes within our dwarf sample show differences in asymmetry,
they show significant overlap in clumpiness. The dwarf featureless galaxies
show the lowest median value of asymmetry. After that, the galaxies with the
lowest asymmetries are dwarf and massive ETGs, while those with the highest
asymmetries are late-type systems (consistent with what is seen in other work
e.g. Bershady et al., 2000; Taylor-Mager et al., 2007).

Our dwarf ETGs reside in similar regions of this plane as their C03
counterparts. Our dwarf LTGs and the massive LTGs from C03 show reasonable
overlap in asymmetry. However our dwarf LTGs show a significant offset in the
median values of clumpiness, with both dwarf and massive LTGs from C03 (the
latter having clumpiness values which are a factor of $\sim$5 higher than our
dwarf LTGs). The difference between the dwarf LTGs in our sample and those in
C03 could be driven by the fact that the local Universe galaxies are better
resolved, although the very small numbers make it difficult to come to a
definitive conclusion. A potential reason for the significant difference in
clumpiness between dwarf and massive LTGs is that the SFRs are higher in the
massive-galaxy regime, where the potential wells are steeper and gas accretion
takes place more efficiently. This is likely to cause the galactic structure
to contain more HII regions which, in turn, would tend to increase the
‘patchiness’ (or clumpiness) of the system. Interestingly, the same
differences are seen when we compare our dwarfs to massive galaxies from the
DES survey, which are resolved slightly worse than our HSC dwarfs (see Section
4.8 below), suggesting that the trend may indeed be driven by differences in
physical properties, such as SFR, than simply the resolution of the images.

The middle and bottom panels of Figure 11 present the asymmetry vs
concentration and the clumpiness vs concentration planes. The concentrations
of our dwarf ETGs are similar to those measured in their counterparts from
C03.  However, massive ETGs show, on average, higher concentration values than
the dwarf ETGs (both from our sample and C03) by a factor of $\sim$1.7. As
noted already in C03, the structural differences between dwarf and massive
ETGs suggest that they form via different evolutionary channels. The observed
differences in terms of morphological parameters appear aligned with the
results of Section 3.3, which demonstrates that dwarf ETGs appear to exhibit a
lower incidence of interactions than their high mass counterparts. Thus, while
massive ETGs are known to experience minor and major merger events, which are
likely to increase the concentration of these systems (e.g. Martin et al.,
2018), the lower concentrations and lack of interaction signatures in dwarf
ETGs suggest an evolutionary history that is dominated by secular accretion.
We explore this point further in Section 5.1.

In Figure 12, we complete the comparison of our dwarfs to galaxies in the very
local Universe by considering the M20 – Gini plane. L04 demonstrate that, in
the massive-galaxy regime, ETGs reside at relatively high and low values of
Gini and M20 respectively, while the opposite is true for the LTG population.
In other words, these morphological classes are reasonably well separated in
the M20 – Gini plane. However, this figure indicates that dwarf ETGs and LTGs
show significant overlap in the M20 – Gini plane. The lower concentrations of
dwarf ETGs, seen in Figure 11, are mirrored in lower values of the Gini
coefficient, while dwarf LTGs do not share the low and high values of M20 and
Gini respectively like their massive counterparts. Overall, the M20 – Gini
plane is unable to cleanly separate the ETG and LTG classes in the dwarf
regime like it does in the massive-galaxy regime.

###  4.8 Comparison to massive galaxies in the nearby Universe ($z<0.1$)

We proceed by comparing our dwarf sample with massive (M⋆ > 1010 M⊙) galaxies
observed in the Dark Energy Survey (DES; Abbott et al. (2018)) at low redshift
($z<0.1$). Note that, given the relatively small ($\sim$2 deg2) area of COSMOS
(as opposed to $\sim$5000 deg2 in DES), there are only a handful of massive
galaxies in the COSMOS2020 catalogue at $z<0.08$, making it impossible to do a
statistical comparison between dwarfs and massive galaxies within this
footprint alone. We restrict our DES comparison to massive galaxies only. This
is because, while DES is deeper than the SDSS, the magnitude limits of the
training set used for the DES classifications ($16<i<18$) mean that DES dwarfs
with reliable morphological classifications remain biased towards blue, star-
forming objects (in a similar fashion to what is the case for SDSS). As we
discuss below, and demonstrate in Appendix A, this biases the DES dwarfs in
the catalogues we use towards blue, morphologically late-type systems.

Given the upper redshift limit of our DES sample and a median seeing of 0.9
arcseconds for the DES images, the physical scale that is resolved in these
images is $\sim$1.6 kpc or better. The DES sample used for our comparisons is
constructed by cross-matching three catalogues:

  * •

Zou et al. (2022) provide physical properties of galaxies, including
photometric redshifts, stellar masses and SFRs of around 300 million galaxies
from DES DR2 data. The photometric redshifts and their uncertainties are
calculated using $ugrizyW1W2$ photometry, from the SCUSS (Zou et al., 2016),
SDSS (Strauss et al., 2002) and WISE (Wright et al., 2010) surveys in a hybrid
way via local regression on a spectroscopic training set combined with
template fitting. The accuracy of the photometric redshifts for galaxies in
our mass range of interest is $\sim$0.024 at $z<1.2$.

  * •

Tarsitano et al. (2018) provides measurements of morphological parameters
including concentration, asymmetry, clumpiness, M20, Gini coefficient and the
Sérsic index in the $g$, $r$ and $i$ bands for 45 million galaxies from DES
Year 1 data.

  * •

Cheng et al. (2021) provides one of the largest catalogues of morphological
classifications to date, comprising measurements for over 20 million galaxies
using the DES Y3 data, based on convolutional neural networks. The training
sets used in this work are taken from the Galaxy Zoo 1 (GZ1) catalogue
(Lintott et al., 2011) which consist of bright galaxies with $16<i<18$ at
$z<0.25$. The accuracy of the ‘superior confidence’ ($i<18$) classifications,
which we use here, reaches 99 per cent for galaxies when compared to the GZ1
data. This makes this catalogue ideal for comparing the morphological
properties of our dwarfs to those of massive galaxies in the nearby Universe.
The final catalogue provides probabilities for two galaxy types: ETGs and
LTGs.

For the comparison with our HSC dwarf population,  we first cross-match and
combine the three catalogues mentioned above. We then use this combined
catalogue to select galaxies with M⋆ > 1010 M⊙ at $z<0.1$, which have
probabilities of being ETG or LTG higher than 90 per cent, redshift and
stellar mass errors less than 0.02 and 0.2 dex respectively and which have the
highest (‘superior’) confidence flag of 4. Importantly, galaxies with the
superior confidence flag span the same magnitude range ($16<i<18$) as that of
the Galaxy Zoo training set used in Cheng et al. (2021) and will, therefore,
have the most reliable morphological classifications. Our final sample
contains 809 objects out of which 103 are ETGs and 706 are LTGs.  For
consistency with the DES studies described above, we calculate the
morphological parameters for our HSC sample using pixels within
$R\rm_{petro}$, as in Tarsitano et al. (2018).

Figure 13: Sérsic index distribution for our dwarf sample and massive galaxies
in DES. Median values (together with their associated uncertainties) are shown
using the vertical lines and horoizontal error bars. ‘m’ and ‘d’ correspond to
the massive (M⋆ > 1010 M⊙) and dwarf (108 M⊙ < M⋆ < 109.5 M⊙) regime,
respectively. ETG = early-type galaxy, LTG = late-type galaxy, F = featureless
galaxy.

Figure 14: Combinations of CAS parameters for various morphological classes in
our dwarf sample and massive galaxies in the DES sample (contours).
Distributions of parameters and median values (together with their associated
uncertainties) are shown on the sides of all panels. ‘m’ and ‘d’ correspond to
the massive (M⋆ > 1010 M⊙) and dwarf (108 M⊙ < M⋆ < 109.5 M⊙) regimes,
respectively. ETG = early-type galaxy, LTG = late-type galaxy, F = featureless
galaxy. Each DES distribution contains 4 equidistant contours starting with 2
counts pixel-1 and ending with the maximum pixel value.

We begin, in Figure 13, by presenting the Sérsic indices of different
morphological classes in both the dwarf and massive galaxy regimes. Median
values are shown using the dashed vertical lines. The bootstrapped standard
errors in the medians are shown using the small horizontal bars. The massive-
galaxy regime exhibits the known trends in Sérsic index, with the ETG
population (which has a median of $\sim$3.5) exhibiting larger values than
their LTG counterparts (which has a median of $\sim$1.3).  As originally noted
by Faber & Lin (1983), unlike their massive counterparts, dwarf ETGs exhibit
relatively low values of Sérsic index (with a median of $\sim$ 1.5 in their
study), mirroring the differences in concentration between dwarf and massive
ETGs seen earlier in Section 4.7). The different dwarf morphological classes
span similar values of Sérsic index, indicating that this parameter is not a
reliable discriminator between morphological classes in the dwarf regime.

In Figures 14 and 15 we compare the morphological parameters of our dwarf
sample to the massive galaxy population from DES. The trends we find here are
broadly similar to those from the local Universe comparison in Section 4.7.
But the much larger number of DES galaxies enables us to put these trends on a
firmer statistical footing. The top panel of Figure 14 indicates that dwarf
ETGs exhibit similar values of asymmetry as their massive counterparts
(similar to our findings for the very local Universe in Section 4.7). The
locations of dwarf LTGs are virtually orthogonal to their massive counterparts
in the clumpiness vs asymmetry plane. While dwarf LTGs exhibit relatively high
asymmetry and low clumpiness values, massive LTGs show high clumpiness and low
asymmetry values. As we noted above, the difference in clumpiness between the
dwarf and high mass LTGs, which is seen both in the very local Universe and
DES comparisons, could be caused by the higher SFRs in the massive LTGs.
Indeed, the median SFR of massive LTGs in DES is a factor of 3 higher than the
median SFR of the HSC dwarf LTGs (SFR $\rm{}_{HSC,dLTG}\sim$0.05 M⊙ yr-1; SFR
$\rm{}_{DES,mLTG}\sim$0.15 M⊙ yr-1). The fact that clumpiness typically
correlates strongly with the SFR (as also seen in e.g. C03) suggests that
massive LTGs are likely to show higher values of clumpiness.

The middle panel of Figure 14 shows that, like in the very local Universe
comparison, dwarf ETGs show much lower values of concentration than their
massive counterparts, with the median concentration of dwarf ETGs being around
a factor of 1.4 smaller than that in the massive ETG population. As noted in
the previous section, past studies have shown that the M20 – Gini plane can be
used to separate ETGs and LTGs in the massive-galaxy regime, using various
instruments at different redshifts e.g. HST at intermediate and high redshift
(e.g. Lotz et al., 2008; Lee et al., 2013), DECaM via DES at $z<0.25$ (Cheng
et al., 2021) and Spitzer via the S4G survey (Holwerda et al., 2014)) at
distances up to $\sim$40 Mpc. Figure 15 shows the ETG – LTG separation
criterion (dashed blue line), defined by Lotz et al. (2008), applied to the
DES galaxies from Cheng et al. (2021) and confirms that this plane can
separate massive ETGs and LTGs well. However, dwarf ETGs and LTGs show a
reasonable degree of overlap in the M20 – Gini plane, which makes it difficult
to cleanly separate these morphological classes in the dwarf regime using
these parameters.

Figure 15: M20 vs Gini for our dwarf sample and massive galaxies in the DES
sample (contours). The light green dashed line represents the interaction
criterion from Lotz et al. (2008). The dashed blue line represents the
separation relation between ETGs and LTGs described in Lotz et al. (2008).
Distributions of parameters and median values (together with their associated
uncertainties) are shown on the sides of all panels. ‘m’ and ‘d’ correspond to
the massive (M⋆ > 1010 M⊙) and dwarf (108 M⊙ < M⋆ < 109.5 M⊙) regimes,
respectively. ETG = early-type galaxy, LTG = late-type galaxy, F = featureless
galaxy. Each DES distribution contains 4 equidistant contours starting with 2
counts pixel-1 and ending with the maximum pixel value.

###  4.9 Can interacting and non-interacting dwarfs be separated using
morphological parameters?

We now explore whether morphological parameters could be used to separate
interacting dwarfs from their non-interacting counterparts. In the massive-
galaxy regime, an asymmetry threshold of $A=0.35$ has often been used to
identify interacting systems during a significant fraction of the interaction
(e.g. Conselice et al., 2000a; Conselice, 2003). While galaxies such as
ULIRGs, which are undergoing significant merging, span a wide range of
asymmetry values, non-interacting galaxies in the massive regime appear not to
extend beyond $A\sim 0.35$, which makes this a reasonable criterion for
selecting strongly interacting systems.

In Figure 16, we compare the values of asymmetry for dwarf galaxies which have
been flagged as being interacting to those that have not.  The dwarf ETGs and
LTGs which are interacting exhibit median asymmetry values that are larger by
around a factor of 4 and 3, respectively, than that of their non-interacting
counterparts (see the top panel of this figure). As might be expected, the
presence of visually-identifiable morphological disturbances correlates with
larger values of asymmetry. There is some overlap between the interacting and
non-interacting populations (at least in the relatively small dwarf sample in
this study), which means that using asymmetry to cleanly separate disturbed
and undisturbed dwarfs is challenging.

Nevertheless, the fraction of interacting galaxies increases for progressively
higher thresholds of asymmetry (see the bottom panel of this figure).  For
example, in dwarf ETGs which have asymmetry values larger than $\sim$0.05,
more than 50 per cent of galaxies are interacting. The corresponding value for
dwarf LTGs is $\sim$0.08. These thresholds can be used to select samples of
dwarfs in which a majority are likely to be interacting (in images that have
similar depth and resolution to the ones used in this study). We note that
these thresholds may change for systems outside the stellar mass range probed
in this paper (108 M⊙ < M⋆ < 109.5 M⊙) or at higher redshift.

In a similar vein, L04 and Lotz et al. (2008) have formulated an interaction
criterion in the M20 – Gini plane for massive galaxies, which is represented
by the green dashed line in Figure 17. Using ULIRGs as proxies for strongly
interacting galaxies, they have shown that most ULIRGs reside on the right-
hand side of this line. However, this discriminator does not separate
interacting and non-interacting dwarfs and performs worse than asymmetry.

Figure 16: Top: Asymmetry distributions for interacting (starred in legend)
and non-interacting (not starred) early (dETG) and late (dLTG) type dwarf
galaxies. Median values (together with their associated uncertainties) are
shown using vertical lines and horizontal error bars. Bottom: Fractions of
interacting galaxies for different lower asymmetry thresholds, shown on the
x-axis. The green horizontal dashed line indicates an interaction fraction of
50 per cent. Figure 17: M20 vs Gini coefficient for our dwarf sample. The
light green dashed line represents the criterion from Lotz et al. (2008) which
is often used to separate interacting galaxies in the massive-galaxy regime.
The black circles represent dwarf galaxies which are interacting.

##  5 Implications for the evolutionary histories of dwarf morphological
classes

In this section, we complete our study by bringing together our results and
discussing their implications for the evolutionary histories of the various
dwarf morphological classes.

###  5.1 Dwarf ETGs have different evolutionary histories to massive ETGs

Section 3.3 indicates several interesting differences between dwarf and
massive ETGs. Contrary to what is found in the massive-galaxy regime, the
incidence of interactions in dwarf ETGs is lower than that in dwarf LTGs. The
interaction fraction in dwarf ETGs appears to be around a factor of 5 lower
than that in their massive counterparts. In a similar vein, the frequency of
dust lanes, which are signposts of interactions with lower mass companions,
are several factors lower in dwarf ETGs than in massive ETGs. While the
majority of massive ETGs have redder colours than their LTG counterparts, the
majority of dwarf ETGs are blue like their LTG counterparts (Section 3.4), due
to a high incidence of features such as blue cores. Finally, Section 4
demonstrates that dwarf ETGs have lower concentrations, Sérsic indices and
Gini coefficients (all of which are measures of how concentrated the light
profile is within a galaxy) than massive ETGs. The strong differences in both
the structural properties and rest-frame colours (which trace recent star
formation histories) suggest that the evolutionary histories of dwarf ETGs is
likely to be different from that of their massive counterparts.

The lower incidence of interactions and the less concentrated light profiles
both suggest that the origin of dwarf ETGs might have less to do with
interactions and merging than their massive counterparts. This appears to be
in line with the findings of recent observational work that suggests that
secular accretion from the cosmic web is the dominant evolutionary channel for
these systems (Lazar et al., 2023). This observational picture also appears
consistent with theoretical studies which have explored the formation
mechanisms of dwarf ETGs.

For example, some studies postulate the formation of dwarf ETGs through
monolithic collapse, with the subsequent star formation history regulated by
internal processes like stellar and supernova feedback (e..g Yoshii & Arimoto,
1987; Chiosi & Carraro, 2002). Other studies postulate a ‘harassment’
scenario, in which dwarf ETGs are created from dwarf LTGs as they orbit
massive galaxies. This takes place both via tidal perturbations, which remove
angular momentum and make the system more dispersion dominated, and the tidal
stripping of gas (e.g. Mayer et al., 2001; Marcolini et al., 2003). While such
a scenario is more likely in dense environments like groups and clusters, it
is plausible that it also operates is relatively less dense environments like
the ones explored in this study. A further potential channel of dwarf ETG
formation is in the tidal tails created by the gas-rich interactions of
massive galaxies (e.g. Duc et al., 2004), although the overall fraction of
dwarfs that is likely to be created via this channel is expected to be very
small (e.g. Kaviraj et al., 2012) and a tidal origin does not easily explain
the formation of large numbers of dwarf ETGs in low-density environments (such
as the ones studied here).

###  5.2 Featureless dwarfs in low-density environments are formed via
baryonic feedback

Section 3 indicates that a minority ($\sim$10 per cent) of our dwarfs fall in
the featureless category. Interestingly, all of these systems are in the lower
half of the dwarf stellar mass range considered in this study (108 M⊙ < M⋆ <
108.75 M⊙), suggesting that the formation of these featureless galaxies
becomes progressively easier as stellar mass decreases. This, in turn,
suggests that the formation of featureless galaxies is driven by processes
whose impact becomes stronger as the depth of the gravitational potential well
becomes shallower e.g. environmental processes like tidal perturbations and
ram pressure or baryonic feedback from supernovae or AGN.

However, the featureless systems are found at similar local densities as the
other morphological classes (Section 3.2) and we have shown that the
COSMOS2020 footprint does not contain dense environments in the redshift range
of our study (Section 2.1). Finally, Section 3.4 shows that the featureless
galaxies exhibit a range of rest-frame colours, indicating that they are not
quenched as a population and that many show evidence for recent star
formation. These points suggest that featureless galaxies in low-density
environments, at least in our dwarf sample, are likely to be created, not by
environmental processes but by internal mechanisms such as baryonic feedback,
either from supernovae and/or AGN (e.g. Kaviraj et al., 2019; Koudmani et al.,
2022).

###  5.3 Shallower potential wells cause late-type dwarfs to be structurally
more asymmetric than massive late-types

Figure 14 indicates that dwarf LTGs show higher median asymmetry than their
massive counterparts. They also extend to much larger asymmetry values than
massive LTGs. This is likely caused by the fact that the shallower potential
wells in the dwarf LTGs make them more susceptible to internal displacement of
material. For example, baryonic feedback may be able to move gas around more
easily, making the gas reservoir more asymmetric. Stars that form from this
gas will then inherit this asymmetry. Alternatively, tidal perturbations due
to nearby large-scale structure are likely to be able to alter the stellar
distribution in dwarfs more easily, also inducing larger asymmetries.

##  6 Summary

Dwarf galaxies dominate the galaxy number density at all epochs, making them
fundamental to understanding the evolution of the Universe. While dwarfs have
been studied in detail in the very local Universe (e.g. within around 50 Mpc),
typical dwarfs are difficult to study at cosmological distances in past large
surveys (e.g. the SDSS), because they are too shallow. Outside the local
neighbourhood, shallow surveys typically detect dwarfs that have high SFRs,
which temporarily boost the luminosity of these galaxies, lifting them above
the detection threshold of shallow surveys. However, this also makes the small
subset of dwarfs that exist in such surveys biased which, in terms of
morphology, skews these samples towards predominantly blue late-type galaxies
(as we have shown in Appendix A).

Quantifying the morphological mix of dwarfs, outside our immediate
neighbourhood, in low-density environments requires surveys that are both deep
and wide and which can therefore provide unbiased statistical samples of dwarf
galaxies. Here, we have constructed such a sample of 257 dwarfs, which lie in
the stellar mass range 108 M⊙ < M⋆ < 109.5 M⊙ and in the redshift range
$z<0.08$. We have first performed visual inspection, using ultra-deep HSC
images (and their unsharp-masked counterparts) that are around 5 magnitudes
deeper than standard-depth SDSS imaging, to establish the principal
morphological classes in the dwarf regime. We have then explored the local
densities, the role of interactions, rest-frame colours and the incidence of
bars in these morphological classes. This is followed by an exploration of
commonly-used morphological parameters in the dwarf regime and a comparison to
both dwarf and massive galaxies in the very local Universe (within 50 Mpc) and
the massive-galaxy population in the nearby Universe, using DES at $z<0.1$.
The overall aim has been to provide a pilot study that offers a useful
benchmark for the study of dwarf morphology using new and forthcoming deep-
wide surveys such as Euclid and LSST. Our main results are as follows:

  * •

Visual inspection reveals three broad morphological classes in the dwarf
population in our stellar mass range of interest (108 M⊙ < M⋆ < 109.5 M⊙).
Around 43 and 45 per cent of our dwarfs exhibit early-type (elliptical/S0) and
late-type (spiral) morphology respectively. Around 10 per cent of dwarfs
populate a ‘featureless’ class, that lacks both the central light
concentration seen in early-types and any spiral structure. While the dwarf
ETGs and LTGs are visually similar to the ETG and LTG classes found in massive
galaxies, the featureless class does not have a counterpart in the massive-
galaxy regime.

  * •

Dwarf ETGs diverge strongly from their massive counterparts in both their
structural and photometric properties. They show an incidence of interactions
and dust lanes which are several factors lower than that seen in massive ETGs.
They are also significantly less concentrated and, unlike massive ETGs, share
similar rest-frame colours as dwarf LTGs. This suggests that, unlike their
massive counterparts, the formation of dwarf ETGs may be driven less by
interactions and more by secular processes over cosmic time.

  * •

The COSMOS footprint does not contain large groups or clusters at $z<0.08$ and
the local density of the various dwarf morphological classes, traced via
projected distances to the first to the tenth nearest massive neighbours, do
not show significant differences. This implies that the creation of the
featureless dwarfs in low-density environments is likely to be driven by
internal baryonic (stellar or AGN) feedback rather than by environmental
processes.

  * •

Around 20 per cent of the star formation activity in dwarfs, in the stellar
mass and redshift range probed in this study, is likely to be driven by
interactions.

  * •

The (strong) bar fraction in dwarf galaxies is around 11 per cent, consistent
with the recent literature and lower than that found in the massive-galaxy
regime ($\sim$20 per cent). Unlike the massive galaxy regime, the median rest-
frame colour of (strongly) barred dwarfs is not significantly redder than that
of unbarred dwarfs.

  * •

It is challenging to separate different dwarf morphological classes using
commonly-used parameters like the Sérsic index, CAS, M20 and the Gini
coefficient. This is largely driven by the fact that dwarf ETGs are less
concentrated than their massive counterparts. Thus, the light concentration,
which is a key separator between morphological classes in the massive-galaxy
regime, does not offer the same level of discrimination in the dwarf regime.

  * •

The asymmetry of dwarf ETGs and LTGs that are interacting is larger, by
approximately factors of 4 and 3 respectively, than their non-interacting
counterparts. Asymmetry thresholds of 0.05 and 0.08 respectively are able to
select samples of dwarf ETGs and LTGs in which more than 50 per cent of the
galaxies are interacting (in images that have similar resolution and depth to
the ones used in this study).

Broadly speaking, there is evidence that a transition in morphological
behaviour occurs between the dwarf and massive regimes (i.e. around M⋆ $\sim$
109.5 M⊙). While similar morphological classes (ETGs and LTGs) exist in both
regimes, they have different formation mechanisms and star formation
histories. In addition, new morphological classes, such as the featureless
objects emerge in the dwarf regime, which do not share the characteristics of
the classical ETG and LTG populations. It is likely that galaxies may show
even more morphological diversity at stellar masses lower than the limit of
our study (i.e. at M⋆ < 108 M⊙).

Our study poses several questions that need to be addressed in future work.
What is the relationship between the different dwarf morphological classes?
Can dwarf LTGs transform into dwarf ETGs as is seen in the massive-galaxy
regime and, if so, via what processes? Could the featureless dwarfs be short-
lived systems, as might be suggested by their low number fractions? Or do they
transform, over short timescales, into the other morphological types? How do
these relationships vary as a function of stellar mass and environment?
Answering these questions requires statistical explorations of how the
morphological mix of dwarfs evolves over cosmic time. While this is beyond the
scope of this study, it will form the basis of future investigations using
both ground and space-based data from surveys like LSST and Euclid.

Given the time-consuming nature of visual inspection, the challenges in
separating dwarf morphological classes using parameters and the fact that
millions of dwarfs will be imaged by forthcoming deep-wide surveys (e.g. LSST
and Euclid), future statistical studies of dwarf morphology will likely need
to leverage machine-learning techniques. Given the differences between the
dwarf and massive regimes, there is a need to construct training sets (e.g.
using systems like Galaxy Zoo) that can be used for dwarf classifications
based on supervised machine-learning (e.g. Walmsley et al., 2022).
Unsupervised machine learning techniques (e.g. Martin et al., 2020; Lazar et
al., 2023), which can perform morphological clustering of arbitrarily large
galaxy populations from wide-area surveys, are also likely to be important for
future morphological studies in the dwarf regime.

To conclude, studying the evolution of dwarfs over the lifetime of the
Universe, using statistically significant samples of dwarf galaxies from deep-
wide surveys like LSST and Euclid, is likely to become a significant endeavour
in the coming decades. Such studies will be capable of bringing revolutionary
advances in our understanding of the physical processes that drive galaxy
evolution.

## Acknowledgements

We are grateful to the referee, Benne Holwerda, for many insightful comments
that improved the quality of the paper. We thank Pierre-Alain Duc, Elizabeth
Sola and Liza Sazonova for many interesting discussions. IL acknowledges a PhD
studentship from the Centre for Astrophysics Research at the University of
Hertfordshire. SK and AEW acknowledge support from the STFC [grant numbers
ST/S00615X/1 and ST/X001318/1]. SK also acknowledges a Senior Research
Fellowship from Worcester College Oxford.

## Data Availability

The morphological parameters produced in this work are available via common
online repositories. They can also be obtained by contacting the authors.

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##  Appendix A Dwarfs in the DES comparison sample are biased towards blue,
late-type galaxies

As noted in Section 4.8, DES dwarfs that conform to the selection criteria we
use to construct the DES comparison sample are strongly biased towards, blue
galaxies which are dominated by late-type morphologies. This prevents us from
comparing our dwarfs to those in DES (as a result of which our DES comparison
is restricted to massive galaxies only). Here, we demonstrate these biases.
Figure 18 presents the rest-frame $(g-i)$ colour vs stellar mass for HSC
galaxies in the COSMOS2020 catalogue (shown using the heatmap) compared to the
DES galaxies which satisfy the selection criteria described in Section 4.8
i.e. which have probabilities of being ETG or LTG higher than 90 per cent,
redshift and stellar mass errors less than 0.02 and 0.2 dex respectively and
the highest confidence flag for morphological classifications of 4. The DES
population is shown using the orange contours. A random 1 per cent of the DES
galaxies are shown overplotted using red points. While massive galaxies are
visible in DES regardless of whether they are red or blue, this is not the
case for dwarf galaxies. The DES galaxies become progressively bluer at lower
stellar masses. Indeed, towards the lower end of the stellar mass range
considered in this study, the small fraction of DES objects that do appear in
the DES comparison sample are some of the most extreme in terms of their blue
colour.

Figure 19 shows a random sample of 35 DES dwarfs. Visual inspection of a
random sample of 300 galaxies in this DES dwarf population (using $gri$ colour
composite images) indicates that the ETG fraction is $\sim$11 per cent, a
factor of 4 lower than the ETG fraction observed in the significantly deeper
COSMOS2020 catalogue ($\sim$44 per cent, see Section 3). Not unexpectedly, a
consequence of the DES dwarfs being dominated by blue galaxies is that the
morphological mix is also skewed towards late-type systems. Note that reducing
the confidence_flag parameter to 3 does not change these results.

Figure 18: $(g-i)$ colour vs stellar mass for galaxies in the COSMOS2020
catalogue (shown using the heatmap) compared to the DES galaxies (shown using
the orange contours) described in Section 4.8 (i.e. those which have
probabilities of being ETG or LTG higher than 90 per cent, redshift and
stellar mass errors less than 0.02 and 0.2 dex respectively and which have the
highest morphological confidence flag of 4). A random 1 per cent of the DES
galaxies are shown overplotted using red points. Figure 19: $gri$ colour
composite images of a random sample of DES dwarfs which satisfy the selection
criteria for the DES comparison sample i.e. galaxies which have probabilities
of being ETG or LTG higher than 90 per cent, redshift and stellar mass errors
less than 0.02 and 0.2 dex respectively and the highest confidence flag for
morphological classifications of 4.