MNRAS 000, 1–22 (2019) Preprint 14 February 2019 Compiled using MNRAS LATEX style file v3.0
The formation and evolution of low-surface-brightness galaxies
G. Martin,1? S. Kaviraj,1 C. Laigle,2 J. E. G. Devriendt,2 R. A. Jackson,1 S. Peirani3,4
Y. Dubois,3 C. Pichon,3,5,6 and A. Slyz2
1Centre for Astrophysics Research, School of Physics, Astronomy and Mathematics, University of Hertfordshire, College Lane, Hatfield AL10 9AB, UK
2Dept of Physics, University of Oxford, Keble Road, Oxford OX1 3RH UK
3Institut d’Astrophysique de Paris, Sorbonne Universités, UMPC Univ Paris 06 et CNRS, UMP 7095, 98 bis bd Arago, 75014 Paris, France
4 Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Bd de l’Observatoire, CS 34229, 06304 Nice Cedex 4, France
5Korea Institute of Advanced Studies (KIAS) 85 Hoegiro, Dongdaemun-gu, Seoul, 02455, Republic of Korea
6Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, United Kingdom
14 February 2019
ABSTRACT
Our statistical understanding of galaxy evolution is fundamentally driven by objects that lie
above the surface-brightness limits of current wide-area surveys (µ ∼ 23 mag arcsec−2).
While both theory and small, deep surveys have hinted at a rich population of low-
surface-brightness galaxies (LSBGs) fainter than these limits, their formation remains
poorly understood. We use Horizon-AGN, a cosmological hydrodynamical simulation to
study how LSBGs, and in particular the population of ultra-diffuse galaxies (UDGs; µ >
24.5 mag arcsec−2), form and evolve over time. For M∗>108 M, LSBGs contribute 47, 7
and 6 per cent of the local number, mass and luminosity densities respectively (∼85/11/10
per cent for M∗>107 M). Today’s LSBGs have similar dark-matter fractions and angular
momenta to high-surface-brightness galaxies (HSBGs; µ < 23 mag arcsec−2), but larger ef-
fective radii (×2.5 for UDGs) and lower fractions of dense, star-forming gas (more than ×6
less in UDGs than HSBGs). LSBGs originate from the same progenitors as HSBGs at z > 2.
However, LSBG progenitors form stars more rapidly at early epochs. The higher resultant
rate of supernova-energy injection flattens their gas-density profiles, which, in turn, creates
shallower stellar profiles that are more susceptible to tidal processes. After z ∼ 1, tidal per-
turbations broaden LSBG stellar distributions and heat their cold gas, creating the diffuse,
largely gas-poor LSBGs seen today. In clusters, ram-pressure stripping provides an additional
mechanism that assists in gas removal in LSBG progenitors. Our results offer insights into
the formation of a galaxy population that is central to a complete understanding of galaxy
evolution, and which will be a key topic of research using new and forthcoming deep-wide
surveys.
Key words: Galaxies: evolution – formation – dwarf – structure
1 INTRODUCTION
Our understanding of galaxy evolution is intimately linked to the
part of the galaxy population that is visible at the surface-brightness
limits of past and current wide-area surveys. Not only do these
thresholds determine the extent of our empirical knowledge, but
the calibration of our theoretical models (and therefore our under-
standing of the physics of galaxy evolution) is strongly influenced
by these limits. In recent decades, a convergence of wide-area sur-
veys like the SDSS (Abazajian et al. 2009) and large-scale numeri-
cal simulations (e.g. Croton et al. 2006; Dubois et al. 2014; Vogels-
berger et al. 2014) has had a transformational impact on our un-
? E-mail: g.martin4@herts.ac.uk
derstanding of galaxy evolution. While these surveys have mapped
the statistical properties of galaxies, comparison to cosmological
simulations – first via semi-analytical models (e.g. Somerville &
Primack 1999; Cole et al. 2000; Benson et al. 2003; Bower et al.
2006; Croton et al. 2006) and more recently via their hydrodynam-
ical counterparts (e.g. Dubois et al. 2014; Vogelsberger et al. 2014;
Schaye et al. 2015; Kaviraj et al. 2017) – has enabled us to under-
stand the physical drivers of galaxy formation over much of cosmic
time.
The SDSS, which has provided much of the discovery space
at low and intermediate redshift, starts becoming incomplete at an
© 2019 The Authors
ar
X
iv
:1
90
2.
04
58
0v
1 
 [a
str
o-
ph
.G
A]
  1
2 F
eb
 20
19
2 G. Martin et al.
r-band effective surface-brightness, 〈µ〉e1, of ∼23 mag arcsec−2
(e.g. Driver et al. 2005; Blanton et al. 2005; Zhong et al. 2008;
Bakos & Trujillo 2012). This is primarily due to the lack of depth
of the survey but also due, in part, to the standard SDSS pipeline
not being optimised for structures that are close to the sky back-
ground. Indeed, while bespoke sky subtraction on SDSS images
is able to mitigate some of these issues and reveal low-surface-
brightness galaxies (LSBGs), these objects do not form the bulk of
the population that are visible in such surveys (e.g. Kniazev et al.
2004; Williams et al. 2016). Thus, while it is clear that a (largely)
hidden Universe exists just below the surface-brightness limits of
current large-area surveys, the detailed nature of galaxies in this
LSB domain remains largely unexplored, both observationally and
in our theoretical models of galaxy evolution. Indeed, the existence
of large numbers of faint, undiscovered galaxies has deep implica-
tions for our understanding of galaxy evolution. Since our current
view of how galaxies evolve is largely predicated on high-surface-
brightness galaxies (HSBGs; 〈µ〉e <23 mag arcsec−2), this almost
certainly leads to potentially significant biases in our understanding
of the evolution of the baryonic Universe. Mapping the LSB do-
main empirically, and exploring the mechanisms by which galaxies
in this regime form and evolve, is central to a complete understand-
ing of galaxy evolution.
The existence of a population of faint, diffuse, (typically) low-
mass galaxies has been known since the mid-1980s (e.g. Sandage
& Binggeli 1984). However, in the decades following their discov-
ery, very few additional examples were identified (e.g. Impey et al.
1988; Bothun et al. 1991; Turner et al. 1993; Dalcanton et al. 1997),
largely due to the surface-brightness limits of contemporary obser-
vations. Only very recently, thanks to advances in the sensitivity
and field of view of modern instruments (e.g. Miyazaki et al. 2002;
Kuijken et al. 2002; Miyazaki et al. 2012; Diehl & Dark Energy
Survey Collaboration 2012; Abraham & van Dokkum 2014; Tor-
realba et al. 2018) and the introduction of new observational and
data-analysis techniques (e.g. Akhlaghi & Ichikawa 2015; Prole
et al. 2018), has the identification of significant samples of LSBGs
become possible (e.g. van Dokkum et al. 2015; Koda et al. 2015;
Muñoz et al. 2015; van der Burg et al. 2016; Janssens et al. 2017;
Venhola et al. 2017; Greco et al. 2018b).
While modern instruments are enabling the study of systems at
significantly fainter surface-brightnesses than was previously pos-
sible, deep-wide surveys and spectroscopic follow-up of areas large
enough to contain significant populations of LSBGs outside dense,
cluster environments remain prohibitively expensive. As a result,
the LSB domain remains poorly explored in groups (e.g Smith
Castelli et al. 2016; Merritt et al. 2016; Román & Trujillo 2017a,b)
and the field (e.g Martínez-Delgado et al. 2016; Papastergis et al.
2017; Leisman et al. 2017). This is particularly true for the ex-
tremely faint, diffuse end of the LSB population, often referred to,
in the contemporary literature, as ‘ultra-diffuse’ galaxies (UDGs;
van Dokkum et al. (2015)).
Recent work suggests that, while LSBGs may be ubiquitous
in clusters (e.g Koda et al. 2015), they occur across all environ-
ments (Román & Trujillo 2017a; Merritt et al. 2016; Papastergis
et al. 2017). However, the contribution of the LSB population to
the number, mass and luminosity density of the Universe remains
unclear. A number of studies (e.g. Davies et al. 1990; Dalcanton
et al. 1997; O’Neil & Bothun 2000; Minchin et al. 2004; Haberzettl
1 The effective surface-brightness, 〈µ〉e, is defined as the mean surface-
brightness within an effective radius.
et al. 2007) have argued that LSBGs represent a significant fraction
of objects at the faint end of the luminosity function and dominate
the number density of galaxies at the present day. They may also ac-
count for a significant fraction of the dynamical mass budget (∼ 15
per cent) (e.g. Driver 1999; O’Neil & Bothun 2000; Minchin et al.
2004) and the neutral hydrogen density (Minchin et al. 2004) in
today’s Universe, although they are thought to contribute a minor-
ity (a few per cent) of the local luminosity and stellar mass density
(Bernstein et al. 1995; Driver 1999; Hayward et al. 2005).
While new observations are opening up the LSB domain,
the formation mechanisms of LSBGs and their relationship to the
HSBG population, on which our understanding of galaxy evolution
is predicated, remains poorly understood. Compared to the HSBG
population, LSBGs, and UDGs in particular, appear to be relatively
quenched, dispersion-dominated systems which largely occupy the
red sequence (van Dokkum et al. 2015, 2016; Ferré-Mateu et al.
2018; Ruiz-Lara et al. 2018). In lower-density environments, how-
ever, they are typically bluer (i.e. unquenched) possibly reflecting
a wide range of formation scenarios across different environments
(e.g. Román & Trujillo 2017b; Zaritsky et al. 2019). LSBGs are
typically extremely extended systems for their stellar mass, with
low (n . 1) Sérsic indices (Koda et al. 2015). While there does
not appear to be a single evolutionary path that is able to explain
the formation of these objects, a number of mechanisms capable of
producing such extended, relatively quenched systems have been
proposed.
For example, van Dokkum et al. (2015) have proposed that
UDGs may be failed Milky Way-like (L?) galaxies, which were
quenched at high redshift as a result of gas stripping. However, ob-
servational evidence using globular cluster abundances (Beasley &
Trujillo 2016; Peng & Lim 2016; Amorisco et al. 2018), velocity
dispersions (e.g Toloba et al. 2018), weak lensing measurements
(e.g Sifón et al. 2018), stellar populations (e.g Ferré-Mateu et al.
2018; Ruiz-Lara et al. 2018), and the spatial distributions and abun-
dances of the galaxies themselves (e.g Román & Trujillo 2017a),
largely supports the idea that the vast majority of LSBGs are low-
mass (i.e. dwarf) galaxies that are hosted by correspondingly low
mass dark-matter haloes, except perhaps in a small number of ex-
treme cases (e.g van Dokkum et al. 2016; Beasley et al. 2016).
UDGs, for example, have been suggested to form as the result
of various channels, including anomalously high spin (e.g Amor-
isco & Loeb 2016; Amorisco et al. 2016; Rong et al. 2017; Leis-
man et al. 2017), gas outflows due to supernova (SN) feedback (e.g
Di Cintio et al. 2017; Chan et al. 2018) and strong tidal fields or
mergers (e.g. Carleton et al. 2018; Conselice 2018; Abraham et al.
2018; Baushev 2018, but see Mowla et al. 2017). Thus, while the
exact mechanisms responsible for producing UDGs are still de-
bated, there is broad consensus that the progenitors of the major-
ity of UDGs are galaxies in low mass haloes, rather than ‘failed’
high mass haloes where galaxies were prevented from forming in
the first place.
In this paper, we use Horizon-AGN, a cosmological hydro-
dynamical simulation (Dubois et al. 2014; Kaviraj et al. 2017), to
perform a comprehensive study of galaxies in the LSB domain.
The use of a cosmological simulation is essential for this exercise,
since it enables us to study baryonic processes that are likely to
drive LSBG formation (e.g. SN feedback, ram-pressure stripping
and tidal perturbations) within fully resolved cosmological struc-
ture. We explore the predicted properties of a complete sample of
LSBGs in today’s Universe across all environments, investigate the
evolution of their progenitors over cosmic time and study the role
MNRAS 000, 1–22 (2019)
Low surface-brightness galaxies 3
of key processes (e.g. SN feedback, tidal perturbations and ram-
pressure stripping) in creating these systems.
This paper is structured as follows. In Section 2, we present an
overview of the Horizon-AGN simulation, including the treatment
of baryonic physics, the definition of galaxies and their merger
trees, and the identification of LSBGs. In Section 3, we compare the
present-day properties of LSBGs to a sample of their HSB counter-
parts that have the same distribution of stellar masses. In Section
4, we explore the evolution of key properties in which LSBGs and
HSBGs diverge the most (gas fractions, effective radii and density
profiles) and which are, therefore, central to the formation of LSB
systems. In Section 5, we quantify the processes (SN feedback, ram
pressure stripping and tidal perturbations) that are responsible for
creating LSBGs over cosmic time. We summarise our results in
Section 6.
2 THE HORIZON-AGN SIMULATION
In this study we employ Horizon-AGN, a cosmological-volume
hydrodynamical simulation (Dubois et al. 2014), that is based on
RAMSES (Teyssier 2002), an adaptive mesh refinement (AMR) Eu-
lerian hydrodynamics code. Horizon-AGN simulates a box with
a length of 100 h−1 coMpc. Initial conditions are taken from a
WMAP7 ΛCDM cosmology (Komatsu et al. 2011), using 10243
dark matter (DM) particles, with a mass resolution of 8×107 M.
An initially uniform 10243 cell grid is refined, according to a quasi
Lagrangian criterion (when 8 times the initial total matter resolu-
tion is reached in a cell), with the refinement continuing until a
minimum cell size of 1kpc in proper units is achieved. Additional
refinement is allowed at each doubling of the scale factor, in order
to keep the resolution constant in physical units. Note that, in ad-
dition to the hydrodynamics, the AMR cells also define the force
softening for the dark matter and baryons. We direct readers to Ap-
pendix B for a discussion of the effect of the resolution of Horizon-
AGN on the sizes of galaxies.
Horizon-AGN produces good agreement with key observables
that trace the cumulative evolution of galaxies across at least 95%
of cosmic time: stellar mass/luminosity functions, the star forma-
tion main sequence, rest-frame UV-optical-near infrared colours
and the merger and star formation histories of galaxies (Kaviraj
et al. 2015, 2017). The simulation also reproduces black-hole (BH)
demographics, such as the luminosity and mass functions of BHs,
the evolution of BH mass density over cosmic time and correlations
between BH and galaxy mass from z = 3 to z = 0 (Volonteri et al.
2016; Martin et al. 2018c). Finally, Horizon-AGN produces good
agreement with the morphological mix of the local Universe, with
the predicted galaxy morphologies reproducing the observed frac-
tions of early and late-type galaxies that have intermediate and high
stellar masses (Dubois et al. 2016; Martin et al. 2018b).
In the following sections, we describe aspects of the simu-
lation that are particularly relevant to this study: the treatment of
baryonic matter (gas and stars), the identification of galaxies, con-
struction of their merger trees and the selection of LSBGs.
2.1 Baryons
Gas cooling is assumed to take place via H, He and metals (Suther-
land & Dopita 1993), down to a temperature of 104 K. A uni-
form UV background is switched on at z = 10, following Haardt
& Madau (1996). Star formation proceeds via a standard 2 per cent
efficiency (e.g. Kennicutt 1998), when the hydrogen gas density
reaches 0.1 H cm−3. The stellar-mass resolution in Horizon-AGN
is 4×106 M.
The simulation employs continuous stellar feedback that in-
cludes momentum, mechanical energy and metals from stellar
winds and both Type II and Type Ia supernovae (SNe). Feedback
from stellar winds and Type II SNe is implemented using STAR-
BURST99 (Leitherer et al. 1999, 2010), via the Padova model (Gi-
rardi et al. 2000) with thermally pulsating asymptotic giant branch
stars (Vassiliadis & Wood 1993). The ‘Evolution’ model of Lei-
therer et al. (1992) is used to calculate the kinetic energy of stellar
winds. Matteucci & Greggio (1986) is used to determine the im-
plementation of Type Ia SNe, assuming a binary fraction of 5%
(Matteucci & Recchi 2001), with chemical yields taken from the
W7 model of Nomoto et al. (2007). Stellar feedback is assumed to
be a heat source after 50 Myrs, because after this timescale the bulk
of the energy is liberated via Type Ia SNe that have time delays of
several hundred Myrs to a few Gyrs (e.g. Maoz et al. 2012). These
systems are not susceptible to large radiative losses, since stars will
disrupt or migrate away from their birth clouds after a few tens of
Myrs (see e.g. Blitz & Shu 1980; Hartmann et al. 2001).
We note that using an AMR refinement scheme based on total
matter density allows us to resolve the gas content of galaxies out
to larger radii, since the resolution in the outskirts of the galaxy
is principally set by the DM mass, where it dominates rather than
the gas mass, which is generally small (as would be the case in
smoothed particle hydrodynamics schemes, for example). This is
important for the study of diffuse galaxies, particularly those with
small gas fractions.
2.2 Identifying galaxies and merger trees
To identify galaxies we use the ADAPTAHOP structure finder
(Aubert et al. 2004; Tweed et al. 2009), applied to the distribution
of star particles. Structures are identified if the local density ex-
ceeds 178 times the average matter density, with the local density
being calculated using the 20 nearest particles. A minimum num-
ber of 50 particles is required to identify a structure. This imposes
a minimum galaxy stellar mass of 2× 108 M. We then produce
merger trees for each galaxy in the final snapshot (z ∼ 0.06), with
an average timestep of ∼130 Myr, which enables us to track the
main progenitors (and thus the assembly histories) of individual
galaxies.
We note that, due to the minimum mass limit described above
(2×108 M), the LSBGs we study in this paper have masses in ex-
cess of this threshold. These systems are, therefore, typically at the
higher mass end of the LSBG populations that have been studied in
recent observational work.
2.3 Surface-brightness maps and selection of LSBGs
We use the Bruzual & Charlot (2003, BC03 hereafter) stellar pop-
ulation synthesis models, with a Chabrier (2003) initial mass func-
tion, to calculate the intrinsic spectral energy distribution (SED) for
each star particle within a galaxy, given its metallicity. We assume
that each star particle represents a simple stellar population, where
all stars are formed at the same redshift and have the same metal-
licity. The SEDs are then multiplied by the initial mass of each
particle to obtain their intrinsic flux.
We use the SUNSET code to measure dust attenuation, as de-
scribed in Kaviraj et al. (2017). Briefly, we first extract the density
and metallicity of the gas cells in the galaxy and convert the gas
MNRAS 000, 1–22 (2019)
4 G. Martin et al.
mass within each cell to a dust mass, assuming a dust-to-metal ratio
of 0.4 (e.g. Draine et al. 2007). The column density of dust is used
to compute the line-of-sight optical depth for each star particle, and
dust-attenuated SEDs are then calculated assuming a dust screen in
front of each star particle. As shown in Kaviraj et al. (2017), for
optical filters, this produces comparable results to a full radiative
transfer approach. The attenuated SEDs are then convolved with
the SDSS r band filter response curve and binned to a spatial reso-
lution of 1 kpc.
Following the convention in the observational literature, we
identify LSBGs using their effective surface-brightness, 〈µ〉e, de-
fined as the average surface-brightness within the effective radius
(Reff). We calculate Reff by performing photometry using isophotal
ellipses as apertures, with Reff defined as the semi-major axis of
an isophote containing half of the total galaxy flux. The effective
surface-brightness is then calculated using the total flux contained
within this ellipse divided by the area of the aperture. We note that
the r band surface-brightness is largely insensitive to the specific
dust attenuation recipe, especially for LSBGs, which are largely
dust poor.
It is worth noting that the labelling of galaxies as ‘LSB’ sys-
tems is strongly determined by the surface-brightness limits of sur-
veys that were available, when the term was coined (e.g. Disney
1976). Galaxies we define as LSBGs in this study are those that are
largely invisible at the depth of current wide-area surveys, like the
SDSS. Indeed, if contemporary large surveys were deeper (e.g. like
the forthcoming LSST survey, which will be 5 magnitudes deeper
than the SDSS) then our definition of an LSB galaxy would be very
different. Surveys like the SDSS start becoming incomplete around
〈µ〉e < 23 mag arcsec−2 (e.g Kniazev et al. 2004; Bakos & Trujillo
2012; Williams et al. 2016) in the r band. The nominal complete-
ness of the survey is∼70 per cent at∼23 mag arcsec−2 (e.g. Zhong
et al. 2008; Driver et al. 2005), falling rapidly to ∼10 per cent for
galaxies that are fainter than∼24 mag arcsec−2 (e.g. Kniazev et al.
2004). In our analysis below, we split our galaxies into three cate-
gories, defined using effective surface-brightness:
(i) ‘High-surface-brightness galaxies’ (HSBGs): These are
defined as galaxies with 〈µ〉e < 23 mag arcsec−2 in the r band.
They represent the overwhelming majority of galaxies that are
detectable in past surveys like the SDSS, and which underpin our
current understanding of galaxy evolution.
(ii) ‘Classical low-surface-brightness galaxies’ (Cl. LSBGs):
These are defined as galaxies with 24.5 > 〈µ〉e > 23 mag arcsec−2
in the r band. They represent the brighter end of the LSBG
population and are the ‘classical’ LSB galaxy populations that
have been studied in the past literature, particularly that which
preceded the SDSS.
(iii) ‘Ultra-diffuse galaxies’ (UDGs): These are defined as
galaxies with 〈µ〉e > 24.5 mag arcsec−2 in the r band (e.g. La-
porte et al. 2018). They represent the fainter end of the LSB galaxy
population.
We note that there is no standard definition in the literature of
what constitutes a UDG, owing to the often specialised nature of the
instruments and techniques involved in their detection. However,
most definitions are roughly equivalent. For example, van Dokkum
et al. (2015) and Román & Trujillo (2017b) both use a g band cen-
tral surface-brightness (µ0) of 24 mag arcsec−2, Koda et al. (2015)
use an R band effective surface-brightness of 24 mag arcsec−2 and
van der Burg et al. (2016) use an r band effective surface-brightness
of 24 mag arcsec−2. Often, UDGs are also selected using an effec-
tive radius threshold of Reff & 1.5 in order to differentiate them
from more compact, lower mass objects with equivalent surface-
brightnesses (e.g. van Dokkum et al. 2015; Koda et al. 2015; van
der Burg et al. 2016; Román & Trujillo 2017b). While this is an im-
portant consideration over the mass ranges that these observational
studies examine (M? < 108 M), the range of masses that we con-
sider in Section 3.2 onwards (108.5–1010 M) precludes such ob-
jects.
Note that, in the following sections, we use ‘low surface-
brightness galaxy’ (LSBG) to refer to any galaxy in Horizon-AGN
with 〈µ〉e > 23 mag arcsec−2 (i.e. any galaxy that falls in either the
Cl. LSBG or UDG categories). As we describe below, the thresh-
old 〈µ〉e ∼ 24.5 mag arcsec−2 between our two LSBG categories
(Cl. LSBGs and UDGs), appears to demarcate two galaxy popu-
lations that are reasonably distinct, both in terms of the redshift
evolution of their properties and their formation mechanisms. The
Cl. LSBGs are much closer to the HSBGs in terms of their forma-
tion histories, with the real distinctions emerging between HSBGs
and UDGs. The differences between the evolution of HSBGs and
UDGs is therefore the principal focus of this study.
Figure 1 shows an example of a galaxy from our three pop-
ulations, with the dashed ellipses indicating the apertures used to
calculate the effective surface-brightness. Figure 2 shows the ef-
fective radii and stellar masses of a random selection of Horizon-
AGN galaxies that fall into each of the three categories described
above. For comparison, we show observed galaxy populations in
the nearby Universe. We note that, even for relatively low stellar
masses (M? ∼ 108.5M), the LSBGs in Horizon-AGN are well-
resolved enough to recover accurate effective radii. However, de-
pending on the implementation of sub-grid physics (e.g. prescrip-
tions for feedback), effects other than resolution can produce some
systematic offset in galaxy sizes (see Appendix B for a full discus-
sion).
Our simulated HSBGs fall along the same locus as observed
HSBGs and dwarf ellipticals from Cappellari et al. (2011) and
Dabringhausen & Kroupa (2013). Although the mass resolution of
Horizon-AGN (2×108 M) does not allow us to probe the stel-
lar mass regime where the majority of UDGs have been discov-
ered observationally, many observed UDGs from e.g. van Dokkum
et al. (2015), Mihos et al. (2015) and Yagi et al. (2016) that are
massive enough do occupy the same region in parameter space as
their model counterparts. Furthermore, as we describe in Appendix
C, while past observational studies are dominated by low-mass
LSBGs, this is largely due to the small volumes probed in these
works. These small volumes do not preclude the existence of mas-
sive LSBGs in new and forthcoming deep-wide surveys. Indeed,
some massive LSBGs, such as Malin 1 and UGC 1382, are already
known (see Figure 2 below), although the small observational vol-
umes probed so far mean that such objects are rare in current (and
past) datasets.
3 THE LOW-SURFACE-BRIGHTNESS UNIVERSE AT
THE PRESENT-DAY
We begin by studying the contributions of LSBGs to the number,
mass and luminosity densities at low redshift (Section 3.1).We then
compare key properties of LSBGs (effective radii, local environ-
ments, dark matter fractions, stellar ages and star-formation histo-
ries) to their HSB counterparts at z∼ 0 (Section 3.2).
MNRAS 000, 1–22 (2019)
Low surface-brightness galaxies 5
I T  
NQI
/ /¯  
4GHH  MRE
MRE
7&)
I T  
NQI
/ /¯  
4GHH  MRE
%N.5$)
I T  
NQI
/ /¯  
4GHH  MRE
*5$)
Figure 1. Example g r i band false colour images of low-mass Horizon-AGN galaxies. The left, middle and right hand panels show a typical example of
galaxies identified as UDGs, Cl. LSBGs and HSBGs respectively. The dotted white ellipses are isophotes which contain half of the galaxy’s r band flux. A
common spatial scale (indicated in the top-left corner of the left-hand panel) is used for all three images.










/ /¯






4
GH
H=
MR
E?
/CNKP

7)%
*5$)
%N.5$)
7&)
%QOC
8KTIQ7&)U
&YCTH'
'
5R
Figure 2. Effective radius (Reff) vs. stellar mass (M?) for a random selection
of galaxies from Horizon-AGN, compared to observed galaxies in the local
Universe. Blue, orange and red filled circles show simulated galaxies identi-
fied as HSBGs, Cl. LSBGs and UDGs respectively. Open red squares show
UDGs from the Coma and Virgo clusters (van Dokkum et al. 2015; Mihos
et al. 2015; Yagi et al. 2016; Gu et al. 2018). Dark blue crosses indicate
dwarf ellipticals, and open dark blue circles indicate high mass ellipticals
and spirals, from Dabringhausen & Kroupa (2013) and Cappellari et al.
(2011). Large open red squares show the giant LSBGs Malin 1 and UGC
1382 (Bothun et al. 1987; Hagen et al. 2016). The grey hatched region falls
below the mass resolution limit of the simulation.
3.1 Contribution of LSBGs to the local number, stellar mass
and luminosity densities
Figure 3 shows the surface-brightness function in Horizon-AGN
i.e. the number density of galaxies as a function of 〈µ〉e in the r
band (solid line). The coloured lines indicate galaxies in different
environments. Following Martin et al. (2018b), environment is de-
fined according to the 3-D local number density of objects around
each galaxy. Local density is calculated using an adaptive kernel
 〈
µ
〉
G=OCICTEUGE

?








NQ
I 


F
0

F〈 µ〉
G
=C
TE
UG
E
O
CI

/
RE

?
%N
.5$)
7&) *5$)
'ZVTCRQNCVGF
#NNGPXKTQPOGPVU
.QYFGPUKV[
HKGNF
+PVGTOGFKCVGFGPUKV[
ITQWRU
*KIJFGPUKV[
ENWUVGTU
Figure 3. The surface-brightness function, showing the number density of
galaxies as a function of their r band effective surface-brightness at z =
0. We show separate curves for low (green), intermediate (blue) and high
(red) density environments and all environments (black). Low, intermediate
and high density environments roughly correspond to the field, groups and
clusters respectively. The dashed line shows the surface-brightness function
that is produced by extrapolating the stellar mass function down to 107 M,
as described in Appendix A.
density estimation method2 (Breiman et al. 1977; Ferdosi et al.
2011; Martin et al. 2018b). The density estimate takes into account
all galaxies above 2×108M.
Galaxies are then split into three bins in local density: ‘low
density’ corresponds to galaxies in the 0th – 40th density per-
centiles, ‘intermediate density’ correspond to the 40th – 90th per-
2 The sharpness of the kernel used for multivariate density estimation is
responsive to the local density of the region, such that the error between the
density estimate and the true density is minimised.
MNRAS 000, 1–22 (2019)
6 G. Martin et al.
centiles and ‘high density’ corresponds to galaxies in the 90th
– 100th percentiles. The low, intermediate and high density bins
roughly correspond to the field, groups and clusters (see Martin
et al. (2018b) for more details). Typically, galaxies in the inter-
mediate and high density bins are found in halos with masses
1012.5 < Mhalo < 1013.5 M and Mhalo > 13.5 M respectively. In
the low density bin, most galaxies (∼ 70 per cent) are isolated (i.e.
they are not a sub-halo of a larger halo). Of the galaxies in the low-
density bin that are satellites, typical halo masses are ∼ 1012 M.
We note that there is no perfect correspondence between number
density and halo mass - for example, at fixed density, UDGs are
typically hosted by haloes that are ∼0.5 dex more massive than
HSBGs.
Since we do not consider objects with stellar masses be-
low 2× 108 M, the predicted surface-brightness function starts
becoming incomplete as we approach this limit. In order to ac-
count for this when estimating the LSBG contribution to the local
number, mass and luminosity densities, we extrapolate the galaxy
stellar-mass function down to 107M (as described in Appendix
A). The dashed black line indicates the corresponding extrapo-
lated surface-brightness function, using a combination of surface-
brightnesses drawn from the extrapolated fits (between 107 M and
109 M) and the raw simulation data (108 M to 1012 M) - see
Appendix A for more details.
Table 1 summarises the absolute numbers and number frac-
tions of HSBGs and LSBGs in the present-day Universe, as a func-
tion of local environment. The numbers in brackets indicate the cor-
responding values using the extrapolated mass function. For galax-
ies with stellar masses above the resolution limit of the simulation
(2×108 M), LSBGs account for a significant fraction (over half)
of the galaxy population in clusters and a significant minority (40-
50 per cent) of objects in low-density environments (groups and the
field).
However, for stellar masses down to 107 M, LSBGs are ex-
pected to overwhelmingly dominate the number density of the Uni-
verse, accounting for more than 70 per cent of galaxies, irrespective
of the local environment being considered. It is worth noting that
the absolute numbers of LSBGs across different environments (see
col 4, 5 in Table 1) are similar. For example, the absolute numbers
of UDGs in the Horizon-AGN volume that inhabit the field and
those that inhabit clusters are predicted to be almost the same (col
5 in Table 1). This is because, although the LSBG fraction is higher
in clusters, the total number of galaxies that inhabit low-density
environments (e.g. the field) is much larger.
Table 2 summarises the contribution of HSBGs and LSBGs to
the mass, luminosity and number density budgets of the local Uni-
verse. For galaxies with stellar masses greater than 2× 108 M,
LSBGs contribute around 47 per cent of the total number density
and make a small but non-negligible contribution to the stellar mass
(7.5 per cent) and luminosity (6 per cent) budgets. These numbers
change to 85 (number density), 10 (mass density) and 11 (lumi-
nosity density) per cent respectively, when we extrapolate down to
a stellar mass of 107 M. Although they account for the major-
ity of the number density budget (76 per cent with extrapolation to
107 M) at low redshift, the extreme end of the LSBG population,
i.e. UDGs (〈µ〉e > 24.5), account for only a small fraction of the
mass or luminosity budget (less than 4 per cent in both cases).
We note that the extrapolated quantities above are used only
to estimate the overall contribution of LSBGs to the number, stellar
mass and luminosity density down to a stellar mass of 107 M. For
the rest of the analysis that follows, we use galaxies that are actually
      
∆Z=/RE?







∆
[
=/
RE
?
7&)
%N.5$)
*5$)
Figure 4. The spatial distribution, within the cosmic web, of the UDG, Cl.
LSBG and HSBG populations. Red, orange and blue coloured points show
the positions of individual UDGs, Cl. LSBGs and HSBGs. Contours indi-
cate the surface density, calculated using all objects in the simulation, with
lighter colours indicating higher densities.
resolved in the simulation and for which the minimum stellar mass
is 2×108 M.
3.2 Properties of LSB galaxies at the present day
In this section we compare the properties of LSBGs to their HSB
counterparts at the present day. Figure 4 shows the spatial distri-
bution of a random selection of UDGs, Cl. LSBGs and HSBGs
within the cosmic web. The contours indicate the surface density
of galaxies calculated using all objects in the simulation. Although
they appear to exist preferentially in regions of high number den-
sity, many UDGs occur in regions of much lower density. On the
other hand HSBGs appear to be essentially uniformly distributed.
In Figure 5, we show contour plots of the distribution of galax-
ies as a function of r band effective surface-brightness, 〈µ〉e, and
stellar mass at z = 0, split by local environment. The histogram for
all galaxies across all environments is bimodal. However, the bi-
modality varies strongly with environment. At a given stellar mass,
the frequency of LSBGs is higher in denser environments. While in
the field most galaxies inhabit the HSB peak, the LSB peak progres-
sively dominates as we move to higher density environments. In-
deed, for low-mass galaxies, in clusters, the LSB peak overwhelm-
ingly dominates the population (this is partly the reason why much
of the UDG literature has been focussed on clusters to date).
Since the frequency of LSBGs is a strong function of stellar
mass (see e.g. Figure 5), we first construct mass-matched samples
of 2000 HSBGs, LSBGs and UDGs with stellar masses between
109M and 1010M, each of which have the same distribution in
stellar mass. Due to the shape of the UDG mass function (see Ap-
pendix C), the stellar mass distribution of our sample peaks close
to 109M and declines such that ∼ 95 per cent of galaxies are less
massive than 109.5M. We then use these mass-matched samples to
explore key properties of LSB systems – effective radii, dark-matter
fractions, specific angular momenta, gas densities, specific star for-
mation rates and mean stellar ages. Note that the analysis presented
MNRAS 000, 1–22 (2019)
Low surface-brightness galaxies 7
Table 1. The frequency (col 2, 3) and number (col 4, 5) of LSBGs of different surface-brightnesses (in r band mag arcsec−2) as a function of environment in the
present-day universe in the Horizon-AGN simulation, for stellar masses greater than 2×108 M. The numbers in brackets indicate the corresponding fractions
produced by extrapolating the stellar mass function down to 107 M. The ‘low’ (local number density in the 0th – 40th density percentile), ‘intermediate’ (40th
– 90th density percentile) and ‘high’ (90th – 100th density percentile) density bins correspond roughly to field, group and cluster environments respectively
(see Martin et al. 2018b).
f (24.5 > 〈µ〉e > 23) f (〈µ〉e > 24.5) N(24.5 > 〈µ〉e > 23) N(〈µ〉e > 24.5)
Low density (Field) 0.23 (0.09) 0.18 (0.77) 10760 5634
Intermediate density (Groups) 0.21 (0.09) 0.27 (0.74) 12691 12119
High density (Clusters) 0.19 (0.07) 0.46 (0.83) 2310 4572
  
NQI
/ /¯





〈 µ〉 G
=O
CI
C
TE
UG
E

? .QYFGPUKV[

HKGNF
  
NQI
/ /¯





〈 µ〉 G
=O
CI
C
TE
UG
E

? +PVGTOGFKCVG
FGPUKV[
ITQWRU
  
NQI
/ /¯





〈 µ〉 G
=O
CI
C
TE
UG
E

? *KIJFGPUKV[

ENWUVGTU
  
NQI
/ /¯





〈 µ〉 G
=O
CI
C
TE
UG
E

? #NN
Figure 5. Contour plots showing the number density of galaxies as a function of effective surface-brightness (〈µ〉e) and stellar mass (M?) at z = 0.06, split
by local environment. Low, intermediate and high density environments correspond roughly to field, group and cluster environments respectively. A random
sample of galaxies is plotted using points in each panel. The right-hand panel shows the same for all galaxies in the simulation.
Table 2. The fraction of the local stellar mass, luminosity and number den-
sity budget contributed by galaxies of different r band surface-brightnesses
(in units of mag arcsec−2) in the Horizon-AGN simulation, for stellar
masses greater than 2×108 M. The numbers in brackets indicate the cor-
responding fractions produced by extrapolating the stellar mass function
down to 107 M.
〈µ〉e < 23 24.5 > 〈µ〉e > 23 〈µ〉e > 24.5
fM? 0.924 (0.902) 0.059 (0.067) 0.014 (0.030)
fL 0.939 (0.892) 0.049 (0.071) 0.012 (0.037)
fN 0.534 (0.145) 0.214 (0.093) 0.252 (0.762)
in all subsequent sections, which explore how LSBG progenitors
evolve with time, is also based on these mass-matched samples.
Figure 6 shows histograms of these properties. LSBGs have
larger effective radii (panel (a)), with the mean effective radii of
UDGs around 2.5 times larger than HSBGs. The dark-matter (DM)
fractions in LSBGs and HSBGs (panel (b)) are similar, with the
median value for LSBGs predicted to be slightly (∼ 5 per cent)
higher than in HSBGs. The overwhelming majority of LSBGs are,
therefore, not devoid of DM, nor do they have anomalously large
DM fractions for their stellar mass. Contamination due to galaxies
being embedded in more massive DM haloes does not appear to
have a significant impact on the ratios shown - when we restrict
our sample to field galaxies only (dotted histograms), there is no
difference in the median DM to stellar mass ratio. This suggests that
high-DM-fraction UDGs (i.e. failed L? galaxies) (e.g. van Dokkum
et al. 2016; Beasley et al. 2016) are extremely uncommon, at least
in the stellar mass range we study here (109 M< M? <1010 M).
It is worth noting here that, while recent observations have
suggested that at least some UDGs may have very low dark mat-
ter fractions (e.g. van Dokkum et al. 2018, but see Laporte et al.
2018; Trujillo et al. 2018), a small fraction of low mass DM-free
galaxies can form naturally within the LCDM paradigm as tidal
dwarf galaxies in galaxy mergers (e.g. Barnes & Hernquist 1992;
Okazaki & Taniguchi 2000; Bournaud & Duc 2006; Kaviraj et al.
2012). However, mergers typically produce tidal dwarfs with very
low stellar masses (Kaviraj et al. 2012), and the mass range that
we consider (M? > 109M) precludes significant numbers of these
objects in our sample. It may not be surprising, therefore, that we
do not find any evidence of UDGs with anomalously low DM frac-
tions in Horizon-AGN, even if this were a significant channel for
their production.
The distribution of the stellar specific angular momenta (panel
(c)) of LSBGs and HSBGs is similar, indicating that the forma-
tion of LSBGs, and UDGs in particular, is not primarily due to
them being the high spin tail of the angular momentum distribu-
tion (e.g. Yozin & Bekki 2015; Amorisco & Loeb 2016; Amorisco
et al. 2016; Rong et al. 2017). The LSBGs in this study typically
have spins that are not significantly different from, or indeed, are
slightly below, those seen in HSBGs (see also Di Cintio et al. 2017;
Chan et al. 2018).
Finally, we consider quantities that trace the star forma-
tion properties of galaxies. Panel (d) shows the ‘star-forming’
gas fraction, defined as the ratio of the gas mass that is dense
enough to form stars (ρgas cell > 0.1H cm−3) to the stellar mass
(Mgas,SF/(Mgas,SF +M?)), measured within the central 2 Reff3. Gas
fractions in LSBGs are lower than those in their HSB counter-
parts. For example, the gas fractions of UDGs mostly lie around
zero, with 4 out of 5 UDGs being completely devoid of star form-
ing gas in their central 2 Reff. HSBGs, on the other hand, still re-
tain fairly significant fractions of star-forming gas ( fgas,SF ∼ 0.3).
UDGs that do contain some star-forming gas at the present day
have median values that are around one sixth of this value. The
lower gas fractions are reflected in lower specific star formation
rates (sSFRs; panel (e)) and higher mass-weighted mean stellar
3 We note that calculating the gas fraction within a fixed radius does not
alter our conclusions.
MNRAS 000, 1–22 (2019)
8 G. Martin et al.
   
4GHH=MRE?





 7&)
%N.5$)
*5$)
(a)
    
H&/
4GHH






HKGNF
(b)
    
NQIL =MREMOU

?






(c)
   
HICU 5(









(d)
   
NQIU5(4=[T

?





(e)
  
/GCPUVGNNCTCIG=)[T?





(f)
Figure 6. Properties of present-day UDGs and Cl. LSBGs compared to those of HSBGs at z ∼ 0 (red, orange and blue histograms respectively). Coloured
arrows indicate the median values of each population. Fainter dashed arrows indicate the median values for field populations only. Panels are as follows: (a)
effective radius measured using the stellar distribution of each galaxy (b) the dark-matter fraction (MDM/(MDM +M?)) measured within the central 2 Reff,
for all galaxies (solid line) and galaxies in the field (dotted lines) - note that the histograms are normalised in order to easily compare the two populations
(c) stellar specific angular momentum (d) star-forming (ρgas cell > 0.1H cm−3) gas fraction measured within 2 Reff (Mgas,SF/(M?+Mgas,SF)) (e) specific star
formation rate - the bar to the left indicates galaxies with sSFRs of 0 (f) mass-weighted mean stellar age ((∑i ageim?,i)/∑i m?,i).
ages (∑i ageim?,i)/∑i m?,i; panel (f)) in LSB systems. For exam-
ple, the sSFRs in UDGs are an order of magnitude lower than in
HSBGs, when galaxies with zero sSFR (again, around 4 out of 5
UDGs) are neglected. The median age of UDG stellar populations
is 9 Gyrs, 50 per cent older than their HSB counterparts. The large
age differences between LSBGs and HSBGs indicates that the LSB
nature of these systems must be partly driven by gas exhaustion at
early epochs and consequently a more quiescent recent star history.
We note here that the production of UDGs may be too efficient
in clusters leading to quenched HSB galaxies being relatively un-
represented. Additionally, since the quenched fraction (especially
at low redshift) is somewhat inconsistent with observations, and
produces an offset in the star formation main sequence between the
observed and theoretical populations in low-mass galaxies (e.g. see
Kaviraj et al. 2017), this may lead to relatively diffuse HSB or LSB
galaxies becoming UDGs due to fading stellar populations.
4 REDSHIFT EVOLUTION OF LSBG PROGENITORS
We proceed by comparing the redshift evolution of LSBG progen-
itors to the progenitors of their HSB counterparts. We focus, in
particular, on the evolution of the effective radii and gas fractions
which, as we showed in Section 3, are the quantities in which HS-
BGs and LSBGs diverge the most at the present day. We note that,
since we restrict our study to resolved progenitors, There is some
incompleteness in the sample at higher redshifts. This is due to the
limit of 50 particles that we impose on the structure finder (see Sec-
tion 2.2), which renders their merger trees incomplete after galaxies
fall below this level. The merger trees of the LSBG and UDG sam-
ples are largely complete after z = 2 (80 and 90 per cent of main
progenitors at z = 2 are accounted for respectively) owing to their
rapid assembly histories (see Section 5.1 below). For the HSBG
sample, around 60 per cent of main progenitors are accounted for
at z = 2 (rising to 100 per cent by z = 1), which may lead to the
exclusion of more slowly evolving HSBGs before z = 1.
MNRAS 000, 1–22 (2019)
Low surface-brightness galaxies 9
   

\









4
GH
H=
MR
E?
#NN
(KGNF
7&)
%N.5$)
*5$)
   

\






H I
CU
5(ICU
HKGNF
#NNICU
HKGNF
5(ICU
#NNICU
Figure 7. Top: The redshift evolution of effective radii. Solid blue, orange
and red coloured points show the redshift evolution of the median effec-
tive radii of the HSBG, Cl. LSBG and UDG populations respectively. The
dashed lines shows the evolution of Reff for galaxies in the field only. Note
that rather than attempt to emulate observational methods to calculate Reff
at all redshifts, we instead use the average projected half mass radius in the
xy, xz and yz planes here Bottom: The redshift evolution of the median gas
fraction, defined as Mgas/(Mgas +M?), for total gas (solid coloured points)
and star-forming gas (open coloured points) for the HSBG, LSBG and UDG
populations. Dashed and dotted lines without points show the evolution of
fgas for total gas and star-forming gas respectively for field galaxies only.
Pale red and blue lines show tracks for the effective radii and star-forming
gas fractions of a random sample of individual UDGs and HSBGs.
4.1 Gas fractions and effective radii
The top panel of Figure 7 describes how the effective radii of the
main progenitors of LSBGs and HSBGs evolve as a function of
redshift. LSBGs, and UDGs in particular, are consistently larger, on
average, than their HSB counterparts. Furthermore, after z∼ 1, the
rate of increase in the effective radii of UDGs is higher compared
to that in HSBGs. Figure 7 shows that the evolution of the effective
radii of all galaxy populations is not abrupt but relatively steady
and smooth with time, both galaxy by galaxy (pale lines) and as a
population. It is unlikely, therefore, that the large radii of LSBGs
today are the result of single, violent events at early epochs.
The dashed lines indicate the evolution of galaxy populations
in field environments only. As the dashed red line indicates, the
evolution of the effective radii of field UDGs proceeds almost iden-
tically to the general UDG population, despite the frequency of
UDGs being higher in very dense (cluster) environments. This im-
plies that the process(es) that produce the large sizes seen in today’s
UDGs are the same regardless of environment (although they may
occur less frequently in the field). In particular, the principal mech-
anism for UDG production is not cluster-specific i.e. galaxies do
not have to inhabit cluster environments to be the progenitors of
UDGs at the present day.
The bottom panel of Figure 7 describes how the gas fractions
of the main progenitors of LSBGs and HSBGs evolve as a function
of redshift. While the gas fractions are similar for progenitors of
all galaxies at high redshift, they begin to diverge rapidly at z ∼ 2.
The total gas fractions in HSBGs and Cl. LSBGs evolve similarly
to each other and both HSBGs and Cl. LSBGs retain relatively high
total gas fractions at z = 0. In these populations the reduction in the
average gas fraction is primarily due to gas being converted into
stars, rather than as a result of gas being expelled from the galaxy.
As we will also show in Section 5, most of this gas in HSBGs that
is turned into stars is not replenished, at least after z = 1, so that the
decreasing gas fractions are due the gas masses steadily decreasing
rather than the stellar masses simply increasing in these galaxies.
There is a more pronounced divergence in terms of the fraction
of star-forming gas. By z = 0, Cl. LSBGs have significantly lower
fractions of star-forming gas compared to their HSB counterparts.
While Cl. LSBGs and HSBGs retain relatively significant
reservoirs of gas as they evolve, the same is not true of UDGs.
By z = 0.5, the majority of UDGs have lost almost all of their
star-forming gas, essentially terminating star formation, and by
z = 0.25, the majority of UDGs have been almost completely
stripped of all of their gas. In around half of the cases, the gas frac-
tions of the main progenitors of UDGs do not evolve linearly with
time. Instead they undergo a phase of rapid gas loss lasting a few
Gyrs around z ∼ 0.5, which significantly reduces their gas content
towards the present day.
The evolution of UDGs in field environments (dotted red
lines) is slightly different from that of the global UDG population.
There is no phase of rapid gas stripping and both the total and star-
forming gas fractions in field UDGs evolve with a similar pattern
to their HSB counterparts, albeit much more rapidly. Ultimately,
the rate of gas heating is intense enough that the star-forming gas
fraction is still reduced to similar levels to the wider UDG popula-
tion (< 5 per cent by z = 0) by the present day. Note that the loss
of star-forming gas is not due to gas being physically removed (i.e.
gas stripping), since field UDGs retain fairly high total gas fractions
(∼ 30 per cent on average, as shown by the dotted red line).
The complete removal of gas is, therefore, not a necessary cri-
terion for the production of UDGs. Gas heating alone produces the
low star-forming gas fractions in these objects (regardless of local
environment), without requiring that the gas be removed from the
galaxy entirely. Whether UDGs have had their gas entirely removed
or have just undergone heating makes little difference to their stel-
lar populations at z = 0. The median stellar ages of UDGs that have
been completely stripped of gas, and those in field environments
that have only undergone heating, are 8.7 Gyrs and 8.5 Gyrs re-
MNRAS 000, 1–22 (2019)
10 G. Martin et al.
spectively. In Section 5, we explore the processes that lead to the
removal or heating of gas in the LSBG population.
Note that although some galaxies (∼ 30 per cent) in the low-
density ‘field’ environment are actually satellites of another galaxy,
the average properties of field UDGs (or LSBGs and HSBGs) do
not change significantly if we select genuinely isolated galaxies
only (i.e. those that are not satellites). Isolated UDGs have typical
effective radii that are only slightly larger than field UDGs gener-
ally (5.15 kpc) and have slightly higher gas fractions (0.11).
In Figure 8, we show the redshift evolution of LSBGs and HS-
BGs in the star-forming gas fraction vs effective radius plane. As
shown in the left-hand panel, the main progenitors of the different
populations are very similar at high redshift (z∼ 3). Although they
differ somewhat in terms of their other properties (e.g. stellar mass
and environment), the progenitors of today’s LSBGs and HSBGs
share essentially identical effective radii and gas fractions in the
early Universe. This indicates that LSBGs emerged from a common
population of progenitors as HSBGs. The three populations only
begin to diverge significantly around z∼ 2 (see Figure 7) and then
separate rapidly at intermediate redshifts (z < 1). UDGs, in partic-
ular, diverge quickly from their HSB counterparts, both in terms of
rapidly increasing their effective radii and losing significant frac-
tions of their gas reservoirs at these redshifts.
We note that LSBGs appear to be part of a smooth distribu-
tion of properties across the general galaxy population. The dashed
blue, orange and red lines in the right-hand panel show the average
evolutionary tracks followed by HSBGs, Cl. LSBGs and UDGs re-
spectively over cosmic time. LSBGs do not take a different route
through the fgas–Reff plane. Instead, they follow very similar locii,
although their evolution (particularly for the UDG population) is
more rapid. Together with the fact that their high-redshift progen-
itors share very similar properties with the progenitors of HSBGs,
this suggests that LSBGs are not a special class of object in terms
of the populations from which they originate.
4.2 Density profiles
Our mass-matched population of LSBGs exhibit somewhat larger
effective radii compared to their HSB counterparts, even at high
redshift. This can either be a result of processes that directly in-
fluence the distribution of the stellar component of the galaxy, or
a result of processes that influence the distribution of the gas from
which these stars form. Establishing which of these is the case is
important for understanding what triggers the formation of LSBGs
at early epochs.
In this section, we consider how the slope of the median
gas and stellar density profiles of the different galaxy populations
evolve over time. The slope of the stellar density profile determines
the measured effective radius of the galaxy, with shallower slopes
typically resulting in larger effective radii at a given stellar mass.
Shallower density slopes (and therefore shallower gravitational po-
tentials) also reduce the energy required to displace material in the
system. In the case of the gas content, the shape of the potential
defines the distribution of stellar mass that forms from this gas.
Galaxies with shallower slopes are more vulnerable to the effects of
encounters with other galaxies or interactions between the galaxy
and the intergalactic medium (tidal heating, harassment, gas strip-
ping etc.), which may be important factors in their subsequent evo-
lution.
We calculate the mass-weighted log-log slope of each galaxy’s
gas and stellar outer density profile between 0.5Reff and 3Reff. We
calculate the density profile using radial bins of 30 particles. The
log-log density slope is parametrised by γ ′ (Dutton & Treu 2014):
γ ′ =
1
M(3Reff)−M(0.5Reff)
∫ 3Reff
0.5Reff
γ(r)4pir2ρ(r)dr, (1)
where γ =−d log(ρ)/d log(r) is the local log-log slope of the den-
sity profile, M(R) is the mass enclosed within a radius R, and ρ(r)
is the local density at radius r. Lower values of γ indicate shallower
density slopes. The density slopes that we recover are consistent
with previous studies using the Horizon-AGN simulation (Peirani
et al. 2017).
The main panel of Figure 9 shows the redshift evolution of the
median stellar density slopes for HSBGs, Cl. LSBGs and UDGs.
The inset shows the evolution of the median gas density slopes for
the same populations between z = 3 and z = 1. This is an epoch
at which galaxies are forming significant fractions of their present-
day stellar mass. This is particularly true of UDGs which, as we
show in Section 5.1 below, form the bulk (∼75 per cent) of their
stellar mass by z = 1. At these early epochs, therefore, the gas dis-
tribution is actively driving the creation of the stellar distribution. In
calculating the median gas density slope, we exclude any galaxies
with star-forming gas fractions (Mgas,SF/(Mgas,SF + M?)) smaller
than 0.05, so as to remove galaxies where the gas is no longer in-
fluencing the stellar distribution (since the star-forming gas mass is
negligible and star-formation has effectively ceased).
At high redshift, the median value of γ ′(gas) is lower (i.e. the
gas density slopes are shallower) in UDGs compared to both Cl.
LSBGs and HSBGs (∼1.56 at z = 2 compared with ∼1.8 for Cl.
LSBGs and HSBGs). Between z = 3 and z = 1, the gas density
slopes in the UDGs remain at a level significantly below the Cl.
LSBG and HSBG populations, while their stellar density slopes
decline faster than those of the Cl. LSBG and HSBG populations.
Thus, at the epochs where UDGs are actively forming the bulk of
their stellar mass, their gas density profiles are significantly flatter
than that of the HSBGs (and also the Cl. LSBGs).
After z = 1, the stellar density slopes decline rapidly, even
though most LSBGs have assembled the majority of their stellar
mass by this time. By z = 0.06 the median value of γ ′(?) for UDGs
has fallen by ∼ 0.32, from 1.67 at z = 1 to 1.35. The median value
of γ ′(?) for HSBGs (most of which have not yet assembled the ma-
jority of their stellar mass at z = 1), falls from 2.0 to 1.8 between
z = 1 and z = 0.06.
Figure 10 shows the distributions of the gas and stellar den-
sity slopes at two epochs: z = 0.06 and z = 1.03 (where the diver-
gence in the effective radii, gas fractions and stellar density slopes
between the LSB and HSB populations accelerates). At z = 1.03,
the distribution of γ ′(gas) strongly resembles that of γ ′(?) for all
three populations. For example, for the UDG gas and stellar den-
sity slope distributions, a two-sample Kolmogorov–Smirnov test
(Smirnov 1939) yields a D-statistic of 0.033 and a p-value of 0.28,
indicating a strong likelihood that the two samples are drawn from
the same distribution. This is a natural consequence of the fact that,
at early epochs (z > 1), the gas distribution is the principal factor
driving the development of the stellar profile, especially in UDGs,
which form the bulk of their stellar mass at these redshifts. The
stellar density slope is, therefore, gradually driven towards the gas
density slope over this epoch.
After z ∼ 1 the gas and stellar slopes progressively diverge,
with the divergence being fastest in UDG progenitors. By z = 0.06,
the stellar density slopes in UDGs have decoupled completely from
the gas density slopes, with the average stellar density slope becom-
MNRAS 000, 1–22 (2019)
Low surface-brightness galaxies 11
 
4GHH=MRE?






H I
CU
5
(
\
*5$)
%N.5$)
7&)
 
4GHH=MRE?
\
 
4GHH=MRE?
\
 
4GHH=MRE?
\
 
4GHH=MRE?
\
Figure 8. Redshift evolution of the star-forming gas fraction, defined as Mgas,SF/(Mgas,SF +M?), and effective radii of the progenitors of the HSBG (blue),
Cl. LSBG (orange) and UDG (red) populations. The time between each redshift snapshot is ∼ 2.5 Gyr. Coloured points indicate the position of individual
galaxies in the fgas–Reff plane. The error bars in each panel show the median values and 1σ dispersions for the distributions of the HSBG, Cl. LSBG and UDG
populations at each redshift. The dashed lines in the right-hand panel indicate the average locii followed by the main progenitors of HSBGs, Cl. LSBGs and
UDGs in the fgas–Reff plane over cosmic time.
   

\








γ
′ 


7&)
%N.5$)
*5$)
  

\



γ
′ 
I
CU

Figure 9. The evolution of the median log-log stellar density slope, γ ′(?),
calculated within 0.5 < Reff < 3 for UDGs, Cl. LSBGs and HSBGs as a
function of redshift. Error bars indicate the error on the median value of γ ′
at each redshift and solid filled regions show the 1σ confidence interval for a
Gaussian process regression to these points. Inset: the corresponding plots
for the log-log star-forming gas density slope, γ ′(gas). Note that, in the case
of the gas density slope, galaxies with very low star-forming gas fractions,
i.e. those less than 0.05, are excluded when we calculate the median values
of γ ′(gas).
ing much shallower than the average gas density slope. Thus, the
trigger for the initial divergence of HSBGs and UDGs at high red-
shift is likely to be processes that act on the gas profiles in UDGs
to make them shallower, rather than those that directly affect the
stellar components of these galaxies.
In the next section we explore some of the processes that lead
  
γ
′

ICU



 \  
  
γ
′

 




 7&)
%N.5$)
*5$)
(a)
  
γ
′

ICU



 \  
  
γ
′

 




(b)
Figure 10. (a) The distribution of the gas (top) and stellar (bottom) log-log
density slopes, γ ′, calculated within 0.5 < Reff < 3 for UDGs, Cl. LSBGs
and HSBGs at z = 0.06 . Coloured arrows indicate the median value for
each histogram. (b) The same for the distribution of the log-log density
slopes at z = 1.03. As in Figure 9, we exclude galaxies with star-forming
gas fractions smaller than 0.05 when plotting the gas density slopes.
to the divergence in the evolution in effective radius, gas fraction
and density slopes of LSBGs compared to their HSB counterparts.
MNRAS 000, 1–22 (2019)
12 G. Martin et al.


 5VCTHQTOCVKQP
6KFCNUVTKRRKPI
  \  
/GTIGTU
(QTDKFFGP
\  



∆
/
∆
V
=

/
¯
)
[T

?
  
∆/ICU 5(∆V =

/¯)[T

?



)CUCEETGVKQP
)CUTGOQXCN
  
5VGNNCTUVTKRRKPI
&T[OGTIGTU
Figure 11. Contour plots showing the distribution of the rate of change
in star-forming gas mass vs the rate of change in stellar mass, in units of
109M Gyr−1. A random selection of the data is plotted using the coloured
points in each panel. Each point represents the change between two consec-
utive timesteps. The left panels show changes in the redshift range 1< z< 3
and the right panels show the same for z < 1. The top, middle and bottom
rows show distributions for HSBGs, Cl. LSBGs and UDGs respectively.
Labels in each quadrant of the top panels indicate the main processes op-
erating in that section of the parameter space. Labels in the bottom panels
indicate the processes that cause points to fall close to the horizontal and
vertical axes.
5 HOW DO LOW-SURFACE-BRIGHTNESS GALAXIES
FORM?
The analysis presented above shows that the formation mechanisms
that produce LSBGs act to both increase the effective radii of their
progenitors and drive the steady loss of star-forming gas (either by
ejection from the galaxy or by heating). This produces diffuse sys-
tems with low SFRs and older stellar populations which, together,
result in systems that exhibit low surface-brightnesses. In this sec-
tion, we study the mechanisms which drive these changes over cos-
mic time: SN feedback, perturbations due to the ambient tidal field
and ram-pressure stripping.
We begin our analysis by taking an aggregate view of the role
of key processes that could drive LSBG formation. Figure 11 shows
distributions of the change in star-forming gas and stellar mass (in
units of 109M Gyr−1), for approximately evenly spaced simula-
tion outputs (∼250 Myrs), in the redshift range 1 < z < 3 (left) and
at z < 1 (when the HSB and LSB populations diverge most rapidly;
right). The top, middle and bottom panels show distributions for
the progenitors of HSBGs, Cl. LSBGs and UDGs respectively.
Different regions in this plot indicate different processes that
act to produce each of these galaxy populations. For example, star
formation will increase the stellar mass while decreasing the gas
mass, as it fuels the star formation. Galaxies undergoing star for-
mation will, therefore, populate the upper-left quadrant of this plot.
Mergers increase both stellar and gas mass (upper right quadrant),
with dry mergers towards the left-hand side of this quadrant. The
signature of gas removal (e.g. ram-pressure stripping and/or gas
heating) is a decrease in gas mass which is not accompanied by
a corresponding change in stellar mass (i.e. the negative half of
the x-axis), while gas accretion causes points to accumulate close
to the positive half of the x-axis. Tidal stripping (which is driven
by tidal heating) results in stripping of both stellar and gas mass
(lower left quadrant), typically from the outskirts of a galaxy. Tidal
heating will also cause the entire distribution of stars to expand, al-
though this is not possible to show in this plot. Finally, the lower
right quadrant is typically forbidden, because galaxies tend not to
increase their gas mass while simultaneously losing stars.
The top panel in Figure 11 indicates that HSBG evolution at
all epochs is largely driven by gas accretion, star formation and
mergers, with little impact from processes such as ram-pressure or
tidal stripping/heating. Star formation at high redshift is smooth
and the gas mass lost to star formation is typically replenished by
accretion. At lower redshifts, star formation remains at similar lev-
els, but accretion is typically no longer fast enough to offset the gas
that is transformed into stars. The plots show that the degree of gas
stripping and heating experienced by HSBGs must be small as, in
the vast majority of cases, any decrease in gas mass is accompanied
by an increase in stellar mass of a similar magnitude.
However, as we transition to populations that have lower
surface-brightnesses at the present day, the relative role of these
processes changes. Cl. LSBGs and UDGs both show similar evolu-
tion to HSBGs at z > 1, the epoch at which the bulk of their stellar
mass forms (see Section 5.1 below). However at z < 1, Cl. LSBGs
and, in particular, UDGs, have both experienced large decreases in
gas mass that are not the result of star formation. In the case of
UDGs, ram pressure stripping and tidal stripping/heating of both
stars and gas are clearly important processes in their evolution-
ary history (particularly at lower redshifts), as shown by the much
higher fraction of such systems that inhabit the lower left quadrant
compared to HSBGs. In the following sections, we study the mech-
anisms that drive these processes and explore their relative role in
creating LSB systems over cosmic time.
5.1 Supernova feedback - a trigger for LSBG formation
Theoretical studies by Di Cintio et al. (2017) and Chan et al. (2018)
show that, at least at low stellar masses, SN feedback may be ca-
pable of producing UDGs by fuelling outflows which create flat-
tened total density profiles (e.g. Navarro et al. 1996; Governato
et al. 2010; Pontzen & Governato 2012; Teyssier et al. 2013; Er-
rani et al. 2015; Oñorbe et al. 2015; Carleton et al. 2018; Sanders
et al. 2018). These outflows may be effective, not only at removing
gas from the galaxy, but also at producing shallower gas density
profiles (Brook et al. 2011, 2012; Pontzen & Governato 2014; Di
Cintio et al. 2014a,b; Dutton et al. 2016; Di Cintio et al. 2017) and
through the dynamical heating of stars, increasing their effective
radii (Chan et al. 2015; El-Badry et al. 2016) (although there may
be some tension with observations e.g. Patel et al. 2018). It may
also be the case, as we show later, that, rather than directly influ-
encing the size and gas content of galaxies, SN feedback instead
allows other processes to work more efficiently (e.g. tidal heating
and ram-pressure stripping).
It has been shown using the Horizon suite of simulations that
the inclusion of baryons and their associated feedback processes re-
sults in shallower stellar density slopes, compared to an otherwise
MNRAS 000, 1–22 (2019)
Low surface-brightness galaxies 13
    
V=)[T?





 7&)
%N.5$)
*5$)
Figure 12. Distribution of t50, (i.e. the minimum time required to form 50
per cent of a galaxy’s present-day stellar mass) for UDGs, Cl. LSBGs and
HSBGs. Coloured arrows indicate the median value for each histogram.
identical DM-only simulation (Peirani et al. 2017). As we have al-
ready shown in Section 3, the DM masses of UDGs and Cl. LSBGs
are not dissimilar to that in their HSB counterparts. It is therefore
not the case that UDGs are massive haloes that have been quenched
before their reservoir of star-forming gas has been used up. Instead,
it is worth considering whether differences in the actual stellar as-
sembly history of LSBGs, especially at early epochs where the bulk
of the stellar mass was formed, may be a contributing factor to cre-
ating their LSB nature over cosmic time.
Since the amount of SN feedback energy deposited in the po-
tential well will be sensitive to the star formation history, we con-
sider the burstiness of star formation in our different galaxy pop-
ulations. To quantify the burstiness we define t50, which measures
the minimum amount of time required to form 50 per cent of the
stellar mass in a galaxy4. Figure 12 shows the distribution of t50
values for the HSBG, Cl. LSBG and UDG populations. The me-
dian value of t50 for HSBGs is typically ∼3 Gyrs, while for UDGs
it is ∼1.5 Gyr (with the value for Cl. LSBGs falling in between
these values). This indicates that the formation of UDGs is much
more rapid than HSBGs of similar stellar masses. UDGs typically
assemble earlier and, on average, they have already formed 75 per
cent of their stellar mass by z = 1 (i.e. as a result of halo assembly
bias, Sheth & Tormen 2004).
On the other hand, HSBGs have formed only 30 per cent of
their stellar mass by this time. The median SFR for HSBGs falls
only modestly between z = 3 and the present day. As a result, en-
ergy released by supernovae (SNe) and stellar winds is distributed
over most of the lifetime of the galaxy, whereas feedback energy
is almost entirely concentrated before z = 1 in the case of UDGs.
This, in turn, means that the maximum instantaneous energy im-
4 In order to calculate t50, we first produce a histogram of the distribution of
star-particle ages in each galaxy at z = 0.06, using bin widths of 100 Myrs.
The bins in each histogram are then re-sorted, in order of decreasing fre-
quency, and the cumulative distribution function (CDF) is calculated. t50 is
the time at which this CDF reaches 50 per cent.
   

\







NQ
I 

'
5
0
=G
TI
U


/
[T

?
7&)
%N.5$)
*5$)






H
+PUVCPVCPGQWU50GPGTI[
%WOWNCVKXGHTCEVKQP
Figure 13. Median mechanical and thermal energy injected as a result of
Type Ia and Type II SNe and stellar winds. Solid lines indicate the SN en-
ergy released per 100 Myr as a function of redshift. Dotted lines show the
average cumulative energy as a fraction of the value at z = 0.06. The frac-
tions are indicated by the values on the right-hand axis.
parted into the gas is much larger in UDGs than in their HSB coun-
terparts.
We proceed by quantifying the impact that SN and stellar feed-
back may have on the galaxy populations due to their disparate
formation histories. We define the total mechanical and thermal en-
ergy released by stellar processes between two timesteps, t0 and t1,
by summing the energy released by each star particle within this
interval:
ESN =∑
i
m?,i(E(z1,Z)i−E(z0,Z)i) (2)
where m?,i is the mass of a star particle and E(z,Z)i is the cumula-
tive mechanical and thermal energy released by that star particle as
a result of Type Ia SNe, Type II SNe and stellar winds per unit stel-
lar mass, for a metallicity Z, and between the time of its formation
and a redshift of z.
Figure 13 shows the median mechanical and thermal energy
released by stars over the last 100 Myr, as a function of redshift.
Since our samples are matched in stellar mass, the total cumulative
feedback energy for each sample reaches the same value at z = 0.06
but the pattern of energy injection differs between the populations.
Since they form the majority of their stellar mass early on (75 per
cent before z = 1), the progenitors of UDGs release energy over a
shorter period of time.
As a result, UDGs experience high levels of SN feedback at
early times. Between z = 3 and z = 1, UDGs have already released
75 per cent of their integrated stellar feedback energy, compared
with 50 per cent for Cl. LSBGs and only 30 per cent for HSBGs.
The SN energy released in HSBGs remains roughly constant as a
function of redshift, decreasing by only 0.25 dex between the peak
at z∼ 1 and z = 0. In comparison, the SN energy released in UDGs
peaks between z = 2 and z = 1 and then declines rapidly towards
z = 0 to a value 1.5 dex lower.
We note that the same patterns are not observed for AGN feed-
back. As Figure 14 shows, the evolution of AGN feedback energy
in UDGs, Cl. LSBGs and HSBGs proceeds similarly at high red-
shift (z > 1), falling rapidly for low redshift UDGs as hot gas in
MNRAS 000, 1–22 (2019)
14 G. Martin et al.
   

\







NQ
I 

'
#
)
0
=G
TI
U


/
[T

?
7&)
%..5$)
*5$)
Figure 14. Median mechanical and thermal energy released as a result of
AGN feedback. Solid lines indicate the AGN energy released per 100 Myr
as a function of redshift.
cluster environments quenches the Bondi accretion rates of their
BHs. Additionally, BH growth in low-mass haloes is regulated
by SN feedback (e.g. Volonteri et al. 2015; Habouzit et al. 2017;
Bower et al. 2017), so that SN feedback is the principal feedback
process in the UDG population.
As we have shown in Section 4.2 (Figure 9), the gas density
slopes of UDG progenitors are significantly and consistently shal-
lower than their HSB counterparts in the early Universe (between
z = 1 and z = 3). This coincides with the period where instanta-
neous SN feedback energy is at its peak in the UDG progenitor
population. It is worth noting that the profiles of HSBG progeni-
tors behave very differently at these early epochs. Both their gas
and stellar density slopes tend to increase with time at these early
epochs, as baryons accumulate in the centres of their gravitational
potential wells. SN feedback therefore has a much greater impact
on LSBG progenitors than it does on their HSB counterparts.
We note that, while large amounts of energy are released into
the gas in UDG progenitors at these early epochs, the fraction of
star-forming gas (Figure 7, bottom panel) in UDG progenitors re-
mains significant ( fgas,SF > 0.4) at these times. This indicates that,
while the slope of the gas density profile is made shallower due
to this SN feedback, the feedback is not so strong that the gas is
completely removed and star-formation quenched.
As was noted in Section 4.2, stars forming from this gas pro-
gressively flatten the stellar density slopes, leading to the decrease
in γ ′(?) shown in Figure 9. SN feedback, therefore, appears to be
the mechanism that drives the creation of shallower gas and stellar
density slopes in UDG progenitors at high redshift, which leaves
these systems more vulnerable to tidal processes (e.g. tidal heating
and, additionally, ram-pressure stripping in dense environments)
over cosmic time. It is worth noting here that the specific angu-
lar momenta of LSBG and HSBG progenitors are very similar at
z ∼ 3, indicating that the flatter density profiles of LSBG progeni-
tors is not due to them initially forming with higher values of spin.
Although UDGs clearly increase in size (Figure 7, top panel)
and gain flatter density slopes (Figure 9, bottom panel) compared
to HSBGs and other LSBGs at z > 1, the difference is fairly modest
compared to the much greater divergence in effective radii and gas
fractions seen after z = 1 (Figure 7, top panel). Thus, SN feedback
appears to be the initial trigger for the divergence of UDGs from
the rest of the galaxy population, rather than the principal cause of
their large sizes at z = 0. A combination of a shallower potential
and a broader distribution of stars is likely to contribute to the steep
rise in the effective radii of UDG progenitors, in contrast to their
HSB counterparts seen after z = 1.
Much of this evolution must be due to external processes that
act to increase the effective radii steadily over cosmic time. Since
they would be expected to operate more efficiently on systems
where galaxies have shallower gravitational potentials (and where
the material, at least in the outer regions, is more weakly bound),
environmental processes such as perturbations from the ambient
tidal field and ram-pressure stripping are likely to amplify the ini-
tial divergence produced by SN feedback (Pontzen & Governato
2012; Errani et al. 2015; Carleton et al. 2018; Sanders et al. 2018).
We explore the effect of these processes in the next two sections.
It is worth noting here that processes other than SN feedback
could assist in the initial creation of shallower density slopes in
UDG progenitors. For example, an accretion history that is rich in
low-mass-ratio (i.e. minor) mergers may also act to broaden the
stellar distribution (e.g. Naab et al. 2009; Bezanson et al. 2009;
Hopkins et al. 2010; Bédorf & Portegies Zwart 2013). However,
while there is some evidence that LSBG progenitors do exhibit
some level of enhancement in their merger histories in the early
Universe (∼ twice the number of major mergers undergone by HS-
BGs between z = 3 and z = 1), it is difficult to draw concrete con-
clusions, as the merger histories of low mass-ratio mergers are typ-
ically highly incomplete in the simulation at high redshift (Martin
et al. 2018a)5.
In order to quantify the relative (and probably additive) roles
of feedback (e.g. Dashyan et al. 2018) and minor mergers (e.g. Di
Cintio et al. 2019) in triggering the initial shallower gas density
profiles, a higher resolution simulation is required. In a forthcoming
paper (Jackson et al. in prep) we will use New-Horizon (Dubois et
al. in prep), a 4000 Mpc3 zoom-in of a region of Horizon-AGN,
which has 64 times better spatial resolution to probe this ‘trigger
epoch’ in more detail.
5.2 Perturbations due to the ambient tidal field - a key driver
of LSBG evolution
Recall first from the arguments above that the processes that pro-
duce LSBGs operate steadily over cosmic time (since the effective
radii and gas fractions change gradually with redshift) and are not
specific to cluster environments (since UDGs are found in all en-
vironments). Mergers and tidal interactions with nearby objects of-
fer an attractive mechanism for LSBG formation because they act
to dynamically heat galaxies and destroy cold, ordered structures
(Moore et al. 1996, 1998; Gnedin 2003; Johansson et al. 2009).
These processes are therefore likely contributors to both the ob-
served increase in the effective radii and the decrease in the star-
forming gas fractions seen in the LSBG population, regardless of
local environment.
5 Due to the stellar mass resolution of the simulation, only objects that are
more massive than 2×108 M are detectable. As a result, only 50 per cent
and 20 per cent of the (z = 0) progenitors of 109.5 M galaxies are massive
enough for a 1:10 mass ratio merger to be detectable at z = 2 and z = 3
respectively (Martin et al. 2018a, Figure 1)
MNRAS 000, 1–22 (2019)
Low surface-brightness galaxies 15
It is worth noting first that, compared to HSBGs and Cl. LS-
BGs, UDGs in our sample are considerably more ‘spheroidal’ (i.e.
a larger fraction of their stars are on random orbits compared to
ordered, rotational ones). While the median value of the ratio of ro-
tational to dispersional velocities of the stellar component, (V/σ)?,
is 0.4 for Cl. LSBGs, it is only 0.15 for UDGs. In comparison, late-
type i.e. disc-dominated galaxies typically exhibit (V/σ)? > 0.55
(Martin et al. 2018b). Since mergers and interactions are efficient
drivers of (disc-to-spheroid) morphological transformation (Martin
et al. 2018a), this is evidence that the UDGs have indeed undergone
a larger number of interactions (but not necessarily actual mergers)
that have shaped their structural evolution.
Recent observational work lends support to the idea that the
formation of LSBGs is connected to the tidal effects of nearby
galaxies. Some studies have pointed to the idea that UDG progen-
itors may be more massive star-forming dwarfs that are destroyed
as a result of interactions within a cluster environment (e.g Con-
selice 2018). Alternatively, they may be less massive dwarfs that
have undergone considerable expansion (e.g. Carleton et al. 2018)
due to tidal interactions. It has also been suggested that at least
some UDGs may be tidal dwarfs (e.g. van Dokkum et al. 2018;
Ogiya 2018; Greco et al. 2018a), formed when material is stripped
from larger galaxies. However, since mergers typically produce
tidal dwarfs with low stellar masses (less than 1 per cent of the mass
of the merging progenitors, see e.g. Barnes & Hernquist (1992);
Okazaki & Taniguchi (2000); Kaviraj et al. (2012)), the mass range
that we consider in this study (M > 108) precludes significant
numbers of these objects in our sample.
In the context of mergers (i.e. interactions which result in the
actual coalescence of the interacting progenitors) it is worth noting
that both LSBGs and HSBGs undergo very few actual mergers at
low redshift, where the effective radii and star-forming gas frac-
tions change significantly. Indeed, only a few percent of galaxies
have undergone mergers of mass ratios larger than 1:4 since z = 1;
see e.g. Darg et al. 2010; Martin et al. 2018c,a). While UDGs do
undergo more mergers than HSBGs at high redshift (as was noted
earlier in Section 5.1), they experience a relative dearth of merg-
ers (a factor of 2.5 fewer major mergers) than their HSB counter-
parts between z = 1 and the present day, when much of the increase
in radii and decrease in gas content takes place. Galaxy mergers,
therefore, are unlikely to be the principal driver of LSBG evolution
over cosmic time.
However, tidal interactions (or fly bys) between galaxies can
produce similar effects to that due to actual mergers (e.g. Martin
et al. 2018a; Choi et al. 2018). To explore the effect of tidal interac-
tions on LSBGs and HSBGs, we employ a perturbation index (PI)
which quantifies the environmental tidal field due to objects in the
vicinity of the galaxy in question. We define the PI (e.g. Byrd &
Valtonen 1990; Choi et al. 2018) between z = 3 and the redshift in
question, by calculating the cumulative contribution of all galaxies
within 3 Mpc:
PI =
∫ z
z=3
∑
i
(
Mi
Mgal
)(
Reff
Di
)3
dt / Gyr (3)
where Mgal is the stellar mass of the galaxy in question and Mi is
the stellar mass of the ith perturbing galaxy. Reff is the effective
radius as defined in Section 2.3, Di is the distance from the ith per-
turbing galaxy and dt is in units of Gyrs. By this definition, galax-
ies that are more massive and/or approach more closely will con-
tribute more to the PI, with each galaxy’s contribution dropping off
steeply with distance. For example, a perturbation index PI = 10−1
   

\






NQ
I 

〈 2+
〉
7&)
%N.5$)
*5$)
#NN
(KGNF
    
NQI 2+







 7&)
%N.5$)
*5$)
(KGNF
Figure 15. Top: Median perturbation index (PI), as defined by Equation 3,
between z = 3 and the redshift in question. Error bars indicate the errors on
the median value of the PI at each redshift and solid filled regions show the
1σ confidence intervals for a Gaussian process regression to these points.
Dashed lines indicate the same for galaxies in the field only. Bottom: Distri-
bution of the perturbation index between z = 3 and z = 0. Dotted lines show
the distribution for field galaxies only. Coloured arrows indicate the median
value for each histogram and fainter arrows indicate the median values for
field galaxies. Note that the histograms are normalised so that the field and
general populations can be easily compared.
is equivalent to a single 1:10 mass ratio merger or an equal mass
galaxy moving within 2 effective radii. We note that our definition
of PI is a cumulative one, so that we integrate the perturbations felt
by individual galaxies between z = 3 and the redshift in question
(z). The PI is calculated at evenly spaced timesteps of ∼130 Myr
and we do not attempt to integrate galaxy orbits, as the relatively
coarse time resolution makes this unreliable.
In the top panel of Figure 15 we plot the median value of the PI
in each of our populations, as a function of redshift. At all redshifts
MNRAS 000, 1–22 (2019)
16 G. Martin et al.
galaxies that have lower surface-brightnesses exhibit consistently
higher PI values. The discrepancy between the median PI values in
the LSBG and HSBG populations becomes more pronounced with
time. Compared with HSBGs, UDGs in all environments undergo
more frequent or violent perturbations, exhibiting PI values more
than 2 dex higher towards low redshift (with Cl. LSBGs reaching
values around 1 dex higher). Not unexpectedly, for all populations,
galaxies that inhabit the field exhibit lower PI values.
In the bottom panel, we show the PI over the entire redshift
range of the top panel (0 < z < 3), i.e. Equation 3 evaluated at the
present day, for each of the galaxy populations. In other words, this
is the cumulative impact of the tidal field experienced by the galaxy
over around 90 per cent of cosmic time. The PI values for UDGs are
significantly larger, with the median of the UDG distribution being
around 2 orders of magnitude greater than that for the HSBGs.
We note that, if the definition of the perturbation index is
changed so that it is independent of Reff (by fixing Reff to 1 kpc), the
average perturbation index for UDGs remains significantly larger
than for equivalent HSB galaxies. With such a change in definition,
the median for UDGs remains 40 times higher than for HSBGs
(compared to 160 times higher when radius is considered), indicat-
ing that the PI is a genuine result of stronger perturbations, rather
than simply an effect of galaxy size.
It is important to note that the perturbations felt by UDGs are
not a strong function of environment. As the dashed red line in the
top panel and the dotted histograms in the bottom panel indicate,
the majority of UDGs in field environments have still undergone
very large perturbations compared with their HSB counterparts. In-
deed the PI values of field UDGs are not dissimilar to that of the
general UDG population (which is dominated by UDGs in groups
and clusters). Finally, it is worth noting that if we only consider
galaxies in low-density field environments which are not satellites,
i.e. those that are truly isolated, the cumulative PI of such UDGs re-
mains more than 10 times higher than that of field HSBGs.Together
with the fact that field UDGs have similar effective radii and star-
forming gas fractions at the present day to UDGs in clusters (Figure
7), this indicates that tidal interactions are likely to be the primary
mechanism that drives LSBG evolution and causes these systems
to both expand and lose their reservoir of star-forming gas over
cosmic time.
5.3 Ram pressure stripping - an additional mechanism of gas
removal in cluster LSBGs
While tidal perturbations are capable of acting on galaxies regard-
less of their environment, ram-pressure provides an additional pro-
cess that can shape the evolution of galaxies in denser environ-
ments, particularly in clusters. The ram pressure exerted on the gas
in a galaxy as it travels through a hot intra-cluster medium (ICM)
or intra-group medium (IGM) can remove gas from the galaxy and
quench star formation (Gunn & Gott 1972). This represents an
appealing mechanism for explaining the transformation of galax-
ies from gas-rich, star-forming objects to quiescent systems that
might resemble LSBGs at the present day. Indeed, the interaction
between the ICM/IGM and the inter-stellar media of galaxies that
are traversing hot, dense environments has often been used to ex-
plain the deficiency of gas and the redder colours of galaxies in
clusters (e.g. Chamaraux et al. 1980; Lee et al. 2003; Sabatini et al.
2005; Boselli et al. 2008; Gavazzi et al. 2013; Habas et al. 2018).
This is a particularly effective mechanism in low-mass galaxies
(M? < 1010M), as gravitational potentials are typically shallow
enough to allow the efficient removal of gas (e.g. Vollmer et al.
2001). In this section, we explore whether ram pressure stripping
may play a role in the gas exhaustion that creates our sample of
LSBGs.
5.3.1 Ram pressure
The cumulative ram pressure, Pram, felt between z = 3 and z by a
galaxy moving through the local medium is given by
Pram ∼
∫ z
z=3
ρIGMv2gal dt / Gyr (4)
where vgal is the velocity of the galaxy relative to the bulk velocity
of the surrounding medium and ρIGM is the mean gas density of
the surrounding medium within 10 times the maximum extent of
the stellar distribution of the galaxy.
The top panel of Figure 16 shows the median cumulative value
of Pram for the HSBG, Cl. LSBG and UDG populations as a func-
tion of redshift. The average ram-pressure continues to increase to-
wards the present day for UDGs, Cl. LSBGs and HSBGs. How-
ever, the average ram-pressure felt by HSBGs and Cl. LSBGs is
relatively small at all redshifts (around 2–3 orders of magnitude
smaller than that of the UDG population). Ram-pressure stripping
begins to have a significantly stronger impact on UDG progeni-
tors around z = 1. This is consistent with the typical infall epoch
of galaxies into clusters (e.g. Tormen 1998; Muldrew et al. 2015;
Mistani et al. 2016; Muldrew et al. 2018).
The cumulative ram pressure experienced by the progenitors
of UDGs in the field (dashed red line) is significantly lower (by
an order of magnitude) than the general population of UDG pro-
genitors. Although the level of ram pressure in these field UDGs is
high compared to that in Cl. LSBGs and HSBGs, it is low enough
that significant gas stripping does not occur (as indicated by the
relatively high total gas fractions retained by field UDGs at z = 0,
shown in the bottom panel of Figure 7). The bottom panel of Fig-
ure 16 shows the cumulative ram pressure experienced by HSBGs,
Cl. LSBGs and UDGs between z = 0 and z = 3. Again, the cumu-
lative ram pressure felt by UDGs is, on average, several orders of
magnitude higher than that felt by either the Cl. LSBGs or HSBGs.
It is worth noting here that the ram pressure experienced by
UDGs in the field is higher than that experienced by Cl. LSBGs
and HSBGs. This is a consequence of the fact that a larger fraction
(∼ 65 per cent) of local UDGs are satellites (i.e. their haloes are
identified as sub-structures of a more massive halo) while a major-
ity of low-mass field HSBGs at z = 0 are not (only ∼ 25 per cent
of these galaxies are satellites). UDGs are therefore typically found
in regions of slightly higher gas density and experience ram pres-
sure due to the host halo they are embedded in (e.g. Simpson et al.
2018). When genuinely isolated UDGs are selected (i.e. those that
are not satellites), the ram pressure felt falls significantly so that the
median cumulative ram pressure felt by completely isolated UDGs,
LSBGs and HSBGs agrees to within 0.2 dex.
5.3.2 Bulk flow of gas
Studying the bulk flow of gas within galaxies also allows us to
quantify the degree to which ram-pressure stripping is experi-
enced by our different galaxy populations. We explore the density
weighted average angle, θ , between the relative velocity between
the gas and stars (vrel) and the bulk motion of the stellar component
in the observed frame (v?):
cos(θ) =
1
∑ρi ∑i
vrel,i · 〈v?〉
|vrel,i| · |〈v?〉|
ρi (5)
MNRAS 000, 1–22 (2019)
Low surface-brightness galaxies 17
   

\







NQ
I 

〈 2 TCO
〉 =MI
O

U

?
7&)
%N.5$)
*5$)
#NN
(KGNF
     
NQI2TCO=MIO

U

?






7&)
%N.5$)
*5$)
(KGNF
Figure 16. Top: The cumulative ram pressure felt by galaxies between z = 3
and the redshift in question, as defined by Equation 4. Error bars indicate the
errors on the median value of Pram at each redshift and solid filled regions
show the 1σ confidence intervals for a Gaussian process regression to these
points. Dashed lines show the cumulative ram pressure felt by field galaxies
only. Bottom: Distribution of the cumulative ram pressure felt by galaxies
between z = 3 and z = 0. Coloured arrows indicate the median value for
each histogram and fainter arrows indicate the median values for galaxies
in the field. Dotted lines indicate the total integrated ram pressure for field
galaxies only. Note that the histograms are normalised so that the field and
general populations can be easily compared.
where vrel = vgas−〈v?〉 is the velocity of each gas cell relative to
the average velocity of the galaxy’s stellar component. In the case
where the bulk motion of the gas is in the opposite direction to the
stars, θ will be close to pi radians (and cos(θ) will be close to -
1). When the gas and stellar components are moving together at
roughly the same velocity, the angle between a given component
of vrel and 〈v?〉 is essentially randomly distributed and therefore θ
will be close to pi/2 (i.e. cos(θ) = 0). If the gas is either moving
ahead of the stellar component of the galaxy, or being accreted in a
    
OKPEQU
θ








7&)
%N.5$)
*5$)
(KGNF
Figure 17. The minimum value of cosθ between z = 3 and z = 0, where θ
is the angle between the average direction of the bulk motion of gas relative
to that of the stellar component in galaxies. Dotted lines indicate the largest
value of cosθ for field galaxies only. Coloured arrows indicate the median
value for each histogram and fainter dotted arrows indicate the median val-
ues for field galaxies only. Note that the histograms are normalised so that
the field and general populations can be easily compared.
wake behind the galaxy (e.g Sakelliou 2000), then θ will be close to
0. When ram-pressure stripping occurs, we therefore expect θ to be
close to pi radians and cos(θ) to be close to -1. Note that gas loss as
a result of mechanisms other than ram pressure stripping does not
produce the same signature. For example, in the case of gas loss
driven by harassment or feedback processes, gas moves out of the
galaxy either in a random direction or approximately isotropically,
so the average value of cos(θ) will be close to 0.
Figure 17 shows the minimum value of cos(θ) that galaxies
exhibit over cosmic time. Thus, minimum cos(θ) values close to
0 would indicate that the ram pressure has not operated on the
galaxy at any point over cosmic time. On the contrary, if we con-
sider galaxies to have undergone some ram-pressure stripping when
the minimum value of cos(θ) is less than -0.75, then a large major-
ity (65 per cent) of UDGs have undergone ram pressure stripping
at some point in their history. The same is not true of Cl. LSBG or
HSBG progenitors (or to a large extent, field UDGs). By the same
definition, almost none of the HSBGs in our sample (0.3 per cent)
have ever undergone significant ram-pressure stripping and a small
minority of Cl. LSBGs have (6 per cent). In the field, only a mod-
est fraction (25 per cent) of field UDGs have been ram-pressure
stripped.
Taken together, Figure 16 and Figure 17 indicate that ram-
pressure stripping make a significant contribution to the quench-
ing of UDG progenitors in dense environments. However, UDGs in
the field are not as significantly stripped (as shown by both panels
of Figure 16) but still have very low star-forming gas fractions at
z = 0 (panel d of Figure 6). This indicates that ram-pressure strip-
ping is not a necessary ingredient for the low star formation rates
seen in today’s UDGs. The high total gas fractions and low star-
forming gas fractions of field UDGs indicates that, for this sub-
set of UDGs, their gas has been heated by other processes rather
than been entirely removed from the galaxy. Thus, in cases where
MNRAS 000, 1–22 (2019)
18 G. Martin et al.
ram-pressure stripping is absent, other processes still act to quench
UDGs by heating their gas. While ram-pressure stripping is an im-
portant mechanism for removing gas from UDGs in dense envi-
ronments, UDGs (in all environments) lose their star-forming gas
through tidal perturbations, even in the absence of this process.
Ram-pressure stripping is, therefore, an additional process, to tidal
perturbations, that assists in the removal of gas in LSBGs, partic-
ularly in clusters, but is not necessary for quenching their star for-
mation. Interaction with the tidal field remains the principal driver
of LSBG evolution in all environments.
6 SUMMARY
In the forthcoming era of deep-wide observational surveys, the low-
surface-brightness Universe represents an important new frontier
in the study of galaxy evolution. While largely uncharted, due to
the lack of depth of past wide-area datasets like the SDSS, low-
surface-brightness galaxies (LSBGs) are essential to a complete
understanding of galaxy evolution. Recent work using small deep
surveys has hinted at the significant contribution that LSBGs may
make to the galaxy number density of the local Universe and high-
lighted the need to understand the evolution of these objects across
all local environments. Given the current dearth of data on LSBGs,
theoretical insights, using cosmological simulations, into their de-
mographics, the redshift evolution of their properties and the prin-
cipal mechanisms that drive their formation is highly desirable.
Here, we have used the Horizon-AGN hydrodynamical cos-
mological simulation to perform a comprehensive study of the for-
mation and evolution of LSBGs. We have (1) studied the demo-
graphics and properties of local LSBGs and compared them to that
of their high-surface-brightness (HSB) counterparts, (2) explored
the evolution of the properties of LSBG progenitors with redshift
and (3) quantified the role of key processes, in particular SN feed-
back, tidal perturbations and ram-pressure stripping, that lead to the
formation of LSB systems. Our main conclusions are as follows:
• LSBGs are significant contributors to the number density
of galaxies in the local Universe. For M?>108 M, LSBGs
contribute 47 per cent of the local number density (∼85 per cent
for M?>107 M). They are, however, minority contributors to
the local stellar mass and luminosity densities. For M?>108 M
(M?>107 M), the LSBGs contribute 7 (11) per cent and 6 (10)
per cent to the stellar mass and luminosity densities respectively.
• Local LSBGs have similar dark matter fractions and angular
momenta as their HSB counterparts but exhibit larger effective
radii (2.5× for UDGs), older stellar populations (1.6× for UDGs),
lower gas fractions (no star-forming gas remaining in most UDGs)
and shallower density profiles.
• LSBGs evolve from the same progenitor population as HSBGs
at high redshift. HSBGs and LSBGs originate from populations
with almost identical gas fractions and effective radii at z = 3 and
evolve along the same locii in the fgas−Reff plane. However, the
evolution of LSBGs (and UDGs in particular) is much more rapid,
especially at z < 1.
• UDGs experience more rapid star formation between z = 3
and z = 1, which triggers their creation and ultimate divergence
from the HSB population. More rapid star formation in UDG
progenitors produces more concentrated SN feedback which, in
turn, leads to shallower gas density profiles at high redshift (z > 1)
(i) rapid star formation at high red-
shift drives strong stellar feedback
which creates flatter gas density
slopes which then produce shal-
lower stellar density slopes.
(iia) shallower density slopes
make UDGs more suscepti-
ble to galaxy–galaxy interac-
tions which heat the gas and
‘puff up’ the stellar compo-
nents, producing diffuse, gas-
poor systems.
(iib) cluster UDGs are
processed further as they
fall into these dense en-
vironments, undergoing
ram-pressure stripping in
addition to heating by the
ambient tidal field.
40%
10% / 50%
Figure 18. A summary of the formation mechanisms of our sample of
UDGs. 40 per cent of these galaxies are found in high-density (cluster) en-
vironments at z = 0, while 10 and 50 per cent are found low density (field)
and intermediate density (group) environments, as indicated by the text next
to each arrow.
without quenching star formation. The star formation fuelled
by this gas then produces systems which have shallow stellar
density slopes (and larger effective radii). These systems are more
susceptible to processes like tidal heating of both stars and gas by
the ambient tidal field, and ram-pressure stripping of gas in denser
environments.
• External processes (tidal perturbations and ram-pressure
stripping) that drive most of the evolution of LSBGs are principally
effective at low and intermediate redshifts. At z < 1, the total and
star-forming gas fractions and effective radii of LSBGs, and UDGs
in particular, change drastically after fairly gradual evolution
between z = 3 and z = 1.
• Tidal heating (regardless of local environment) is able to
produce the large sizes and low star-forming gas fractions of
today’s UDGs. Flattened density profiles, produced via stronger
SN feedback, are amplified by the ambient tidal field, further
broadening the stellar distributions. UDGs, regardless of envi-
ronment, undergo tidal perturbations of similar magnitude, with
field UDGs exhibiting similar effective radii to their group/cluster
counterparts at the present day. In a similar vein, tidal heating is
also able to prevent gas from forming stars in UDG progenitors,
regardless of their local environment. Even in field environments,
where field UDGs remain star-forming down to low redshift, the
tidal field is able to continually heat the gas in a large number
of these systems, effectively quenching their star formation by
z = 0.25.
• In clusters, ram-pressure stripping is a significant additional
mechanism that removes gas from in-falling UDG progenitors,
starting around z = 1. Although ram-pressure stripping is very
effective at stripping gas in dense environments, it acts as a sec-
ondary mechanism to tidal heating outside of these environments,
MNRAS 000, 1–22 (2019)
Low surface-brightness galaxies 19
for creating the low fractions of star-forming gas found in UDGs at
the present day. Our analysis shows that tidal heating would likely
produce the low gas fractions found in cluster UDGs, even in the
absence of ram-pressure stripping.
Figure 18 shows a summary of the evolutionary channels for
LSBG formation described above. Our results offer insights into the
formation of galaxies in the LSB regime which, given their dom-
inance of the galaxy number densities, are essential pieces of the
puzzle of galaxy evolution. Furthermore, as we have demonstrated
in the analysis above, LSBGs are much more sensitive tracers of
key processes that shape galaxy evolution (e.g. SN feedback, tidal
perturbations and ram-pressure stripping) than their HSB counter-
parts. Without an understanding of the formation and evolution of
LSBGs, therefore, our comprehension of galaxy evolution remains
incomplete.
The new era of deep-wide surveys like the Hyper Suprime
Cam Subaru Strategic Program (HSC-SSP), and forthcoming
datasets from instruments like LSST, Euclid and WFIRST will rev-
olutionize the study of LSBGs, by yielding statistical samples of
these systems, for the first time, across all environments. These
datasets will enable us to perform the first statistical census of
LSBG properties and their evolution with redshift, producing strin-
gent tests of current theoretical predictions, such as those presented
in this study. Together, this will create a platform for construct-
ing a new generation of cosmological simulations, which offer a
better understanding of processes (e.g. SN feedback, ram pressure
stripping and tidal perturbations) to which the LSBG population
is particularly sensitive, and a better reproduction of galaxies in
the as-yet-unexplored LSB regime. This convergence of deep-wide
surveys and cosmological hydrodynamical simulations is likely to
have a transformational impact on our understanding of galaxy evo-
lution in the coming years.
ACKNOWLEDGEMENTS
We are grateful to the anonymous referee for several constructive
suggestions that improved the quality of the original manuscript.
We thank David Valls-Gabaud, Johan Knapen, Lee Kelvin, Cristina
Martinez-Lombilla, Elias Brinks, Shaun Read and Sebastien Vi-
aene for many interesting discussions. GM acknowledges support
from the STFC [ST/N504105/1]. SK acknowledges support from
the STFC [ST/N002512/1] and a Senior Research Fellowship from
Worcester College Oxford. RAJ acknowledges support from the
STFC [ST/R504786/1]. JD and AS acknowledge funding support
from Adrian Beecroft, the Oxford Martin School and the STFC.
CL is supported by a Beecroft Fellowship. CP acknowledges fund-
ing support from the ERC [670193]. This research has used the
DiRAC facility, jointly funded by the STFC and the Large Facili-
ties Capital Fund of BIS, and has been partially supported by grant
Spin(e) ANR-13-BS05-0005 of the French ANR. This work was
granted access to the HPC resources of CINES under the alloca-
tions 2013047012, 2014047012 and 2015047012 made by GENCI.
This work is part of the Horizon-UK project.
REFERENCES
Abazajian K. N., et al., 2009, ApJS, 182, 543
Abraham R. G., van Dokkum P. G., 2014, Publications of the Astronomical
Society of the Pacific, 126, 55
Abraham R., et al., 2018, Research Notes of the American Astronomical
Society, 2, 16
Akhlaghi M., Ichikawa T., 2015, The Astrophysical Journal Supplement
Series, 220
Amorisco N. C., Loeb A., 2016, MNRAS, 459, L51
Amorisco N. C., Monachesi A., Agnello A., White S. D. M., 2016, preprint,
(arXiv:1610.01595)
Amorisco N. C., Monachesi A., Agnello A., White S. D. M., 2018, MN-
RAS, 475, 4235
Aubert D., Pichon C., Colombi S., 2004, MNRAS, 352, 376
Bakos J., Trujillo I., 2012, preprint, (arXiv:1204.3082)
Baldry I. K., Glazebrook K., Driver S. P., 2008, MNRAS, 388, 945
Barnes J. E., Hernquist L., 1992, Nature, 360, 715
Baushev A. N., 2018, New Astron., 60, 69
Beasley M. A., Trujillo I., 2016, ApJ, 830
Beasley M. A., Romanowsky A. J., Pota V., Navarro I. M., Martinez Del-
gado D., Neyer F., Deich A. L., 2016, ApJ, 819, L20
Bédorf J., Portegies Zwart S., 2013, MNRAS, 431, 767
Benson A. J., Bower R. G., Frenk C. S., Lacey C. G., Baugh C. M., Cole S.,
2003, ApJ, 599, 38
Bernstein G. M., Nichol R. C., Tyson J. A., Ulmer M. P., Wittman D., 1995,
AJ, 110, 1507
Bezanson R., van Dokkum P. G., Tal T., Marchesini D., Kriek M., Franx
M., Coppi P., 2009, ApJ, 697, 1290
Blanton M. R., Lupton R. H., Schlegel D. J., Strauss M. A., Brinkmann J.,
Fukugita M., Loveday J., 2005, ApJ, 631, 208
Blitz L., Shu F. H., 1980, ApJ, 238, 148
Boselli A., Boissier S., Cortese L., Gavazzi G., 2008, ApJ, 674
Bothun G. D., Impey C. D., Malin D. F., Mould J. R., 1987, AJ, 94, 23
Bothun G. D., Impey C. D., Malin D. F., 1991, ApJ, 376, 404
Bournaud F., Duc P.-A., 2006, A&A, 456, 481
Bower R. G., Benson A. J., Malbon R., Helly J. C., Frenk C. S., Baugh
C. M., Cole S., Lacey C. G., 2006, MNRAS, 370, 645
Bower R. G., Schaye J., Frenk C. S., Theuns T., Schaller M., Crain R. A.,
McAlpine S., 2017, MNRAS, 465, 32
Breiman L., Meisel W., Purcell E., 1977, Technometrics, 19, 135
Brook C. B., Di Cintio A., 2015, MNRAS, 450, 3920
Brook C. B., et al., 2011, MNRAS, 415, 1051
Brook C. B., Stinson G., Gibson B. K., Roškar R., Wadsley J., Quinn T.,
2012, MNRAS, 419, 771
Bruzual G., Charlot S., 2003, MNRAS, 344, 1000
Byrd G., Valtonen M., 1990, ApJ, 350, 89
Cappellari M., et al., 2011, MNRAS, 416, 1680
Carleton T., Errani R., Cooper M., Kaplinghat M., Peñarrubia J., 2018,
preprint, p. arXiv:1805.06896 (arXiv:1805.06896)
Chabrier G., 2003, Publications of the Astronomical Society of the Pacific,
115, 763
Chamaraux P., Balkowski C., Gerard E., 1980, A&A, 83, 38
Chan T. K., Kereš D., Oñorbe J., Hopkins P. F., Muratov A. L., Faucher-
Giguère C. A., Quataert E., 2015, MNRAS, 454, 2981
Chan T. K., Kereš D., Wetzel A., Hopkins P. F., Faucher-Giguère C. A., El-
Badry K., Garrison-Kimmel S., Boylan-Kolchin M., 2018, MNRAS,
p. 1094
Choi H., Yi S. K., Dubois Y., Kimm T., Devriendt J. E. G., Pichon C., 2018,
ApJ, 856
Cole S., Lacey C. G., Baugh C. M., Frenk C. S., 2000, MNRAS, 319, 168
Conselice C. J., 2018, Research Notes of the American Astronomical Soci-
ety, 2, 43
Croton D. J., et al., 2006, MNRAS, 365, 11
Dabringhausen J., Kroupa P., 2013, MNRAS, 429, 1858
Dalcanton J. J., Spergel D. N., Gunn J. E., Schmidt M., Schneider D. P.,
1997, AJ, 114, 635
Darg D. W., et al., 2010, MNRAS, 401, 1043
Dashyan G., Silk J., Mamon G. A., Dubois Y., Hartwig T., 2018, MNRAS,
473, 5698
Davies J. I., Phillipps S., Disney M. J., 1990, MNRAS, 244, 385
Di Cintio A., Brook C. B., Macciò A. V., Stinson G. S., Knebe A., Dutton
A. A., Wadsley J., 2014a, MNRAS, 437, 415
MNRAS 000, 1–22 (2019)
20 G. Martin et al.
Di Cintio A., Brook C. B., Dutton A. A., Macciò A. V., Stinson G. S., Knebe
A., 2014b, MNRAS, 441, 2986
Di Cintio A., Brook C. B., Dutton A. A., Macciò A. V., Obreja A., Dekel
A., 2017, MNRAS, 466, L1
Di Cintio A., Brook C. B., Macciò A. V., Dutton A. A., Cardona-Barrero
S., 2019, arXiv e-prints, p. arXiv:1901.08559
Diehl T., Dark Energy Survey Collaboration 2012, Physics Procedia, 37,
1332
Disney M. J., 1976, Nature, 263, 573
Draine B. T., et al., 2007, ApJ, 663, 866
Driver S. P., 1999, ApJ, 526, L69
Driver S. P., Liske J., Cross N. J. G., De Propris R., Allen P. D., 2005,
MNRAS, 360, 81
Dubois Y., et al., 2014, MNRAS, 444, 1453
Dubois Y., Peirani S., Pichon C., Devriendt J., Gavazzi R., Welker C.,
Volonteri M., 2016, MNRAS, 463, 3948
Dutton A. A., Treu T., 2014, MNRAS, 438, 3594
Dutton A. A., et al., 2016, MNRAS, 461, 2658
El-Badry K., Wetzel A., Geha M., Hopkins P. F., Kereš D., Chan T. K.,
Faucher-Giguère C.-A., 2016, ApJ, 820, 131
Errani R., Penarrubia J., Tormen G., 2015, MNRAS, 449, L46
Ferdosi B. J., Buddelmeijer H., Trager S. C., Wilkinson M. H. F., Roerdink
J. B. T. M., 2011, A&A, 531, A114
Ferré-Mateu A., et al., 2018, MNRAS, p. 1525
Gavazzi G., Fumagalli M., Fossati M., Galardo V., Grossetti F., Boselli A.,
Giovanelli R., Haynes M. P., 2013, A&A, 553
Girardi L., Bressan A., Bertelli G., Chiosi C., 2000, A&AS, 141, 371
Gnedin O. Y., 2003, ApJ, 582, 141
Governato F., et al., 2010, Nature, 463, 203
Greco J. P., et al., 2018a, Publications of the Astronomical Society of Japan,
70, S19
Greco J. P., et al., 2018b, ApJ, 857, 104
Gu M., et al., 2018, ApJ, 859, 37
Gunn J. E., Gott J. Richard I., 1972, ApJ, 176, 1
Haardt F., Madau P., 1996, ApJ, 461, 20
Habas R., Fadda D., Marleau F. R., Biviano A., Durret F., 2018, MNRAS,
475, 4544
Haberzettl L., Bomans D. J., Dettmar R. J., 2007, A&A, 471, 787
Habouzit M., Volonteri M., Dubois Y., 2017, MNRAS, 468, 3935
Hagen L. M. Z., et al., 2016, ApJ, 826, 210
Hartmann L., Ballesteros-Paredes J., Bergin E. A., 2001, ApJ, 562, 852
Hayward C. C., Irwin J. A., Bregman J. N., 2005, ApJ, 635, 827
Hopkins P. F., Bundy K., Hernquist L., Wuyts S., Cox T. J., 2010, MNRAS,
401, 1099
Impey C., Bothun G., Malin D., 1988, ApJ, 330, 634
Janssens S., Abraham R., Brodie J., Forbes D., Romanowsky A. J., van
Dokkum P., 2017, ApJ, 839, L17
Johansson P. H., Naab T., Ostriker J. P., 2009, ApJ, 697, L38
Kaviraj S., Darg D., Lintott C., Schawinski K., Silk J., 2012, MNRAS, 419,
70
Kaviraj S., Devriendt J., Dubois Y., Slyz A., Welker C., Pichon C., Peirani
S., Le Borgne D., 2015, MNRAS, 452, 2845
Kaviraj S., et al., 2017, MNRAS, 467, 4739
Kennicutt Jr. R. C., 1998, ApJ, 498, 541
Kniazev A. Y., Grebel E. K., Pustilnik S. A., Pramskij A. G., Kniazeva T. F.,
Prada F., Harbeck D., 2004, AJ, 127, 704
Koda J., Yagi M., Yamanoi H., Komiyama Y., 2015, ApJ, 807
Komatsu E., et al., 2011, ApJS, 192, 18
Kuijken K., et al., 2002, The Messenger, 110, 15
Laporte C. F. P., Agnello A., Navarro J. F., 2018, preprint, p.
arXiv:1804.04139 (arXiv:1804.04139)
Lee H., McCall M. L., Richer M. G., 2003, AJ, 125, 2975
Leisman L., et al., 2017, ApJ, 842, 133
Leitherer C., Robert C., Drissen L., 1992, ApJ, 401, 596
Leitherer C., et al., 1999, ApJS, 123, 3
Leitherer C., Ortiz Otálvaro P. A., Bresolin F., Kudritzki R.-P., Lo Faro B.,
Pauldrach A. W. A., Pettini M., Rix S. A., 2010, ApJS, 189, 309
Maoz D., Mannucci F., Brandt T. D., 2012, MNRAS, 426, 3282
Martin G., Kaviraj S., Devriendt J. E. G., Dubois Y., Pichon C., 2018a,
MNRAS, p. 1855
Martin G., Kaviraj S., Devriendt J. E. G., Dubois Y., Pichon C., Laigle C.,
2018b, MNRAS, 474, 3140
Martin G., et al., 2018c, MNRAS, 476, 2801
Martínez-Delgado D., et al., 2016, AJ, 151, 96
Matteucci F., Greggio L., 1986, A&A, 154, 279
Matteucci F., Recchi S., 2001, ApJ, 558, 351
Merritt A., van Dokkum P., Danieli S., Abraham R., Zhang J., Karachentsev
I. D., Makarova L. N., 2016, ApJ, 833, 168
Mihos J. C., et al., 2015, ApJ, 809, L21
Minchin R. F., et al., 2004, MNRAS, 355, 1303
Mistani P. A., et al., 2016, MNRAS, 455, 2323
Miyazaki S., et al., 2002, Publications of the Astronomical Society of Japan,
54, 833
Miyazaki S., et al., 2012, in Ground-based and Airborne Instrumentation
for Astronomy IV. Proceedings of the SPIE, Volume 8446, article id.
84460Z, 9 pp. (2012).. , doi:10.1117/12.926844
Moore B., Katz N., Lake G., Dressler A., Oemler A., 1996, Nature, 379,
613
Moore B., Governato F., Quinn T., Stadel J., Lake G., 1998, ApJ, 499, L5
Mowla L., van Dokkum P., Merritt A., Abraham R., Yagi M., Koda J., 2017,
ApJ, 851, 27
Muñoz R. P., et al., 2015, ApJ, 813
Muldrew S. I., Hatch N. A., Cooke E. A., 2015, MNRAS, 452, 2528
Muldrew S. I., Hatch N. A., Cooke E. A., 2018, MNRAS, 473, 2335
Naab T., Johansson P. H., Ostriker J. P., 2009, ApJ, 699, L178
Navarro J. F., Eke V. R., Frenk C. S., 1996, MNRAS, 283, L72
Nomoto K., Saio H., Kato M., Hachisu I., 2007, ApJ, 663, 1269
Oñorbe J., Boylan-Kolchin M., Bullock J. S., Hopkins P. F., Kereš D.,
Faucher-Giguère C.-A., Quataert E., Murray N., 2015, MNRAS, 454,
2092
O’Neil K., Bothun G., 2000, ApJ, 529, 811
Ogiya G., 2018, preprint, p. arXiv:1804.06421 (arXiv:1804.06421)
Okazaki T., Taniguchi Y., 2000, ApJ, 543, 149
Papastergis E., Adams E. A. K., Romanowsky A. J., 2017, A&A, 601, L10
Patel S. G., Kelson D. D., Diao N., Tonnesen S., Abramson L. E., 2018,
preprint, p. arXiv:1807.02118 (arXiv:1807.02118)
Peirani S., et al., 2017, MNRAS, 472, 2153
Peirani S., et al., 2018, preprint, (arXiv:1801.09754)
Peng E. W., Lim S., 2016, ApJ, 822
Pontzen A., Governato F., 2012, MNRAS, 421, 3464
Pontzen A., Governato F., 2014, Nature, 506, 171
Prole D. J., Davies J. I., Keenan O. C., Davies L. J. M., 2018, MNRAS,
p. 970
Román J., Trujillo I., 2017a, MNRAS, 468, 703
Román J., Trujillo I., 2017b, MNRAS, 468, 4039
Rong Y., Guo Q., Gao L., Liao S., Xie L., Puzia T. H., Sun S., Pan J., 2017,
MNRAS, 470, 4231
Ruiz-Lara T., et al., 2018, MNRAS, 478, 2034
Sabatini S., Davies J., van Driel W., Baes M., Roberts S., Smith R., Linder
S., O’Neil K., 2005, MNRAS, 357, 819
Sakelliou I., 2000, MNRAS, 318, 1164
Sandage A., Binggeli B., 1984, AJ, 89, 919
Sanders J. L., Evans N. W., Dehnen W., 2018, MNRAS, 478, 3879
Schaye J., et al., 2015, MNRAS, 446, 521
Schechter P., 1976, ApJ, 203, 297
Sheth R. K., Tormen G., 2004, MNRAS, 350, 1385
Sifón C., van der Burg R. F. J., Hoekstra H., Muzzin A., Herbonnet R.,
2018, MNRAS, 473, 3747
Simpson C. M., Grand R. J. J., Gómez F. A., Marinacci F., Pakmor R.,
Springel V., Campbell D. J. R., Frenk C. S., 2018, MNRAS, 478, 548
Smirnov N. V., 1939, Bull. Math. Univ. Moscou, 2, 3
Smith Castelli A. V., Faifer F. R., Escudero C. G., 2016, A&A, 596, A23
Somerville R. S., Primack J. R., 1999, MNRAS, 310, 1087
Sutherland R. S., Dopita M. A., 1993, ApJS, 88, 253
Teyssier R., 2002, A&A, 385, 337
Teyssier R., Pontzen A., Dubois Y., Read J. I., 2013, MNRAS, 429, 3068
MNRAS 000, 1–22 (2019)
Low surface-brightness galaxies 21
Toloba E., et al., 2018, ApJ, 856
Tormen G., 1998, MNRAS, 297, 648
Torrealba G., et al., 2018, preprint, p. arXiv:1811.04082
(arXiv:1811.04082)
Trujillo I., et al., 2018, preprint, (arXiv:1806.10141)
Turner J. A., Phillipps S., Davies J. I., Disney M. J., 1993, MNRAS, 261,
39
Tweed D., Devriendt J., Blaizot J., Colombi S., Slyz A., 2009, A&A, 506,
647
Vassiliadis E., Wood P. R., 1993, ApJ, 413, 641
Venhola A., et al., 2017, A&A, 608
Vogelsberger M., et al., 2014, MNRAS, 444, 1518
Vollmer B., Cayatte V., Balkowski C., Duschl W. J., 2001, ApJ, 561, 708
Volonteri M., Capelo P. R., Netzer H., Bellovary J., Dotti M., Governato F.,
2015, MNRAS, 449, 1470
Volonteri M., Dubois Y., Pichon C., Devriendt J., 2016, MNRAS, 460, 2979
Williams R. P., et al., 2016, MNRAS, 463, 2746
Yagi M., Koda J., Komiyama Y., Yamanoi H., 2016, The Astrophysical
Journal Supplement Series, 225, 11
Yozin C., Bekki K., 2015, MNRAS, 452, 937
Zaritsky D., et al., 2019, The Astrophysical Journal Supplement Series, 240,
1
Zhong G. H., Liang Y. C., Liu F. S., Hammer F., Hu J. Y., Chen X. Y., Deng
L. C., Zhang B., 2008, MNRAS, 391, 986
van Dokkum P. G., Abraham R., Merritt A., Zhang J., Geha M., Conroy C.,
2015, ApJ, 798
van Dokkum P., et al., 2016, ApJ, 828
van Dokkum P., et al., 2018, Nature, 555, 629
van der Burg R. F. J., Muzzin A., Hoekstra H., 2016, A&A, 590
APPENDIX A: EXTRAPOLATING THE MASS AND
SURFACE-BRIGHTNESS FUNCTIONS
Since the Horizon-AGN mass function becomes incomplete as
we approach the galaxy mass resolution limit of the simulation
(M? ∼ 108M), it is necessary to extrapolate the stellar mass and
surface-brightness functions in order to obtain estimates of the con-
tribution of LSBGs to the number, stellar mass and luminosity den-
sities down to M? ∼ 107M.
To do this, we first fit a Schechter function (Schechter 1976) to
the raw Horizon-AGN mass function yielding a slope of 1.23±0.030.05
(Figure A1). We then use a Gaussian mixture model to fit the dis-
tribution of galaxies in the stellar mass – surface-brightness plane,
allowing us to estimate the shape and variance of the data. Beyond
the resolution limit (2× 108M), we linearly extrapolate the vari-
ance down to 107M (Figure A2).
In order to obtain the extrapolated surface-brightness function,
we split the mass function into narrow mass bins and draw N times
from a Gaussian distribution with a variance and mean defined by
our fit to the stellar mass – surface-brightness distribution, where N
is the number of objects in that mass bin. Where the mass function
is complete (above 109M), we fill in the surface-brightness func-
tion using the raw data. The resultant surface-brightness is shown
in Figure 3.
APPENDIX B: EFFECT OF THE SPATIAL RESOLUTION
OF THE SIMULATION
In this section, we discuss the effect of the spatial resolution of the
simulation (1 kpc) on the sizes (and therefore surface-brightnesses)
of low-mass galaxies. Although the locus of the M?–Reff distribu-
tion only barely reaches 1 kpc at our mass limit (2× 108M; e.g.
see Figure 2), it is still possible that the resolution may produce
     
NQI 
/ /¯










φ

F
0
F
/

Figure A1. Schechter function fit to the Horizon-AGN mass function.
Points with error bars indicate binned data with Poisson errors. The grey
region indicates the 99 per cent confidence interval for the fit to the data.
     
NQI 
/ /¯










〈 µ〉 G
HKV
σFKURGTUKQP
Figure A2. Density plot showing the distribution of galaxies in the stellar
mass – surface-brightness plane. The dashed black line indicates the fit to
the data using a mixture of Gaussians and the filled grey region indicates
the 1σ dispersion.
some spurious dynamical support. This problem would likely be
compounded if the maximum resolution is not satisfied in the cells
at the centres of our galaxies.
We first check the refinement level (i.e. the accuracy used by
the gravity and hydrodynamics solvers; see Teyssier (2002)) of the
AMR grid within the central Reff. As noted in Section 2, the AMR
grid is refined according to a semi-Lagrangian criterion, where the
refinement of a cell is approximately proportional to the total mass
within the cell. Table B1 shows the refinement of the AMR cells
within 1 and 2 Reff of each galaxy used for our sample of UDGs and
HSBGs in Section 4. On average almost 100 per cent of the AMR
MNRAS 000, 1–22 (2019)
22 G. Martin et al.
UDGs level 17 (1 kpc) > level 16 (>2 kpc)
R < Reff 98% 100%
Reff < R < 2 Reff 21% 100%
HSBs
R < Reff 100% 100%
Reff < R < 2 Reff 88% 100%
Table B1. The percentage of AMR cells within 1 Reff or 2 Reff that are
refined to level 17 or at least level 16. The table is split between the UDG
sample and the HSB sample.
cells within 1 Reff of each galaxy are refined to the maximum level
(level 17; 1 kpc) for both UDGs and HSBGs and within 2 Reff. The
value falls to 21 per cent for UDGs, owing to their larger effective
radii (i.e. they extend much further from the centre of the total mass
distribution). In both cases, all cells are refined to at least the second
highest level (level 16; 2 kpc).
We also check how the effective radii of equivalent galaxies
in a higher resolution, 4000 Mpc3 zoom-in of a region of Horizon-
AGN (New Horizon; Dubois et al. in preparation) differ from those
in the Horizon-AGN simulation. New Horizon has a spatial resolu-
tion 35 pc (×30 Horizon-AGN) but uses the same underlying code
(RAMSES Teyssier 2002) and implements similar sub-grid prescrip-
tions. The comparison is made at z = 0.7, the lowest redshift to
which the New Horizon simulation has been run.
In order to produce a matching catalogue of galaxies, at the
initial snapshot, the particle IDs of multiple (64) DM particles in
the high resolution simulation were mapped onto each DM particle
in Horizon-AGN. This allows us to match galaxy haloes between
simulations and thereby attempt to find each galaxy’s ‘twin’ in the
New Horizon simulation. We limit ourselves to haloes that share at
least 75 per cent of the same DM particles, have at least 75 per cent
of the mass of their matching halo and which host galaxies with
stellar masses that are no more than a factor of two different from
their twin. This yields a sample of 50 galaxies with masses between
2×108 M and 1010 M.
Figure B1 shows the effective radii and stellar masses of
galaxies that we were able to robustly match between the two simu-
lations, with each pair of twin galaxies joined by a dashed grey line.
While the much higher resolution of the New Horizon simulation
produces differences in the accretion histories and star formation of
haloes compared with their twin haloes in the Horizon-AGN sim-
ulation, the lower resolution of the Horizon-AGN simulation does
not produce a significant systematic offset in galaxy sizes. On aver-
age, galaxies in the Horizon-AGN simulation have only marginally
larger sizes. The mean of the distribution of size offsets in Fig-
ure B1 (denoted by a red arrow) is 0.1± 0.04, so that galaxies in
Horizon-AGN are only 10 per cent larger, on average, than their
twin in New Horizon. Note that the higher-resolution twin is often
the larger of the two (26 per cent of higher-resolution galaxies are
slightly larger).
The black lines in Figure B1 show the trend in Reff vs M?
for the whole sample of galaxies within the same volume as New
Horizon, regardless of whether they are reliably matched. Again,
the average sizes of galaxies in Horizon-AGN are only around 10
per cent larger than equivalent mass galaxies in New Horizon.
We note however, that there is some degree of systematic off-
set between the average sizes of the simulated and observed galax-
ies (e.g. see blue filled points vs blue open points in Figure 2). This
is especially pronounced at the high stellar mass end (∼ 1011.5M),
where, compared to Cappellari et al. (2011, open circles), simulated
   
NQI
/ /¯





4
GH
H
=M
RE
?
0GY*QTK\QP
\  
*QTK\QP#)0
\  
  

4GHH 0* 4GHH *\4GHH *\
Figure B1. Comparison of the effective radius and stellar mass of galax-
ies with haloes matched between the Horizon-AGN simulation and higher-
resolution (35 pc) New Horizon simulation. Square and circle markers of
the same colour linked by a dashed line indicate the stellar mass and ef-
fective radius of a matched galaxy in the New Horizon simulation (open
square) and the Horizon-AGN simulation (open circle). The black solid and
dashed lines show the mean trend in Reff vs M? for New Horizon and the
matching volume in Horizon-AGN respectively. Errors are not shown in the
interest of legibility, but the typical error on the mean is ±0.1 kpc in each
bin. The inset plot shows the distribution of the fractional difference in Reff
between the two simulations and the red arrow shows the mean fractional
difference.
galaxy sizes are around 1.5 – 2 times larger than observed galaxies
of equivalent mass. Towards lower masses (∼ 1010M), the typical
sizes of simulated galaxies are only 1.15 times larger than those of
observed galaxies. This may be an indication that the AGN feed-
back prescription produces artificially large galaxies at high stel-
lar mass (where AGN feedback is most efficient), but is not such
an important effect at low masses, where AGN feedback becomes
relatively unimportant compared to stellar feedback. For example,
Peirani et al. (2018, see their Figure 1) show that the AGN feed-
back implementation used in Horizon-AGN produces galaxies that
are larger than observed galaxies compared to the same simulation
with no AGN feedback at masses of M? ≈ 1011.5M.
APPENDIX C: RELEVANCE OF THIS STUDY TO
OBSERVED LSBG POPULATIONS
In this section, we discuss the relevance and applicability of this
study to observed UDG populations. Figure C1 compares the mass
distribution of cluster UDGs in the Horizon-AGN simulation (with
a correction for incompleteness applied as detailed in Appendix
A) to that of observed UDGs in the Coma and Virgo clusters (van
Dokkum et al. 2015; Mihos et al. 2015; Yagi et al. 2016; Gu
et al. 2018). Within the mass range where both samples overlap,
there is good agreement between the mass distribution of Horizon-
AGN UDGs (red histogram) and the observed cluster UDGs (blue
histogram). Assuming a log-normal distribution for the observed
sample, we also find that Horizon-AGN agrees within a factor
MNRAS 000, 1–22 (2019)
Low surface-brightness galaxies 23
   
NQI
/ /¯






0
QT
O
CN
KU
GF
HT
GS
WG
PE
[
$CNFT[
ªEQPUV
)CWUUKCPHKVVQQDUGTXGF
*QTK\QP#)07&)U
ENWUVGT
%QOC
8KTIQ7&)U
Figure C1. The blue histogram shows the normalised stellar mass distribu-
tion for UDGs in the Coma and Virgo clusters (red open squares in Figure 2)
and the blue dotted line shows a log-normal fit to the full distribution of
masses. The red histogram shows the stellar mass distribution for Horizon-
AGN cluster UDGs after an extrapolation of the stellar mass function has
been performed as detailed in Appendix A. The Horizon-AGN UDG and
observed cluster UDG histograms are both normalised by dividing by the
number of counts in the three bins where the datasets overlay (between
108M) and 109M. The dashed black line indicates the non-parametric
galaxy stellar mass function from Baldry et al. (2008) multiplied by a con-
stant for clarity and the shaded region indicates the error.
of a few with the extrapolated value for the observed sample for
M? > 109M.
Although high mass UDGs (M? > 109M) are largely miss-
ing from observations, the very limited volumes explored obser-
vationally to date do not preclude the existence of galaxies with
significantly larger stellar masses that satisfy the same low-surface-
brightness criteria as their less massive counterparts. Indeed, exam-
ples of such massive LSBGs are already known e.g. Malin 1 and
UGC 1382 (see large open red squares in Figure 2). Furthermore,
the dashed black line in Figure C1 indicates the galaxy stellar mass
function from Baldry et al. (2008). A decline in the UDG frac-
tion towards higher stellar masses should be expected and is likely
driven by a combination of a mass dependence in the efficiency of
the physical processes (e.g. SN feedback) that drive the formation
of LSBGs (e.g. Brook & Di Cintio 2015; van Dokkum et al. 2016;
Toloba et al. 2018) and the steep decline in the galaxy stellar mass
function towards higher stellar masses (which is exacerbated by the
small observational volumes probed so far).
This paper has been typeset from a TEX/LATEX file prepared by the author.
MNRAS 000, 1–22 (2019)