MNRAS 464, 1659–1675 (2017) doi:10.1093/mnras/stw2437
Advance Access publication 2016 September 27
A chronicle of galaxy mass assembly in the EAGLE simulation
Yan Qu,
1‹
John C. Helly,
2
Richard G. Bower,
2
Tom Theuns,
2
Robert A. Crain,
3
Carlos S. Frenk,
2
Michelle Furlong,
2
Stuart McAlpine,
2
Matthieu Schaller,
2
Joop Schaye
4
and Simon D. M. White
5
1
National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang, Beijing 10012, China
2
Institute of Computational Cosmology, Durham University, South Road, Durham DH1 3LE, UK
3
Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK
4
Leiden Observatory, Leiden University, Postbus 9513, NL-2300 RA Leiden, the Netherlands
5
Max-Planck-Institut f
¨
ur Astrophysik, Karl-Schwarzschild-Strae 1, D-85741 Garching, Germany
Accepted 2016 September 26. Received 2016 August 29; in original form 2016 March 28
ABSTRACT
We analyse the mass assembly of central galaxies in the Evolution and Assembly of Galaxies
and their Environments (EAGLE) hydrodynamical simulations. We build merger trees to
connect galaxies to their progenitors at different redshifts and characterize their assembly
histories by focusing on the time when half of the galaxy stellar mass was assembled into the
main progenitor. We show that galaxies with stellar mass M
∗
< 10
10.5
M
⊙
assemble most of
their stellar mass through star formation in the main progenitor (‘in situ’ star formation). This
can be understood as a consequence of the steep rise in star formation efficiency with halo
mass for these galaxies. For more massive galaxies, however, an increasing fraction of their
stellar mass is formed outside the main progenitor and subsequently accreted. Consequently,
while for low-mass galaxies, the assembly time is close to the stellar formation time, the stars
in high-mass galaxies typically formed long before half of the present-day stellar mass was
assembled into a single object, giving rise to the observed antihierarchical downsizing trend.
In a typical present-day M
∗
≥ 10
11
M
⊙
galaxy, around 20 per cent of the stellar mass has an
external origin. This fraction decreases with increasing redshift. Bearing in mind that mergers
only make an important contribution to the stellar mass growth of massive galaxies, we find
that the dominant contribution comes from mergers with galaxies of mass greater than one-
tenth of the main progenitor’s mass. The galaxy merger fraction derived from our simulations
agrees with recent observational estimates.
Key words: galaxies: evolution – galaxies: formation – galaxies: high-redshift – galaxies:
interactions – galaxies: stellar content.
1 INTRODUCTION
In the cold dark matter (CDM) cosmological model, the growth
of dark matter haloes is largely self-similar, with larger haloes be-
ing formed more recently than their low-mass counterparts. The
formation and assembly of galaxies are, however, much more com-
plex. Feedback from massive stars and the formation of black holes
generates a strongly non-linear relationship between the masses of
dark matter haloes and those of the galaxies they host. For low-mass
haloes (with mass 10
11.5
M
⊙
), the stellar mass increases rapidly,
with a slope of ∼2, but in higher mass haloes, the stellar mass of
the main (or ‘central’) galaxy increases much more slowly than the
⋆
E-mail:
quyan@nao.cas.cn
halo mass, with a slope of ∼0.5 (e.g. Benson et al. 2003; Behroozi,
Wechsler & Conroy
2013; Moster, Naab & White 2013). The mass
assembly of galaxies will therefore be quite different from those of
their parent haloes. Establishing how galaxies assemble their stars
over cosmic time is then central to understanding galaxy formation
and evolution.
One question we need to answer is the relative importance of the
growth of galaxies via internal ongoing star formation (‘in situ’),
in comparison to the mass contributions of external processes (e.g.
Guo & White
2008; Zolotov et al. 2009;Oseretal.2010; Font et al.
2011; McCarthy et al. 2012; Pillepich, Madau & Mayer 2015).
These external processes can be further divided to distinguish be-
tween the mass growth due to mergers with galaxies of comparable
mass (‘major mergers’), and the mass gained from much smaller
galaxies (‘minor mergers’) or barely resolved systems and diffuse
C
2016 The Authors
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1660 Y. Qu et al.
mass (‘accretion’). While major mergers can rapidly increase a
galaxy’s stellar mass, minor mergers are much more common (e.g.
Hopkins et al.
2008; Parry, Eke & Frenk 2009).
To evaluate the relative importance of mergers to galaxy assem-
bly, we need to know their merging histories. From an observational
perspective, counts of close galaxy pairs (e.g. Williams, Quadri &
Franx
2011;Man,Zirm&Toft2014), or galaxies with disturbed
morphologies (e.g. Lotz et al.
2008; Conselice, Yang & Bluck 2009;
L
´
opez-Sanjuan et al.
2011; Stott et al. 2013), provide a census of
galaxy mergers. These values can be further converted into galaxy
merger rates t hrough the use of a merger time-scale (e.g. Kitzbichler
& White
2008). Unfortunately, those methods have their own lim-
itations: galaxies in close-pairs may not be physically related, and
may be chance line-of-sight superpositions; morphological distur-
bances are not unique to galaxy mergers. For example, clumpy star
formation driven by gravitational instability can also foster the for-
mation of galaxies with irregular morphologies (Lotz et al.
2008).
In addition, these methods are sensitive to the merger stage and
the mass ratio of the merging galaxies. Due to these limitations, the
scatter between merger rate measurements is large, and it is difficult
to make a reliable assessment of the complementary contribution
of mergers to galaxy growth. Recently, deep surveys have begun
to shed more light on the galaxy merger rate at high redshifts (e.g.
Man et al.
2014). Even so, the evolution of the merger rate remains
controversial. An alternative approach is to extract the merger rates
of galaxies from a model that reproduces the observed abundance
of galaxies (and their distribution in mass), and its evolution with
redshift, in a full cosmological context.
In the hierarchical structure formation scenario, the assembly of
galaxies is believed to be closely related to the formation histories
of their parent haloes. The practice of using halo merger histories
to understand the build-up of galaxies can be traced back to Bower
(
1991), Cole (1991), and Kauffmann, White & Guiderdoni (1993).
In these pioneering works, the growth of haloes is described by
analytical methods. Numerical techniques like N-body numerical
simulations can deal more accurately with the gravitational pro-
cesses underlying the evolution of cosmic structure. The clustering
of haloes is tracked, snapshot by snapshot, and stored in a tree
form (‘merger tree’). Halo merger trees therefore record, in a direct
way, when and how haloes assemble by accreting other building
blocks, and are widely used to rebuild galaxy assembly histories
(e.g. Kauffmann et al.
1993, 1999; Roukema et al. 1997; Springel
et al.
2001).
To compute galaxy merger rates, one possibility is to combine
the halo merger trees with a redshift-dependent abundance match-
ing model that statistically assigns galaxies to dark matter haloes
(Fakhouri & Ma
2008;Behroozietal.2013; Moster et al. 2013).
In this fashion, the observed abundance of galaxies can be inverted
to estimate the galaxy merger rate as a function of halo mass and
redshift. This provides a great deal of insight, but relies on the
accuracy of the statistical model. Although appealing because of
its close relation to the real data, the approach may miss physical
correlations between the merging objects. A preferable approach is
therefore to form galaxies within dark matter haloes using a physical
galaxy formation model. It is important to note, however, that reli-
able conclusions can only be obtained if the overall galaxy stellar
mass function accurately reproduces observational measurements
(Benson et al.
2003; Schaye et al. 2015).
One approach is to use ‘semi-analytic’ models of galaxy forma-
tion. By introducing phenomenological descriptions for feedback
from star formation and active galactic nuclei (AGN), such mod-
els are able to reproduce the observed galaxy stellar mass function
(e.g. Bower et al.
2006; Croton et al. 2006
, for a recent review, see
Knebe et al.
2015). De Lucia et al. (2006) study the assembly of
elliptical galaxies in a semi-analytic model based on the model of
Croton et al. (
2006). They find that stars in massive galaxies (with
stellar mass M
∗
≥ 10
11
M
⊙
) are formed earlier (z 2.5) but are as-
sembled later (by z ≈ 0.8). De Lucia & Blaizot (
2007) show further
that massive members in galaxy clusters assemble through mergers
late in the history of the Universe, with half of their present-day
mass being in place in their main progenitor by z ≈ 0.5. In contrast,
less massive galaxies undergo relatively few mergers, acquiring
only 20 per cent of their final stellar mass from external objects.
Parry et al. (
2009) study the assembly and morphology of galaxies
in the semi-analytic model of Bower et al. (
2006). They found many
similarities, but also important disagreements, stemming primarily
from the differing importance of disc instabilities in the two mod-
els. Parry et al. (
2009) find that major mergers are not the primary
mass contributors to most spheroids except the brightest ellipticals.
This, instead, is brought in by minor mergers and disc instabilities.
In their model, the majority of ellipticals, and the overwhelming
majority of spirals, never experience a major merger.
Semi-analytic studies such as those above give important insights
but suffer from the limitations inherent to the approach, for example,
the neglect of tidal stripping of infalling satellites and the absence of
information about the spatial distribution of stars, as well as being
limited by the overall accuracy of the model. Numerical simulations
have fewer limitations, and have thus become an alternative useful
tool for these studies. Hopkins et al. (
2010) compare the galaxy
merger rates derived from a variety of analytical models and hydro-
dynamical simulations. They find that the predicted galaxy merger
rates depend strongly on the prescriptions for baryonic physical pro-
cesses, especially those in satellite galaxies. For example, the lack
of strong feedback can result in a difference in predicted merger
rates by as much as a factor of 5. Mass ratios used in merger clas-
sification also have an impact on merger rate prediction. Using the
stellar mass ratio, rather than the halo mass ratio, can result in an
order of magnitude change in the derived merger rate.
With rapidly increasing computational power and much pro-
gresses in modelling physical processes on subgrid scales, cosmo-
logical N-body hydrodynamical simulations are increasingly capa-
ble of capturing the physics of galaxy formation (e.g. Hopkins et al.
2013; Vogelsberger et al. 2014). The Evolution and Assembly of
Galaxies and their Environments (EAGLE) simulation project ac-
curately reproduces the observed properties of galaxies, including
their stellar mass, sizes, and formation histories, within a large and
representative cosmological volume (Schaye et al.
2015; Furlong
et al.
2015a,b). This degree of fidelity makes the EAGLE simu-
lations a powerful tool for understanding and interpreting a wide
range of observational measurements. Previous papers have focused
on the evolution of the mass function and the size distribution of
galaxies (Furlong et al.
2015a,b), the luminosity function and colour
diagram (Trayford et al.
2015) and galaxy rotation curves (Schaller
et al.
2015a), as well as many aspects of the H
I and H
2
distribution
of galaxies (Lagos et al.
2015;Bah
´
eetal.2016; Crain et al. 2016)
in the EAGLE Universe. But none has tracked the assembly of in-
dividual galaxies and decipher the underlying mechanisms as yet.
As an attempt to shed some light on the issue, in this work, we
connect galaxies seen at different redshifts, creating a merger
tree that enables us to establish which high-redshift fragments col-
lapse to form which present-day galaxies (and vice versa). In this
way, we can quantify the importance of in situ star formation rel-
ative to the mass gain from galaxy mergers and diffuse accretion.
Throughout the paper, we will focus on the main, or ‘central’,
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Galaxy mass assembly in the EAGLE simulation 1661
galaxies, avoiding the complications of environmental processes
such as ram pressure stripping and strangulation that suppress star
formation and strip stellar mass from satellites. Unless otherwise
stated, stellar masses refer to the stellar mass of a galaxy at the
redshift of observation, not to the initial mass of stars formed.
The outline of this paper is as follows. In Section 2, we provide
a brief overview of the numerical techniques and subgrid physi-
cal models employed by the EAGLE simulations, and describe the
methodology used to construct merger trees from simulation out-
puts. We investigate the assembly histories and merger histories of
galaxies and discuss the impact of feedback on galaxy mass build-
up in Section 3. We compare our results with some previous works
in Section 4, and finally summarize in Section 5. The appendices
present the detailed criteria we use to define galaxy mergers and
show the impacts of our choices of galaxy mass on our results. The
cosmological parameters used in this work is from the Planck mis-
sion (Planck Collaboration XVI
2014),
= 0.693,
m
= 0.307,
h = 0.677, n
s
= 0.96, and σ
8
= 0.829.
2 EAGLE SIMULATION AND MERGER TREE
2.1 EAGLE simulation
The galaxy samples for this study are selected from the EAGLE
simulation suite (Crain et al.
2015; Schaye et al. 2015). The
EAGLE simulations follow the evolution (and, where appropri-
ate, the formation) of dark matter, gas, stars, and black holes from
redshift z = 127 to the present day at z = 0. They were carried
out with a modified version of the
GADGET 3 code (Springel 2005)
using a pressure–entropy-based formulation of smoothed particle
hydrodynamics method (Hopkins
2013), coupled to several other
improvements to the hydrodynamic calculation (Dalla Vecchia., in
preparation; Schaye et al.
2015; Schaller et al. 2015b). The simula-
tions include subgrid descriptions for radiative cooling (Wiersma,
Schaye & Smith
2009), star formation (Schaye & Dalla Vecchia
2008), multi-element metal enrichment (Wiersma et al. 2009), black
hole formation (Rosas-Guevara et al.
2015; Springel, Di Matteo &
Hernquist
2005), as well as feedback from massive stars (Dalla
Vecchia & Schaye
2012) and AGN (for a complete description, see
Schaye et al.
2015). The subgrid models are calibrated using a well-
defined set of local observational constraints on the present-day
galaxy stellar mass function and galaxy sizes (Crain et al.
2015).
Each simulation outputs 29 snapshots to store particle properties
over the redshift range of 0 ≤ z ≤ 20. The corresponding time inter-
val between snapshot outputs ranges from ∼0.3 to ∼1.35 Gyr. The
largest EAGLE simulation, hereafter referred to as Ref-L100N1504,
employs 1504
3
dark matter particles and an initially equal number
of gas particles in a periodic cube with side-length 100 comoving
Mpc (cMpc) on each side. This setup results in a particle mass of
9.7 × 10
6
M
⊙
and 1.81 × 10
6
M
⊙
(initial mass) for dark matter and
gas particles, respectively. The gravitational force between particles
is calculated using a Plummer potential with a softening length set
to the smaller of 2.66 comoving kpc (ckpc) and 0.7 physical kpc
(pkpc).
The formation of galaxies involves physical processes operating
on a huge range of scales, from the gravitational forces that drive the
formation of large-scale structure on 10–100 Mpc scales, to the pro-
cesses that lead to the formation of individual stars and black holes
on 0.1 pc and smaller scales. Such a dynamic range, 10
9
in length
and perhaps 10
27
in mass, cannot be computed efficiently without
the use of subgrid models. Such models are inevitably approximate
and uncertain. In EAGLE, we require that the subgrid models are
physically plausible, numerically stable, and as simple as possible.
The uncertainty in these models introduces parameters whose val-
ues must be calibrated by comparison to observational data (Vernon,
Goldstein & Bower
2010). We explicitly recognize that these mod-
els are approximate and adopt the clear methodology for selecting
parameters and validating the model that is described in detail in
Schaye et al. (
2015) and Crain et al. (2015). The subgrid parame-
ters calibrated by requiring that the model fits three key properties
of local galaxies well: the galaxy stellar mass function, the galaxy
size – mass relation and the normalization of the black hole mass –
galaxy mass relation and that variations of the parameters alter the
simulation outcome in predictable ways (Crain et al.
2015). We find
that these data sets can be described well with physically plausible
values for the subgrid parameters. We then compare the s imulation
with further observational data to validate the simulation. We find
that it describes many aspects of the observed universe well (i.e.
within the plausible observational uncertainties), including the evo-
lution of the galaxy stellar mass function and star formation rates
(Furlong et al.
2015b), evolution of galaxy colours and luminosity
functions (Trayford et al.
2015). It also provides a good match to
observed O
VI column densities (Rahmati et al. 2016) and molecu-
lar content of galaxies (Lagos et al.
2015), as well as a reasonable
description of the X-ray luminosities of AGN (Rosas-Guevara et al.
2015). The good agreement with these diverse data sets, especially
those distantly related to the calibration data, provides good rea-
son to believe that the simulation provides a good description of
the evolution of galaxies in the observed Universe. It can therefore
be used to explore galaxy assembly histories in ways that are not
accessible to observational studies.
2.2 Halo identification and subhalo merger tree
Building subhalo merger trees from cosmological simulations in-
volves two steps: first, we identify haloes and subhaloes as gravi-
tationally self-bound structures; secondly, we identify the descen-
dants of each subhalo across snapshot outputs and establish the
descendant–progenitor relationship over time.
2.2.1 Halo identification
Dark matter structures in the EAGLE simulations are initially iden-
tified using the ‘Friends-of-Friends’ (FoF) algorithm with a linking
length of 0.2 times the mean inter-particle spacing (Davis et al.
1985). Other particles (gas, stars and black holes) are assigned to
the same FoF group as their nearest linked dark matter neighbours.
The gravitationally bound substructures within the FoF groups are
then identified by the SUBFIND algorithm (Springel et al.
2001;
Dolag et al.
2009). Unlike the FoF group finder, SUBFIND consid-
ers all species of particle and identifies self-bound subunits within
a bound structure which we refer to as ‘subhaloes’. Briefly, the
algorithm assigns a mass density at the position of every particle
through a kernel interpolation over a certain number of its nearest
neighbours. The local minima in the gravitational potential field
are the centres of subhalo candidates. The particle membership of
the subhaloes is determined by the iso-density contours defined
by the density saddle points. Particles are assigned to at most one
subhalo. The subhalo with a minimum value of the gravitational
potential within an FoF group is defined as the main subhalo of the
group. Any particle bound to the group but not assigned to any other
subhaloes within the group are assigned to the main subhalo.
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1662 Y. Qu et al.
2.2.2 Subhalo merger tree
Although they orbit within an FoF group, subhaloes survive as
distinct objects for an extended period of time. We therefore use
subhaloes as the base units of our merger trees: FoF group merger
trees can be rebuilt from subhalo merger trees if required. The first
and main step in building the merger tree is to link subhaloes across
snapshots. As in Springel et al. (
2005), we search the descendant
of a subhalo by tracing the most bound particles of the subhalo. We
use the D-Trees algorithm (Jiang et al.
2014) to locate the where-
abouts of the N
link
= min(N
linkmax
,max(f
trace
N, N
linkmin
)) most bound
particles of the subhalo, where N is the total particle number in the
subhalo. We use parameters N
linkmin
= 10, N
linkmax
= 100, f
trace
= 0.1
in the descendant search. The advantages of focusing on the N
link
most bound particles are two-fold. On the one hand, D-Trees can
identify a descendant even if most particles are stripped away leav-
ing only a dense core. On the other hand, the criterion minimises
misprediction of mergers during flyby encounters (Fakhouri & Ma
2008; Genel et al. 2009).
The descendant identification proceeds as follows. For a subhalo
A at a given snapshot, any subhalo at the subsequent snapshot that
receives at least one particle from A is labelled as a descendant
candidate. From those candidates, we pick the one that receives the
largest fraction of A’s N
link
most bound particles (denoted as B)as
the descendant of A. A is the progenitor of B.IfB receives a larger
fraction of its own N
link
most bound particles from A than from any
other subhalo at previous snapshot, A is the principal progenitor
of B. A descendant can have more than one progenitor, but only
one principal progenitor. The principal progenitor can be thought
of as ‘surviving’ the merger while the other progenitors lose their
individual identity.
Subhaloes sometimes exhibit unstable behaviour during merg-
ers, complicating the descendant/progenitor search. When a sub-
halo passes through the dense core of another subhalo, it may not
be identifiable as a separate object at the next snapshot, but will
then reappear in a later snapshot. From a single snapshot, there
is no way to know whether the subhalo has merged with another
subhalo, or has just disappeared temporarily, and we need to search
a few snapshots ahead in order to know which case it falls into.
In practice, we search up to N
step
= 5 consecutive snapshots ahead
for the missing descendants. This gives us between one and N
step
descendant candidates. If the subhalo is the principal progenitor of
one or more candidates, the earliest candidate that does not have a
principal progenitor is chosen to be the descendant. If there is no
such candidate, then the earliest one will be chosen. If the subhalo is
not the principal progenitor of any candidates, it will be considered
to have merged with another subhalo and no longer appears as an
identifiable object.
Occasionally, two subhaloes enter into a competition for bound
particles. This occurs as the participants orbit each other prior to
merging. In SUBFIND, the influence of a subhalo is based on its
gravitational potential well. When two subhaloes are close to each
other, their volumes of influence become intertwined and the def-
inition of the main halo may become unclear. For example, when
a satellite subhalo orbits closely to its primary host, the satellite
can be tidally compressed at some stage and become denser than
the host. At this point, the satellite may be classified as the central
object of the halo so that most of the halo particles are assigned
to it. At a later time, the original central, however, can surpass the
satellite in density and reclaim the halo particles. This contest can
last for several successive snapshots, accompanied by a see-saw
exchange of their physical properties during the merging. Fig.
1
Figure 1. A section of a subhalo merger tree illustrating how subhaloes
following branches A and B exchange particles before merging. The colour
of the solid symbol reflects the halo mass, while the size of the circle
represents the ‘branch mass’, which is the sum of the total mass of all the
progenitors sitting on the same branch. A see-saw behaviour is clearly seen
in the evolution of the halo mass, which may confuse identification of the
most important branch. Instead, we use branch mass to locate the main
branch of the tree. In this plot, branch A has the largest branch mass and
is therefore chosen as the main branch, even though its progenitors are not
always the most massive ones.
shows an example in which merging haloes take turns to be classi-
fied as the central host during the merging process. Overall, fewer
than 5 per cent of subhalo mergers in the EAGLE simulations ex-
hibit this behaviour, compatible with the statistics found by Wetzel,
Cohn & White (
2009). The fact that a fierce contest between sub-
haloes is sometimes seen during the merging process highlights the
inherent difficulties in appropriately describing subhalo properties
at that stage.
The property exchanges during such periods are not physical,
but rather stem from the requirement that particles be assigned to
a unique subhalo on the basis of the spatial coordinates and the
local density field in a single snapshot. The history of an object
is, however, conveniently simplified by modifying the definition
of the most massive progenitor to account for its mass in earlier
snapshots. We refer to this progenitor as the ‘main progenitor’, and
the branch they stay on in the object’s merger tree as the ‘main
branch’. Because of the mass exchange discussed above, we track
the main branch using the ‘branch mass’, the sum of the mass over all
particle species of all progenitors on the same branch ( De Lucia &
Blaizot
2007). The main progenitor is then the progenitor that has
the maximum branch mass among its contemporaries. This can
avoid the misidentification of main progenitors due to the property
exchanges occurring for merging subhaloes as we see in Fig.
1.
It is worth noting that according to this definition, a lower mass
progenitor which has existed for a long time can sometimes be
preferred over a more massive progenitor which has formed quickly,
when locating main progenitors.
The subhalo merger trees derived by the method described above
are publicly available through an
SQL data base
1
similar to that used
for the Millennium simulations (see McAlpine et al.
2016, for more
details).
1
http://www.eaglesim.org
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Galaxy mass assembly in the EAGLE simulation 1663
2.3 Galaxy sample, galaxy merger tree, and merger type
In this work, galaxies are identified as the stellar components of
the subhaloes. The main subhalo of a FoF halo hosts the ‘central’
galaxy, while other subhaloes within the group host satellite galax-
ies. We will focus on the central galaxies in our study, avoiding
the complications of environmental processes such as ram pressure
stripping and strangulation that suppress star formation and strip
stellar mass from satellite galaxies (e.g. Wetzel et al.
2013; McGee,
Bower & Balogh
2014;Barberetal.2016).
The stellar mass of a galaxy is measured using a spherical aper-
ture. This gives similar results to the commonly used 2D Petrosian
aperture used in observational work, but provides an orientation-
independent mass measurement for each galaxy. Previous studies
based on the EAGLE simulations adopt an aperture of 30 pkpc to
measure galaxy stellar mass (e.g. Furlong et al.
2015b; Schaye et al.
2015). Nevertheless, subhaloes do contain a significant population
of diffuse stars, particularly in more massive haloes (Furlong et al.
2015b). Such stars are probably deposited by interactions and tidal
stripping, and sometimes observed as low-surface brightness intr-
acluster/intragroup light (Theuns & Warren
1997; Zibetti & White
2004; McGee & Balogh 2010). Since the formation of massive
galaxies is a particular focus of this paper, we use a larger aperture,
with a radius of 100 pkpc, to calculate galaxy mass. Note that this
mass does not include the stellar mass of satellites lying within the
100 pkpc aperture. As we will show in Appendix C, this aperture
choice has little impact on galaxy properties for galaxies with stellar
mass M
∗
< 10
11
M
⊙
(see also Schaye et al. 2015).
Unless otherwise stated, the galaxy stellar mass in this work refers
to the actual mass of stars in the galaxy at the epoch of ‘observa-
tion’. Using actual mass replicates what an ideal observer would
measure and directly addresses the question of when the current
stellar population of the galaxy was formed/assembled. Neverthe-
less, we should note that the mass budget of the current stellar
population is a combination of two processes: stellar mass gain
via star formation, accretion and merging, and mass-loss through
stellar evolution processes. However, using the actual stellar mass
complicates interpretation of the relative mass contribution from
different types of merger events since it depends on the age of the
stellar population that is accreted. We therefore use the stellar mass
initially formed (‘initial mass’), not the actual stellar mass, to evalu-
ate the contributions from internal and external processes to galaxy
assembly. In practice, this distinction has little effect on the results
and we show the effect of using initial stellar mass throughout in
Appendix B.
2.3.1 Galaxy sample
Our study is based on the formation histories of 62 543 galax-
ies in the largest EAGLE simulation R ef-L100N1504, spanning
a stellar mass range of 10
9.5
–10
12
M
⊙
over redshift z = 0–3. In
order to test the robustness of our results to resolution, we also
extract 1381 galaxies within the same mass range, as a com-
parison sample, from the EAGLE simulation Recal-L025N0752
(2 × 752
3
dark matter and gas particles in a 25 cMpc box),
which has eight times better mass resolution and the same snap-
shot frequency as Ref-L100N1504. We use subgrid physical mod-
els with parameters recalibrated to the present-day observations,
as this provides the best match to the observed galaxy popula-
tion (see Schaye et al.
2015). In order to study the mass de-
pendence of galaxy assembly, we split our samples into three
stellar mass bins: a low-mass bin (10
9.5
≤ M
∗
< 10
10.5
M
⊙
), an
intermediate-mass bin (10
10.5
≤ M
∗
< 10
11
M
⊙
), and a high-mass
bin (10
11
≤ M
∗
< 10
12
M
⊙
).
2.3.2 Galaxy merger tree
We construct galaxy merger trees by focusing on the stellar com-
ponent of the subhalo merger trees. Fig.
2 shows such a tree for a
galaxy with M
∗
= 1.7 × 10
11
M
⊙
at z = 0, together with images of
its star distribution highlighting its morphological evolution since
z = 1. The main branch of the tree is marked by the thick black
line. It is important to bear in mind that the identification of the
main branch is always based on t he branch mass; at any particular
epoch, the most massive galaxy progenitor may not lie on the main
branch. However, for the reasons described in Section 2.2.2, using
the branch mass yields more stable and intuitive results.
Galaxy merger trees appear broadly similar to subhalo merger
trees, except that the latter contain more fine branches corresponding
to small subhaloes within which no stars have formed. Galaxy trees
are also less affected by the mass exchange issue than subhalo trees,
as star particles are more spatially concentrated.
2.3.3 Merger type
The effects of tidal forces and torques during a merger depend on
the mass r atio of the merging systems (e.g. Barnes & Hernquist
1992). A merger between a low-mass satellite and a more massive
host is generally less violent than a merger between systems of
comparable mass, and has a less dramatic impact on the dynamics
and morphology of the host. It is therefore useful to classify mergers
into different t ypes according to the mass ratio between the two
merging systems, μ ≡ M
2
/M
1
(M
1
> M
2
). For galaxy mergers, μ
is the ratio of stellar masses between two merging galaxies. While
for halo mergers, it is the halo mass ratio.
While this is straightforward in semi-analytic models (since
galaxies are uniquely defined entities), in numerical simulations
(and in nature as well), merging systems experience mass-loss due
to tidal stripping throughout the merging process. Our strategy is
therefore to choose a separation criterion, R
merge
, and determine
the merger type when the merging systems are separated, for the
first time, by that distance or less. For galaxy mergers, we adopt
R
merge
= 5 × R
1/2
,whereR
1/2
is the half-stellar mass radius of the
primary galaxy (note that R
merge
is not a projected but a 3D separa-
tion). The value of R
merge
ranges from ∼20 to 200 pkpc in the stellar
mass range explored in this work (see Appendix A), and is s imilar
to the projected separation criteria adopted in observational galaxy
pair studies. For subhalo mergers, R
merge
= r
200
,wherer
200
is the
radius of a region around the FoF group of the subhaloes within
which the density is 200 times the cosmological critical density. In
the rare event that an object is located within the R
merge
of more than
one other object, i t is considered to be the merging companion of
the nearest one.
More often than not, the secondary object may have suffered
tidal stripping of mass when the merger type is determined due to
the finite time sampling of our snapshot outputs. To alleviate the
resulting misestimate of the mass ratio, we compare the mass of
the merging systems at the start of the merging event with that at
the previous snapshot, and use the maximum to calculate the mass
ratio μ. In our study, merging events are classified as major mergers
if μ ≥ 1/4; as minor mergers if 1/4 >μ≥ 1/10; and as diffuse
accretion, when μ<1/10. Our major merger definition is different
from that of C ole et al. (
2000) or De L ucia & Blaizot (2007)who
adopt a larger mass ratio ≥1/3, but is similar to more recent studies
MNRAS 464, 1659–1675 (2017)
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