The Baryons in the Milky Way Satellites

Abstract

We investigate the formation and evolution of satellite galaxies using
smoothed particle hydrodynamics (SPH) simulations of a Milky Way(MW)-like
system, focussing on the best resolved examples, analogous to the classical MW
satellites. Comparing with a pure dark matter simulation, we find that the
condensation of baryons has had a relatively minor effect on the structure of
the satellites' dark matter halos. The stellar mass that forms in each
satellite agrees relatively well over three levels of resolution (a factor of
~64 in particle mass) and scales with (sub)halo mass in a similar way in an
independent semi-analytical model. Our model provides a relatively good match
to the average luminosity function of the MW and M31. To establish whether the
potential wells of our satellites are realistic, we measure their masses within
observationally determined half-light radii, finding that the most massive
examples have somewhat higher mass-to-light ratios than those derived for the
MW dSphs from stellar kinematic data. A statistical test yields a ~9 percent
probability that the simulated and observationally derived distributions of
masses are consistent. Our results may suggest that either the MW halo is less
massive than assumed in our simulations (~1.4e12 M_sun) or that there is
substantial scatter in the satellite luminosity function or distribution of
mass-to-light ratios at fixed host halo mass. Alternatively, feedback processes
not properly captured by our simulations may have reduced the central densities
of (sub)halos, or the subhalos may have initially formed with lower
concentrations as would be the case, for example, if the dark matter were made
of warm, rather than cold particles.

Full text

Page 1

arXiv:1105.3474v2 [astro-ph.GA] 22 Jun 2011
Mon. Not. R. Astron. Soc. 000, 1–16 (201?) Printed 23 June 2011(MN LATEX style file v2.2)
The Baryons in the Milky Way Satellites
O. H. Parry1⋆, V. R. Eke1, C. S. Frenk1and T. Okamoto1,2
1Institute for Computational Cosmology, Department of Physics, University of Durham, Science Laboratories, South Road, Durham DH1 3LE
2Center for Computational Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8577 Ibaraki, Japan
Accepted 201? . Received 201? ; in original form 201?
ABSTRACT
We investigate the formation and evolution of satellite galaxies using smoothed particle
hydrodynamics (SPH) simulations of a Milky Way (MW)-like system, focussing on
the best resolved examples, analogous to the classical MW satellites. Comparing with
a pure dark matter simulation, we find that the condensation of baryons has had
a relatively minor effect on the structure of the satellites’ dark matter halos. The
stellar mass that forms in each satellite agrees relatively well over three levels of
resolution (a factor of ∼ 64 in particle mass) and scales with (sub)halo mass in a
similar way in an independent semi-analytical model. Our model provides a relatively
good match to the average luminosity function of the MW and M31. To establish
whether the potential wells of our satellites are realistic, we measure their masses
within observationally determined half-light radii, finding that they have somewhat
higher mass-to-light ratios than those derived for the MW dSphs from stellar kinematic
data; the most massive examples are most discrepant. A statistical test yields a ∼ 6
percent probability that the simulated and observationally derived distributions of
masses are consistent. If the satellite population of the MW is typical, our results
could imply that feedback processes not properly captured by our simulations have
reduced the central densities of subhalos, or that they initially formed with lower
concentrations, as would be the case, for example, if the dark matter were made of
warm, rather than cold particles.
Key words: methods: numerical – galaxies: evolution – galaxies: formation – cos-
mology: theory.
1 INTRODUCTION
Substantial progress has been made over the last few years
in modelling the formation of galactic dark matter halos us-
ing high resolution N-body simulations (Springel et al. 2008;
Diemand et al. 2008; Stadel et al. 2009). Hydrodynamical
simulations of such systems inevitably lag behind in terms
of resolution, but are now reaching a point where they can
be used to investigate the detailed evolution of the baryonic
component of satellite galaxies, as demonstrated by several
recent studies. Okamoto et al. (2010) studied the effects of
different feedback models on the chemical properties and lu-
minosities of the satellite populations around three Milky
Way (MW)-mass halos. Okamoto & Frenk (2009) showed
that a combination of the early reionisation of pregalac-
tic gas at high redshift and the injection of supernovae
energy is sufficient to suppress star formation in the myr-
iad of low mass subhalos that form in the ΛCDM cosmol-
ogy, confirming results from earlier semi-analytic modelling
(Benson et al. 2002; Somerville 2002). Wadepuhl & Springel
⋆E-mail:o.h.parry@durham.ac.uk
(2010) further argued that cosmic rays generated by super-
novae may play an important role in suppressing star for-
mation in satellites.
From an observational point of view, the release of data
from the Sloan Digital Sky Survey (SDSS) (York et al. 2000)
over the last decade has transformed the study of the Lo-
cal Group satellites. The ∼ 30 faint dwarf galaxies discov-
ered using those data (e.g., Zucker et al. 2004; Martin et al.
2006; Belokurov et al. 2007; McConnachie et al. 2008) have
prompted a new phase of detailed testing of current galaxy
formation theories on smaller scales and in more detail than
ever before. The SDSS data also reduced the discrepancy
that existed between the number of low mass dark matter
halos predicted by the ΛCDM cosmological model and the
number of faint satellites identified around the MW: the
‘missing satellite problem’ (Klypin et al. 1999; Moore et al.
1999). Over the same period, numerous theoretical mod-
els (e.g., Li et al. 2010; Macci` o et al. 2010; Font et al. 2011)
have confirmed early conclusions that a combination of a
photoionising background and feedback processes from su-
pernovae (SNe) are capable of bringing the two into good
agreement.
c ? 201? RAS

Page 2

2 O. H. Parry et al.
However, it is important to recognise that the satel-
lite problem is not simply a statement that star formation
must be suppressed in low mass halos. A more subtle, but
equally important test of any cosmological model is whether
the potential wells in which satellite galaxies form are capa-
ble of supporting stellar systems with realistic kinematics.
Strigari et al. (2010) demonstrated that all of the classical
MW satellites for which high quality kinematic data are
available are consistent with having formed in dark matter
subhalos selected from the high resolution ΛCDM N-body
simulations of the Aquarius project (Springel et al. 2008).
However, successful models must satisfy both constraints,
producing realistic luminosity functions and forming stars
in potentials like those inferred from observations.
Boylan-Kolchin et al. (2011) have recently argued that
the most massive subhalos in high resolution simulations
of cold dark matter halos are too concentrated to be able
to host the brightest observed satellites of the Milky Way.
Lovell et al. (2011) have shown that subhalos formed from
warm, rather than cold, dark matter have suitably low con-
centrations, but both they and Boylan-Kolchin et al. empha-
sise that other solutions to the discrepancy are possible. One
promising possibility is the mechanism originally proposed
by Navarro, Eke & Frenk (1996a), whereby the rapid expul-
sion of dense central gas in a starburst can unbind the inner
parts of the halo, significantly reducing its concentration.
We find an example of this process in one of the subhalos
formed in the simulations analysed in this paper.
From a theoretical perspective, ab initio hydrodynamic
simulations are uniquely well-suited to investigating the ef-
fects of galaxy formation on the dark matter halos of satel-
lite galaxies. It has been known for some time that baryons
may significantly alter the behaviour of dark matter on some
scales. Dissipative processes such as gas cooling, star forma-
tion and feedback decouple the dynamical evolution of the
baryons from that of the dark matter. The resulting change
in the shape of the overall potential in turn affects the phase
space structure of the dark matter halo.
Central concentrations of cold baryonic matter can in-
duce an adiabatic, radial contraction of the central re-
gions (Blumenthal et al. 1986; Gnedin et al. 2004), while
the opposite effect can be achieved if dense clumps
of baryonic material heat the central distribution of
dark matter (Mo & Mao 2004; Mashchenko et al. 2006,
2008), or if the blowout mechanism of Navarro, Eke and
Frenk is effective (see also Gelato & Sommer-Larsen 1999;
Gnedin & Zhao 2002; Mo & Mao 2004; Read & Gilmore
2005; Governato et al. 2010; Pontzen & Governato 2011).
This latter mechanism was originally proposed as a means
to erase the central dark matter cusps in dwarf galax-
ies, though whether or not such ‘cored’ profiles are re-
quired by the observations remains a matter of ongo-
ing debate (Goerdt et al. 2006; S´ anchez-Salcedo et al. 2006;
Strigari et al. 2006; Gilmore et al. 2007; Walker et al. 2009).
If baryons really do modify the dark matter in satellites
on sub-kpc scales significantly, then the value of studying
dwarf galaxies with post-processed N-body simulations may
be very limited.
In this paper, we make use of a model that has already
had success in reproducing some properties of the Local
Group satellites, including the shape and approximate nor-
malisation of their luminosity function and the metallicity-
Table 1. Numerical parameters adopted for the three different
resolution simulations: dark matter and gas particle masses and
the gravitational softening in physical units.
MDM[M⊙]Mgas[M⊙]
ǫphys[pc]
Aq-C-4
Aq-C-5
Aq-C-6
2.6 × 105
2.1 × 106
1.7 × 107
5.8 × 104
4.7 × 105
3.7 × 106
257
514
1028
luminosity relation (Okamoto et al. 2010). In Section 2 we
outline the details of our simulations, including the initial
conditions, simulation code and modelling of various key
baryonic physical processes. In Section 3, we expand on the
theoretical predictions of the model by examining what ef-
fect baryons have had on the dark matter profiles of satel-
lites. We perform tests in Section 4 to ensure that key prop-
erties of our satellite population do not depend on the nu-
merical resolution. In Section 5 we compare several observ-
able and derived properties of the simulated satellites to
Local Group data. Finally, in Section 6 we discuss the evo-
lution of one particularly interesting satellite in the simula-
tion, which is dominated by its stellar component at z = 0.
Our main results are summarised in Section 7.
2 THE SIMULATIONS
To investigate the properties of a simulated MW-satellite
system, we select one of the six halos from the Aquar-
ius project described in Springel et al. (2008), halo ‘C’ in
their labelling system. These halos were extracted from
a cosmological simulation in a cube of comoving volume
(100Mpc)3and were chosen to have masses close to that of
the Milky Way (∼ 1012M⊙) and avoid dense environments
(no neighbour exceeding half its mass within 1h−1Mpc)
(Navarro et al. 2010).
As in Aquarius, we employ a ‘zoom’ resimulation tech-
nique, with higher mass boundary particles used to model
the large scale potential and lower mass particles in a
∼ 5h−1Mpc region surrounding the target halo. Extra power
is added to the initial particle distribution on small scales
in the high resolution region, as described by Frenk et al.
(1996). We assume a ΛCDM cosmology, with parameters
Ωm = 0.25, ΩΛ = 0.75, Ωb = 0.045, σ8 = 0.9, ns = 1 and
H0 = 100hkms−1Mpc−1= 73kms−1Mpc−1.
The highest resolution realisation of halo C in Aquarius
had a dark matter particle mass of 1.4 × 104M⊙. However,
the extra computational time associated with hydrodynamic
simulations makes such a resolution impractical; our high-
est resolution instead corresponds to a dark matter particle
mass of ∼ 2.6 × 105M⊙ and an initial gas particle mass of
5.8 × 104M⊙. In order to conduct convergence studies, we
also simulated the halo at two lower resolutions, with par-
ticle masses ∼ 8 and ∼ 64 times larger. We adopt the same
naming convention as Springel et al. (2008), labelling the
three runs (in order of decreasing resolution) Aq-C-4, Aq-
C-5 and Aq-C-6. Table 1 lists the numerical parameters of
each simulation.
Our simulation code is based on an early version of the
PM-Tree-SPH code gadget-3. Baryonic processes are mod-
elled as described in Okamoto et al. (2010), with a num-
c ? 201? RAS, MNRAS 000, 1–16

Page 3

The Baryons in the MW Satellites3
ber of modifications designed to improve the treatment of
supernovae-driven winds. In the following subsections, we
summarise some of the most important features of the code
with emphasis on aspects that have the greatest impact on
satellite formation.
2.1 Radiative cooling and the equation of state
Radiative processes in our model are implemented as de-
scribed in Wiersma et al. (2009a) and include inverse Comp-
ton scattering of CMB photons, thermal Bremsstrahlung,
atomic line cooling and photoionisation heating from Hy-
drogen and Helium. All gas in the simulation volume is
ionised and heated by a spatially uniform, time evolving
UV background, as calculated by Haardt & Madau (2001).
During the reionisation of H and He I (z = 9) and He II
(z = 3.5), an extra two eV per atom of thermal energy is
added to the gas, smoothed over Gaussian distributions with
widths ∆z = 0.0001 and 0.5 respectively, in order to approx-
imately account for non-equilibrium and radiative-transfer
effects (Abel & Haehnelt 1999). The contributions to heat-
ing and cooling from eleven elements (H, He, C, N, O, Ne,
Mg, Si, S, Ca and Fe) are interpolated from tables output by
cloudy (Ferland et al. 1998), using elemental abundances
smoothed over the SPH kernel, to approximate the mixing
of metals in the interstellar medium (ISM). This avoids un-
physical small scale fluctuations in the cooling time that
arise if the abundances associated with individual particles
are used (Wiersma et al. 2009b).
Failure to resolve the Jeans mass (MJ) or Jeans
Length (λJ) is known to lead to spurious fragmenta-
tion through gravitational instability (Bate & Burkert 1997;
Truelove et al. 1997). Techniques employed to avoid this
problem typically involve some form of energy injection
to maintain an effective pressure that guarantees that the
available resolution is sufficient (e.g., Machacek et al. 2001;
Robertson & Kravtsov 2008; Springel & Hernquist 2003;
Ceverino et al. 2010; Schaye et al. 2010). This pressure sup-
port has been identified with, for example, a hot phase main-
tained through energy input by SNe (Springel & Hernquist
2003) and turbulence induced by the disk’s self gravity
and rotation (Wada & Norman 2007). We include a min-
imum pressure explicitly by adopting a polytropic equa-
tion of state (EoS) with Pmin ∝ ργefffor gas above the
density threshold for star formation and adopt γeff = 1.4.
For γeff > 4/3, the Jeans mass increases with density
(e.g., Schaye & Dalla Vecchia 2008), such that, if it is re-
solved at the threshold density, it is resolved everywhere.
Schaye et al. (2010) showed that, in models where star for-
mation is strongly regulated by stellar feedback, as it is in
ours, the choice of γeff has very little impact on the global
star formation rate. The star formation threshold density is
nH > 0.1cm−3for the Aq-C-6 simulation and a factor of four
and sixteen higher for the Aq-C-5 and Aq-C-4 simulations
respectively. This scaling is chosen since, for irradiated pri-
mordial gas with an isothermal density profile, halving the
gravitational softening will increase the maximum density
that is resolved by a factor of four.
2.2 Multiphase ISM and Star Formation
At sufficiently high pressures, the ISM is known to exist
in distinct phases. We follow Springel & Hernquist (2003),
modelling gas above the threshold density using hybrid SPH
particles, which are assumed to consist of a series of cold
clouds in pressure equilibrium with a surrounding hot phase.
The total mass in the cold phase can increase through ther-
mal instability and decrease through star formation and
cloud evaporation by SNe, but the mass spectrum of clouds
is kept fixed as
Φ(m) =dNc
dm∝ m−α. (1)
We adopt α = 1.7, guided by observations that sug-
gest a plausible range of 1.5 − 1.9 (Solomon & Rivolo
1989; Fukui et al. 2001; Heyer et al. 2001). We follow
Samland & Gerhard (2003) in assuming clouds to be spher-
ical, with size at a fixed mass determined solely by the am-
bient pressure (Elmegreen 1989):
?
m
M⊙
??r(m)
pc
?−2
= 190P1/2
4
, (2)
where P4 =
dependence of each cloud’s dynamical time on the effective
pressure follows directly from Eqn. 2:
P/k
104Kcm−3and k is the Boltzmann constant. The
tdyn=
?
3π
32Gρ(m)
?1/2
≃ 0.32P−3/8
4
?
m
M⊙
?1/4
Myr, (3)
and we assume that the star formation rate in each cloud is
inversely proportional to its dynamical time (tdyn):
˙ m∗ = c∗
m
tdyn, (4)
where c∗ is the star formation efficiency, which is set to
reproduce the normalisation of the Kennicutt-Schmidt law
(Kennicutt 1998). The total star formation rate for each
SPH particle is obtained by integrating Eqn. 4 over all clouds
deemed capable of supporting star formation (which we as-
sume to be in the mass range 104− 106M⊙).
SPH particles spawn new collisionless star particles in a
stochastic fashion, with a probability that depends on their
star formation rate and on the mass in the cold phase. Each
star particle represents a single stellar population, forming
with a Chabrier (2003) initial mass function (IMF). Energy,
mass and metals are returned to the ISM by AGB stars, type
Ia and type II SNe on timescales appropriate for the age and
metallicity of the stellar population, with yields and stel-
lar lifetimes taken from Portinari et al. (1998) and Marigo
(2001). Rather than performing this calculation at every dy-
namical timestep, which is very expensive computationally,
we use coarser steps, chosen such that the timescales asso-
ciated with type II and type Ia SNe can be adequately sam-
pled. Initially, each step has length t8M⊙/50, where t8M⊙is
the lifetime of an 8M⊙ star1. When the age of the stellar
population exceeds t8M⊙, the timesteps lengthen to 100Myr,
which is short enough to model the release of mass and en-
ergy from type Ia SNe and from AGB stars.
1t8M⊙∼ 40 Myr at solar metallicity
c ? 201? RAS, MNRAS 000, 1–16

Page 4

4 O. H. Parry et al.
2.3 Supernovae Winds
The perennial problem with the distribution of stellar feed-
back energy in cosmological hydrodynamical simulations has
been that the star-forming gas that receives the energy is
dense enough to radiate it away before it can have any dy-
namical effect (Katz et al. 1996). This is likely to be a conse-
quence of the inability to resolve the detailed structure of the
ISM (e.g., Dalla Vecchia & Schaye 2008; Ceverino & Klypin
2009). We employ a commonly used technique to circum-
vent this limitation, which consists of imparting kinetic en-
ergy to gas particles directly (e.g., Navarro & White 1993;
Mihos & Hernquist 1994; Springel & Hernquist 2003). The
velocity we choose to give gas particles that receive SNe en-
ergy is motivated by observations that suggest that large
scale outflows have velocities that scale with the circular ve-
locity of their host galaxies (Martin 2005). As a proxy for the
host halo’s circular velocity, which is computationally expen-
sive to calculate for each particle on-the-fly, we use the local
one-dimensional velocity dispersion, determined from neigh-
bouring dark matter particles. This quantity is strongly cor-
related with the maximum circular velocity, vmax, in a way
that does not evolve with redshift (Okamoto et al. 2010).
Our prescription results in a wind speed that increases as
the halo grows and hence, from energy conservation, in a
mass loading (wind mass per unit star formation rate) that
is highest at early times. This scaling has been shown to
give a much better match to the luminosity function of the
Milky Way satellites than models that use a constant wind
velocity (Okamoto et al. 2010).
One further addition
to ensurethat SNedriven
Dalla Vecchia & Schaye (2008) showed that standard kinetic
feedback is more effective in low mass galaxies, where wind
particles tend to drag neighbouring gas out with them. In
high mass galaxies on the other hand, the pressure of the
ISM can be sufficient to prevent much of the mass in the
wind from escaping. Since we wish to be able to prescribe
the mass loading and wind velocity directly, we choose to
decouple wind particles from the hydrodynamic calculation
for a short time in order to allow them to escape the high
density star forming regions. When the density has fallen to
nH = 0.01cm−3, the particles feel the usual hydrodynamic
force again. If they do not reach sufficiently low densities
after a time 10kpc/vwind, they are recoupled anyway.
When a gas particle receives SNe energy from a neigh-
bouring star particle, the wind speed (vw) is obtained from
the local velocity dispersion and then the particle is assigned
a probability to be added to the wind:
to the model
act
is needed
intended.winds as
pw =
∆Q
1
2msphv2
w, (5)
where ∆Q is the total feedback energy received by the gas
particle and msph is the current mass of the SPH particle.
Note that an SPH particle’s mass may increase if it receives
mass from SNe or AGB stars in neighbouring star particles,
or decrease if it spawns a new star particle, which has a
mass of half the original gas particle mass. If pw exceeds
unity, that is, if there is energy available in excess of that
needed to add the particle to the wind, then the extra energy
is distributed to the gas particle’s neighbours as an increase
in internal energy. The direction in which wind particles are
propelled is chosen at random to be parallel or anti-parallel
to the vector (? v0−?v)×? agrav where v0 is the velocity of the
gas particle before it receives feedback energy, ? agrav is the
gravitational acceleration vector, pointing approximately to
the local potential minimum (halo centre) and v is the bulk
velocity of the halo, which we take to be the mean velocity
of the gas particle’s dark matter neighbours. The result of
this treatment is a wind launched preferentially along an ob-
ject’s rotation axis (Springel & Hernquist 2003). Our model
for SNe winds differs from that described by Okamoto et al.
(2010) in two ways. Firstly, we allow all gas particles, not
just those above the star formation density threshold, to be
added to the wind if they receive feedback energy. The orig-
inal prescription can result in a variable wind mass loading
depending on how well the star forming region is resolved.
Secondly, only type II SNe contribute to the winds, type Ia
SNe energy is added to the gas as thermal energy.
2.4Satellite Identification
Galaxies are identified using a version of the subfind algo-
rithm (Springel et al. 2001) adapted by Dolag et al. (2009),
which identifies self-bound structures and includes the inter-
nal energy of gas when computing particle binding energies.
From the ∼ 5Mpc high resolution region, we select all galax-
ies within 280kpc of the centre of the most massive (cen-
tral) galaxy. This distance was chosen to match the limiting
magnitude of the completeness-corrected satellite luminosity
function constructed by Koposov et al. (2008). The largest
satellite in our Aq-C-4 run is resolved with about 1.5 × 105
particles in total, ∼ 3 × 104of which are star particles. In
the following, we consider all galaxies with more than ten
star particles, which, taking into account the typical mass
fraction lost through stellar evolution for our choice of IMF,
implies a stellar mass limit of ∼ 1.2 × 105M⊙ for Aq-C-4.
3 THE EFFECT OF BARYONS ON
SATELLITE DARK MATTER HALOS
Using a dark matter only (DMO) counterpart of our
Aq-C-4 run, simulated as part of the Aquarius project
(Springel et al. 2008), we have examined the extent to which
the dynamics of the baryons alter the structure of dark mat-
ter (sub)halos of satellite galaxies over the course of their
formation. The DMO run had identical initial conditions
to our Aq-C-4, but for the absence of baryons and a cor-
respondingly higher dark matter particle mass by a factor
∼ 1/(1 − Ωb/Ωm).
Naively, one might simply compare each subhalo with
its DMO equivalent at z = 0, but this turns out to be prob-
lematic. As has been noted in previous N-body simulations
at different resolutions, small phase deviations in subhalo
orbits get amplified over time, such that subhalos can be in
quite different positions at z = 0 (e.g., Frenk et al. 1999;
Springel et al. 2008). We see similar differences between Aq-
C-4 and the DMO run. Subhalo orbits are also affected by
other factors such as subhalo-subhalo scattering and varia-
tions in the potential due to small differences in the growth
history of the main halo.
Since the strength of tidal shocking is strongly
dependent on pericentric distance (Gnedin et al. 1999;
c ? 201? RAS, MNRAS 000, 1–16

Page 5

The Baryons in the MW Satellites5
Mayer et al. 2001), small orbital deviations can cause large
differences in subhalo structure, which are entirely unrelated
to the presence or absence of baryons. This complication can
be avoided, either by choosing subhalos with no close peri-
centre, or by making the comparison at the epoch when the
satellite is first accreted into the halo of the main galaxy, be-
fore the orbits have had a chance to diverge. We choose the
latter option, since the former restricts us to a very small
number of cases, although we note that one massive halo
in a low eccentricity (∼ 0.2) orbit with a distant pericentre
(∼ 200kpc) shows comparatively small differences in its dark
matter density profile at z = 0 relative to the DMO case. In
the few instances where the accretion times of the subhalo
differ slightly between the hydrodynamical and DMO runs,
we choose the earlier of the two epochs.
In Fig. 1 we show spherically averaged profiles for the
dark matter density (plotted as ρr2to emphasise small dif-
ferences) of our most massive satellites, for Aq-C-4 and the
DMO run at the output time when each satellite first joins
the main friend-of-friends (FOF; Davis et al. 1985) group.2
The differences in the subhalo density profiles with and with-
out baryons clearly exceed the uncertainties associated with
finite sampling, indicated by the error bars. They are also
greater than, for example, the differences expected between
dark matter realisations of the same subhalo at different res-
olutions (Springel et al. 2008). Some subhalos (e.g. top left
and centre right panels) appear to have been largely unaf-
fected, whilst others (e.g. top and bottom right panels) show
more substantial changes of up to thirty percent in some ra-
dial bins. In Section 6, we describe an extreme example of
a subhalo which suffered much more extensive damage as a
result of baryonic processes. In general, however, there does
not seem to be any consistent trend for baryons to increase
or decrease the central density of the dark matter.
In Fig. 2, we show spherically averaged dark matter
velocity dispersion profiles for the same selection of satellites
in Aq-C-4 and the DMO run. The largest differences are seen
in those subhalos that show the most change in their density
profiles in Fig. 1. Once again, the differences are typically
less than ten percent in any given radial bin, but as much as
thirty percent in some instances, with no apparent trend for
baryons to raise or lower the dark matter velocity dispersion.
From these results, we conclude that the baryons have
had a relatively small impact on the dark matter phase-space
structure of the subhalos, with the important caveat that it
is unclear whether such effects are limited by the resolution
of our simulations. Another important factor contributing
to this conclusion is the strength of our feedback, since it
dictates how easily baryons are able to condense in the cen-
tre of low mass halos and affect the dynamics of the dark
matter. Models with much weaker feedback might achieve
more pronounced differences than we see here, but as we
will show in Section 5.1, such models typically overpredict
the luminosities of satellite galaxies.
Although some satellites are accreted at fairly high red-
shift (see the labels on each panel in Fig. 1), it is unlikely
that the baryons would have an increased effect in the re-
2In practice, we require the subhalo to be counted in the main
FOF group for two consecutive snapshots to avoid instances where
subhalos are spuriously joined to the main group for a short time.
maining time to z = 0. In all but the largest satellites, gas
is lost fairly rapidly following accretion, as we will show in
Section 4.2.
4 CONVERGENCE OF SATELLITE
PROPERTIES
In this section we investigate the convergence of various key
properties of our simulated satellite galaxies. We make the
comparison on an object-to-object basis, matching up satel-
lites between runs. As explained in Section 3, this cannot be
accomplished simply by choosing subhalos that are spatially
closest at the final time. Instead, we trace particles back to
the initial conditions and match them spatially there. In the
following analysis we consider the most massive satellites in
Aq-C-4 for which resolved counterparts exist in Aq-C-5 and
often also in Aq-C-6.
4.1 Stellar Mass
We begin by considering the total stellar mass in each satel-
lite at z = 0. This is a function of the rate at which gas can
cool onto the galaxy and the efficiency of star formation,
dictated by the gas physics and feedback. As well as check-
ing that our results do not depend on resolution, we com-
pare with an independent modelling technique, presented by
Cooper et al. (2010), hereafter C10. They used the Aquarius
simulations to track the formation of dark matter substruc-
tures in six different halos and a version of the semi-analytic
galaxy formation code galform to compute the baryonic
properties of satellite galaxies.3At each output time, the
stellar mass formed since the last simulation snapshot is as-
signed to some fraction of the most tightly gravitationally
bound dark matter particles in the subhalo, providing spa-
tial and kinematic information for the stars. The ‘tagged’
fraction was chosen to match the distribution of sizes (half-
light radii) for Local Group satellites and also to produce
results robust to changes in resolution.
Fig. 3 demonstrates that the stellar mass in each sub-
halo agrees relatively well between the three resolutions,
particularly for the most massive examples, although the
difference is as large as a factor of six in one case. Some of
this scatter (between different resolutions and between the
semi-analytic and hydrodynamical realisations) is likely re-
lated to the deviations in subhalo orbits between simulation
runs described in Section 3. Small differences in pericentric
distance and eccentricity can strongly affect the tidal field
and hence the extent to which stars can be stripped from
subhalos. Examples of subhalos that have lost more than 50
percent of their peak stellar mass (excluding the effects of
stellar evolution) in one or more of the runs are indicated in
Fig. 3 by circled points.
The semi-analytic prescription typically predicts a lower
stellar mass in each subhalo, although the correlation indi-
cates that the ranking of subhalos by stellar mass is similar
3Their semi-analytic model is essentially that presented by
Bower et al. (2006), but with a lower circular velocity threshold
(30 kms−1) to identify halos in which cooling is suppressed by
reionisation. This value is motivated by recent hydrodynamical
simulations (Hoeft et al. 2006; Okamoto et al. 2008).
c ? 201? RAS, MNRAS 000, 1–16

Page 6

6 O. H. Parry et al.
Figure 1. The spherically averaged dark matter density profiles of the nine most massive satellite galaxies in our high resolution
hydrodynamic (red) and dark matter only (black) runs. Error bars are obtained by bootstrap resampling. The comparisons are made at
the redshift where the galaxy is first accreted as a satellite, which is shown as a label at the top of each panel. Black dashed vertical lines
indicate the scale on which softened gravitational forces become fully Newtonian. Blue dashed vertical lines indicate the convergence
radius of Power et al. (2003).
to that in our simulations. This offset between the two tech-
niques is not obviously attributable to a single aspect of
either model, but one mechanism that may be important
is ram pressure stripping. In the semi-analytic model, any
hot gas is instantaneously stripped from satellites upon in-
fall. In combination with strong SNe feedback, this quenches
star formation in satellites very rapidly following accretion.
As we will show in the next subsection, ram pressure and
feedback act to produce a similar effect in our simulations,
but star formation is able to continue for an appreciable time
after accretion and right up to z = 0 for the most massive
satellites.
4.2Mass evolution
We now examine how satellites in the three runs acquire
their dark and baryonic mass and form stars. Fig. 4 shows
the gravitationally bound mass of dark matter, stars and gas
for the nine most massive satellites as a function of redshift.
For reference, we also include Table 2, which lists the masses
at z = 0. Reionisation (z = 9) is marked with a vertical
dashed line and arrows indicate the accretion time, that is,
the time when the galaxy first becomes a satellite in the
high resolution run. Where the accretion times differ slightly
between runs, the value for the high resolution case is shown.
Apart from numerical convergence, which we will dis-
cuss next, there are a number of interesting features to note
in Fig. 4, many of which were also observed in the simula-
tions of Okamoto et al. (2010), Wadepuhl & Springel (2010)
and Sawala et al. (2011). There are instances of satellites
being periodically stripped of mass as they pass through
pericentre, most obviously the satellite tracked in the bot-
tom right panel, which loses dark matter and gas from its
outer parts in two close approaches. None of these massive
satellites appear to be on orbits with sufficiently high ec-
centricity and/or a close pericentre to strip the more tightly
c ? 201? RAS, MNRAS 000, 1–16

Page 7

The Baryons in the MW Satellites7
Figure 2. The spherically averaged 1D velocity dispersion profiles of the most massive satellite galaxies in our high resolution hydro-
dynamic (red) and dark matter only (black) runs. Error bars are obtained by bootstrap resampling. The comparisons are made at the
redshift when the galaxy is first accreted as a satellite, which is indicated on the corresponding panels in Fig. 1. Black dashed vertical
lines indicate the scale on which softened gravitational forces become fully Newtonian. Blue dashed vertical lines indicate the convergence
radius of Power et al. (2003).
bound stellar component, although there are several exam-
ples of satellites in the simulation that were heavily stripped
or disrupted entirely and hence are not among the most mas-
sive at z = 0.
The loss of gas following accretion in most cases is fairly
rapid and is brought about through a combination of ram
pressure stripping and stellar feedback. As noted by both
Okamoto & Frenk (2009) and Wadepuhl & Springel (2010),
reionisation appears to have virtually no impact on satellites
this large (the lowest mass example in Fig. 4 has final total
mass of 5 × 108M⊙); the gas mass rises steadily through
z = 9, and star formation continues unabated. We note that
the three largest satellites retain a substantial amount of gas
and are still increasing their stellar mass at the present day,
analogously to the ongoing star formation in the MW dIrrs.
In terms of numerical convergence, in most respects,
there is good agreement between the three resolutions. The
exceptions to this are the rate at which gas is lost from
some satellites following accretion and the resulting effect
on the late-time star formation rates. In most cases, there
is a clear tendency for more efficient ram pressure strip-
ping with decreasing resolution. This affect appears to be
related to the force resolution, which results in gas particles
in lower resolution runs being less tightly bound and hence
more susceptible to ram pressure stripping. The slightly dif-
ferent timescales over which satellites are able to retain their
gas and continue to form stars account, at least in part, for
the often lower final stellar masses in Aq-C-5 and Aq-C-6
noted in the previous subsection.
5 OBSERVED PROPERTIES
In the previous section, we demonstrated that our model
produces satellite galaxies with properties that show rea-
sonable convergence with resolution and stellar masses that
c ? 201? RAS, MNRAS 000, 1–16

Page 8

8 O. H. Parry et al.
Figure 4. The mass evolution in dark matter (solid lines), stars (dashed lines) and gas (dotted lines) for the nine most massive satellite
galaxies in our Aq-C-4 (red), Aq-C-5 (green) and Aq-C-6 (blue) simulations. Note that no resolved counterpart was identified in the
Aq-C-6 simulation for the satellites tracked in the bottom row of panels. Stellar masses are scaled up by a factor of ten to reduce the
range of the ordinate axis. The vertical dashed line indicates the redshift of reionisation and arrows the epoch at which the galaxy was
first accreted as a satellite in Aq-C-4. The panels are ordered by total mass, from left to right along each row, beginning at the top.
MDM
[106M⊙]
Mgas
[106M⊙]
M∗
[106M⊙]
14822.3
14236.2
5436.6
4634.8
1548.1
1496.5
1229.1
1049.7
1001.8
1734.8
584.1
678.1
215.2
0.0
40.6
0.0
0.0
37.6
250.5
27.7
47.2
4.8
3.2
12.2
2.6
55.4
2.6
Table 2. The mass in dark matter, gas and stars gravitationally
bound to the nine most massive satellites at z = 0
scale with subhalo mass in a fashion expected from an al-
ternative modelling technique. We now proceed to exam-
ine how well their observable properties match those of
the Local Group satellites. Where photometric quantities
are required, we use the stellar population synthesis model
PEGAS´E (Fioc & Rocca-Volmerange 1997), summing the
luminosities of all star particles gravitationally bound to the
subhalo at z = 0.
5.1 Satellite Luminosity Function
One of the most fundamental properties of any galaxy pop-
ulation is its luminosity function. Encoded in its shape and
normalisation are a range of physical processes that are key
to understanding the formation and evolution of the popu-
lation.
In Fig. 5 we plot the luminosity function of sim-
ulated satellites at each resolution. Also plotted is the
(completeness-corrected) average luminosity function for
c ? 201? RAS, MNRAS 000, 1–16

Page 9

The Baryons in the MW Satellites9
Figure 3. A comparison of the stellar mass that forms in each
satellite at the three different resolutions of our hydrodynamical
runs, as well as in the independent semi-analytic model presented
by Cooper et al. (2010). Note that not all satellites in the high
resolution run have resolved counterparts at intermediate and low
resolution. Points that lie on the abscissa correspond to subhalos
with Mstellar< 5 × 104M⊙. Data points are plotted for all satel-
lites in the high resolution run with more than ten star particles.
If the satellite also has ten star particles in the lower resolution
run, it is plotted as a filled, rather than open symbol. Satellites
that have lost more than 50 percent of their maximum stellar
mass through tidal stripping are indicated by circled points. The
dark and light gray shaded regions represent factors of two and
five respectively away from the line of equality.
MW and M31 satellites from Koposov et al. (2008) that in-
cludes the SDSS ultra-faint objects. We find good agreement
between resolutions at all resolved luminosities, consistent
with the convergence of stellar masses and star formation
histories demonstrated in Section 4. The simulated popula-
tions provide good matches to the Local Group average at
the faint end, consistent with the findings of Okamoto et al.
(2010) in another of the Aquarius halos, but have no galaxy
as bright as the Large Magellanic Cloud (LMC). The bright-
est galaxy (in Aq-C-4) has a similar V-band magnitude to
that of the Small Magellanic Cloud (SMC).
Note that there is still a significant observational un-
certainty in the total mass of the MW. Current estimates
put it between 0.8 and 3 × 1012M⊙ (Dehnen et al. 2006;
Li & White 2008; Xue et al. 2008; Watkins et al. 2010). Our
halo has a mass slightly closer to the lower end of this range
of Mcrit,200 = 1.42 × 1012M⊙. Clearly, if we are simulating
a halo twice or half as massive as the MW, we should not
expect to reproduce the luminosity function of its satellites
exactly. A further consideration is whether the MW has a
typical satellite population for its halo mass or total lumi-
nosity. To this end, we have also plotted a black solid line
and two shaded regions indicating the mean and spread of
the luminosity function (see figure caption for details) for
satellite systems in the SDSS around central galaxies with
r-band luminosity close to that of the MW (Guo et al. 2011).
These data suggest that the Local Group is fairly typical,
although satellites like the Magellanic Clouds are found in
fewer than half of the systems in the sample. In another
Figure 5. The rest frame, V-band luminosity function of satellite
galaxies in our high (red), intermediate (green) and low (blue) res-
olution simulations. Circles with error bars indicate the average
MW+M31 satellite luminosity function, corrected for complete-
ness, by Koposov et al. (2008). For consistency with their data,
only simulated satellites within 280kpc of the central galaxy are
included. The solid black line and shaded regions indicate the
mean and spread in the satellite luminosity functions of Milky
Way mass galaxies in an analysis of SDSS data by Guo et al.
(2011). The light grey region shows the RMS scatter about the
mean in each bin.
study, Liu et al. (2010) found that > 80 percent of MW-
like galaxies have no satellite as bright as the SMC within
150 kpc. In this statistical context, perhaps the lack of very
bright satellites in our simulations should not be a major
cause for concern.
5.2 Sizes
An important and readily observable property of the most
massive Local Group satellites is the distribution of their
sizes, usually measured as the radius containing half the lu-
minosity in projection. Unfortunately, a combination of the
spatial resolution and the limitations of our subgrid model
for star formation mean that we cannot hope to reproduce
the observed sizes in our simulations. As explained in Sec-
tion 2, a minimum pressure is maintained in star forming
gas to ensure that the Jeans length on the equation of state,
λJ,EoS, is always resolved. Our subgrid model assumes that
stars form on much smaller (unresolved) scales, inside molec-
ular clouds, but the star particles that are created must
nonetheless inherit the dynamical properties of the SPH par-
ticle from which they formed. As a result, the minimum size
of star-forming regions will be dictated by the warm/hot
phase density and temperature, through λJ,EoS, or by the
gravitational softening, if this is larger.
These limits are apparent in Fig. 6, where we plot
the absolute V-band magnitude of simulated satellites as
a function of their half-light radius. The observed half-light
radii are de-projected by multiplying by a factor of 4/3,
an approximation that is accurate to 2% for the exponen-
tial, Gaussian, King, Plummer and Sersic profiles commonly
c ? 201? RAS, MNRAS 000, 1–16

Page 10

10 O. H. Parry et al.
Figure 6. Absolute V-band magnitude as a function of de-
projected half-light radius for satellite galaxies in our Aq-C-4
(red filled circles) and Aq-C-5 (green filled circles) runs. The
Magellanic Clouds are represented by purple crosses. Their pro-
jected half-light radii were derived from angular values taken
from Bothun & Thompson (1988) and distance estimates from
Hilditch et al. (2005) and Pietrzy´ nski et al. (2009). 3D half-light
radii were calculated by multiplying these values by 4/3, as sug-
gested by Wolf et al. (2010). All other MW satellites brighter than
−7.5 (except Saggitarius) are shown as blue triangles with lu-
minosity and de-projected half-light radii taken from Wolf et al.
(2010). The solid blue line is a least-squares fit to all the observa-
tional data points. Arrows indicate the scales on which softened
gravitational forces become fully Newtonian for each resolution.
used to fit the MW satellites (Wolf et al. 2010). The stars
in both the Aq-C-4 and Aq-C-5 runs typically have much
less concentrated distributions than the observed satellites.
An exception to this is the third brightest satellite in Aq-C-
4, which has a V-band magnitude of −12.2 and a half-light
radius of ∼ 480pc. It has a very high mass fraction in stars
and an unusual history, forming in a series of violent major
mergers at z ∼ 4 before being subjected to strong tidal dis-
ruption between z = 2 and z = 0. We discuss this satellite
in detail in Section 6.
In the highest resolution run, Aq-C-4, we expect the
gravitational softening to be the main factor limiting the
minimum sizes of star forming regions, since it is always
larger than λJ,EoS. In Aq-C-5 and Aq-C-6 (not shown here),
which have lower threshold densities for star formation by
factors of four and sixteen respectively, λJ,EoS at the thresh-
old is comparable to the softening, so should also be impor-
tant in setting the sizes of the stellar component. For both
Aq-C-4 and Aq-C-5, the half-light radius of the most mas-
sive galaxy should not be limited by either effect and is
consistent with the observations, given the large scatter.
5.3 Dynamical Masses
The stellar kinematical properties of Local Group dwarf
galaxies provide an important test of the ΛCDM cosmol-
ogy. Subhalos that form in N-body simulations of MW-mass
systems appear to have potentials compatible with the stel-
lar kinematics of the brightest MW satellites (Stoehr et al.
2002; Strigari et al. 2010). Nonetheless, the analytic calcu-
lations required to reach such conclusions necessarily in-
Figure 7. The total mass contained within the projected half-
light radius (Rhl) of simulated satellites, measured in the high
resolution, dark matter only, Aquarius-C-2 simulation (open and
filled black circles). The radii are inferred from the observed
luminosity-size relation (see text for details). The filled circles
indicate those satellites that are used in the statistical compari-
son with the observed data, illustrated in Fig. 8. The error bars on
the simulated data points show the masses obtained by assuming
half-light radii 1σ above and below the mean fitted values, where
σ is determined by the scatter about the fit to the observed data.
Red crosses with error bars are estimates from Wolf et al. (2010)
for a selection of MW satellites.
clude simplifying assumptions. Hydrodynamic simulations
attempting to model star formation self consistently in a cos-
mological setting are inevitably some way behind the best
N-body simulations in terms of resolution and must also
model uncertain baryonic physics on sub-kiloparsec scales.
As such, our simulations are not suitable for studying the de-
tailed kinematics of the stars directly; instead, we resort to a
somewhat cruder comparison and ask whether our satellites
form in realistic potential wells, by comparing simulated and
observationally determined masses.
Historically there has been significant uncertainty asso-
ciated with determining satellite masses from observations.
Typically, estimates are derived from the line-of-sight stellar
velocity dispersion with three key assumptions: i) the system
is spherically symmetric, ii) stellar orbits are isotropic and
iii) the system is in equilibrium. Two recent studies have at-
tempted a more general approach, with the aim of reducing
the systematic uncertainties. Using an approach based on
the spherical Jeans equation, Walker et al. (2009) showed
that for the brightest MW dSphs, the mass within the pro-
jected half-light radius is robust to changes in the anisotropy
and underlying density profile. This relation was explained
analytically by Wolf et al. (2010) who demonstrated that,
if the stellar velocity dispersion profile remains relatively
flat in the centre, as observations suggest (e.g., Walker et al.
2007), then the uncertainty introduced by assuming a par-
ticular anisotropy is minimised at the (3D) radius where
the logarithmic slope of the stellar number density profile,
−dlnn∗/dlnr = 3. They also showed that, for a range of re-
alistic light profiles that have been used to model the MW
dSphs, this minimum lies close to the (de-projected) half-
light radius. It is this radius, therefore, at which we choose
to compare the enclosed masses of satellites in the simula-
tions and observations.
c ? 201? RAS, MNRAS 000, 1–16

Page 11

The Baryons in the MW Satellites11
In the previous subsection we described how aspects of
our simulations, particularly the limitations of the subgrid
treatment of the ISM and the gravitational softening scale,
can set an artificial lower limit to the sizes of the stellar
components of the satellites. However, we also demonstrated
that the luminosity function of the simulated satellites is
close to that observed, the stellar mass in each satellite is
relatively well converged and stellar mass is found to scale
with subhalo mass similarly using an alternative modelling
technique.
With these checks in mind, we proceed with the as-
sumption that the cooling, star formation and feedback pre-
scriptions in our model result in a realistic stellar mass in
each satellite, but that stars form in a configuration that is
too diffuse. We then ask what the projected half-light radius
of each simulated satellite should be at a fixed luminosity,
based on the observed sizes of the brightest MW satellites.
We take a simple least-squares fit to the data points in Fig. 6
(minimising the sum of the squared differences in the mag-
nitude coordinate) and compute the scatter in the (log) ra-
dius coordinate about this line. For each simulated satellite,
we assume a Gaussian distribution of possible sizes, with a
mean equal to the fit evaluated at the satellite’s luminosity
and dispersion defined by the observed scatter.
Following this procedure we find that, for magnitudes
MV> −12, our fit to the observed data implies sizes be-
low the scale at which softened gravitational forces become
non-Newtonian in the Aq-C-4 simulation, which leads to an
underestimation of the enclosed mass. We choose instead
to measure the mass of each satellite in a much higher
resolution dark matter only realisation of the simulation,
Aquarius-C-2, which has a smaller softening scale by a fac-
tor of ∼ 4, such that the fitted half-light radii of satellites
down to MV∼ −7.5 are larger than the force resolution.
The central masses measured in the higher resolution sim-
ulation are typically forty to eighty percent higher for the
ten brightest satellites, but the difference can be a factor
of three for satellites with MV∼ −8. Given the results pre-
sented in Section 3, we do not expect the omission of baryons
from Aquarius-C-2 to have had a large impact on the central
densities and hence the measured masses of these satellites.
Fig. 7 shows the mass enclosed within the mean half-
light radius chosen for each satellite, with error bars indi-
cating the masses corresponding to ±1σ sizes. Although the
range of plausible values is large, the brightest simulated
satellites have mean masses three to five times higher than
the MW satellites of the same luminosity. While there is less
of a discrepancy at fainter magnitudes, our model seems to
show a more gradual increase in luminosity with mass than
is suggested by the observational data. We note that, start-
ing from identical initial conditions to our Aq-C-4 simula-
tion, Wadepuhl & Springel (2010) found that the mass-to-
light ratios of their satellites were typically higher than those
quoted observationally by a very similar factor and were also
more discrepant in the most massive satellites (see their Fig.
15). In a hydrodynamic simulation of the Local Group, again
with resolution similar to our Aq-C-4, Knebe et al. (2010)
found a similar result for satellites bound to their MW and
M31 analogues, with mass-to-light ratios a factor ∼ 7 too
high. We note, however, that they measured half-light radii
for their satellites using the star particles forming in their
Figure 8. The cumulative fraction of the 4th − 12th brightest
satellites as a function of the mass contained within the half-
light radius in three model distributions (solid blue, green and red
lines) and those derived for MW satellites by Wolf et al. (2010)
(dashed line). Labels in the top left indicate the number of times
we repeat the process of drawing masses for our sample of nine
satellites in order to define the model distribution, along with
the probability that each model is consistent with the observed
masses.
simulation, which, as we have shown, can be too large when
the scales associated with star formation are not resolved.
To quantify the discrepancy in Fig. 7 statistically, we
construct multiple realisations of the half-light masses of the
simulated satellites by drawing sizes from the distributions
described above and computing the mass enclosed in the
corresponding high resolution Aquarius-C-2 satellites. We
then combine the samples to define a model distribution for
the cumulative fraction of satellites with mass larger than a
given value and calculate the probability that the observed
masses could have been drawn from it, using a one-tailed
Kolmogorov-Smirnov (KS) test.
In order to make a like-for-like comparison with the
masses quoted by Wolf et al. (2010), we consider only the
4th− 12thbrightest simulated satellites in our Aq-C-4 sim-
ulation that are within 280kpc, corresponding to all of the
classical MW satellites except the Magellanic Clouds and
Sagittarius, and including Canes Venatici (which is approx-
imately the same luminosity as Draco). The sample is indi-
cated in Fig. 7 by filled circles. Note that the third brightest
satellite in Aq-C-4 is in the midst of tidal disruption (see Sec-
tion 6), a process that, as a result of small differences in the
orbits of the subhalos, is already complete in Aquarius-C-2,
hence no counterpart is found. Although Wolf et al. (2010)
derived masses for fainter satellites, these correspond to sim-
ulated galaxies with fewer than ten star particles, whose lu-
minosities are uncertain in our simulations and which we
therefore choose to exclude. In Fig. 8 we plot cumulative
model distributions, drawing masses for the sample of nine
satellites multiple times to define each distribution, as indi-
cated by the labels in the top left of the plot. The probabil-
ities that the observationally derived masses are consistent
with those distributions are found to be around six percent.
As both Fig. 7 and Fig. 8 demonstrate, the masses of the
brightest simulated satellites are too high compared to those
derived for the MW satellites. This is another manifestation
of the problem recently highlighted by Boylan-Kolchin et al.
c ? 201? RAS, MNRAS 000, 1–16

Page 12

12 O. H. Parry et al.
(2011) who compared the measured masses within the half-
light radii of the same satellites considered here with results
from high-resolution simulations of cold dark matter halos,
including the Aquarius suite. Assuming an NFW density
profile (Navarro et al. 1996b, 1997), they showed that the
most massive subhalos in the simulations are too concen-
trated to be able to host the brightest observed satellites.
The mismatch seen in Fig. 7 and in the results of
Boylan-Kolchin et al. (2011) could, in principle, be due to an
underestimate of the central masses of the observed satel-
lites. However, for the errors quoted by Wolf et al. (2010)
to be substantially underestimated would require rather ex-
treme variations in the anisotropy profile, which would be
poorly fit by their fairly general parameterised form. This
seems unlikely to be the sole source of the disagreement be-
tween model and data.
While the discrepancy could be simply due to statis-
tics, it might also reflect a serious shortcoming either of the
standard CDM cosmogony or of current models of galaxy
formation, such as those assumed in our simulations. A pos-
sible explanation of the discrepancy between the mass-to-
light ratios measured for the real and simulated satellites
is that the central dark matter densities predicted in the
CDM model are reduced by baryonic physics. One mecha-
nism for achieving this, proposed by Navarro et al. (1996a),
is the condensation of a dense baryonic component followed
by the rapid expulsion of gas by stellar feedback. The dark
matter adjusts to this change in the potential by develop-
ing a central “core”, shifting the rotation curve maximum
to a larger radius and reducing the mass-to-light ratio in
the central parts. This process does indeed appear to play
an important role in the evolution of one satellite in Aq-C-
4 (see Section 6), which forms in the subhalo that has the
largest mass prior to accretion. If this process is common, it
is possible that it is not seen here in less massive subhalos
due to lack of resolution.
A more radical explanation of the discrepancy is that
the dark matter consists of warm, rather than cold, par-
ticles. In this case, subhalos of a given mass form later
and have lower concentrations than in the CDM model (see
Navarro et al. 1997; Hogan & Dalcanton 2000). Lovell et al.
(2011) have recently shown explicitly that the masses and
concentrations of subhalos in a warm dark matter model
agree well with the data.
6 A STAR-DOMINATED SATELLITE
The formation history of one of the satellite galaxies in our
high resolution hydrodynamical simulation is particularly
interesting. By z = 0, we find that it has become dominated
by its stellar component, with a mass-to-light ratio of ∼ 2.4
and its dark matter has become much less concentrated than
otherwise similar subhalos. It appears as an outlier in Fig. 6,
as it has a very small half-light radius for its luminosity. In
this section, we briefly describe its formation history and
explain why it develops into such an unusual object.
At z = 0 the satellite is, in fact, in the process of being
tidally disrupted and has a substantial stellar stream asso-
ciated with it. Fig. 9 illustrates the structure of the stream
in two orthogonal projections centred on the main galaxy.
The dense stellar nucleus of the satellite that remains iden-
tifiable as a bound structure is also visible. We track all star
particles associated with the satellite at the epoch when it
is accreted and plot their projected mass density at z = 0.
The stripped stars account for the majority of the stellar
halo by mass.
The stream is a result of a fairly eccentric orbit with
several close pericentres, illustrated in the bottom panel of
Fig. 10, which shows the distance of the satellite from the
centre of the main galaxy as a function of redshift. The
dashed line indicates the virial radius of the main halo. The
accretion time is the point where the two lines intersect.
The top panel tracks the mass in gas, dark matter and stars
bound to the satellite over the same redshift interval, as
well as the total mass fraction in stars. At accretion, it is
the brightest satellite of the central galaxy, but only the
third brightest at z = 0, as a result of the reduction in
stellar mass through tidal stripping. The stellar fraction at
accretion (∼ 0.02) is fairly typical of the surviving satellites.
Note that it is very common for the stellar fraction of a
satellite to increase with time after it is accreted, since the
outer parts of the dark matter halo are less tightly bound
than the stars and hence more susceptible to tidal stripping
(e.g. Pe˜ narrubia et al. 2008; Sawala et al. 2011). The middle
panel of Fig. 10 shows the evolution of the central (r < 1kpc)
density of the subhalo in gas and dark matter, both of which
drop sharply when the satellite is close to pericentre. A de-
cline is also evident after z ∼ 3, well before the satellite is
accreted, the origin of which we discuss in more detail below.
During the first few orbits, the stellar component re-
mains unaffected while the dark matter lying beyond the
radial extent of the stellar component is stripped. In fact,
some of the dark matter particles with pericentres within
the stellar component are also stripped, as a result of the
dark matter having a higher radial velocity dispersion than
the stars. The final masses of the stellar and dark matter
components are factors of ∼ 50 and 2×104lower than their
peak values respectively.
The extent to which the two components are stripped is
strongly affected by their radial density profiles, which are
shown in Fig. 11 at the time of accretion. The overplotted
regions indicate the range of densities (±1σ) in each bin
for the nine most massive surviving satellites. Clearly, the
stellar component of this galaxy is unsually concentrated
relative to those other galaxies, whilst the dark matter and
gas have shallower than average central density profiles. It
is unclear how much effect the gravitational softening has in
this respect, since forces begin to become sub-Newtonian on
scales less than∼
< 720pc, but we note that the profiles also
differ outside that radius. The highly ‘cusped’ stellar profile
allows the central stellar nucleus to resist the strong tidal
forces that unbind the majority of the dark matter. It also
accounts for the unusually small half-light radius shown in
Fig. 6.
The origin of these density profiles is related to the
satellite’s violent formation history. In a series of major
mergers at z ∼ 3, gas is funnelled to the centre of the main
progenitor, initiating an intense burst of star formation that
gives rise to a highly concentrated stellar distribution. The
subsequent burst of feedback energy rapidly removes a large
fraction of the gas and leads to a fall in the mean binding
energy of the central dark matter. This episode is clearly vis-
ible in the bottom panel of Fig. 10, which shows the central
c ? 201? RAS, MNRAS 000, 1–16

Page 13

The Baryons in the MW Satellites13
Figure 9. Two orthogonal projections of the stellar stream associated with the satellite. The centre of the main halo is at the origin. The
stream is defined by selecting all stars associated with the satellite at the time of accretion and locating them at z = 0. The surviving
satellite is clearly seen as the bright concentrated object lying along the stream.
gas density drop as it is expelled by feedback and turned
into stars, followed by a decline in the dark matter density
in response to the change in the potential. This sequence
of events is effectively the process originally proposed by
Navarro et al. (1996a). The reduced binding energy of its
central dark matter, along with an extreme orbit, combine
to produce the unusual properties of this satellite at z = 0.
7 CONCLUSIONS
We have investigated the formation and evolution of a Milky
Way-like satellite system in an SPH simulation over three
levels of resolution, in which particle masses vary by a fac-
tor of 64. The properties of our simulated satellites show
relatively good numerical convergence, with the final stel-
lar masses typically agreeing to within a factor of two, and
always to within a factor of six. We also compared to an in-
dependent estimate of the stellar mass expected to form in
each subhalo, using the semi-analytic model of Cooper et al.
(2010). The two theoretical techniques produce a similar
ranking of the subhalos by stellar mass, although our simu-
lations typically form a higher mass of stars by a factor of
between two and six. This discrepancy may be partly ex-
plained by the assumption in the semi-analytic model that
gas is stripped instantaneously when a galaxy becomes a
satellite. The mass evolution in gas, stars and dark matter
of each satellite agrees well between resolutions, except that
gas is stripped more rapidly at lower resolution following
accretion onto the main halo. Poorer force resolution causes
gas particles to be more loosely bound to the subhalo and
hence more susceptible to ram pressure stripping. This phe-
nomenon may account for many of the differences in the
final stellar masses between resolutions.
By comparing the dark matter halos of our satellite
galaxies to those that form in a dissipationless version of
the same simulation, we were able to quantify the expected
impact of baryons on the phase-space structure of the dark
matter. Due to small deviations in satellite orbits between
different realisations of the same halo, it is necessary to make
this comparison when the satellite first falls in rather than
at z = 0. Although in some radial bins, in a few subha-
los, the density and velocity dispersion profiles are found
to change by ∼ 30 percent, the differences were typically
less than 10 percent. With the caveat that the resolution
of our simulation may limit the magnitude of such effects,
we conclude that baryons have a relatively small impact on
the structure of the dark matter halos of satellite galaxies
around MW-like hosts.
Our model provides a reasonable match to the faint end
of the Local Group satellite luminosity function averaged
between the Milky Way and M31, although there is a slight
deficit at the bright end, with no LMC analogue. However,
SDSS data (Liu et al. 2010; Guo et al. 2011) suggest that it
is quite common for galaxies with luminosities like the MW
to have no satellites as bright as the LMC and SMC.
Due to the limitations of the spatial resolution and the
implementation of baryonic physics in our simulations, par-
ticularly the modelling of the multiphase ISM, stars do not
form in sufficiently concentrated distributions to match the
half-light radii of Local Group satellites. However, the rea-
sonable agreement between the stellar masses in simulations
with different resolution and different modelling techniques,
combined with the match to the observed satellite luminos-
ity function, suggest that the baryonic mass that is able to
cool in each (sub)halo and form stars is realistic.
In order to test whether satellites of a given luminosity
form in halos with masses consistent with those observed, we
compare their ‘half-light masses’ with values derived for a se-
lection of the brightest MW satellites by Wolf et al. (2010).
For this comparison, each satellite is assigned a distribu-
tion of half-light radii from the best fit to the observed
luminosity-size relation and its variance. In the hydrody-
namical simulation, the gravitational softening is compara-
c ? 201? RAS, MNRAS 000, 1–16

Page 14

14 O. H. Parry et al.
Figure 10. Top panel: the mass in gas (blue), dark matter (black)
and stars (red) gravitationally bound to the satellite’s main pro-
genitor, and the stellar fraction (magenta,dashed line, measured
on the right vertical axis) as a function of redshift. Some of the
small variations in the masses (and hence also the stellar fraction)
at z < 1 are due to the difficulty in identifying the subhalo’s par-
ticles against the high background density at the centre of the
main halo. Centre panel: the density of dark matter (black) and
gas (blue) within the central 1kpc. Bottom panel: the distance to
the satellite from the centre of the main halo. The dashed line
indicates the virial radius of the main halo.
ble to these fitted half-light radii, so we instead measure the
masses in a much higher resolution, dark matter only re-
alisation of the simulation. We hence explicitly ignore any
effects baryons may have had on the central density profiles,
which, in any case, the results in Section 3 suggest are small.
The large scatter about the observed relation translates into
a broad range of possible masses for each simulated satellite,
but nonetheless, the mean masses for the brightest examples
(Mv < −11) are about three to five times higher than their
observed counterparts. The observed mass-luminosity rela-
tion seems to be somewhat steeper than that produced by
our model, although due to the small sample sizes, the slope
of the relation and the scatter about it are relatively poorly
defined in both cases. A KS test, taking into account the un-
certainties in the half-light radii assigned to the simulated
Figure 11. The dark matter (black), stellar (red) and gas (blue)
density profiles of the galaxy at z ∼ 2, when it is first accreted as
a satellite. Regions of the same colour indicate the spread of val-
ues (±1σ) in each radial bin for the nine most massive surviving
satellites at z = 0.
satellites, returns a six percent probability that the observed
masses could have been drawn from the distribution defined
by the simulation data.
Although the apparent disagreement between the simu-
lations and the data could be simply due to statistics, there
are also a number of plausible physical explanations. It could
be that baryonic processes significantly reduce the central
dark matter densities of satellite galaxies. Possible mecha-
nisms to achieve this include, for instance, a sudden change
in the local potential, induced by the rapid expulsion of
baryonic mass through stellar feedback (e.g. Navarro et al.
1996a) or heating due to bulk motions of dense clumps of
gas (e.g. Mashchenko et al. 2006). The results in Section 3
imply that, if such processes are important, they are either
not resolved in the Aq-C-4 simulation, or are not properly
captured by our feedback prescription, except in one case,
which happens to be the most massive subhalo at accretion.
Less concentrated dark matter profiles would also result if
the dark matter consists of warm, rather than cold particles
(e.g. Lovell et al. 2011).
The broad range of possible explanations of the discrep-
ancy highlighted by our results illustrates how uncertain our
understanding of galaxy formation still is on the scale of
dwarf galaxies. Determining which, if any, is correct will be
of critical importance in assessing the viability of the CDM
cosmology and the success of galaxy formation models.
ACKNOWLEDGMENTS
We thank Joop Schaye for helpful comments in the early
stages of this work and Adrian Jenkins for creating the
initial conditions for the simulations. We are also grateful
to Andrew Cooper for giving us access to his semi-analytic
satellite data and for helpful discussions. OHP acknowledges
the receipt of an STFC studentship. TO acknowledges fi-
nancial support by Grant-in-Aid for Scientific Research (S)
by JSPS (20224002) and by Grant-in-Aid for Young Scien-
tists (start-up: 21840015). Simulations associated with this
c ? 201? RAS, MNRAS 000, 1–16

Page 15

The Baryons in the MW Satellites15
work were run on the IBM pSeries Power6 at the Rechen-
zentrum, Garching, the Cosmology Machine at the Institute
for Computational Cosmology (ICC) in Durham, the Cray
XT4 at the National Astronomical Observatory of Japan’s
Centre for Computational Astrophysics and at the Centre
for Computational Sciences in the University of Tsukuba.
CSF acknowledges a Royal Society Wolfson research merit
award. We thank the DEISA Consortium (www.deisa.eu),
co-funded through the EU FP6 project RI-031513 and the
FP7 project RI-222919, for support within the DEISA Ex-
treme Computing Initiative. This work was supported in
part by a STFC rolling grant to the ICC and ERC Advanced
Investigator grant 267291 COSMIWAY.
REFERENCES
Abel T., Haehnelt M. G., 1999, ApJ, 520, L13
Bate M. R., Burkert A., 1997, MNRAS, 288, 1060
Belokurov V. et al., 2007, ApJ, 654, 897
Benson A. J., Frenk C. S., Lacey C. G., Baugh C. M., Cole
S., 2002, MNRAS, 333, 177
Blumenthal G. R., Faber S. M., Flores R., Primack J. R.,
1986, ApJ, 301, 27
Bothun G. D., Thompson I. B., 1988, AJ, 96, 877
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
Boylan-Kolchin M., Bullock J. S., Kaplinghat M., 2011,
ArXiv e-prints
Ceverino D., Dekel A., Bournaud F., 2010, MNRAS, 404,
2151
Ceverino D., Klypin A., 2009, ApJ, 695, 292
Chabrier G., 2003, PASP, 115, 763
Cooper A. P. et al., 2010, MNRAS, 406, 744
Dalla Vecchia C., Schaye J., 2008, MNRAS, 387, 1431
Davis M., Efstathiou G., Frenk C. S., White S. D. M., 1985,
ApJ, 292, 371
Dehnen W., McLaughlin D. E., Sachania J., 2006, MNRAS,
369, 1688
Diemand J., Kuhlen M., Madau P., Zemp M., Moore B.,
Potter D., Stadel J., 2008, Nature, 454, 735
Dolag K., Borgani S., Murante G., Springel V., 2009, MN-
RAS, 399, 497
Elmegreen B. G., 1989, ApJ, 338, 178
Ferland G. J., Korista K. T., Verner D. A., Ferguson J. W.,
Kingdon J. B., Verner E. M., 1998, PASP, 110, 761
Fioc M., Rocca-Volmerange B., 1997, A&A, 326, 950
Font A. S. et al., 2011, ArXiv e-prints
Frenk C. S., Evrard A. E., White S. D. M., Summers F. J.,
1996, ApJ, 472, 460
Frenk C. S., White S. D. M., Bode P., Bond J. R., Bryan
G. L., Cen R., Couchman H. M. P., Evrard A. E., 1999,
ApJ, 525, 554
Fukui Y., Mizuno N., Yamaguchi R., Mizuno A., Onishi T.,
2001, PASJ, 53, L41
Gelato S., Sommer-Larsen J., 1999, MNRAS, 303, 321
Gilmore G., Wilkinson M. I., Wyse R. F. G., Kleyna J. T.,
Koch A., Evans N. W., Grebel E. K., 2007, ApJ, 663, 948
Gnedin O. Y., Hernquist L., Ostriker J. P., 1999, ApJ, 514,
109
Gnedin O. Y., Kravtsov A. V., Klypin A. A., Nagai D.,
2004, ApJ, 616, 16
Gnedin O. Y., Zhao H., 2002, MNRAS, 333, 299
Goerdt T., Moore B., Read J. I., Stadel J., Zemp M., 2006,
MNRAS, 368, 1073
Governato F. et al., 2010, Nature, 463, 203
Guo Q., Cole S., Eke V., Frenk C., 2011, ArXiv e-prints
Haardt F., Madau P., 2001, in Clusters of Galaxies and the
High Redshift Universe Observed in X-rays, D. M. Neu-
mann & J. T. V. Tran, ed.
Heyer M. H., Carpenter J. M., Snell R. L., 2001, ApJ, 551,
852
Hilditch R. W., Howarth I. D., Harries T. J., 2005, MN-
RAS, 357, 304
Hoeft M., Yepes G., Gottl¨ ober S., Springel V., 2006, MN-
RAS, 371, 401
Hogan C. J., Dalcanton J. J., 2000, Phys. Rev. D, 62,
063511
Katz N., Weinberg D. H., Hernquist L., 1996, ApJS, 105,
19
Kennicutt, Jr. R. C., 1998, ApJ, 498, 541
Klypin A., Kravtsov A. V., Valenzuela O., Prada F., 1999,
ApJ, 522, 82
Knebe A., Libeskind N. I., Knollmann S. R., Martinez-
Vaquero L. A., Yepes G., Gottl¨ ober S., Hoffman Y., 2010,
MNRAS, 1863
Koposov S., Belokurov V., Evans N. W., Hewett P. C.,
Irwin M. J., 2008, ApJ, 686, 279
Li Y., De Lucia G., Helmi A., 2010, MNRAS, 401, 2036
Li Y., White S. D. M., 2008, MNRAS, 384, 1459
Liu L., Gerke B. F., Wechsler R. H., Behroozi P. S., Busha
M. T., 2010, ArXiv e-prints
Lovell M. et al., 2011, ArXiv e-prints
Macci` o A. V., Kang X., Fontanot F., Somerville R. S., Ko-
posov S., Monaco P., 2010, MNRAS, 402, 1995
Machacek M. E., Bryan G. L., Abel T., 2001, ApJ, 548,
509
Marigo P., 2001, A&A, 370, 194
Martin C. L., 2005, ApJ, 621, 227
Martin N. F., Ibata R. A., Irwin M. J., Chapman S., Lewis
G. F., Ferguson A. M. N., Tanvir N., McConnachie A. W.,
2006, MNRAS, 371, 1983
Mashchenko S., Couchman H. M. P., Wadsley J., 2006,
Nature, 442, 539
Mashchenko S., Wadsley J., Couchman H. M. P., 2008,
Science, 319, 174
Mayer L., Governato F., Colpi M., Moore B., Quinn T.,
Wadsley J., Stadel J., Lake G., 2001, ApJ, 547, L123
McConnachie A. W. et al., 2008, ApJ, 688, 1009
Mihos J. C., Hernquist L., 1994, ApJ, 437, 611
Mo H. J., Mao S., 2004, MNRAS, 353, 829
Moore B., Ghigna S., Governato F., Lake G., Quinn T.,
Stadel J., Tozzi P., 1999, ApJ, 524, L19
Navarro J. F., Eke V. R., Frenk C. S., 1996a, MNRAS, 283,
L72
Navarro J. F., Frenk C. S., White S. D. M., 1996b, ApJ,
462, 563
—, 1997, ApJ, 490, 493
Navarro J. F. et al., 2010, MNRAS, 402, 21
Navarro J. F., White S. D. M., 1993, MNRAS, 265, 271
Okamoto T., Frenk C. S., 2009, MNRAS, 399, L174
Okamoto T., Frenk C. S., Jenkins A., Theuns T., 2010,
c ? 201? RAS, MNRAS 000, 1–16