A dark matter core in M31 - Pierre Boldrini1 , Roya Mohayaee1, Joseph Silk1,2,3
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MNRAS 000, 1–5 (2020) Preprint 28 February 2020 Compiled using MNRAS LATEX style file v3.0
A dark matter core in M31
Pierre
1
Boldrini1? , Roya Mohayaee1 , Joseph Silk1,2,3
Sorbonne Université, CNRS, UMR 7095, Institut d’Astrophysique de Paris, 98 bis bd Arago, 75014 Paris, France
2 Department of Physics and Astronomy, The Johns Hopkins University, Baltimore MD 21218, USA
3 Beecroft Institute for Particle Astrophysics and Cosmology, Department of Physics, University of Oxford, Oxford OX1 3RH, UK
In original form 2020 February 4.
arXiv:2002.12192v1 [astro-ph.GA] 27 Feb 2020
ABSTRACT
We run state-of-the-art high resolution fully GPU N-body simulations to show that M31
harbours a dark matter core. Observational data in the inner halo of M31 provide stringent
constraints on the initial conditions of our simulations. We demonstrate that an infalling
satellite on a highly eccentric orbit is at the origin of the giant stellar stream and the shell-like
features of M31. The infalling satellite heats up the central parts of its host and triggers a
cusp-core transition in the dark matter halo of M31, generating a universal core independently
of the initial conditions. Our results imply that cores in massive galaxies are a common and
natural feature of cold dark matter haloes that have been initially cuspy but have accreted
subhaloes on highly eccentric orbits
Key words: halo dynamics , cusp, core, dark matter -methods: N-body simulations - galaxies:
M31 - galaxies: satellite - galaxies: halos
1 INTRODUCTION satellite through the centre of M31 would perturb the disk and warp
it as known for some time. Previously to our work, it was usually
Due to its proximity, the Andromeda galaxy (M31) provides a wealth
assumed that warps of discs of galaxies are due to tidal interactions.
of high precision observational data for understanding the history
We demonstrated that accretion of smaller galaxies can also be at
of M31 and the Local Group, and more generally, galaxy formation
the origin of warpy discs.
models in a cold dark matter-dominated universe. M31 exhibits
challenging features on different scales ranging from the double M31 is embedded in a dark matter halo. The density profile
nucleus at its centre on a scale of a few parsecs (Tremaine 1995; of halos of galaxies provides important constraints on the nature
Kormendy & Bender 1999) to the giant stellar stream (GSS) in its of dark matter (DM). In a cold dark matter-dominated Universe,
outskirts which extends to tens of kiloparsecs (Ibata, et al. 2001). the halos have profiles that diverge at the centre or known as cuspy
It is widely believed that the phased features of M31, namely its profiles (Navarro et al. 1997; Fukushige & Makino 1997; Moore
giant stream and its shell-like features, are results of the accretion et al. 1998; Navarro, et al. 2010). This is not the case for other
of a satellite galaxy (Ibata, et al. 2004; Font, et al. 2006; Fardal, candidates for dark matter such as warm dark matter, fuzzy dark
et al. 2006, 2007). The mass, radial velocity and distance to the matter or self-interacting dark matter, where the velocity dispersion
stream are observed with good accuracy. The accretion scenario is non-negligible and the dark matter haloes have constant density
has been simulated with high resolution and the high quality data profiles or "cores" at their centres. Core profiles have been supported
on the stream and the shell-like features have been used to strongly by observations of dwarf galaxies (Moore 1994; Flores & Primack
limit the initial parameter space. In a previous work, we ran high 1994) and are believed to present a challenge for Λ cold dark mat-
resolution simulations of a live M31 and an infalling satellite, and ter (ΛCDM). In previous work, mainly concentrating on the dwarf
showed that in the cosmological scenario, the infalling satellite spheroidal satellite in the Local Group, Fornax, we showed that
moved on a highly eccentric orbit after it reached its turn-around cores can arise in a cold-dark-matter-dominated Universe due to the
radius, and then fell towards the centre of M31 (Sadoun, et al. passages of globular clusters embedded in DM minihalos (Boldrini,
2014). The satellite was disrupted by M31 and formed the giant Mohayaee & Silk 2020). We showed how accretion of globular clus-
stream and its subsequent passages through the centre of M31, led ters could solve the cusp-core and the so-called "timing problem"
to the formation of the shell-like features that we observe today. for Fornax (Oh, Lin & Richer 2000; Read, et al. 2006; Cole, et al.
Our work showed that the infalling satellite was dark matter-rich 2012; Boldrini, Mohayaee & Silk 2019).
and in the same plane as most of the present-day satellites of M31. In this work, we show yet another consequence of the subhalo
We also demonstrated that the passage of such a dark matter-rich accretion in a ΛCDM Universe and show that the density profile of
M31 could have been strongly influenced by this mechanism. We
demonstrate that the passage of the satellite, which is at the origin
? Contact e-mail: boldrini@iap.fr of the giant stream, the shells and the warp of the disc of M31,
© 2020 The Authors
2 P. Boldrini, R. Mohayaee, J. Silk
should have also caused a cusp-to-core transition at the centre of al. 2004; Brown, et al. 2006; Richardson, et al. 2008; McConnachie,
the dark matter distribution in M31. A more general consequence et al. 2009). The GSS is a faint stellar tail located at the southeast
of our work is that accreting satellites on highly eccentric orbits can part of M31. It extends radially outwards of the central region of
induce a cusp-to-core transition in cold dark matter halos. These M31 for approximately 5◦ , corresponding to a projected radius of
cores are a common feature of many dark matter halos that have about 68 kpc on the sky. The stream luminosity is 3.4 × 107 L
been initially cuspy but have accreted subhalos in highly eccentric corresponding to a stellar mass of 2.4 × 108 M for a mass-to-light
orbits. ratio of 7 (Ibata, et al. 2001; Fardal, et al. 2006). In the follow-
Most cosmological simulations cannot probe these cusp-to- up observations of the GSS, two other structures corresponding to
core transitions in the DM halos of dwarf galaxies because of the stellar overdensities, which are now believed to be two shells, have
lack of resolution. We expect to see this effect also for DM halos been discovered (Ferguson, et al. 2002; Fardal, et al. 2007; Tanaka,
with masses higher than 1012 M , in simulations which have suffi- et al. 2010; Fardal, et al. 2012). The colourâĂŞmagnitude diagram
cient resolution to determine the shapes of DM density profiles. The of the north-eastern shelf is similar to that of the GSS (Ferguson, et
DM density profile of the Aquarius simulation revealed that density al. 2005; Richardson, et al. 2008). This similarity has been a strong
profiles become shallower inwards down to the innermost resolved argument in favour of models which predict that both the GSS and
radius (Navarro, et al. 2010). This slight deviation from the NFW the NE are the results of a single merger event between M31 and a
model could be evidence for our proposed cusp-to-core mechanism. satellite galaxy (Ibata, et al. 2004; Font, et al. 2006; Fardal, et al.
Indeed, most halos have suffered multiple subhalo mergers, espe- 2007).
cially at early epochs (z∼ 2-3) (Neistein & Dekel 2008). At these
redshifts, the number of subhalo accretions is high andthe energy A major merger scenario, dating back to a few Gyr, from which
transfer to the central DM region of the galaxy will be efficient in M31, its giant stream, and many of its dwarf galaxies emerged, has
generating cores. As the cusp can regenerate itself, the cuspy pro- been proposed (Hammer, et al. 2010, 2013). An empirical minor
files are more common in recent epochs, which could explain the merger scenario has also been studied extensively, in which a satel-
presence of transient cores (see Boldrini, Mohayaee & Silk (2020)) lite galaxy falls on to M31, from a distance of a few tens of kpc, on a
In this work, we perform state-of-the-art N-body simulations highly radial orbit (of pericentre of a few kpc) less than one billion
with GPUs, which allow parsec resolution, to study the effect of years ago. The satellite is tidally disrupted at the pericentre passage
the accretion of a satellite on the central density profile of the and forms the observed M31 stream and the two shell-like features
dark matter halo of M31. The initial conditions of our simulations (Fardal, et al. 2006, 2007). Although these empirical models pro-
are determined by observations of the mass, density profile, radial vide good fits to the observations, they suffer from simplifications.
velocities and distances of the giant stream which provide high First, M31 is not modelled as a live galaxy but is only represented
precision tests of our model. We consider infalling satellite scenarios by a static potential, and consequently the effects of dynamical fric-
from Sadoun, et al. (2014) and Fardal, et al. (2007). By analysing tion are not properly taken into account. Secondly, there is no dark
the density profile of the halo of M31, we clearly show that our matter in the progenitor satellite whereas a good fraction of satellite
initially cuspy profile is flattened as the dark matter particles are galaxies in the Local Group seems to be dark matter-rich. Finally,
heated during the satellite passage and migrate outwards from the the origin of the infalling satellite and its trajectory in the past has
central region of M31. As the cusp-to-core transition occurs for been overlooked. It is highly implausible that a satellite on a highly
both these scenarios, we conclude that the central core of M31 is radial orbit could have survived to arrive within easy reach of M31.
universal and independent of initial conditions. We have proposed an alternative cosmologically-plausible scenario
The paper is organized as follows. In Section 2 we present a for the origin of the giant stream and also the warped structure of
brief summary of observational data. Section 3 provides a descrip- the M31 disc itself (Sadoun, et al. 2014). In our model, a dark-
tion of the N-body modelling of M31 and its satellite, along with matter-rich satellite is accreted and falls from its first turnaround
details of our numerical simulations. In Section 4, we present our radius, via an eccentric orbit onto M31. The best agreement with
simulation results and discuss the implications for the cusp-core the observational data is obtained when the satellite lies on the same
problem. Section 5 presents our conclusions. plane that contains many of the present dwarfs of M31 (Conn, et
al. 2013; Ibata, et al. 2013). Unlike previous empirical models, the
disc of M31 is perturbed by the infall of the massive satellite in our
2 OBSERVATION: GIANT STELLAR STREAM AND model and becomes warped.
SHELL-LIKE FEATURES OF M31
A significant fraction of observed galaxies exhibit tidal features such In this paper, we use this cosmologically-motivated scenario
as tidal tails, streams and shells (Malin and Carter 1980; Malin & to set up our simulations. To show that our results are universal and
Carter 1983). These features are widely believed to be the products hold for a wide range of initial conditions, we also run simulations
of merger events (Hernquist & Quinn 1988, 1989). The observations for the model proposed by Fardal, et al. (2007) in which the satellite
of tidal structures that could arise during mergers of galaxies – as is dark matter poor and starts its infall from a much closer distance
shown by numerical simulations – have been used to put bounds on to the centre of M31.
various parameters, such as the orbital parameters and the masses
of the host galaxies and their satellites. However here we use a fully GPU-scaled code which allows
In this work, we consider M31 which is an example of a spiral us to increase the resolution by a factor of 100 and study the impact
galaxy that exhibits tidal features, such as streams and shells. The of the infalling satellite not just on the outer parts of M31 but also
Andromeda galaxy contains two rings of star formation off-centred on the dark matter distribution at its centre. The rich observational
from the nucleus (Block, et al. 2006, and references therein) and data on the giant stream and shells of M31 provide rather demanding
most notably a Giant Southern Stream (GSS) (Ibata, et al. 2001, tests of our model. In the following section we discuss the details
2005, 2007; Ferguson, et al. 2002; Bellazzini, et al. 2003; Zucker, et of our numerical simulations.
MNRAS 000, 1–5 (2020)
A dark matter core in M31 3
250
4 M GSS = 2. 34 × 10 8 M ¯ T = 2. 29 Gyr Field 1
300
Radial velocity [km. s −1 ]
Field 2
2 350
η [degrees]
400
0
Field a3
450
78 500 Field 6
2 6
47 550
23
4
1 Sadoun scenario 600 Field 8 Sadoun scenario
4 2 0 2 4 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
ζ [degrees] Direction along stream [degrees]
Figure 1. Giant south stream of M31: Simulated stellar density maps in Figure 2. Comparison with kinematic data of the observed GSS: Simulated
standard sky coordinates corresponding to particles of satellite stars at 2.29 radial velocity of satellite particles as a function of the distance along the
Gyr. We overplot particles (in red) from one of our shells. We represent stream. We represent the radial velocity measurements in five fields by
the observed stream fields by black boxes (McConnachie, et al. 2003). We red points with error-bars (Ibata, et al. 2004; Fardal, et al. 2006). A good
find MGSS = 2.32 × 108 M in excellent agreement with the value of agreement with observations for the radial velocity measurement is shown.
2.4 × 108 M derived from observations (Ibata, et al. 2001; Fardal, et al.
2006)
0. 0 Gyr
3 SIMULATION: HIGH RESOLUTION FULLY GPU No satellite (2. 29 Gyr)
Fardal scenario (0. 85 Gyr)
CODE Sadoun scenario (2. 29 Gyr)
ρ [M ¯ kpc −3 ]
The initial conditions for the M31 satellite are taken from Sadoun, 10 9
et al. (2014) and Fardal, et al. (2007) (see details in Table. 1). To
generate our live objects, we use the initial condition code magi
(Miki and Umemura 2017). Adopting a distribution-function-based
method, it ensures that the final realization of the galaxy is in dy-
namical equilibrium (Miki and Umemura 2017). We perform our
simulations with the high performance collisionless N-body code
gothic (Miki and Umemura 2017). This gravitational octree code
runs entirely on GPU and is accelerated by the use of hierarchi- 10 8
cal time steps in which a group of particles has the same time step 10 0
(Miki and Umemura 2017). We evolve the M31 galaxy-satellite sys- r [kpc]
tem over 3 Gyr in each scenario. We set the particle resolution of
all the live objects to 4.4 × 104 M and the gravitational softening
Figure 3. Cusp-to-core transition in M31: DM density profiles for the dif-
length to 10 pc. ferent scenarios. Initially, the M31 DM halo assumes a NFW profile (black
curve). We consider DM particles from both the M31 and satellite halos to
determine the DM density profile of M31. The fitting function described
by Equation 1 reproduces the simulated density structures and capturs the
4 RESULT: CUSP-CORE TRANSITION IN M31
rapid transition from the cusp to the core. We set Poissonian errors for fit-
4.1 Comparison with M31 observations ting weights. The DM distribution of M31 halo is divided in bins of groups
composed of Ng = 2046 particles. The density profile of the M31 at 2.29
First, we confirm our model by making a detailed comparison with (green curve) confirms that our halo is stable over the simulation time in
M31 observations in the Sadoun scenario (see Table. 1). Fig. 1 shows the absence of satellite. We observe a DM core of about 220 (90) pc for the
the stellar density maps in standard sky coordinates corresponding M31 halo in Sadoun (Fardal) scenario. As the Sadoun satellite is 20 times
to particles of satellite stars at 2.29 Gyr. We colour particles in red more massive than the Fardal satellite, the core size is larger in the former
in order to highlight one of the two shells. We also represent the scenario. Hovewer, in both scenarios, the cusp-to-core transition takes place,
which highlight the universality of core formation in CDM universe.
observed stream fields as solid rectangles with proper scaling. We
note that the simulated stream is in good agreement with the ob-
servations regarding the morphology and spatial extent of the GSS.
4.2 Cusp-Core transition in M31
We find MGSS = 2.32 × 108 M in excellent agreement with the
value of 2.4×108 M derived from observations (Ibata, et al. 2001; Our GPU simulations allow us to study the impact of the accretion
Fardal, et al. 2006). Furthermore, we test the Sadoun model against of a DM-rich satellite on the evolution of the density profile of M31.
kinematic data. Fig. 2 shows radial velocities of satellite particles We have centered our system on the stellar component of M31 for
as a function of the distance along the stream. We obtain a good all our results by using the shrinking sphere method of Power, et al.
agreement with observations for the radial velocity measurement in (2003). We observe the formation of a core in the cold dark matter
the five fields (Ibata, et al. 2004; Fardal, et al. 2006). halo of M31. The satellite perturbs the DM inner structure of the
MNRAS 000, 1–5 (2020)4 P. Boldrini, R. Mohayaee, J. Silk
Scenario Component Profile a r200 Mass (x0 ,y0 ,z0 ) (vx0 ,vy0 ,vz0 )
[kpc] [kpc] [1010 M ] [pc] [kpc] [km.s −1 ]
M31 halo NFW 7.63 195 88 10 0 0
M31 bulge Hernquist 0.61 - 3.24 10 0 0
Sadoun et al. 2014 Satellite halo Hernquist 12.5 20 4.18 10 (-84.41,152.47,-97.08) 0
Satellite stars Plummer 1.03 - 0.22 10 (-84.41,152.47,-97.08) 0
Fardal et al. 2007 Satellite stars Plummer 1.03 - 0.22 10 (-34.75,19.37,-13.99) (67.34,-26.12,13.5)
Table 1. Simulation parameters: From left to right, the columns give for each component: the density profile; the scale length; the virial radius; the mass; the
softening length; the initial positions in a reference frame centered on M31 with the x-axis pointing east, the y-axis pointing north and the z-axis corresponding
to the line-of-sight direction; the velocities in this reference frame. We consider both infalling satellite scenarios (Sadoun, et al. 2014; Fardal, et al. 2007). We
set the particle resolution of all the live objects to 4.4 × 104 M .
720
250 T = 0. 0 Gyr T = 2. 29 Gyr in the central region, the DM density profile changes until core
640 formation occurs. This figure demonstrates that core formation is a
150 560 consequence of dynamical heating of DM halo by infalling satellite.
kVk [km s −1 ]
480
50 To test the impact of softening length on the density profile of
y [kpc]
400 the DM component, we ran simulations in the Sadoun scenario with
50 320 two different softening lengths = 5 and 10 pc in order to ensure that
240
150 our simulations do not suffer from numerical noise. Figure 5 reveals
160
that softening length (or particle size) does not affect the density
250 Sadoun scenario 80
profile of the DM component. In addition, the density profile at 2.29
250 150 50 50 150 250 250 150 50 50 150 250 Gyr (green curve) in Figure 3 shows that our halo is stable over the
x [kpc] x [kpc] simulation time in the absence of satellite. Thus, numerical artifacts
Figure 4. Cusp-to-core transition due to heating by the satellite: Maps of
are not responsible for core formation.
the DM mass-weighted velocity distribution projected face-on through a
500 pc slice at 0 and 2.29 Gyr for the Sadoun scenario. As the DM velocity
increases in the central region, the DM density profile changes until core
5 CONCLUSION
formation occurs (see Fig 3). Core formation is a consequence of dynamical
heating of DM halo by infalling satellite. The giant stellar stream and the shell-like features of M31 are likely
outcomes of accretion of satellites on highly eccentric orbits in both
of the infalling satellite scenarios proposed in Sadoun, et al. (2014)
M31 halo during the merger by forming the tidal structures such
and Fardal, et al. (2007), as shown by high resolution numerical
as the GSS and shells. Initially, the M31 DM halo assumes a NFW
simulations in the past and reaffirmed here. In this work, we have
profile. We consider DM particles from both M31 and satellite halos
further increased the resolution of simulations by using a fully
to determine the DM density profile of M31 over the time. In order
GPU state-of-the-art code and have focused on the impact of such
to determine if there is core formation in the M31 halo, we did a fit
an accretion event on the dark matter density profile of M31 in
for the DM profile. As shown in Fig. 3, we find that our profile is
its central regions. We have shown that the initial NFW profile
well fitted by the following five-parameter formula:
of M31 is perturbed by the accretion of the satellite. The satellite
energy is transferred to the dark matter particles; they are heated
ρ(r) = ρcW(r) + [1 − W(r)]ρNFW (r), (1) and consequently migrate out of the central regions of M31. The
density profile is hence flatten out resulting in a constant density
where ρc is the core constant density and W(r) is defined as
r − r and a cusp-core transition in M31. We find that the infalling satellite
2W(r) = 1 − erf ,
c generates a universal core independently of the initial conditions.
(2)
2δ Our work highlights a general mechanism for core formation in a
where rc is the core radius and δ is a parameter to control the sharp- ΛCDM Universe during accretion of subhalos on highly eccentric
ness of the transition from the cusp to the core and the converse. It orbits. Satellites with larger ratios between the satellite and the
reproduces the simulated density structures and captures the rapid host halo masses move along slightly more eccentric orbits with
transition from the cusp to the core (see Fig. 3). We set Poisso- lower angular momentum Moreover, satellites around more massive
nian errors for fitting weights. The DM distribution of M31 halo is haloes seem to be on more radial orbits at fixed mass ratio (Tormen
divided in bins of groups composed of Ng = 2046 particles. The 1997; Wetzel 2011; Jiang, et al. 2015). Hence, we expect that a
satellite has induced a cusp-to-core transition by heating the central noticeable fraction of galaxies in ΛCDM Universe to harbour cores
region of the DM halo of M31. As the satellite has a radial orbit, that have been formed during the merger and accretion events. In
its crossings near the centre perturb the M31 halo by heating its this work, we have ignored the presence of a central black hole and
DM particles via dynamical friction. By gaining energy, the DM have assumed an initially NFW profile for M31. The initially cuspy
particles migrate out of the central regions of M31. It results in profile must have been cuspier, due to the redistribution of dark
a DM core of about 220 (90) pc for the M31 halo in the Sadoun matter around black holes (Bahcall & Wolf 1976; Gondolo & Silk
(Fardal) scenario. As the value of the core size depends on the fitted 1999). We however expect that the cusp-core transition mechanism
DM profile, we do not use this precised radius as a constraint on will not be influenced by a central black hole. A study of the fate of
the M31 core. In addition, Figure 4 shows the DM mass-weighted the black hole and the spiky central profile that develops transiently
velocity distribution projected face-on through a 500 pc slice at 0 during the accretion of the satellite in M31 will be presented in the
and 2.29 Gyr in the Sadoun scenario. As the DM velocity increases forthcoming work.
MNRAS 000, 1–5 (2020)A dark matter core in M31 5
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