Local Group candidates in cosmological
simulations
Luis A. Martı́nez1, Gustavo Yepes1 , Mira Sivan2 , Yaniv Dover2 , and Yehuda
Hoffman2
1
2
Dpto. Fı́sica Teórica, Universidad Autónoma de Madrid,
Racah Institute of Physics, Hebrew University, Jerusalem
Summary. We present results from an ongoing collaboration to make realistic cosmological simulations of our Local Universe by means of constrained initial conditions. In this contribution we will focus on the analyses of the kinematic and
dynamical properties of objects similar to the real Local Group (LG) that have
been identified in large N-body simulations.
1 N-body Simulations
We have performed several collisionless numerical simulations in different cosmological models, (i.e ΛCDM, OCDM and SCDM), of a computational box
of 64h−1 Mpc on a side. We used the publicly available Tree-PM parallel Nbody code GADGET [1] to run all of them. High resolution initial conditions
(20483 particles within the 64 Mpc/h box) have been set up for the three
cosmological models. We then resampled them in order to have a reasonable
mass resolution (2563 ). With this technique, we can zoom in at any particular
place in the simulation down to the maximum number of particles initially
generated. We generated both constrained and unconstrained (i.e random)
realizations of the initial power spectra for each model3 . Several observational
data to put constrains on the initial conditions have been used. The first data
set is made of radial velocities of galaxies drawn from the MARK III [2], SBF
[3] and the Karachentsev [4] catalogs. Peculiar velocities are less affected by
non-linear effects and are used as constraints as if they are linear quantities
[5]. The other constrains are obtained from the catalog of nearby X-ray selected clusters of galaxies [6]. Given the virial parameters of a cluster and
assuming the spherical top-hat model one can derive the linear overdensity of
the cluster. The estimated linear overdensity is imposed on the mass scale of
3
Note we call ΛCDM, OCDM and SCDM to the constrain simulations (depending
on the cosmological model used) and ΛCDMu and OCDMu to the unconstrain
ones.
2
Martı́nez et al.
the cluster as a constraint. Different CSs with different random realizations
have been calculated and they all exhibit a clear and unambiguous LSC-like
structure that dominates the entire simulation, much in the same way as in
the actual universe in which the LSC dominates the nearby LSS. The simulations do vary with respect to the particular details of the LG-like object that
is formed roughly in its actual position. The simulations used here are based
on the same constrained realization of the initial conditions.
2 Selection of objects
The halos were found using two methods: The BDM algorithm [7] and the
AmigaHaloFinder [8] based on finding local density maxima from an adaptive
mesh hierachy. In both cases, we found almost the same objects.
To identify candidates for the Local Group, we selected those objects that
fulfill the strict conditions as given in [9], shown in Table 1. In summary, we
searched two halos similar to Milky Way and Andromeda, without neighbours
with masses as high as any of the LG components and with a Virgo-like halo
separate an appropiate distance.
Table 1. Constrains to find LG candidates following the [9] criterion. The circular
velocity has been used in the mass contrains.
Components
Kind
MW + M31
Mass
125 ≤ Vc ≤ 270 km/s
Separation
s ≤ 1 Mpc/h
Relative velocity
Vr < 0
No neighbours
Distance to LG
Mass
Virgo halos
Distance to LG 5 ≤ dV irgo ≤ 12 Mpc/h
Mass
500 ≤ Vc ≤ 1500 km/s
dneigh < 3 Mpc/h
Vc ≥ Vc,comp
We also used another searching criterion that was slightly less restrictive
than the above constrains, but looking for the candidates only in the center
region of the box. The reason of this criterion is because of the goal of the
constrained simulation is building the local universe around our Local Group,
so there should be a good candidate close to the center.
3 The Local Hubble Flow
Our local neighborhood is the most suited region to study the temperature of
the clustered galaxy distribution. The local dispersion of the peculiar velocities
Local Group candidates in cosmological simulations
3
Fig. 1. Local Hubble flow vs. local overdensity of each LG candidate for constrained
(left) and unconstrained (right) simulations.
Fig. 2. Percentage of cold LG candidates found in constrained (left) and unconstrained (right) simulations.
around a uniform Hubble flow is observed to be cold, compared with theoretical expectations (from cosmological simulations mainly). This dispersion is
defined as:
r
1 X
σH =
[(vi − Hloc Di )− < v − Hloc D >]2
(1)
n−1
The nearby galaxy distribution, on the other hand, follows the general
pattern of the cosmic web in accordance with the simulations and observations.
This coldness of the local Hubble flow was first pointed out by Sandage et al.
[10]. This was immediately recognized either as an anomaly or as a problem.
Maccio et al. [9] have recently compiled all the existing data on the coldness
of the local flow and have fitted the observed scatter around the Hubble flow
(out to about 7 h−1 Mpc) by:
4
Martı́nez et al.
σH = 88 ± 20 km/s ×
R
4.9
h−1 M pc
(2)
Taking Eq. 2 as a guide flows with σH (5 h−1 M pc) ≤ 80 km/s are labeled here
as cold.
Using N-body simulations of dark energy dominated cosmologies, Maccio
et al [9] found several cold LG candidates. However this kind of LGs were not
found in previous simulations [11] of dark matter dominated cosmologies (i.e
OCDM and SCDM models). This fact led them [9] to propose that the cold
Hubble flow is a manifestation of the dark energy.
In order to check this surprising result, we have measured the Hubble flow
for every LG candidate in our simulations. In Figure 1, we plot the velocity
dispersion as function of overdensity for each simulation. One can realize that
we only obtain cold candidates low density regions. Therefore, we find the
problem of the coldness of the Hubble flow in our simulations, too. A possible
explanation for this problem would rely on the fact that the Zone of Avoidance
(ZOA) (i.e. the region of the sky where the galactic plane is located) goes in
the direction of the Great Attractor. Those galaxies that are hidden in the
ZOA could have a substantial contribution to the velocity dispersion around
Hubble flow. If they could have been taken into account, the Hubble Flow
would be hotter and in better agreement with simulation predictions. Another
reason could be a bias between the galaxies and the dark matter halos used
in simulations.
In Figure 2, one can observe that the number of cold Local Group candidates is not correlated at all with the amount of dark energy. In fact, we
find similar, or even more, number of cold objects in low density cosmological
models (OCDM) than in dark energy dominated models (ΛCDM). So dark
energy seems not to be responsible of the coldness of the local Hubble flow,
contrary to the results of previous studies.
4 Dynamics in the Local Volume
Whiting [12] carried out an analysis of the distribution and peculiar velocities
of 149 galaxies in the Local Volume (LV), defined as the sphere of radius 7
h−1 Mpc centered on the Local Group. Using the high-quality data of these
galaxies, he [12] has mapped the mass distribution within the LV, assuming
it is traced by the galaxies, and calculated the gravitational field within the
LV. The gravitational field has been calculated by summing over the pairwise
Newtonian interaction for each galaxy and by weighting the galaxies by their
luminosity in the K and B bands. No clear correlation has been found between the gravitational and the velocity fields and this has led [12] to claim
that either dark matter is not distributed in the same way as luminous matter in this region, or peculiar velocities are not due to fluctuations in mass.
Local Group candidates in cosmological simulations
5
Fig. 3. Local vs. global acceleration, local acceleration vs. velocity, and global acceleration vs. velocity, respectively, for a Local Volume of the constrained ΛCDM
simulation.
The implication that follows is that, at the least in the LV, structure has not
formed by means of the gravitational inestability.
Again, this represent a strong statement that can be tested in full detail
using our numerical simulations. For each of our LG candidates, we found
all the halos within a distance of 10 Mpc around them. For them, we have
computed the gravitational field in two ways:
•
The local gravitational field: was derived by computing all the pairwise
newtonian forces due to the rest of halos in this volume, with a smoothing
factor A of 1.2 Mpc:
0
gl,i
= −G
X
j6=i
•
Mj
rj − ri
·r̂i
[(rj − ri )2 + A2 ]3/2
(3)
and the outer of the LV was considered as a homogeneous medium.
The global Gravitational field: was computed by averaging the gravitational accelerations of all of the dark matter particles belonging to each
halo. The particle accelerations are stored as an output from the N-body
integration and are derived from the gravitational field due to all matter
in the simulation.
All accelerations will be scaled by their linear theory prediction, i.e. considering the velocity proportional to the acceleration [13], [14], getting:
2f
g0
3H0 ΩM
1
1
0.6
f ≈ ΩM
+ ΩΛ 1 + ΩM
70
2
g=
(4)
(5)
The aim of this scaling is to make an easier comparsion between accelerations
and velocities.
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Martı́nez et al.
We have checked that there is almost no correlation between local and
global accelerations for all the LVs in all our simulations. Moreover, the correlation between peculiar velocities and accelerations (both local and global)
is very low. In Figure 3, a representative example of this fact is shown.
The main conclusions that can be derived from the results presented above
are the following:
•
•
Accelerations measured using Whiting’s method [12] do not agree with the
real ones obtained from simulations. This is because the main hypotheses
of Whiting are not compatible with what we see in the simulated universes, i.e. considering a limited Local Volume neglicting the rest of the
Universe, and, above all, taking into account only the matter contained
in the galaxies (halos in our case). The contribution of the difffuse matter
distributed in filamentary structure linking the halos, as is shown in CDM
models, have an important contribution to the total dynamical state of
the halos. So, if the Universe is in fact described by a CDM dominated
cosmology, then we should expect to have a strong bias between the light
(galaxies) and dark matter.
Peculiar velocity and accelerations are not correlated. Actually, the reason
of this is because the formation and evolution of the Local Volume is a
strongly non-linear process that erase all the correlations from the early
epochs.
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