The Bound Mass of Substructures in Dark
Matter Halos
Shaw et al. (astro-ph/0603150)
Jochen Weller (UCL)
Jerry Ostriker (Princeton)
Paul Bode (Princeton)
OMM – 16/03/07
• The Hierarchy of
structure in the
universe:
•
•
•
•
•
‘cosmic web’
Superclusters
Clusters
Substructure
subsubstructures
Motivation for studying
substructure?
•
How to relate observed spatial clustering of
galaxies with the underlying dark matter
density field:
can matching structure/substructure to
galaxies in an empirical manner provide a
better basis for using galaxies to test
cosmology?
•
Non-parametric method adopts a statistical
method of linking observed clustering of
galaxies with subhalo populations of dark
matter halos in an empirical way
– Combine halo occupation distribution with
galaxy luminosity function (e.g. Vale &
Ostriker, 2005)
– Populate subhalos in simulations with
galaxies from surveys and compare
correlation statistics (e.g. Conroy et al. 2006)
(Vale & Ostriker, 2005)
Further motivation.
• 1) strong Gravitational lensing: Can the expected CDM
substructure explain the observed image ratios? (Mao et
al, 2004)
• 2) Effect of substructures on weak lensing shear (Hagan,
2005)
• Dark matter diagnostic: can the amount of small scale
structure found (as compared to modeling) constrain the
nature of dark matter?
Algorithm Depends on Purpose
•
Some methods are geometrical, others also aim at finding dynamically
coherent structures, ALL contain dimensionless parameters
•
Most basic level of identification is to use a geometrical routine
Friends of Friends (Lacey and Cole 1994)
Denmax (and variants) (Bertschinger & Gelb 1991)
•
Use only instantaneous particle positions to group nearby particles.
•
Sufficient for sampling the projected potential field within objects (e.g.
lensing studies)
•
No dynamical analysis to check whether particles are actually bound
1st Refinement: Dynamical Analysis
(the standard approach)
•
Now wish to separate the particles belonging to substructure from the
local underlying background matter distribution (unbinding)
•
For finding groups which live/have lived together: refine geometric
identification by hunting for cold structures in phase space:
SKID (Stadel 2001)
BDM (Klypin et al. 1999)
SUBFIND (Springel et al. 2001)
•
Assumes that subhalo is in complete isolation: only bound particles are
accounted for when calculating potential of subhalo
•
Not taken into account in energy calculation:
Unbound particles located spatially within subhalo
Disruptive effect of tidal forces from the particles surrounding the subhalo
Standard Approach: Ebind < 0; if and only if
A Second Refinement
(a new, coherent, definition of substructure)
•
If purpose is to identify objects that correspond to galaxies, must
find groups of particles that will stay together:
•
Must account for all the forces that influence the state of a
subhalo:
1. those due to the particles in the unit considered
2. those due to particles within the unit considered, but not
bound to that unit
3. those due to particles outside the unit considered (tidal
forces)
Adopted Algorithm to find Coherent Structures
2: Results
• TPM Simulation of Bode & Ostriker (2003)
Model
ΛCDM
z
0.05
Ωb
0.04
Ωc
0.26
ΩΛ
0.7
H0 [km/s/Mpc]
σ8
70
0.975
n
Ν
1.0
L [Mpc/h]
320
Mp [Msun/h]
2.54x109
ε [kpc/h]
3.2
10243
Mass distribution of subhalos
•
Previous studies measure α
= -1.1 to -0.7 (e.g. Gao et al.
(2004), De Lucia (2004))
•
Greater number of high
mass subhalos (Msub > 0.2
Mh) for coherent sample
•
High mass subhalos
typically reside near the core
of lower mass halos
α = −0.79
α = −0.91
Fraction of mass contained in subhalos
•
Early studies have suggested
that halos are self-similar in
terms of their subhalo
populations (Moore et al. 1999,
De Lucia et al. 2004, Reed, 2005)
•
Figure shows that higher mass
halos contain a higher fraction
of their mass in substructure:
Halos are NOT self-similar
•
Higher fs results in a lower
concentration, less spherical
morphology and higher spin
(Shaw et al. 2005)
Slopes:
0.44 ± 0.09 (coh)
0.40 ± 0.09 (sta)
Comparison: Standard vs Coherent Criterion
Does it produce less Sub-structure or More ?
• Using all particles interior to the structure to
compute gravitational forces and potential ->
MORE sub-structure.
• Removing particles that cannot survive tidal forces
for one dynamical time -> LESS substructure.
• -----------------------------------------------------• Result: a trade-off with amount of sub-structure
changed only moderately.
Radial distribution of subhalos
•
Simplest assumption is that the radial distribution of galaxies (or their
host subhalos) follows that of the background dark matter distribution
•
Subhalo distribution is
typically found to be less
concentrated than the
smooth background matter
distribution (see also Reed,
2005, Faltenbacher and
Diemand, 2006)
•
Nagai & Kravtsov, 2006,
found that selecting
subhalos by their mass at
the time of accretion results
in a radial distribution that
follows that of the dark
matter much more closely.
Nagai & Kravtsov (2006)
Radial distribution of subhalos
•
Within 0.6 Rvir, subhalo
distribution does not follow
that of the dark matter
•
Lack of substructure in inner
regions more pronounced for
the standard sample
•
In the inner regions of a
halo, binding effect of
‘background’ particles is
greater than the tidal forces
 Increases total substructure mass in inner regions of halos
Conclusions
•
•
Presented an improved definition of substructure which allows for all
forces exerted on a subhalo, internal and external
Applied both standard and coherent subhalo definitions to a sample
of 2000 cluster mass halos finding:
– Similar subhalo mass functions, small increase of the number of high
mass subhalos
– Slightly greater fraction of mass in substructure
– Subhalos have slightly greater mass in the inner regions of halos with
the coherent halo definition: better identification of bound mass than in
standard procedure
– Halos are NOT self-similar in terms of their subhalo populations
•
Overall, contribution of ‘background’ particles to the binding energy,
and disruptive effect of tidal forces tend to cancel