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Population of Dark
Matter Subhaloes
Department of Astronomy - UniPD
INAF - Observatory of Padova
Carlo Giocoli
prof. Giuseppe Tormen
Blois
May 21 2008
OUTLINE





Introduction: galaxy formation and dark matter
clustering in a CDM-universe
N-body simulations
Satellite mass function
Subhalo definition and mass-loss rate
Present-day subhalo mass function
INTRODUCTION

Dark Energy (DE): unknown form of
energy permeating all of space and
increasing the expansion rate of the
universe.

Dark Matter (DM): unknown weakly
interacting elementary particle not emitting
any radiation, whose presence can be
inferred indirectly from gravitational effects
on visible matter.

Baryons: “common” and visible matter: hot
and cold gas, stars …
INTRODUCTION
Dark Matter :
Cold, i.e. its velocity is non-relativistic (v«c) at all epochs relevant for structure
formation.
Non-Baryonic & Collisionless.
DM density fluctuations grow with the expansion of the universe, become non-linear
and form collapsed structures: dark matter haloes.
In the last twenty or so years, physicists
have proposed different candidates for
DM. Among these, two classes of particles
are sufficiently promising to motivate
major experimental search:
‫ﮪ‬
‫ﮪ‬
WIMPS – e.g. from supersymmetric
extensions of the standard model (SUSY):
neutralino.
Axion – to solve the strong-CP problem.
Dimopulos 1990; Bertone et al. 2005;
Giocoli, Pieri & Tormen 2008; Pieri, Bertone & Branchini 2008
Springel et al. 2005
INTRODUCTION
Galaxies reside inside dark matter haloes, where baryons can shock, cool and eventually form
stars (White & Rees 1978).
The structure formation process is hierarchical: smaller haloes collapse first, and later merge to
form larger systems.
The cores of progenitor haloes may survive this process, and constitute the so-called
substructure population of a halo.
INTRODUCTION
Understanding the clustering of DM is a
fundamental topic in modern cosmology.
Semi-analytical models of galaxy formation
provide links between observations
(galaxy colour, clustering, etc) and DM
haloes and subhaloes.
Semi analytical models start from Monte
Carlo merger trees or, more realistically,
from N-body numerical simulations.
Halo and Subhalo Mass Functions are also
important to constrain the g-ray emission
from DM particles annihilation.
Kauffman & White 1993; Kauffmann et al. 1999; Springel et al. 2001;
Diaferio et al. 2001; De Lucia et al. 2004, Gao et al. 2004, van den Bosch,
Tormen, Giocoli 2005, Giocoli, Pieri & Tormen 2008
Colberg & Diaferio (GIF – project)
N-BODY SIMULATIONS
N-body simulations model the expanding universe as a system
of DM particles in a large box, and evolve it in time under the
action of its own gravity. They are used to study structure
formation and clustering in the non-linear regime.
• GIF
(Kauffman et al 1999)
& GIF2
(Gao et al 2004)
Cosmological Simulations
Wm
W
h
s8
N
L (Mpc/h)
mp (Msun/h)
e (kpc/h)
GIF
0.3
0.7
0.7
0.9
2563
141.1
1.4x1010
20
GIF2
0.3
0.7
0.7
0.9
4003
110
1.73x109
6.6
• Resimulated Galaxy Clusters
Resim (17)
(Dolag et al 2004 – DM run)
Wm
W
h
s8
N (hr)
L (Mpc/h)
mp (Msun/h)
e (kpc/h)
0.3
0.7
0.7
0.9
643 - 2563
479
1.3x109
5
N-BODY SIMULATIONS - GIF2
MERGER HISTORY TREES

Halo Finder:

Follow each halo along its merging-history tree, and store all information
about satellites accreted by the main halo progenitor at any z > z0 ;
time
main progenitor;
z0 = [ 0, 0.5, 1, 2, 4 ]
satellites: progenitor haloes
accreted by the main prog.
Giocoli, Tormen & van den Bosch 2008 - MNRAS
SATELLITE MASS FUNCTION
(AKA unevolved subhalo mass function)
fitting function
van den Bosch, Tormen, Giocoli (2005)
Giocoli, Tormen, van den Bosch (2008)
SATELLITE MASS FUNCTION
The mass function of
satellites accreted at all
redshift is universal:

Independent on final
(observation) redshift

Independent on final host
halo mass.
SATELLITE MASS FUNCTION
before and after the formation redshift zf
(zf = earliest redshift when the main halo progenitor assemble half of its final mass)
•Distribution slopes are identical, while normalisations can be obtained from the
main halo progenitor mass distribution at zf (Sheth & Tormen 2004b).
•More mass is accreted in satellites before the formation redshift (57%).
WHAT ABOUT THE
evolved POPULATION?

Evolved: tidal stripping, gravitational heating and
dynamical effects reduce the mass of satellites
after they enter the environment of the host halo.
SATELLITE EVOLUTION
PRESENT-DAY SUBHALOES
z=0
satellite self-bound mass
Giocoli, Tormen & van den Bosch 2008 - MNRAS
PRESENT-DAY SUBHALOES
broken universality
Satellites orbiting within the host
halo lose (part of) their mass due to:
gravitational heating and
tidal effects.
correlation
Giocoli, Tormen & van den Bosch 2008 - MNRAS
MASS LOSS RATE
van den Bosch, Tormen & Giocoli (2005) propose a simple model for the satellite mass
loss in a steady-state (dM/dt≈0) halo:
yes
Assuming the host halo in
a steady-state: ok!
Can we check this in numerical simulations?
Giocoli, Tormen & van den Bosch 2008 - MNRAS
MASS LOSS RATE
characteristic time-scale for
subhalo mass loss at z= 0

msb (z)
e
mv
t(z) t(zacc )
τ z 
o The fractional mass loss
rate is constant.
o The slope of the un-evolved
mass function is preserved.
o Small haloes are denser
and form at higher redshifts.
Why the universality is broken?
• Compared to massive haloes,
smaller haloes form at higher
redshifts.
• Smaller haloes thus accrete
satellites at earlier times.
• These satellites suffer mass
loss for longer times.
• The time scale for mass loss
rate is shorter at higher redshift.
• Due to both effects, small
haloes possess fewer
subhaloes today.
Thanks so much for the attention