Population of Dark Matter Subhaloes

Department of Astronomy - UniPDINAF - Observatory of Padova

Carlo GiocoliCarlo Giocoli prof. Giuseppe Tormenprof. Giuseppe Tormen

May 21 2008Blois

OUTLINEOUTLINE

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

INTRODUCTIONINTRODUCTION Dark Energy (DE): unknown form Dark Energy (DE): unknown form

of energy permeating all of space of energy permeating all of space and increasing the expansion rate and increasing the expansion rate of the universe.of the universe.

Dark Matter (DM): unknown Dark Matter (DM): unknown weakly interacting elementary weakly interacting elementary particle not emitting any radiation, particle not emitting any radiation, whose presence can be inferred whose presence can be inferred indirectly from gravitational indirectly from gravitational effects on visible matter.effects on visible matter.

Baryons: “commonBaryons: “common”” and visible and visible matter: hot and cold gas, stars … matter: hot and cold gas, stars …

INTRODUCTIONINTRODUCTIONDark Matter Dark Matter :ColdCold, i.e. its velocity is non-relativistic (v«c) at all epochs relevant for

structure formation.

Non-Baryonic Non-Baryonic && Collisionless. DM density fluctuations grow with the expansion of the universe,

become non-linear and form collapsed structures: dark matter haloes.

Springel et al. 2005

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 WIMPS – e.g. from supersymmetric extensions of the standard model (SUSY): neutralino.

ھ Axion – to solve the strong-CP problem.

Dimopulos 1990; Bertone et al. 2005;

Giocoli, Pieri & Tormen 2008; Pieri, Bertone & Branchini 2008

INTRODUCTIONINTRODUCTION

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.

INTRODUCTIONINTRODUCTION Understanding the clustering of DM is a

fundamental topic in modern cosmology.

Semi-analytical models of galaxy Semi-analytical models of galaxy formationformation 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 -ray-ray

emission from DM particles annihilation.

Colberg & Diaferio (GIF – project)

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

N-BODY SIMULATIONSN-BODY SIMULATIONSN-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

• Resimulated Galaxy Clusters (Dolag et al 2004 – DM run)

m h N L (Mpc/h) mp (Msun/h) (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

m h N (hr) L (Mpc/h) mp (Msun/h)

(kpc/h)

Resim (17)

0.3 0.7 0.7 0.9 643 - 2563

479 1.3x109 5

N-BODY SIMULATIONS - GIF2N-BODY SIMULATIONS - GIF2

MERGER HISTORY TREESMERGER 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 ;

main progenitormain progenitor;

satellitessatellites: progenitor haloes accreted by the main prog.

z0 = [ 0, 0.5, 1, 2, 4 ]

time

SATELLITE MASS FUNCTIONSATELLITE MASS FUNCTION(AKA unevolved subhalo mass function)

fitting function van den Bosch, Tormen, Giocoli (2005)

Giocoli, Tormen, van den Bosch (2008)

Giocoli, Tormen & van den Bosch 2008 - MNRAS

SATELLITE MASS FUNCTIONSATELLITE 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 FUNCTIONSATELLITE MASS FUNCTIONbefore 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 WHAT ABOUT THE evolvedevolved POPULATION? POPULATION?

Evolved: Evolved: tidal stripping, gravitational heating and dynamical effects reduce the mass of satellites after they enter the environment of the host halo.

SATELLITE EVOLUTIONSATELLITE EVOLUTION

PRESENT-DAY SUBHALOESPRESENT-DAY SUBHALOES

satellitesatelliteself-bound self-bound massmass

z=0

PRESENT-DAY SUBHALOESPRESENT-DAY SUBHALOES

Satellites orbiting within the host halo lose (part of) their mass due to: gravitational heating and tidal effects.

correlation

broken universality

Giocoli, Tormen & van den Bosch 2008 - MNRAS

MASS LOSS RATEMASS LOSS RATEvan den Bosch, Tormen & Giocoli (2005) propose a simple model for the satellite mass loss in a steady-state (dM/dt≈0) halo:

yesyesAssuming the host halo Assuming the host halo in a steady-state: ok!in a steady-state: ok!

Giocoli, Tormen & van den Bosch 2008 - MNRAS

Can we check this in numerical simulations?

MASS LOSS RATEMASS LOSS RATE

zτ)t(zt(z)

v

sbacc

em

(z)m

o The fractional mass loss The fractional mass loss rate is constant.rate is constant.

o The slope of the The slope of the un-un-evolvedevolved mass function is mass function is preserved. preserved.

o Small haloes are denser Small haloes are denser and form at higher and form at higher redshifts.redshifts.

Giocoli, Tormen & van den Bosch 2008 - MNRAS

characteristic time-scale for subhalo mass loss at z= 0

Why the universality is broken?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 attentionThanks so much for the attention