Population of Dark Matter Subhaloes Department of Astronomy - UniPD INAF - Observatory of Padova Carlo Giocoli prof. Giuseppe Tormen May Blois

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 Dark Matter : Cold Cold, 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 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

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 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.  -ray Halo and Subhalo Mass Functions are also important to constrain the  -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 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 Resimulated Galaxy Clusters (Dolag et al 2004 – DM run) mm  h  NL (Mpc/h)m p (M sun /h)  (kpc/h) GIF x GIF x mm  h  N (hr)L (Mpc/h)m p (M sun /h)  (kpc/h) Resim (17) x

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 > z 0 ; main progenitor main progenitor; satellites satellites: progenitor haloes accreted by the main prog. z 0 = [ 0, 0.5, 1, 2, 4 ] time

SATELLITE 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 MNRAS

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 z f ( z f = 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 z f (Sheth & Tormen 2004b). More mass is accreted in satellites before the formation redshift (57%).

WHAT ABOUT THE evolved 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 EVOLUTION

PRESENT-DAY SUBHALOES satellite self-bound mass z=0

PRESENT-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 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! Giocoli, Tormen & van den Bosch MNRAS Can we check this in numerical simulations?

MASS LOSS RATE o To To To The fractional mass loss rate is constant. o To To To The slope of the un-evolved mass function is preserved. o So So So Small haloes are denser and form at higher redshifts. Giocoli, Tormen & van den Bosch MNRAS characteristic time-scale for subhalo mass loss at z= 0

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