MODELING MODELING INTRACLUSTER MEDIUM INTRACLUSTER MEDIUM

AND DARK MATTER IN AND DARK MATTER IN GALAXY CLUSTERSGALAXY CLUSTERS

Elena Rasia Dipartimento di Astronomia

Università di Padova

Padova, April 9th, 2002

Goals

• Provide new models, in a simple analytic form, that describe the average radial profiles of the main quantities of the baryonic and non baryonic components

• They can be used to derive and test mass estimates• The density profile gives useful indications on the

lensing properties of clusters and on the characteristics of their emission in the X and millimetric (Sunyaev-Zel’dovich effect) bands

Simulations• Risimulation:

– Initial conditions: ZIC (Zoom Initial Condition) (Tormen et al. 1997)– Evolution:GADGET (GAlaxies with Dark matter and Gas intEracT) TREESPH

(Springel et al. 2001)– Very high mass resolution: NDM = NGAS 106 , mDM25 109, mGAS25 108

M/h– Very high dynamical range 105: Lbox 480 Mpc/h; gravitational softening

5kpc/h• Cosmological model: CDM; DM =0.27; B =0.03; =0.7; h=0.7• Sample:17 Galaxy Clusters(z=0) Mvir 3.6 10141.5 1015 M /h; Rvir

1.52.5 Mpc/h; NVIR 5 105

the largest sample of simulated galaxy clusters at this resolution

DARK MATTER:Density profile

• We fit the phase-space density profiles by a power law (Taylor & Navarro 2001) and, using the model of the velocity dispersion profile, we found a new model that describes the (usual) average density profile more properly than NFW for r < 0.7 rvir

• The fluctuactions for r < 0.014 rvir are due to numerical effects

NFW fitr 0 (r) r -1 r>>rs (r) r -3 Our fit:

r 0 (r) r-1

r>>rs(r) r-2.5

N=2 107 N=6 105

DARK MATTER:Velocity profiles

•Velocity anisotropy: (r)=1–t

2(r)/2r2(r)

•In the inner part the velocity field is nearly isotropic ( 0 ), while radial motions predominate ( >0 ) at large radii•On average, infall motions are present (v(rvir)<0 ) •Models are dynamically self-consistent

DARK MATTER:Mass estimates

• Jeans equation:

• Integral of NFW model:

• Integral of our model:)1/()1ln(

)1/()1ln()(ccccxcxcxx

MxM

vir

NFW

ppp

ppp

vir xxx

xxxxx

MxM

2)1(/)21(

2)(/)2()(~

For r>0.02 rvir Jeans equation properly estimates the total mass (error < 10%)

GAS:Density profile

• The gas and dark matter density profiles are self-similar for r>0.1 rvir

• In the center the gas distribution is less concentrated (due to pressure forces that counterbalance the gravitational forces)

• The NFW model is not appropriate to describe the gas density profile

• Thanks to the resolution and to the large sample we can give a new model for the gas density.

• Asymptotic behaviour:– r 0 (r) cost.– r >> rp (r) r -2.5

GAS:Temperature and entropy profiles

• On average the gas temperature is nearly constant in the cluster center (r<0.2rvir)

• At the virial radius the gas has a temperature that is almost half of the central value

• The entropy profile is always increasing up to the external regions

GAS:Velocity profiles

• The radial velocity profile is always negative demonstrating that gas is infalling now. Probably this is due to the presence of merging events in some cluster of the sample

• Slight predominance of tangential motions around r=0.1rvir

• The IntraCluster Medium is not really in hydrostatic equilibrium within the cluster, in fact some residual, non negligible velocities are present

this influences the traditional mass estimates.

GAS:Mass estimates

• Isothermal sphere model:

• Hydrostatic equilibrium equation:

• Hydro(dynamic?) equilibrium equation

21 TxMM

vir

E

xdTd

xddxT

MxM

vir

E

lnln

lnln)(3

2ln

lnlnln

lnln

lnln)( 2

22

xdd

xdd

xdTd

xddTx

MxM r

rvir

E

Dependence on dynamical state

• Using several tests (virial model/ residuals/ statistica dello center-of-mass shift / evolution of the dynamic state), we selected a subsample of clusters that appear more relaxed

• In coincidence with merging events:– The total mass grows by

20100% r grows on account of the cinetic

energy of the infalling substructure

– T increases because of shocks• From the analysis of all radial

profiles we found that the proposed models still agree with the simulations, except the radial velocity, that is closer to zero for relaxed clusters. Velocity dispersions have the same asymptotic behaviour, but now are systematically lower

M T r

Conclusions• We proposed a model that describes the

distribution of dark matter more accurately than the NFW model for r/rvir < 0.7.

• We found new models for other dark mater radial profiles and used them to construct a self-consistent dynamical model, useful also for mass estimates.

• We proposed an analytic model for the gas distribution: density, temperature and velocity dispersions.

• These models describe the average properties of galaxy clusters, and have immediate applications for X-Ray, SZ and lensing observations.

Future goals

• Study with more details the system dynamical state and the consequencies on the dark matter and gas distribution in order to give other models ad hoc for the relaxed clusters and to have a better mass estimate for these objects

• Extend the study to high redshift to probe and to quantify if models have some temporal dependences

• Analyse other simulations with pre-heating gas