Transcript Simulazioni di ammassi di galassie: modelli per la

MODELING
INTRACLUSTER MEDIUM
AND DARK MATTER IN
GALAXY 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 , mDM25 109,
mGAS25 108 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 10141.5 1015
M /h; Rvir  1.52.5 Mpc/h; NVIR 5 105
 the largest sample of simulated galaxy clusters at
this resolution
NFW fit
r  0  (r)  r -1
r>>rs  (r)  r -3
N=2 107
N=6 105
DARK MATTER:
Density profile
Our fit:
r  0  (r)  r-1
r>>rs(r)    r-2.5
• 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
DARK MATTER:
Velocity profiles
•Velocity anisotropy:
(r)=1–t2(r)/2r2(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 selfconsistent
DARK MATTER:
Mass estimates
• Jeans equation:
• Integral of NFW
model:
M NFW ( x )

M vir
x
ln( 1  cx )  cx /(1  cx )
ln( 1  c )  c /(1  c )
• Integral of our model:
~
 (x  2xp ) /
M ( x)

M vir

 (1  2 x p ) /
(x  xp )  2
(1  x p )  2
For r>0.02 rvir Jeans equation properly estimates the total mass
(error < 10%)
xp 

xp 

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:
M 1E
  xT  2
M vir
• Hydrostatic
equilibrium equation:
M 3E ( x)
d ln T 
 d ln 
  xT 

M vir
d ln x 
 d ln x

• Hydro(dynamic?)
equilibrium equation

  d ln  d ln T  2  d ln  d ln  r2
M 2E ( x)
  x T 





2


 r  d ln x d ln x
M vir
  d ln x d ln x 


Dependence on
dynamical state
M
T
r
• Using several tests (virial model/
residuals/ statistica dello center-ofmass 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
20100%
– 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
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 selfconsistent 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