X-RAY CLUSTERS IN CONFORMAL GRAVITY

Antonaldo Diaferio

Universita' degli Studi di TorinoDipartimento di Fisica Generale

“Amedeo Avogadro”

Edinburgh, April 21st, 2006

Introduction on conformal factor: photon and massive particle geodesics

Gravitational potential energy of extended objects

Virial theorem and average temperature in X-ray clusters

Hydro-static equilibrium and temperature profile

SPH simulations of self-gravitating gas

OUTLINE

X-RAY CLUSTERS: OBSERVED

CL0016+16 ROSAT PSPC

X-ray spectrum Temperature

ICM mass

radiusT

em

pe

ratu

re

15 clusters observed with XMM-Newton

(De Grandi et al . 2004)

X-RAY CLUSTERS: SIMULATED(WITH GR + DM)

(Diaferio et al. 2005) (Borgani et al. 2004)

The Mannheim-Kazanas (MK) parameterization:

(Walker 1994, Edery & Paranjape 1998, Pireaux 2004a,b)

> 0 0

gravitational potentialdeflection angle

metric

geodesicequation

CONFORMAL GRAVITY BASICS (1)

massive particles: E>0photons: E=0

independent of 2

action

CONFORMAL GRAVITY BASICS (2)

The Mannheim-Kazanas (MK) parameterization

The Horne parameterization (adopted here)

POTENTIAL OF A STATIC POINT SOURCE

To fit galaxy rotation curves:

POTENTIAL GRADIENT OF SPHERICALLY SYMMETRIC

EXTENDED OBJECTS

Newtoniancomponent

Conformalcomponent

THE VIRIAL THEOREM (1)

Euler theorem on homogeneous functions

potential energies

THE VIRIAL THEOREM (2)

Example: sphere of radius “a”with a power-law density profile

<0

>0

1012 Msol

1013 Msol

mas

s

a = 1 Mpc

= 5/3

Applying the virial theorem

CLUSTERS IN VIRIAL EQUILIBRIUM

ARE HOTTER THAN OBSERVED.

ICM TEMPERATURE PROFILE

Hydro-static eq.

Solution

Power-lawdensity profile

AT LARGE RADII,

CLUSTERS IN HYDROSTATIC EQUILIBRIUM

HAVE A TEMPERATURE PROFILE

WHICH INCREASES AT LEAST AS r2.

SPH SIMULATIONSModified version of Gadget-1.1 (Springel et al. 2001)

extended particles

Potential

Acceleration

x=r/h

GRAVITATIONAL ACCELERATION DUE TO INDIVIDUAL PARTICLES

Newtonian term

Conformalterm

A TEST SIMULATION

initial density profile from A2199:

-model with rc=134 kpc

total mass M = 2.7x1013 Msol

# of SPH particles = 4096softening =0.1 kpc

adiabatic simulation with Tin=0

vacuum boundary conditions

NO MULTIPOLE EXPANSION DIRECT SUMMATION

SIMULATION RESULTS (1)

X-ray surf. bright. evolution

2 Mpc

SIMULATION RESULTS (2)

Temperature evolution

2 Mpc

SIMULATION RESULTS (3)

Energy evolution Size evolutionenergy conservation

pot. en.

tot. en.

th. en.

kin. en.

temperature virial ratio

90%

10%

SIMULATION RESULTS (4)Density profile at eq. Temperature profile at eq.

0=1.6x10-25 g cm-3

rc=142 kpc

=1.65

r2

r1/2

CONCLUSION X-ray clusters are too hot and have an increasing temperature profile when the MK conformal factor choice is implemented in conformal gravity

N-body simulations confirm the virial theorem estimates

Appropriate boundary conditions needed

Conformal factor choice to be revised?

We have got an SPH/N-body code that can be used for simulations with physically motivated initial conditions