1. X-RAY CLUSTERS IN CONFORMAL GRAVITY Antonaldo Diaferio Universita' degli Studi di Torino Dipartimento di Fisica Generale “Amedeo Avogadro” Edinburgh, April 21 st, 2006

2. 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

3. X-RAY CLUSTERS: OBSERVED CL0016+16 ROSAT PSPC X-ray spectrum Temperature ICM mass radius Temperature 15 clusters observed with XMM-Newton (De Grandi et al. 2004)

4. X-RAY CLUSTERS: SIMULATED (WITH GR + DM) (Diaferio et al. 2005)(Borgani et al. 2004)

5. CONFORMAL GRAVITY BASICS (1) Conformal action Schwarzschild metric where However: current choice:

6. The Mannheim-Kazanas (MK) parameterization: (Walker 1994, Edery & Paranjape 1998, Pireaux 2004a,b)  > 0  0 gravitational potential deflection angle metric geodesic equation CONFORMAL GRAVITY BASICS (1) massive particles: E>0 photons: E=0 independent of  2 action

7. 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:

8. POTENTIAL GRADIENT OF SPHERICALLY SYMMETRIC EXTENDED OBJECTS Newtonian component Conformal component

9. THE VIRIAL THEOREM (1) Euler theorem on homogeneous functions potential energies

10. THE VIRIAL THEOREM (2) Example: sphere of radius “a” with a power-law density profile <0 >0 10 12 Msol 10 13 Msol mass a = 1 Mpc  = 5/3 Applying the virial theorem

11. CLUSTERS IN VIRIAL EQUILIBRIUM ARE HOTTER THAN OBSERVED.

12. ICM TEMPERATURE PROFILE Hydro-static eq. Solution Power-law density profile

13. AT LARGE RADII, CLUSTERS IN HYDROSTATIC EQUILIBRIUM HAVE A TEMPERATURE PROFILE WHICH INCREASES AT LEAST AS r 2.

14. SPH SIMULATIONS Modified version of Gadget-1.1 (Springel et al. 2001) extended particles Potential Acceleration x=r/h

15. GRAVITATIONAL ACCELERATION DUE TO INDIVIDUAL PARTICLES Newtonian term Conformal term

16. A TEST SIMULATION initial density profile from A2199:  -model with r c =134 kpc total mass M = 2.7x10 13 Msol # of SPH particles = 4096 softening  =0.1 kpc adiabatic simulation with T in =0 vacuum boundary conditions NO MULTIPOLE EXPANSION DIRECT SUMMATION

17. SIMULATION RESULTS (1) X-ray surf. bright. evolution 2 Mpc

18. SIMULATION RESULTS (2) Temperature evolution 2 Mpc

19. SIMULATION RESULTS (3) Energy evolution Size evolution energy conservation pot. en. tot. en. th. en. kin. en. temperature virial ratio 90% 10%

20. SIMULATION RESULTS (4) Density profile at eq.Temperature profile at eq.  0 =1.6x10 -25 g cm -3 r c =142 kpc  =1.65 r2r2 r 1/2

21. 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