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X-RAY CLUSTERS IN CONFORMAL GRAVITY

X-RAY CLUSTERS IN CONFORMAL GRAVITY. Antonaldo Diaferio Universita' degli Studi di Torino Dipartimento di Fisica Generale “Amedeo Avogadro”. Edinburgh, April 21 st , 2006. OUTLINE. Introduction on conformal factor : photon and massive particle geodesics

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X-RAY CLUSTERS IN CONFORMAL GRAVITY

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

  2. OUTLINE • 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

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

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

  5. CONFORMAL GRAVITY BASICS (1) action metric geodesic equation photons: E=0 massive particles: E>0 independent of c2 The Mannheim-Kazanas (MK) parameterization: gravitational potential deflection angle g > 0 g< 0 (Walker 1994, Edery & Paranjape 1998, Pireaux 2004a,b)

  6. CONFORMAL GRAVITY BASICS (2) POTENTIAL OF A STATIC POINT SOURCE The Mannheim-Kazanas (MK) parameterization The Horne parameterization (adopted here) To fit galaxy rotation curves:

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

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

  9. THE VIRIAL THEOREM (2) a = 1 Mpc Example: sphere of radius “a” with a power-law density profile 1013 Msol 1012 Msol <0 >0 Applying the virial theorem mass g = 5/3

  10. CLUSTERS IN VIRIAL EQUILIBRIUM ARE HOTTER THAN OBSERVED.

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

  12. AT LARGE RADII, CLUSTERS IN HYDROSTATIC EQUILIBRIUM HAVE A TEMPERATURE PROFILE WHICH INCREASES AT LEAST AS r2.

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

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

  15. A TEST SIMULATION • initial density profile from A2199: • b-model with rc=134 kpc • total mass M = 2.7x1013 Msol • # of SPH particles = 4096 • softening =0.1 kpc • adiabatic simulation with Tin=0 • vacuum boundary conditions NO MULTIPOLE EXPANSION DIRECT SUMMATION

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

  17. SIMULATION RESULTS (2) Temperature evolution 2 Mpc

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

  19. SIMULATION RESULTS (4) Density profile at eq. Temperature profile at eq. r2 r1/2 0=1.6x10-25 g cm-3 rc=142 kpc =1.65

  20. 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

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