Presentazione di PowerPoint

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

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X-RAY CLUSTERS OBSERVED
15 clusters observed with XMM-Newton
CL001616 ROSAT PSPC
Temperature
radius
(De Grandi et al . 2004)
X-ray spectrum
Temperature
ICM mass
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X-RAY CLUSTERS SIMULATED
(WITH GR DM)
(Diaferio et al. 2005)
(Borgani et al. 2004)
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CONFORMAL GRAVITY BASICS (1)
Conformal action
Schwarzschild metric
where
current choice
However
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CONFORMAL GRAVITY BASICS (1)
action
metric
geodesic equation
photons E0
massive particles Egt0
independent of c2
The Mannheim-Kazanas (MK) parameterization
gravitational potential
deflection angle
g gt 0
g lt 0
(Walker 1994, Edery Paranjape 1998, Pireaux
2004a,b)
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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
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POTENTIAL GRADIENT OF SPHERICALLY SYMMETRIC
EXTENDED OBJECTS
Newtonian component
Conformal component
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THE VIRIAL THEOREM (1)
Euler theorem on homogeneous functions
potential energies
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THE VIRIAL THEOREM (2)
a 1 Mpc
Example sphere of radius a with a power-law
density profile
1013 Msol
1012 Msol
lt0
gt0
Applying the virial theorem
mass
g 5/3
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CLUSTERS IN VIRIAL EQUILIBRIUM ARE HOTTER THAN
OBSERVED.
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ICM TEMPERATURE PROFILE
Hydro-static eq.
Solution
Power-law density profile
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AT LARGE RADII, CLUSTERS IN HYDROSTATIC
EQUILIBRIUM HAVE A TEMPERATURE PROFILE WHICH
INCREASES AT LEAST AS r2.
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SPH SIMULATIONS
Modified version of Gadget-1.1 (Springel et al.
2001)
extended particles
xr/h
Potential
Acceleration
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GRAVITATIONAL ACCELERATION DUE TO INDIVIDUAL
PARTICLES
Newtonian term
Conformal term
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A TEST SIMULATION

• initial density profile from A2199
• b-model with rc134 kpc
• total mass M 2.7x1013 Msol
• of SPH particles 4096
• softening ?0.1 kpc
• adiabatic simulation with Tin0
• vacuum boundary conditions

NO MULTIPOLE EXPANSION DIRECT SUMMATION
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SIMULATION RESULTS (1)
X-ray surf. bright. evolution
2 Mpc
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SIMULATION RESULTS (2)
Temperature evolution
2 Mpc
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SIMULATION RESULTS (3)
Energy evolution
Size evolution
energy conservation
tot. en.
90
pot. en.
th. en.
kin. en.
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virial ratio
temperature
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SIMULATION RESULTS (4)
Density profile at eq.
Temperature profile at eq.
r2
r1/2
?01.6x10-25 g cm-3 rc142 kpc ?1.65
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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