in central cluster regions it can be shorter than the age of the Universe
in fairly relaxed clusters the decrease of the ICM temp. in the central regions has been recognized
supernovae or AGNs as possible feedback mechanisms providing an adequate amount of extra energy to balance overcooling
three ways how an electron can get rid of energy
collisional cooling very efficient but not for completely ionized ICM
Recombination probability 1/velocity gt unimportant for ICM
free-free interaction thermal bremsstrahlung
24 Cooling cont.
about 1000 Msol/yr of gas can cool out of the X-Ray halo
this gas could form stars some cD galaxies show filaments of gas emission and blue colors in the central region
others do not show the lower central temperatures that would be expected if cooling was efficient
presumably cooling will lead to enhanced accretion of gas onto the black hole in the cD galaxy
it in turn may become active and provide high energy particles to heat the gas
thus a quasi equilibrium may be established that prevents the gas from ever forming stars
still under debate
25 Cooling cont.
Mixing via turbulence could counteract cooling towards the outside
Central AGNs can produce relativistic jets which directly inject energy into the ICM
and may cause shocks. Jets also inflate bubbles which rise buoyantly pushing colder gas upwards out of the core.
Acoustic waves produced by AGN outbursts can also transfer energy to the ICM if it is viscous enough
26 Characteristic time-scales
Mean free path for the ions and electrons of the ICM
is ltlt cluster size
ICM can be described by fluid dynamics
Timescale for pressure equilibrium
if a region of gas undergoes a compression how long does it take for the pressure wave to propagate across the cluster
this is short compared to Hubble time we can assume that the gas is in pressure eq.
27 Characteristic time-scales cont.
Timescale for cooling
due to thermal emission
longer than a Hubble time
gt hot gas stays hot!
time-change to equil.
28 Cluster mass estimates
From the virial theorem
From X-ray data
hydrostatic equilibrium condition
µ ... mean molecular weight (0.59 for primordial composition)
distribution of ICM
ß ... ratio between the kinetic energy of any tracer of the grav. potential and the thermal energy of the gas
From gravitational lensing
29 Mass estimate from gravitational lensing
clusters act as grav. lenses on more distant galaxies
one of the most important methods for the mass determination of galaxy clusters
the only method working for non-equilibrium systems!
There are two rather different regimes
background galaxies are strongly distorted
good for massive clusters
background galaxies only slightly distorted
For a symmetric potential the galaxies are elongated slightly in the axial direction
This is a shearing effect and only reveals the gradient in the potential not its integrated depth
By measuring thousands of faint galaxy images the effect is identified statistically.
shape and radial trend of the weak shear and strong lensing effects yield the cluster mass distribution independent of the nature of the mass and therefore allow reliable total mass estimates including the dark matter
30 Mass from lensing
Newtonian deflection angle
In general relativity
thin lens approximation
angular radius of Einstein ring
critical surface density
lensing occurs when Sgt Scrit
Jacobian matrix of lens eq.
a complex shear Since and are derived from the same potential it is possible to determine the surface mass density. 31 Results of lensing
Comparison between the ICM temperatures inferred by the fitting of isothermal profiles to the shear data and from X-ray measurements.
Comparison between the velocity dispersion found by fitting isothermal profiles to the shear data and those estimated through spectroscopic measurements.
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