cooling, heating and temperature oscillation

From: Yves Revaz <yves.revaz_at_obspm.fr>
Date: Fri, 30 Mar 2007 11:49:25 +0200

I encounter problems in reproducing the Temperature-Density distribution
of gas particles in a LCDM model (see for example Fig. 3 of Katz et al
96 or Fig.11 of
Springel & Hernquist 2002).

The overall distribution is correct, however, I fail to reproduce the
thinness
of the horizontal branch, corresponding to high density regions
((rho/rhom)>1e4, T<1e5K).
In my simulations, the temperature dispersion of the horizontal branch
is high,
with some particles having temperature up to 1e6 K !

This problem comes from the competition between cooling (dA/dt)_rad and
viscosity heating (dA/dt)_visc, where A is the entropy.
For a particle with a density (rho/rhom)>1e4 and temperature > 1e4K,
we have:
|(dA/dt)_rad| >> |(dA/dt)_visc| => dA/dt)_tot << 0,

the cooling dominates and the temperature quickly decreases. When the
temperature of
the particle goes below 1e4K, (dA/dt)_rad drops nearly to zero (cutoff
in the cooling function),
and the entropy variation is only due to the (dA/dt)_visc therm, which,
in some cases is so high
that the particle temperature instantaneously rises up to 1e6K !!!
In summary, in the horizontal branch, instead of being more or less
constant at 1e4K (equilibrium between
viscosity heating and radiative cooling), the temperature of the
particles oscillate between 1e4 and 1e5-1e6K.

This behavior is the result of the cooling and heating time scale, much
shorter than
the time-step imposed by the currant condition. The cooling is limited
by the condition
that :
dA/dt > -0.5 A.

Imposing also

dA/dt < A,

in not sufficient to damp the temperature oscillation.
There is probably a well known solution to this problem,
but I haven't found it in the literature.

Does anyone has a solution ?

Yves

MY PARAMETERS
---------------

The simulation test contains 2*64^3 particles in 20 Mpc^3 h^-3

I use the following parameters :

ErrTolIntAccuracy 0.025
CourantFac 0.15
MaxSizeTimestep 0.03
MinSizeTimestep 0

ErrTolTheta 0.8
TypeOfOpeningCriterion 0
ErrTolForceAcc 0.005

DesNumNgb 32
MaxNumNgbDeviation 2
ArtBulkViscConst 0.8

MinGasHsmlFractional 0.25
SofteningGas 8.
SofteningHalo 8.

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