ICM Temperature models
If no temperature map is provided, then it is necessary to provide a temperature model in order to compute the different ICM observables (X-ray surface brightness, SZ effect temperature contrast, etc.). For purely lensing, this is not necessary.
Temp0 is the pivot temperature model, eq. (17) in
Allingham 2024:
T_0(z) = T_{500,c} (z) T_{\rm ref}.
It may be computed using routine predT:
predT0 <redshift> <model_type> <M_500,c>
where the mass
M_{500,c} is in
M_{\odot}, and the <model_type> corresponds to the regression used for
P_e (n_e). By default, use polyEv1 for the latter.
Jz_array indicates how to compute the Jz function, relating the potential to the ICM density
n_e.
It takes three arguments:
An integer.
0: do not perform the computation.1: perform it.A string for the model type. By default, use
polyE. Other option ispolyA, which should be more up-to-date.A second string for the name of the output array. If the array is not computed (
0), this array must already exist.
The different temperature models are listed here:
polyEv1: uses the reduction of a polytropic temperature distribution, with a varying index. Reduction over 12 X-COP clusters. See parameters values in the table below.polyAv1: uses the reduction of a polytropic temperature distribution, with a varying index. Reduction over 12 X-COP clusters, and 3 strong lensing clusters’ XMM-Newton spectrocopic data. See parameters values in the table below.
The polytropic index model writes:
T_e &= \eta_T T_{500,c} \left( \frac{n_e E(z)^{-2}}{\eta_n} \right)^{\Gamma (n_e) - 1},
where E(z) = H(z)/H_0 is the scaled Hubble factor at a cluster redshift z. Assuming the polytropic index \Gamma to vary with the ICM density,
\Gamma (n_e) &= \Gamma_0 \left[ 1 + \Gamma_S \arctan \left( \ln \frac{n_e E(z)^{-2}}{\eta_n} \right) \right],
where
\eta_T = (1e6*3.426e-3/8.85)*(\eta_P/\eta_n).
We specify the parameters of different models in the table below.
Id |
\eta_P |
\eta_n [cm ^{-3}] |
\Gamma_0 |
\Gamma_S |
|---|---|---|---|---|
|
||||
|
4.61 |
1.54\times 10^{-3} |
1.02 |
-0.15 |