4.1.4. Cf: isobaric cooling flow differential emission measure model

This model calculates the spectrum of a standard isobaric cooling flow. The differential emission measure distribution \mathrm{d}Y(T)/\mathrm{d}T for the isobaric cooling flow model can be written as

D(T)\equiv \mathrm{d}Y(T)/\mathrm{d}T = \frac{5\dot{M}k}{2\mu m_{\mathrm{H}} \Lambda(T)},

where \dot{M} is the mass deposition rate, k is Boltzmann’s constant, \mu the mean molecular weight (0.618 for a plasma with 0.5 times solar abundances), m_{\mathrm{H}} is the mass of a hydrogen atom, and \Lambda(T) is the cooling function. We have calculated the cooling function \Lambda using our own SPEX code for a grid of temperatures and for 0.5 times solar abundances. The spectrum is evaluated by integrating the above differential emission measure distribution between a lower temperature boundary T_1 and a high temperature boundary T_n. We do this by creating a temperature grid with n bins and calculating the spectrum for each temperature.


Take care that n is not too small in case the relevant temperature is large; on the other hand if n is large, the computational time increases. Usually a spacing with temperature differences between adjacent bins of 0.1 (in \log) is sufficient and optimal.


The physical relevance of this model is a matter of debate.

The parameters of the model are:

norm : The mass deposition rate \dot{M} in \mathrm{M}_{\odot} \mathrm{yr}^{-1}.
t1 : Lower temperature cut-off temperature T_1. Default: 0.1 keV.
tn : Upper temperature cut-off temperature T_n. Default: 1 keV.
nr : Number of temperature bins n used in the integration. Default value: 16
p : Slope p=1/\alpha. Default: 0.25 (\alpha = 4).
cut : Lower temperature cut-off, in units of T_{\max}. Default value: 0.1.
The following parameters are the same as for the cie-model:
hden : Hydrogen density in 10^{20} \mathrm{m}^{-3}
it : Ion temperature in keV
vrms : RMS Velocity broadening in km/s (see Definition of the micro-turbulent velocity in SPEX)
ref : Reference element
01...30 : Abundances of H to Zn
file : Filename for the nonthermal electron distribution

Recommended citation: Kaastra et al. (2004) and Fabian et al. (1984).