# 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 for the isobaric cooling flow model can be written as

where is the mass deposition rate, is Boltzmann’s constant, the mean molecular weight (0.618 for a plasma with 0.5 times solar abundances), is the mass of a hydrogen atom, and is the cooling function. We have calculated the cooling function 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 and a high temperature boundary . We do this by creating a temperature grid with bins and calculating the spectrum for each temperature.

Warning

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

Warning

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

The parameters of the model are:

`norm`

: The mass deposition rate in
.`t1`

: Lower temperature cut-off temperature . Default:
0.1 keV.`tn`

: Upper temperature cut-off temperature . Default:
1 keV.`nr`

: Number of temperature bins used in the integration.
Default value: 16`p`

: Slope . Default: 0.25 ().`cut`

: Lower temperature cut-off, in units of .
Default value: 0.1.`hden`

:
Hydrogen density in `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).