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
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.
Warning
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.
Warning
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: 16p : Slope \(p=1/\alpha\). Default: 0.25 (\(\alpha = 4\)).cut : Lower temperature cut-off, in units of \(T_{\max}\).
Default value: 0.1.hden :
Hydrogen density in \(10^{20}\) \(\mathrm{m}^{-3}\)it : Ion temperature in keVvrms : RMS Velocity broadening in km/s (see Definition of the micro-turbulent velocity in SPEX)ref : Reference element01...30 : Abundances of H to Znfile : Filename for the nonthermal electron distributionRecommended citation: Kaastra et al. (2004) and Fabian et al. (1984).