4.1.31. Pdem: DEM models

The pdem model is intended to be used for differential emission measure analysis, simultaneous with fitting of abundances etc. of an optically thin plasma.

It works as follows. The user gives a a number of temperature grid points n, a minimum temperature T_1, a maximum temperature T_n, a total emission measure Y and relative contributions y_1 \ldots y_n. SPEX assumes that the grid points between T_1 and T_n are distributed logarithmically.

The relative contributions y_1\ldots y_n represents the values of {\mathrm d}Y/{\mathrm d}\ln T (note the logarithm!) at the grid points. SPEX then interpolates in the \log T_i - \log y_i space on a finer grid using splines. That temperature grid on which the data are being evaluated has a fine mesh: step size is about 0.10 in \log T (finer is not useful because uniqueness is no longer guaranteed), with the additional constraint that the number of mesh points is at least n and not larger than 64 (practical limit in order to avoid excessive cpu-time). The emission measure distribution is then simply scaled in such a way that its sum over the fine mesh equals the total emission measure Y that went into the model.

Warning

At least one of the y_i values should be kept frozen during fitting, when Y is a free parameter, otherwise no well defined solution can be obtained! If Y is fixed, then all y_i can be free.

The parameters of the model are:

norm:

Normalisation, i.e. total integrated emission measure Y in units of 10^{64} \mathrm{m}^{-3}.

t1:

Lower temperature T_1 in keV.

tn:

Upper temperature T_n in keV.

npol:

Number of temperature grid points n; minimum value 2, maximum value 8.

y1:

Relative contribution y_1 at T_1.

y2:

Relative contribution y_2 at T_2

\ldots

y8:

Relative contribution y_8 at T_8; note that the higher contributions y_i are neglected if i>n.

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

Note that the true emission measure on the finer mesh can be displayed by using the ascdump term # # dem command; you will get a list of temperature (keV) versus emission measure.