An Xspec model for a log-normal temperature distribution
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Jeremy Sanders

This model is a spectral model for a log-normal distribution of apec
temperature components. As the width of the distribution decreases, it
converges to a single temperature component.

N different temperature components are summed (default N=21). These
have temperatures evenly-spaced in log-temperature between
logT_central-M*logsigma and logT_central+M*logsigma (default M=3). The
normalisation (emission measure) of the components is proportional to
exp(-0.5*((logT_i-logT_central)/logsigma)**2), but normalised to sum to
1. Please note the usage of log base-e, rather than base-10.

There are two models included. lognorm sums apec components with solar
abundance ratios. vlognorm allows individual elemental abundances.

Parameters for lognorm:

kT - central temperature of the distribution
logsigma - width of the distribution (note: log base-e, not log base-10)
Abundanc - standard solar relative abundances
Redshift - redshift of components
norm - total normalisation of the components

xset variables to modify behaviour:

LOGNORM_NTEMPS: number of temperature components, N (default 21)
LOGNORM_MAXSIGMA: number of sigma to include, M (default 3)

Setting chatter to 15 will show which the temperature and
normalisations of the individual components.

For example, if LOGNORM_NTEMS=5, and LOGNORM_MAXSIGMA=2, for a central
temperature of 10 keV and logsigma=0.1, then the following
temperatures (keV) and relative emission measures are produced (before
normalisation):

T=8.18731 em=0.135335
T=9.04837 em=0.606531
T=10 em=1
T=11.0517 em=0.606531
T=12.214 em=0.135335


Build instructions
------------------

Please see the Xspec manual on how to build user models. You can do
something like this to build from source:

XSPEC>initpackage lognorm lmodel.dat dir_name

And to load use this

XSPEC>lmod lognorm dir_name

Where dir_name is where the source is located.

The model may need rebuilding for different Xspec versions