*Astron. Astrophys. 320, 181-184 (1997)*
## 3. Fitting of theoretical X-ray burst spectra
The theoretical X-ray spectra for hot neutron star atmospheres (see
table 1A - 1D in Paper I) can be quite accurately fitted by the
expression
which is a modification of the Planck function with non-zero
chemical potential *µ* and constant
generally not equal to 3. Here denotes the
flux measured in energy units (erg/cm^{2} sec Hz), and
denotes frequency in Hz. Eq. (1) depends on 4
free parameters which have to be determined, ,
, , and *µ*. One
of them, , is the color temperature of an X-ray
burst. One should be aware, that determined from
Eq. (1) can differ slightly from color temperatures obtained from the
standard blackbody fits, as made in many earlier studies.
Eq. (1) can be expressed in logarithmic form,
which is much more useful in the further fitting (decimal
logarithms). Eq. (2) depends non-linearly on two parameters,
and *µ*. Non-linear fitting
procedures did not yield convergence in case of that formula.
Therefore, for each X-ray spectrum given in tabular form (Paper I) a
dense discrete mesh of and *µ* has
been defined within reasonable limits. Then, for each fixed pair of
these parameters, the remaining and
were determined with the usual linear least
squares techniques, minimizing values of in
which all (unknown) errors of theoretical fluxes were arbitrarily set
to unity, .
Numerical FORTRAN procedures for linear fitting were directly taken
from Press et al. (1986).
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998
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