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/cm2 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