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Astron. Astrophys. 320, 181-184 (1997)

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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

[EQUATION]

which is a modification of the Planck function with non-zero chemical potential µ and constant [FORMULA] generally not equal to 3. Here [FORMULA] denotes the flux measured in energy units (erg/cm2 sec Hz), and [FORMULA] denotes frequency in Hz. Eq. (1) depends on 4 free parameters which have to be determined, [FORMULA], [FORMULA], [FORMULA], and µ. One of them, [FORMULA], is the color temperature of an X-ray burst. One should be aware, that [FORMULA] 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,

[EQUATION]

which is much more useful in the further fitting (decimal logarithms). Eq. (2) depends non-linearly on two parameters, [FORMULA] 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 [FORMULA] and µ has been defined within reasonable limits. Then, for each fixed pair of these parameters, the remaining [FORMULA] and [FORMULA] were determined with the usual linear least squares techniques, minimizing values of [FORMULA] in which all (unknown) errors of theoretical fluxes were arbitrarily set to unity, [FORMULA].

Numerical FORTRAN procedures for linear fitting were directly taken from Press et al. (1986).

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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