Distance Estimation for Eclipsing X-ray Pulsars
Distance of an X-ray binary can be computed from a rigorous flux scaling law that connects model stellar atmosphere output with observed standard magnitudes of the optical star via either of two standard magnitude calibrations that agree within 4 percent. Accordingly the corresponding distance disagreement (due to the calibrations only) is only 2 percent, which is negligible compared to several other error sources. The flux-distance scaling is not the usual one for spherical stars but preserves directional (i.e. aspect) information, and therefore is not limited to well detached binaries. Bolometric corrections are not needed, so errors in their estimation are avoided. The procedure also models dependence of system brightness and spectroscopically observable temperature on orbital phase and inclination due to tides, irradiance, and eccentric orbits, although those effects cause only minor distance uncertainties for most X-ray binaries. Not taken into account, due to their largely stochastic nature, are radial velocity variations caused by dynamical tides. Expressions are given for derivatives ∂d/∂p, of distance with respect to various parameters. Some of the derivatives are entirely analytic while others are partly numerical. Upper and lower limits to the relative radius, r= R/a, of an X-ray binary's optical star can be measured, although actual rand inclination are otherwise uncertain. An application to the High Mass X-ray Binary Vela X-1/GP Vel, based on archival pulse arrival times and radial velocities, finds a distance of about 2.2 kiloparsecs and also finds distance uncertainties due to estimated magnitude, interstellar extinction, metallicity, orbit size, optical star size, surface temperature, and surface gravity.
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