Evolution of compact binary systems with X-ray heating

Abstract

The evolution of low-mass X-ray binary systems is calculated with the inclusion of heating of the secondary star by the X-radiation from the primary. The secondary is assumed to be nonsynchronously rotating with the orbit, so that the X-ray heating may be taken to be approximately uniform over its surface. Due to the shadowing effect of a postulated accretion disk, only a portion of the X-ray flux reaches the secondary star. The evolution of binary systems with secondary stars of initial mass 0.4 and 1 M 0 is computed. We find that the expansion of the secondary due to the X-ray heating causes high rates of mass loss from the star for significant intervals of time, for both values of the secondary mass. This mass transfer is typically accompained by an increase in the orbital period. The expansion of the secondary takes place in two distinct phases: (1) an initial phase, during which only the outermost layers of the star are heated and expand rapidly; and (2) A long-term expansion phase, during which the reduced temperature gradient (temporarily an inverse temperature gradient) in the outer regions of the star forms a heat barrier which prevents heat flow from the interior and causes the entire star to swell. The evolution of the two binary systems that we considered are characterized by very high initial mass-loss rates during the first expansion phase, followed by a decreasing (but still super-Eddington) mass-loss rate during the second of the expansion phases. When the mass transfer rate to the neutron star drops below the Eddington limit, the effects of the X-ray heating diminish sufficiently so that the secondary cannot be sustained in its fully bloated state. The secondary then shrinks within its Roche lobe, and mass transfer ceases until magnetic braking can bring the system back into contact. We discuss the relevance of these results to low-mass X-ray binaries and recycled radio pulsars. This includes the high rate of mass transfer and large positive values of P orh observed in a number of low-mass X-ray binaries, as well as the formation of recycled radio pulsars.