A Model for Pulsating X-Ray Sources: Accretion by Pulsating White Dwarfs

Abstract

Accretion of matter by a pulsating white dwarf is studied as a model of pulsating X-ray sources. In our model the X-ray pulse is understood as the difference in X-ray emission between the expanding and the contracting phases of pulsation. The relative strength· of the pulse depends on the radial velocity of pulsation or on the pulsation amplitude. In or'der to account for the observed fraction of pulsed X-rays, the white dwarf should pulsate with a relatively large amplitude, .dR/R~0.14. pulsating X-ray sources such as Cen X-3 and Her X-1 that pulsate with periods of 4.84 sec and 1.24 sec, respectively. 1l' 2l From the sinusoidal variation of the observed periods and the existence of X-ray eclipse2),S) it has been confirmed that they are members of close binary systems with orbital periods of 2.087 day for Cen X-3 and 1.700 day for Her X-1. Furthermore the upper limits of the masses of Cen X-3 and Her X-1 have been determined to be 0.46~0.75M0 and 0.21~ 1.2M0 , respectively. 4l' 5l The uncertainty in the limiting masses, especially in Her X-1, is due mainly to variations in the duration of X-ray eclipse. The variations may be an effect of circumstellar matter overflowing from the Roche lobe. If this is the case we should adopt the smallest duration of X-ray eclipse to determine the dimension of the Roche lobe of the primary. The correspond­ ing limiting masses are 0.7M0 for Cen X-3 and 1.2M0 for Her X-1. In close binary systems it is well known that matter is transferred to the secondary star when the atmosphere of the primary star fills its Roche lobe. In order to emit X-rays of required energies the secondary star must be either a white dwarf or a neutron star or a black hole. Recently, Hoshi6l and Aizu7l have investigated that the mass accretion onto a white dwarf can account for essential properties of SCO X-1. When substantial matter ( ~ 10-3M 0 ) accumulates onto a white dwarf, how­ ever, hydrogen burning begins at the bottom of the accumulated matter. At the same time thermal instability developes at the burning shell as discussed by Giannone and Weigert. 8) Through the course of this instability Rose9l showed that a pulsation could be excited by intense nuclear burning that appeared near