Thermonuclear burning on the accreting X-ray pulsar GRO J1744-28

We investigate the thermal stability of nuclear burning on the accreting X-ray pulsar GRO J1744-28. The neutron star's dipolar magnetic field is less than or similar to 3x10(11) G if persistent spin-up implies that the magnetospheric radius is less than the corotation radius. Bildsten earlier noted that magnetic fields this weak might not quench the vigorous convection sometimes associated with thermonuclear instabilities, so that a convective burning front can propagate around the star in a few seconds and rapidly release the accumulated nuclear energy. After inferring the properties of the neutron star, we study the thermal stability of hydrogen/helium burning and show that thermonuclear instabilities are unlikely causes of the hourly bursts seen at very high accretion rates. Then we discuss how the stability of the thermonuclear burning depends on both the global accretion rate and the neutron star's magnetic field strength. If the accreted matter spreads over the star prior to ignition, then the burning will become unstable when the accretion rate is below 6x10(-9) M. yr(-1). We emphasize that the appearance of the instability (i.e., whether it looks like a type I X-ray burst or a flare lasting a few minutes) will yield crucial information on the neutron star's surface magnetic field and the role of magnetic fields in convection. We suggest that a thermal instability in the accretion disk is the origin of the long (similar to 300 days) outburst and that the recurrence time of these outbursts is more than 50 yr. We also discuss the nature of the binary and point out that a velocity measurement of the stellar companion (most likely a Roche lobe filling giant with m(K) greater than or similar to 17) will constrain the neutron star mass. This is of interest in this binary, where the inferred low mass of the companion implies that 0.5 M. of transfer occurred.