Frame dragging and other precessional effects in black hole pulsar binaries

For radio pulsars in orbit with a compact companion, pulsar timing observat ions have proved to be a powerful tool for identifying the physical nature of the companion. Unfortunately, perhaps the most intriguing system where s uch a tool could be used, a pulsar in orbit with a black hole, has yet to b e discovered. In this paper we give a detailed investigation of what one ca n learn about the black hole companion via timing observations of the pulsa r. We present an analytic calculation for the propagation delay caused by t he frame-dragging effect and show that it has the same functional behavior as the modulation of the observed rotational phase of the pulsar caused by the deflection of the radio signals in the gravitational field of the compa nion (bending delay). Thus, contrary to statements of other authors, the fr ame-dragging delay is unlikely to be separately measurable in pulsar binari es where the companion is a stellar-mass black hole. We demonstrate, howeve r, that the precession of the binary orbit caused by the relativistic spin- orbit coupling can lead to observable effects that can be used to set a low er limit to the black hole spin or possibly allow the determination of its magnitude and orientation. We give parameter estimates for two possible sys tems, a 10 M-. black hole in orbit either with a young (similar to 0.1 s) p ulsar or with a millisecond pulsar. Finally, we discuss the measurability o f the quadrupole moment of the rotating black hole companion that would tes t the presence of a Kerr black hole. As an interesting side result of our c alculations, we can give a further argument why the companion of PSR J0045- 7319 cannot be a Kerr black hole.