Periodic timing residuals in pulsating binary X-ray sources and orbital precession in Hercules X-1

Intrinsic variations of pulse frequency and reflection of pulses produce systematic residuals in pulse arrival times from pulsating binary X-ray sources. We use an iterative technique to calculate higher-order terms in the arrival time curve of a variable-frequency binary source. We also formulate a general framework for studying time delays caused by reflection of pulses. By applying these methods to Her X-1, we find that reflection effects and variations in pulse frequency due to accretion torques, stellar wobble, and changes in pulse shape can mimic the effects of orbital precession with the 35 d period. We suggest observational tests to resolve this ambiguity in the interpretation of the timing data