Burst Oscillation Periods from 4U 1636-53: A Constraint on the Binary Doppler Modulation

The burst oscillations seen during type I X-ray bursts from low-mass X-ray binaries typically evolve in period toward an asymptotic limit that likely reflects the spin of the underlying neutron star. If the underlying period is stable enough, measurement of it at different orbital phases may allow a detection of the Doppler modulation caused by the motion of the neutron star with respect to the center of mass of the binary system. Testing this hypothesis requires enough X-ray bursts and an accurate optical ephemeris to determine the binary phases at which they occurred. We present here a study of the distribution of asymptotic burst oscillation periods for a sample of 26 bursts from 4U 1636-53 observed with the Rossi X-Ray Timing Explorer. The burst sample includes both archival and proprietary data and spans more than 4.5 yr. We also present new optical light curves of V801 Arae, the optical counterpart of 4U 1636-53, obtained during 1998-2001. We use these optical data to refine the binary period measured by Augusteijn et al. to 3.7931206(152) hr. We show that a subset of ∼70% of the bursts form a tightly clustered distribution of asymptotic periods consistent with a period stability of ∼1 × 10 -4. The tightness of this distribution, made up of bursts spanning more than 4 yr in time, suggests that the underlying period is highly stable, with a time to change the period of ∼3 × 10 4 yr. This is comparable to similar numbers derived for X-ray pulsars. We investigate the period and orbital phase data for our burst sample and show that it is consistent with binary motion of the neutron star, with v ns sin i < 38 and 50 km s -1 at 90% and 99% confidence, respectively. We use this limit as well as previous radial velocity data to constrain the binary geometry and component masses in 4U 1636-53. Our results suggest that unless the neutron star is significantly more massive than 1.4 M ⊙, the secondary is unlikely to have a mass as large as 0.36 M ⊙, the mass estimated assuming that it is a main-sequence star that fills its Roche lobe. We show that a factor of ∼3 increase in the number of bursts with asymptotic period measurements should allow a detection of the neutron star velocity.