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We present a study of the distribution of asymptotic burst oscillationperiods for a sample of 26 bursts from 4U 1636-53 observed with the Rossi X-rayTiming Explorer (RXTE). The burst sample includes both archival and proprietarydata and spans more than 4.5 years. We also present new optical light curves ofV801 Arae, the optical counterpart of 4U 1636-53, obtained during 1998-2001. Weuse these optical data to refine the binary period measured by Augusteijn etal. (1998) to 3.7931206(152) hours. We show that a subset of ~70% of the burstsform a tightly clustered distribution of asymptotic periods consistent with aperiod stability of ~ 1/10,000. The tightness of this distribution, made up ofbursts spanning more than 4 years in time, suggests that the underlying periodis highly stable, with a time to change the period of ~30,000 years, comparableto similar numbers derived for X-ray pulsars. We investigate the period andorbital phase data for our burst sample and show that it is consistent withbinary motion of the neutron star with v sin i < 55 km/sec at 90% confidence.We use this limit as well as previous radial velocity data to constrain thebinary geometry and component masses in 4U 1636-53.Comment: AASTEX, 35 pages, 9 figures. Submitted to the Astrophysical Journa

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