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N. R. Nath (Raytheon/GSFC), T. E. Strohmayer, J. H. Swank (NASA/GSFC)
Oscillations during thermonuclear X-ray bursts observed with the Rossi X-Ray Timing Explorer (RXTE) intrinsically contain information on the compactness (mass/radius ratio) of the neutron stars from which the bursts originate. The amplitude of oscillation depends sensitively on the compactness; in general, the greater the amplitude the smaller the compactness. Using a "hot spot" model, with simple assumptions about the emission characteristics of the photons and employing the Schwartzschild metric, we have determined least-squares fits to pulsations detected on the rising edge of bursts from 4U 1636-53 and 4U 1728-34. The model parameters include, in addition to compactness, an initial size, an initial phase, the angular growth rate of the (assumed) circular spot, and the latitudes of the spot center and the observation direction, and both single and antipodal spots are considered. In 4U 1636-53 the apparent detection of a 290 Hz subharmonic suggests that the spin frequency is 290 Hz and that two antipodal spots produce the stronger signal at 580 Hz. We find that with two antipodal spots the observed amplitude of pulsations places a strong constraint on the compactness such that M/R < 0.15 (in natural units). Results obtained from several bursts from 4U 1636-53 are consistent with this value. Assuming that 1.4 solar masses is a lower limit to the mass of the neutron star in 4U 1636-53, then this implies a lower limit on the radius of about 13.8 km, and would require a fairly stiff equation of state. For 4U 1728-34 (or 4U 1636-53) the single spot model is not as constraining, but if future bursts reveal stronger oscillations then useful constraints should follow.