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Coherent oscillations and the evolution of the emission area in the decaying phase of radius-expansion bursts from 4U 1636-53

We analysed all archival data of the low-mass X-ray binary 4U 1636--53 with the Rossi X-ray Timing Explorer (1490 observations). We found a total of 336 type-I X-ray bursts from this source. In the time-resolved spectra of 69 of these bursts, close to the peak of the burst, the best-fitting blackbody radius shows the sharp increase and decrease that is typical of photospheric radius-expansion (PRE) bursts. We found that in 17 of these 69 PRE bursts, after the touchdown point, the blackbody radius increases again quickly after about 1 second, and from then on the radius decreases slightly or it remains more or less constant. In the other 52 PRE bursts, after touchdown, the radius of the blackbody stays more or less constant for $\sim 2 - 8$ seconds, and after that it increases slowly. Interestingly, those PRE bursts in which the blackbody radius remains more or less constant for $\simmore 2$ seconds show coherent oscillations in the tail of the burst, whereas those PRE bursts in which the blackbody radius changes rapidly after touchdown show no coherent oscillations in the tail of the burst. We found that the distribution of durations of the post touchdown phase between these two groups of PRE bursts is significantly different; the Kolmogorov-Smirnov probability that the two groups of PRE bursts come from the same parent populations is only $3.5 \times 10^{-7}$. This is the first time that the presence of burst oscillations in the tail of X-ray bursts is associated with a systematic behaviour of the spectral parameters in that phase of the bursts. This result is consistent with predictions of models that associate the oscillations in the tail of X-ray bursts with the propagation of a cooling wake in the material on the neutron-star surface during the decay of the bursts.