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We analysed all archival data of the low-mass X-ray binary 4U 1636--53 withthe Rossi X-ray Timing Explorer (1490 observations). We found a total of 336type-I X-ray bursts from this source. In the time-resolved spectra of 69 ofthese bursts, close to the peak of the burst, the best-fitting blackbody radiusshows the sharp increase and decrease that is typical of photosphericradius-expansion (PRE) bursts. We found that in 17 of these 69 PRE bursts,after the touchdown point, the blackbody radius increases again quickly afterabout 1 second, and from then on the radius decreases slightly or it remainsmore or less constant. In the other 52 PRE bursts, after touchdown, the radiusof the blackbody stays more or less constant for $\sim 2 - 8$ seconds, andafter that it increases slowly. Interestingly, those PRE bursts in which theblackbody radius remains more or less constant for $\simmore 2$ seconds showcoherent oscillations in the tail of the burst, whereas those PRE bursts inwhich the blackbody radius changes rapidly after touchdown show no coherentoscillations in the tail of the burst. We found that the distribution ofdurations of the post touchdown phase between these two groups of PRE bursts issignificantly different; the Kolmogorov-Smirnov probability that the two groupsof PRE bursts come from the same parent populations is only $3.5 \times10^{-7}$. This is the first time that the presence of burst oscillations in thetail of X-ray bursts is associated with a systematic behaviour of the spectralparameters in that phase of the bursts. This result is consistent withpredictions of models that associate the oscillations in the tail of X-raybursts with the propagation of a cooling wake in the material on theneutron-star surface during the decay of the bursts.

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