Thermonuclear shell flashes on neutron stars are detected as bright X-ray bursts. Traditionally, their decay is modeled with an exponential function. However, this is not what theory predicts. The expected functional form for luminosities below the Eddington limit, at times when there is no significant nuclear burning, is a power law. We tested the exponential and power-law functional forms against the best data available: bursts measured with the high-throughput Proportional Counter Array (PCA) on board the Rossi X-ray Timing Explorer. We selected a sample of 35 clean and ordinary (i.e., shorter than a few minutes) bursts from 14 different neutron stars that 1) show a large dynamic range in luminosity, 2) are the least affected by disturbances by the accretion disk and 3) lack prolonged nuclear burning through the rp-process. We find indeed that for every burst a power law is a better description than an exponential function. We also find that the decay index is steep, 1.8 on average, and different for every burst. This may be explained by contributions from degenerate electrons and photons to the specific heat capacity of the ignited layer and by deviations from the Stefan-Boltzmann law due to changes in the opacity with density and temperature. Detailed verification of this explanation yields inconclusive results. While the values for the decay index are consistent, changes of it with the burst time scale, as a proxy of ignition depth, and with time are not supported by model calculations.
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