  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.
