  The neutron star transient and 11 Hz X-ray pulsar IGR J17480-2446, recently
discovered in the globular cluster Terzan 5, showed unprecedented bursting
activity during its 2010 October-November outburst. We analyzed all X-ray
bursts detected with the Rossi X-ray Timing Explorer and find strong evidence
that they all have a thermonuclear origin, despite the fact that many do not
show the canonical spectral softening along the decay imprinted on type I X-ray
bursts by the cooling of the neutron star photosphere. We show that the
persistent-to-burst power ratio is fully consistent with the
accretion-to-thermonuclear efficiency ratio along the whole outburst, as is
typical for type I X-ray bursts. The burst energy, peak luminosity and
daily-averaged spectral profiles all evolve smoothly throughout the outburst,
in parallel with the persistent (non-burst) luminosity. We also find that the
peak burst to persistent luminosity ratio determines whether or not cooling is
present in the bursts from IGR J17480-2446, and argue that the apparent lack of
cooling is due to the "non-cooling" bursts having both a lower peak temperature
and a higher non-burst (persistent) emission. We conclude that the detection of
cooling along the decay is a sufficient, but not a necessary condition to
identify an X-ray burst as thermonuclear. Finally, we compare these findings
with X-ray bursts from other rapidly accreting neutron stars.
