  We present a comprehensive study of the thermonuclear bursts and millihertz
quasi-periodic oscillations (mHz QPOs) from the neutron star (NS) transient and
11 Hz X-ray pulsar IGR J17480-2446, located in the globular cluster Terzan 5.
The increase in burst rate that we found during its 2010 outburst, when
persistent luminosity rose from 0.1 to 0.5 times the Eddington limit, is in
qualitative agreement with thermonuclear burning theory yet opposite to all
previous observations of thermonuclear bursts. Thermonuclear bursts gradually
evolved into a mHz QPO when the accretion rate increased, and vice versa. The
mHz QPOs from IGR J17480-2446 resemble those previously observed in other
accreting NSs, yet they feature lower frequencies (by a factor ~3) and occur
when the persistent luminosity is higher (by a factor 4-25). We find four
distinct bursting regimes and a steep (close to inverse cubic) decrease of the
burst recurrence time with increasing persistent luminosity. We compare these
findings to nuclear burning models and find evidence for a transition between
the pure helium and mixed hydrogen/helium ignition regimes when the persistent
luminosity was about 0.3 times the Eddington limit. We also point out important
discrepancies between the observed bursts and theory, which predicts brighter
and less frequent bursts, and suggest that an additional source of heat in the
NS envelope is required to reconcile the observed and expected burst
properties. We discuss the impact of NS magnetic field and spin on the expected
nuclear burning regimes, in the context of this particular pulsar.
