  The time-dependence of heating in solar active regions can be studied by
analyzing the slope of the emission measure distribution cool-ward of the peak.
In a previous study we showed that low-frequency heating can account for 0% to
77% of active region core emission measures. We now turn our attention to
heating by a finite succession of impulsive events for which the timescale
between events on a single magnetic strand is shorter than the cooling
timescale. We refer to this scenario as a "nanoflare train" and explore a
parameter space of heating and coronal loop properties with a hydrodynamic
model. Our conclusions are: (1) nanoflare trains are consistent with 86% to
100% of observed active region cores when uncertainties in the atomic data are
properly accounted for; (2) steeper slopes are found for larger values of the
ratio of the train duration $\Delta_H$ to the post-train cooling and draining
timescale $\Delta_C$, where $\Delta_H$ depends on the number of heating events,
the event duration and the time interval between successive events ($\tau_C$);
(3) $\tau_C$ may be diagnosed from the width of the hot component of the
emission measure provided that the temperature bins are much smaller than 0.1
dex; (4) the slope of the emission measure alone is not sufficient to provide
information about any timescale associated with heating - the length and
density of the heated structure must be measured for $\Delta_H$ to be uniquely
extracted from the ratio $\Delta_H/\Delta_C$.
