  When neutron stars reside in transient X-ray binaries, their crustal layers
become heated during accretion outbursts and subsequently cool in quiescence.
Observing and modeling this thermal response has yielded valuable insight into
the physics of neutron star crusts. However, one unresolved problem is the
evidence in several neutron stars for an extra energy source, located at
shallow depth in the crust, that is not accounted for by standard heating
models. Its origin remains puzzling, and it is currently unclear whether this
additional heating occurs in all neutron stars, and if the magnitude is always
the same. Here, we report on Chandra observations that cover two years after
the 2012 outburst of the transient neutron star X-ray binary Swift
J174805.3-244637 in the globular cluster Terzan 5. The temperature of the
neutron star was elevated during the first two months following its ~8 week
accretion episode, but had decayed to the pre-outburst level within ~100 days.
Interpreting this as rapid cooling of the accretion-heated crust, we model the
observed temperature curve with a thermal evolution code. We find that there is
no need to invoke shallow heating for this neutron star, although an extra
energy release up to ~1.4 MeV/nucleon is allowed by the current data (2-sigma
confidence). We also present two new data points on the crust cooling curve of
the 11-Hz X-ray pulsar IGR J17480-2446 in Terzan 5, which was active in 2010.
The temperature of this neutron star remained significantly above its
pre-outburst level, but we detect no temperature change since the previous
measurements of 2013 February. This is consistent with the slower cooling
expected several years post-outburst.
