  Transiently accreting Low Mass X-Ray Binaries have the potential to probe the
core composition of their neutron stars via deep crustal heating caused by
nuclear reactions. We statistically assess this deep crustal heating scenario,
taking into account the various microphysical and astrophysical uncertainties.
We find that despite the sizable uncertainties there is the chance to
discriminate different compositional scenarios. Several observed sources
statistically challenge a minimal hadronic matter composition, where cooling
proceeds exclusively via slow modified Urca reactions. Considering here two
exemplary extended uniform compositions, namely ultra-dense hadronic matter
with direct Urca emission and ungapped quark matter, we find that they are even
within uncertainties distinguishable. We show that although exotic forms of
matter are generally only expected in an inner core, which could in principle
have any size, sufficiently large astrophysical data sets nonetheless have the
potential to statistically discriminate compositional scenarios, in particular
when further mass measurements become available.
