  The discovery of pulsars as heavy as 2 solar masses has led astrophysicists
to rethink the core compositions of neutron stars, ruling out many models for
the nuclear equations of state (EoS). We explore the hybrid stars that occur
when hadronic matter is treated in a relativistic mean-field approximation and
quark matter is modeled by three-flavor local and non-local Nambu Jona-Lasinio
(NJL) models with repulsive vector interactions. The NJL models typically yield
equations of state that feature a first order transition to quark matter.
Assuming that the quark-hadron surface tension is high enough to disfavour
mixed phases, and restricting to EoSes that allow stars to reach 2 solar
masses, we find that the appearance of the quark matter core either
destabilizes the star immediately (this is typical for non-local NJL models) or
leads to a very short hybrid star branch in the mass-radius relation (this is
typical for local NJL models). Using the Constant-Sound-Speed parametrization
we can see that the reason for the near-absence of hybrid stars is that the
transition pressure is fairly high and the transition is strongly first order.
