  The question of whether quark matter exists in neutron stars is a long
standing one. Generally one finds that a first order phase transition from
baryons to quarks softens the equation of state so much that the star would
collapse into a black hole. We consider a crossover equation of state, similar
to the crossover that is found in lattice QCD studies at finite temperature and
zero or small baryon chemical potentials. We find that with reasonable
parameters it may be possible to support neutron stars up to about 2.2 solar
masses. In that case 1 to 10% of the pressure would be contributed by quark
matter in the central core of the highest mass stars.
