  The existence of quark matter inside the cores of heavy neutron stars is a
possibility which can be probed with modern astrophysical observations. We use
an (axial)vector meson extended quark-meson model to describe quark matter in
the core of neutron stars. We discover that an additional parameter constraint
is necessary in the quark model to ensure chiral restoration at high densities.
By investigating hybrid star sequences with various parameter sets we show that
low sigma meson masses are needed to fulfill the upper radius constraints, and
that the maximum mass of stable hybrid stars is only slightly dependent on the
parameters of the crossover-type phase transition. Using this observation and
results from recent astrophysical measurements a constraint of 2.6 < g_V < 4.3
is set for the constituent quark - vector meson coupling. The effect of a
nonzero bag constant is also investigated and we observe that its effect is
small for values adopted in previous works.
