  We found type I critical collapses of compact objects modeled by a polytropic
equation of state (EOS) with polytropic index $\Gamma=2$ without the
ultra-relativistic assumption. The object is formed in head-on collisions of
neutron stars. Further we showed that the critical collapse can occur due to a
change of the EOS, without fine tuning of initial data. This opens the
possibility that a neutron star like compact object, not just those formed in a
collision, may undergo a critical collapse in processes which slowly change the
EOS, such as cooling.
