CP violation in cold dense quark matter and axion effects on the non-radial oscillations of neutron stars

Abstract Charge-conjugation and parity violation in strong interaction for cold dense quark matter is studied with axions of quantum chromodynamics within the three flavor Nambu-Jona-Lasinio model that includes the coupling of axions to quarks. Using the equation of state for quark matter with axions and a hadronic matter equation of state in the ambit of a relativistic mean field theory in quantum hadrodynamics, we discuss the hadron-quark phase transition. We use Gibbs construct for the same satisfying the constraints of beta equilibrium and charge neutrality as appropriate for the neutron star matter. The equation of state obtained is used to investigate the structure of hybrid stars. Inclusion of hyperons softens the equation of state. The hadron-quark phase transition softens it further. It is seen that with the presence of axions, it is possible to have the stable hybrid stars having an inner core of quark matter, both in pure quark matter phase as well as in a mixed phase with hyperonic matter along with an outer core of hyperonic matter. Such a hybrid star is in agreement with modern astrophysical constraints. We also discuss the properties of non-radial oscillations of such hybrid stars. It is observed that the frequencies of quadrupolar fundamental modes ( f modes) for such hybrid stars get substantial increase both due to a larger quark core in the presence of axions and from the hyperons as compared to a canonical nucleonic neutron star.