Axion effects on the non-radial oscillations of neutron stars

The effects of axions on quark matter equation of state (EOS) is studied within the three flavor Nambu--Jona-Lasinio model and its effects on on the non-radial oscillations of neutron stars is investigated. Using such an EOS for quark matter with axions and a EOS for hadronic matter within the relativistic mean field (RMF) theory, we discuss the hadron-quark phase transition (HQPT) using the Gibbs construction. The EOS so obtained is used to investigate the structure of hybrid neutron star (NS)s. It is found that the presence of axions in the core of compact stars stabilizes hybrid NSs in agreement with modern astrophysical constraints. It is further observed that the quadrupolar fundamental modes ($f$-modes) for such hybrid NSs get substantial enhancements both due to a larger quark core in the presence of axions and from the hyperons as compared to a canonical nucleonic neutron stars.