Constraining properties of massive neutron star through R-mode

Taking the GW190814 event as a clue, r-mode of 2.5M${}_{\odot }$ supermassive neutron star along with 1.4M${}_{\odot }$ canonical neutron star is investigated by using RNS code in the framework of rotating neutron star. Our conclusion further confirms that for the secondary star of GW190814, there exists a possibility that it is a rapid rotating supermassive neutron star in r-mode stable state. For super fast rotating neutron star with fixed spin frequency, the lower limit of its mass M${}_{min}$ can be constrained by the critical spin frequency under r-mode. As the M${}_{min}$ is EOS (equation of state) dependent, if the mass of neutron star with very high spin frequency can be observed in the future, the EOS of super-dense nuclear matter can be constrained by comparing the M${}_{min}$ of different EOSs. At last, the effect of crust-core transition densities on r-modes of neutron stars is explored and discussed.