Research On The Non-Radial Oscillations Of Compact Stars

In the first part, we review the researches on the structures and properties of neutron stars,as well as the non-radial oscillation, such as the f-mode of the neutron stars. Then in thefollowing two main parts, the f-mode frequencies and damping times in neutron stars andquark stars are calculated and discussed.In detail, by using the general relativity spherically symmetric ideal hydrostaticequilibrium equation (TOV equation) and employing a reasonable constraint range of thesymmetry energy slope around the saturation nuclear density, the mass-radius relations andthe frequencies and damping times of the f-mode oscillations are calculated and thecorresponding constraint on the frequencies and damping times of the f-mode oscillations arealso obtained. It is shown that a larger symmetry energy slope corresponds to a smalleroscillation frequency and a longer damping time. Similar to Newton’s theory, we also showthat the frequencies of f-modes in general relativity also exist a universal property, that is, thefrequency is proportional to the square root with the average density, which is independent onthe equation of state of the dense matters. In addition, we also obtain a reasonable fitting forthe relation between the damping time and the compactness (M R).On the other hand, as the Non-Newtonian gravity was proposed in order to make the softequation of state to support the observed massive pulsar, which equivalently to provide anadditional repulsive force, similar to the role of dark energy in physics. Here by introducingthe non-Newtonian gravity in quark stars, where the equation of state of the quark star mattersis described by the MIT bag models, we also calculate mass-radius relation and thefrequencies and damping times of the f-mode oscillations. It is found that for a higher bagparameter, such as117MeVfm-3, to support the observations of the massive pulsar, theNon-Newtonian gravity should be introduced. Moreover, our results show that, comparingwith the traditional neutron star model, the quark star has a relative higher frequency of thef-mode oscillation for a fixed stellar mass.