Gravitational waves from slow combustion of a neutron star to quark star

Shailendra Singh, Ritam Mallick, R Prasad

Published 2020-03-02Version 1

Fluctuation at the neutron star center gives rise to a small deconfined quark core very close to the star center. The density discontinuity at the quark-hadron boundary initiates a shock wave, which propagates outwards of the star. The shock is strong enough to combust nuclear matter to 2-flavor quark matter in the star. The 2-flavor quark matter is not stable and there is an excess of down quarks. The 2-flavor matter settles to a stable 3-flavor matter in the weakly interacting time-scale. In this paper particularly study the conversion of 2-flavor matter to 3-flavor matter is carried out. We set up a differential equation for the conversion of the excess of down quarks to strange quarks involving weak reaction and diffusion of quarks. Calculating the reaction rate we solve the differential equation to find the velocity of the conversion front. The conversion velocity is about $0.002$ times of the speed of light and the time taken for the conversion is about $1.96$ millisecond. Once the front velocity is known we find the change in density profile of the star. As the conversion front moves out of the star the density profile changes bringing about a change in the quadrupole moment of the star. The change in the quadrupole moment is reflected in the GW amplitude which is of the order of $10^{-24}-10^{-23}$. The power spectrum has a peak frequencies of around $10-20$ kHz. Such amplitude and peak frequency is a unique signature of shock-induced first-order phase transition.