Gravitational wave signature from phase transition of a combusting neutron star to quark star

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 has enough energy to combust nuclear matter to 2-flavor quark matter in the star. The 2-flavor quark matter is not stable and settles to a stable 3-flavor matter in the weakly interacting timescale. In this paper, we study the conversion of 2-flavor matter to 3-flavor matter. We set up a differential equation to convert 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. As the conversion front moves out, the density profile changes, bringing about a change in the star's quadrupole moment and thereby emitting gravitational waves. We find that the GW signal depends strongly on the star temperature and mass. The GW amplitude of a colder star is well within present detector capability, but the frequency is slightly on the higher side. Relatively hotter stars are on the boundary of present detectors and easily detectable with future detectors, and their frequency is also within the present detectability range. In comparison, PT from galactic pulsars is easily detectable with present detectors.