Differentially rotating strange star in general relativity

Rapidly and differentially rotating compact stars are believed to be formed in binary neutron star merger events, according to both numerical simulations and the multi-messenger observation of GW170817. The lifetime and evolution of such a differentially rotating star, is tightly related to the observations in the post-merger phase. Various studies on the maximum mass of differentially rotating neutron stars have been done in the past, most of which assume the so-called $j$-const law as the rotation profile inside the star and consider only neutron star equations of state. In this paper, we extend the studies to strange star models, as well as to a new rotation profile model. Significant differences are found between differentially rotating strange stars and neutron stars, with both differential rotation laws. A moderate differential rotation rate for neutron stars is found to be too large for strange stars, resulting in a rapid drop in the maximum mass as the differential rotation degree is increased further from $\hat{A}\sim2.0$, where $\hat{A}$ is a parameter characterizing the differential rotation rate for $j$-const law. As a result the maximum mass of a differentially rotating self-bound star drops below the uniformly rotating mass shedding limit for a reasonable degree of differential rotation. The continuous transition to the toroidal sequence is also found to happen at a much smaller differential rotation rate and angular momentum than for neutron stars. In spite of those differences, $\hat{A}$-insensitive relation between the maximum mass for a given angular momentum is still found to hold, even for the new differential rotation law. Astrophysical consequences of these differences and how to distinguish between strange star and neutron star models with future observations are also discussed.