*Introduction to Hypermassive Maximally
Rotating Neutron Stars*

##
**Equilibrium Sequences**

This graph shows the rest mass of an equilibrium star as a
function of the maximum mass-energy density. All stars are supported by a polytropic
equation of state with polytropic index n=1. The bottom curve shows the mass-energy relation for nonrotating spherical neutron stars obeying the TOV equations (dashed line). The top curve shows the mass-density relation for stars rotating uniformly at the mass-shedding limit (solid line). Units on the left and bottom axes are nondimensional; units on the right are chosen so that the maximum nonrotating mass is 2 M.

##
** Differentially Rotating Mass-Shedding Sequences**

The uniformly rotating case only allows a modest increase in the maximum mass over the non-rotating case. If instead, the neutron stars are rotating
differentially, then the maximum allowed mass can grow significantly with increasing differential rotation.

denotes the angular velocity on the rotation axis. The parameter A measures the degree of differential rotation. The quantity (1/A) is varied from 0 (uniform rotation) to 1 (high differential rotation). In the following cases, the curves were numerically determined.

Note as the star's rotation becomes more differential, the maximum allowed mass increases.

The line represents the division between stable (white) and bar-unstable (black)
hypermassive neutron star configurations. The division is at T/W ~ 0.24-0.25, where T is the rotational kinetic and W is the gravitational binding energy. Unstable stars form bars. This is the first calculation in general relativity of the formation of nonlinear bars in unstable stars.

*last updated 11 Sept 00 jjm *