Do triaxial supramassive compact stars exist?

Abstract

We study quasiequilibrium solutions of triaxially deformed rotating compact stars -a generalization of Jacobi ellipsoids under relativistic gravity and compressible equations of state (EOS). For relatively stiff (piecewise) polytropic EOSs, we find supramassive triaxial solutions whose masses exceed the maximum mass of the spherical solution, but are always lower than those of axisymmetric equilibriums. The difference in the maximum masses of triaxial and axisymmetric solutions depends sensitively on the EOS. If the difference turns out to be only about 10%, it will be strong evidence that the EOS of high density matter becomes substantially softer in the core of neutron stars. This finding opens a novel way to probe phase transitions of high density nuclear matter using detections of gravitational waves from new born neutron stars or magnetars under fallback accretion.

Gravitational wave content and stability of uniformly, rotating, triaxial neutron stars in general relativity

“…A higher value of Γ satisfies the necessary conditions for uniformly rotating triaxial solutions to exist, and this is the main reason behind such a choice. As discussed in [45] the softening of the core enables ra = 0 : Radial coordinate where the radial grids start. us to compute for the first time supramassive, triaxially deformed, uniform rotating stars, without increasing further the maximum polytropic exponent.…”

“…As in [45] we employ the same "benchmark" EoSs. The first one is a simple Γ = 4 polytrope, while the second is a piecewise-polytropic EoS with two pieces and a soft core, where {Γ 1 , Γ 2 } = {2.5, 4}.…”

“…According to the authors the reason could be either the nonlinear coupling of various oscillatory modes in the star, or an "elliptic flow" instability which manifests itself when the fluid flow is forced along elliptic streamlines. 1 The critical β for instability in Newtonian Maclaurin spheroids is βsec ∼ 0.14, but decreases in GR as the compaction increases [43] In a previous work [45] we computed for the first time triaxial supramassive neutron stars (uniformly rotating models with rest-mass higher than the maximum rest-mass of a nonrotating star, but lower than the maximum rest-mass when allowing for maximal uniform rotation), by using a piecewise polytropic EoS. In this work we perform the first evolutions of such stars and try to investigate their stability and gravitational wave content.…”

“…However, for the two-piece polytropic EoS, the maximum mass of the triaxial star relative to the spherical counterpart increases, even though the overall averaged stiffness of the EoS is softer. If the mass difference between the maximum axisymmetric and triaxial solutions is ∼ 10% or less, then that implies that the EoS of high density matter becomes substantially softer in the core of neutron stars [45].…”

“…In this work we perform the first evolutions of such stars and try to investigate their stability and gravitational wave content. Following [45] we carefully construct five such models: two normal ones (uniformly rotating but not supramassive) with compactions 0.1 and 0.25 2 adopting a stiff, Γ = 4, EoS, and three supramassive models with compactions 0.23, 0.24, 0.26 adopting a two-piece polytrope that has a soft core. Although these EoSs are rather extreme, our goal is to prove a matter of principle rather than focus on realistic EoSs.…”