Generic conditions for stable hybrid stars

Mark G Alford,Madappa Prakash,Sophia Han

doi:10.1103/physrevd.88.083013

Mark G Alford, Madappa Prakash + Show 1 more

Open Access

https://doi.org/10.1103/physrevd.88.083013

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Abstract

We study the mass-radius curve of hybrid stars, assuming a single first-order phase transition between nuclear and quark matter, with a sharp interface between the quark matter core and nuclear matter mantle. We use a generic parameterization of the quark matter equation of state, which has a constant, i.e. density-independent, speed of sound ("CSS"). We argue that this parameterization provides a framework for comparison and empirical testing of models of quark matter. We obtain the phase diagram of possible forms of the hybrid star mass-radius relation, where the control parameters are the transition pressure, energy density discontinuity, and the quark matter speed of sound. We find that this diagram is sensitive to the quark matter parameters but fairly insensitive to details of the nuclear matter equation of state. We calculate the maximum hybrid star mass as a function of the parameters of the quark matter EoS, and find that there are reasonable values of those parameters that give rise to hybrid stars with mass above $2\,M_\odot$.

Highlights

We parametrize the dense matter equation of state in terms of three parameters: the pressure ptrans of the transition from nuclear matter to quark matter, the discontinuity in energy density Δε at the transition, and the speed of sound cQM in the CSS parameterization of quark matter[1]
We assume that there is a first-order phase transition between nuclear and quark matter, and that the surface tension of the interface is high enough to ensure that the transition occurs at a sharp interface (Maxwell construction) not via a mixed phase (Gibbs construction)
This is a possible scenario, given the uncertainties in the value of the surface tension. (For analysis of generic equations of state that continuously interpolate between the phases to model mixing or percolation, see Refs. [2, 3].) This “CSS” parameterization can be viewed as the lowest-order terms of a Taylor expansion of the quark matter EoS about the transition pressure, ε(p) =

Summary

Introduction

We parametrize the dense matter equation of state in terms of three parameters: the pressure ptrans of the transition from nuclear matter to quark matter, the discontinuity in energy density Δε at the transition, and the speed of sound cQM in the CSS parameterization of quark matter[1]. We assume that there is a first-order phase transition between nuclear and quark matter, and that the surface tension of the interface is high enough to ensure that the transition occurs at a sharp interface (Maxwell construction) not via a mixed phase (Gibbs construction). This is a possible scenario, given the uncertainties in the value of the surface tension. HLPS is a softer equation of state, with a lower value of L and lower pressure at a given energy density (up to p ≈ 3 × 109 MeV4, n ≈ 5.5 n0 where its speed of sound rises above 1 and becomes unphysical). It yields neutron stars that are larger, and can reach a higher maximum mass

Criterion for stable hybrid stars “Absent”

Phase diagram at fixed cQM

Varying cQM and the nuclear EoS

Physical understanding of the phase diagram

Observability of hybrid branches

Maximum mass of hybrid stars