Generic conditions for stable hybrid stars (1302.4732v3)

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 $2\,M_\odot$.

• The paper reveals that energy density discontinuity and transition pressure chiefly determine hybrid star stability during a first-order phase transition.
• It employs a constant speed-of-sound quark matter EoS, enabling unified comparisons of diverse quark matter models on the mass-radius relation.
• The study calculates maximum hybrid star masses above two solar masses, providing vital constraints for astrophysical observations and model validation.

Overview of Generic Conditions for Stable Hybrid Stars

The paper "Generic conditions for stable hybrid stars" by Mark G. Alford, Sophia Han, and Madappa Prakash investigates hybrid stars with a specific focus on the stability conditions that dictate the relationship between their mass and radius. The authors assume a single first-order phase transition between nuclear and quark matter and explore the effects of this transition on the structural properties of hybrid stars.

The paper employs a generic parameterization for the equation of state (EoS) for quark matter characterized by a constant speed of sound, which remains independent of the density. This approach facilitates the empirical testing of various quark matter models by allowing comparisons within a unified framework. The researchers outline a phase diagram that maps possible topologies of the mass-radius relation in hybrid stars, with key parameters including transition pressure, energy density discontinuity, and quark matter speed of sound.

Key Findings

1. Phase Transition and Stability: The paper reveals that the stability of hybrid stars is highly sensitive to the parameters of the quark matter EoS. The energy density discontinuity and the transition pressure are particularly influential in determining whether a stable hybrid star branch, connected to the neutron star branch, exists. The authors derive a critical condition for stability that hinges on these parameters.
2. Impact of Quark Matter Parameters: While the phase diagram shows substantial sensitivity to quark matter parameters, it is relatively insensitive to the specifics of the nuclear matter EoS. This suggests that the properties of quark matter are the principal determinants of hybrid star stability.
3. Observable Branches: The research concludes that the connected branch, where hybrid stars are stable and observable, can be very small or entirely absent based on the phase transition characteristics. A disconnected branch of stable hybrid stars may appear if the conditions are favorable, offering unique observational features through astrophysical measurements.
4. Maximum Mass Calculation: By calculating the maximum hybrid star mass in terms of quark matter EoS parameters, the paper finds plausible parameter values that predict hybrid stars with a mass above two solar masses, consistent with the highest-known neutron star masses. This calculation is crucial for assessing the viability of particular quark matter models against astrophysical data.
5. Implications and Parameterization: The CSS parameterization provides a generalized approach to characterizing the quark matter EoS, addressing a gap for scenarios where quark matter is incompletely understood or untested. This work lays the groundwork for further theoretical studies and observational missions seeking to constrain the properties of dense matter phases within neutron stars.

Implications and Future Directions

The findings have significant implications for both theoretical research and observational astrophysics. By establishing conditions under which stable hybrid star branches exist, the paper offers a predictive framework to evaluate different models of quark matter EoS. This is particularly relevant in the context of recent neutron star mass measurements that challenge traditional nuclear matter models.

Future research could involve expanding the CSS model to include density-dependent speeds of sound or other complexities suggested by quark matter theories. Additionally, observational advancements in neutron star radius and mass estimations could provide empirical constraints to further refine these models. Furthermore, exploring the role of rotation in hybrid stars with these parameterizations may extend the applicability of the theoretical groundwork laid in this paper.

In conclusion, the paper makes a substantial contribution to understanding hybrid stars and the phase transition dynamics between nuclear and quark matter. It provides a quantitative basis for future explorations of neutron star properties and the state of matter at extreme densities.