General-purpose equations of state for hadron-quark matter: first application to accretion-induced phase transitions in neutron stars

The gist: The authors generate a new set of general-purpose equations of state for hadron–quark matter with first-order phase transitions and perform general-relativistic radiation hydrodynamics simulations of neutron stars undergoing accretion-induced phase transitions, finding that these systems do not produce unbound ejecta but are accompanied by intense neutrino emission <ref:2610.30233#pg11>.

Hybrid Equation of State Construction

The hybrid equations of state are constructed based on the method described in Ref. [108], using separate hadronic and quark models and applying the Gibbs condition to realize the transition between the two phases <ref:2610.30233#pg4>. For the hadronic EoS, they choose the relativistic mean field model of Typel et al. (DD2) with density-dependent nuclear interactions <ref:2610.30233#pg5>. For the quark phase, they employ a model described in Ref. [108], which uses a relativistic mean field approach with two quark flavors and a density-dependent potential between the quarks <ref:2610.30233#pg6>. The potential is defined through the (iso)scalar and (iso)vector densities and is given by Equation (1), where ns, nv, and niv are the scalar, vector and isovector densities, respectively <ref:2610.30233#pg6>.

Phase Transition Surface Mapping

To find the phase transition surface within this three-dimensional space of chemical potentials, they apply the Gibbs condition involving thermal equilibrium T H = T Q, mechanical equilibrium p H = p Q, and chemical equilibrium µ H B,C = µ Q B,C for the baryon and charge chemical potentials simultaneously <ref:2610.30233#pg7>. The difficulty lies in parameterizing the EoS as a function of baryon number density and electron fraction by finding the line connecting the (nB, Ye) values in the two phases corresponding to a single transition point. This is done using Equation (10), which defines how extensive quantities like electron number density and baryon number density mix according to a mixing factor χ.

General Relativistic Hydrodynamics Simulations

General-relativistic radiation hydrodynamics simulations are performed using the BAM code, evolving spacetime through a Z4c formulation with constraint damping terms. Matter is evolved as an ideal fluid governed by general relativistic hydrodynamics equations in the Valencia formulation. Neutrino radiation transport is implemented through an energy-integrated (gray) M1 moment scheme. The simulation setup involves adding a small perturbation to a Tolman–Oppenheimer–Volkoff (TOV) solution by increasing the density of the NS uniformly by 0.4% without modifying the spacetime solution.

Simulation Results and Ejecta Analysis

The simulations were performed using EoSs BBKF 2.1, BBKF 2.3 and BBKF 2.5 with progressively weaker transition strengths. Out of the three simulations, only BBKF 2.1 formed a significant quark core because along the migration this model crosses the radially unstable branch (for which radial oscillations are amplified), reaching central densities beyond the upper transition density. The authors find that for all simulations, they find negligible amounts of unbound material, contrary to some previous studies.

Neutrino Emission and Compositional Equilibration

The inclusion of neutrino emission in the quark phase allows them to observe equilibration of quarks and a gas of trapped neutrinos, indicated by a small (within the sub percent level) fractional deviation of the fluid’s net electron fraction with respect to equilibrium. They note that matter in the simulation corresponding to BBKF 2.1 EoS is driven out of equilibrium due to the formation of a pure quark core, as an increased deviation develops around the onset time.

Conclusion on Accretion-Induced Transitions

The paper concludes that accretion-induced phase transitions are unlikely sources of observable electromagnetic transients because they do not produce unbound ejecta for the models considered. However, they find that transitions are accompanied by intense neutrino emission, with peak luminosities reaching ∼ 10 52 erg/s for the strongest transition considered. The use of temperature-dependent EoSs poses a major challenge for the numerical modeling of the migration of a hadronic NS to the hybrid branch because neutrino cooling does not operate on timescales small enough to counteract the rising thermal pressure.

How it works

The construction of hybrid equations of state is based on using separate hadronic and quark models and applying the Gibbs condition to realize the transition between the two phases <ref:2610.30233#pg5>. The hadronic EoS uses the relativistic mean field model of Typel et al. (DD2) with density-dependent nuclear interactions <ref:2610.30233#pg5>. The quark phase employs a model described in Ref. [108], which uses a relativistic mean field approach with two quark flavors and a density-dependent potential between the quarks <ref:2610.30233#pg6>.

Simulation Setup Details

The general-relativistic radiation hydrodynamics simulations use the BAM code, evolving spacetime through a Z4c formulation with constraint damping terms. The initial conditions are set by adding a small perturbation to a TOV solution by increasing the density of the NS uniformly by 0.4% without modifying the spacetime solution.

Neutrino Opacity Treatment

The authors adopt a more realistic description of interaction rates for nucleons provided by the full-kinematics approach, as analytic expressions for interaction rates are no longer available. They calculate neutrino opacities for the charged processes νe + d ↔ u + e− and ν¯e + u ↔ d + e+ according to Refs. [129, 130] using the current-current interaction Lagrangian. The spectral opacities κ(ϵν) are then obtained through a double integral over particle energies.

Key Findings on Phase Transition Strength

The five EoSs were calculated to conform with current astrophysical constraints, display a phase transition at approximately the same NS mass of ∼ 1.4 M⊙, and cover a broad range of phase transition strengths. BBKF 2.1 and 2.2 EoSs showcase twinstar branches, while BBKF 2.3 is a limiting case between EoSs with and without a twin-star branch.

Implications for Astrophysical Observables

The results indicate that transitions are accompanied by intense neutrino emission, with peak luminosities reaching ∼ 10 52 erg/s for the strongest transition considered. The authors suggest that the inclusion of neutrino-quark scattering would allow to better capture the thermalization of neutrinos, possibly contributing to diminishing the observed deviations. The use of temperature-dependent EoSs poses a major challenge for the numerical modeling of the migration of a hadronic NS to the hybrid branch because neutrino cooling does not operate on timescales small enough to counteract the rising thermal pressure.

How it works

The authors study the evolution of accreting NSs with hybrid EoSs right at the onset of the phase transition by performing general relativistic radiation hydrodynamics simulations using the BAM code. They extend previous studies by employing EoSs with different hadron–quark transition strengths and implementing neutrino opacities in the quark phase. The set of EoSs was purposefully created to allow future dynamical studies to investigate the effect of various phase transition strengths in a controlled manner, while keeping the hadronic EoS and the onset of phase transition unchanged.

Simulation Outcomes on Stability

For all our simulations, they find negligible amounts of unbound material instead. The formation of a pure quark core is observed as a non-oscillatory increase of ρc at ∼ 1.3 ms for BBKF 2.1.

Final Summary of Constraints

All five EoSs will be made publicly available through the CompOSE database and neutrino opacities will be shared through Zenodo <ref:2610.

1

The improved AI system can perform systematic exploration of the role of phase transition strength by using a new set of general-purpose EoSs and neutrino opacities that allow for controlled investigation. This enables the AI to map out how different transition strengths affect observables like neutrino emission, which can reach peak luminosities reaching 10 52 erg/s for the strongest transition considered.

2

The system can accurately predict whether accretion-induced phase transitions are unlikely sources of observable electromagnetic transients by running general-relativistic radiation hydrodynamics simulations of neutron stars undergoing accretion. This allows the AI to assess if these systems do not produce unbound ejecta for the models considered.

3

The AI can determine the compositional evolution of a quark core after a transition by calculating the fractional deviation of Ye with respect to equilibrium with a gas of trapped neutrinos using Eq. (23). This capability allows it to quantify how close the system evolves to fluid-radiation equilibrium, achieving accuracy to the sub-percent level.

4

The system can analyze dynamical responses in binary systems by simulating accretion perturbations, specifically testing whether the migration of initially hadronic stars (or stars in a mixed phase) to the hybrid branch can be captured. This helps determine if such accretion-induced transitions are a source of observable multi-messenger transients.

Strong first-order phase transitions in the cores of neutron stars (NSs) can have profound implications for astrophysical observables, however, their existence remains an open question. Since most NSs form in binary systems, they are expected to experience prolonged episodes of mass accretion that gradually increase their central density and can potentially trigger such a transition. This might, in turn, generate observable multi-messenger signals, as suggested by previous studies. Motivated by this prospect, we generate a new set of equations of state for hadron--quark matter with first-order phase transitions of various strengths, including neutrino absorption opacities in the quark phase as well. We then perform general-relativistic radiation hydrodynamics simulations of NSs undergoing accretion-induced phase transitions. In contrast to previous findings, our results indicate that these systems do not produce unbound ejecta for the models considered, making accretion-induced phase transitions unlikely sources of observable electromagnetic transients. However, we find that transitions are accompanied by intense neutrino emission, with peak luminosities reaching about10 52 erg/s for the strongest transition considered. To facilitate future numerical studies, we make the family of equations of state and neutrino opacities used in this work publicly available, enabling the systematic exploration of the role of the phase transition strength.