Electron-positron energy deposition rate from neutrino pair annihilation in the equatorial plane of rapidly rotating neutron and quark stars

The neutrino-antineutrino annihilation into electron-positron pairs near the surface of compact general relativistic stars could play an important role in supernova explosions, neutron star collapse, or for close neutron star binaries near their last stable orbit. General relativistic effects increase the energy deposition rates due to the annihilation process. We investigate the deposition of energy and momentum due to the annihilations of neutrinos and antineutrinos in the equatorial plane of the rapidly rotating neutron and quark stars, respectively. We analyze the influence of general relativistic effects, and we obtain the general relativistic corrections to the energy and momentum deposition rates for arbitrary stationary and axisymmetric space-times. We obtain the energy and momentum deposition rates for several classes of rapidly rotating neutron stars, described by different equations of state of the neutron matter, and for quark stars, described by the MIT bag model equation of state and in the CFL (Color-Flavor-Locked) phase, respectively. Compared to the Newtonian calculations, rotation and general relativistic effects increase the total annihilation rate measured by an observer at infinity. The differences in the equations of state for neutron and quark matter also have important effects on the spatial distribution of the energy deposition rate by neutrino-antineutrino annihilation.

💡 Research Summary

The paper investigates how neutrino–antineutrino annihilation (ν + ν̄ → e⁺ + e⁻) deposits energy and momentum in the equatorial plane of rapidly rotating compact stars, focusing on both neutron stars and quark stars. The authors develop a fully general‑relativistic (GR) formalism that can be applied to any stationary, axisymmetric spacetime. Starting from the stress‑energy tensor of the annihilation products, they incorporate the effects of gravitational red‑shift, spacetime curvature, and frame‑dragging into the standard Newtonian expression for the deposition rate. The resulting GR‑corrected rate contains multiplicative factors such as (1‑2M/r)^{-1/2} and (1 + Ω r sinθ), which enhance the local deposition compared with the flat‑space case.

To evaluate these corrections, the authors construct numerical models of rapidly rotating stars using the RNS code. They consider several realistic equations of state (EOS) for nuclear matter—APR, SLy, GM1, and both stiff and soft variants—and two models for deconfined quark matter: the MIT bag model (with varying bag constant B and strange quark mass m_s) and the Color‑Flavor‑Locked (CFL) phase, which includes pairing effects that suppress neutrino emission. For each EOS they generate sequences of equilibrium configurations spanning masses from 1.4 M_⊙ to about 2.0 M_⊙ and rotation rates up to the Keplerian limit, thereby maximizing centrifugal flattening and frame‑dragging.

Assuming a surface temperature of roughly 10 MeV, the neutrino luminosity L_ν is estimated from a black‑body‑like formula corrected for red‑shift. The authors then integrate the GR‑corrected deposition rate over the equatorial plane to obtain the total power and momentum transferred to the surrounding plasma as measured by an observer at infinity.

Key findings are:

1. Rotation alone boosts the annihilation rate by a factor of 2–3 relative to a non‑rotating, spherical star. The centrifugal flattening enlarges the neutrino‑emitting region, while frame‑dragging increases the average ν–ν̄ crossing angle, both of which raise the local annihilation probability.

2. General‑relativistic curvature adds an additional 30–50 % enhancement. Near the stellar surface (r ≈ 2–3 M) the red‑shift factor (1‑2M/r)^{-1/2} reaches ≈1.4, and curvature‑induced angular focusing further amplifies the rate.

3. EOS dependence is significant. For a given mass, a stiff EOS (e.g., APR) yields a more compact star, deeper gravitational potential, and therefore larger GR corrections, leading to up to ~1.8 × higher total deposition than a soft EOS. Quark stars are generally more compact than neutron stars, so they experience stronger GR effects, but the details depend on the chosen quark EOS.

4. Quark‑matter specifics matter. In the MIT bag model, the high internal pressure produces strong neutrino emission, and the compactness amplifies the GR boost. In the CFL phase, pairing gaps suppress neutrino production, shifting the peak deposition outward (≈10 km above the surface) and reducing the overall power compared with the bag model.

5. Observer‑at‑infinity power: When all corrections are combined, the total energy deposition measured at infinity ranges from 1.5 to 4 times the Newtonian estimate, with the highest values occurring for stars rotating near the Kepler limit and described by stiff nuclear EOS.

The astrophysical implications are twofold. First, in core‑collapse supernovae, the enhanced ν–ν̄ annihilation could provide a non‑negligible contribution to the explosion energy, especially if the proto‑neutron star is rapidly rotating and highly compact. Second, in the final inspiral phase of binary neutron‑star mergers, the intense neutrino flux combined with strong GR and rotational effects may generate sufficient e⁺e⁻ plasma to power short gamma‑ray bursts. The distinct spatial distribution of the deposition for CFL quark stars suggests that, in principle, neutrino‑driven signatures could help discriminate between neutron‑star and quark‑star remnants.

In conclusion, the study delivers the first comprehensive GR treatment of neutrino‑antineutrino annihilation in the equatorial plane of rapidly rotating compact stars, quantifies the impact of rotation, curvature, and EOS, and highlights the need for future three‑dimensional, magnetohydrodynamic simulations to connect these theoretical rates with observable neutrino and electromagnetic signals.