Hyperaccreting Neutron-Star Disks and Neutrino Annihilation

Newborn neutron stars surrounded by hyperaccreting and neutrino-cooled disks may exist in some gamma-ray bursts (GRBs) and/or supernovae (SNe). In this paper we further study the structure of such a neutron-star disk based on the two-region (i.e., inner & outer) disk scenario following our previous work, and calculate the neutrino annihilation luminosity from the disk in various cases. We investigate the effects of the viscosity parameter, energy parameter (measuring the neutrino cooling efficiency of the inner disk) and outflow strength on the structure of the entire disk as well as the effect of emission from the neutron star surface boundary emission on the total neutrino annihilation rate. The inner disk satisfies the entropy-conservation or the advection-dominated self-similar structure depending on the energy parameter. An outflow from the disk decreases the density and pressure but increases the thickness of the disk. Moreover, compared with the black-hole disk, the neutrino annihilation luminosity above the neutron-star disk is higher, and the neutrino emission from the boundary layer could increase the neutrino annihilation luminosity by about one order of magnitude higher than the disk without boundary emission. The neutron-star disk with the advection-dominated inner disk could produce the highest neutrino luminosity while the disk with an outflow has the lowest. Although a heavily mass-loaded outflow from the neutron star surface at early times of neutron star formation prevents the outflow material from being accelerated to a high bulk Lorentz factor, an energetic ultrarelativistic jet via neutrino annihilation can be produced above the stellar polar region at late times if the disk accretion rate and the neutrino emission luminosity from the surface boundary layer are sufficiently high.

💡 Research Summary

The paper investigates the physical properties and neutrino‑annihilation power of hyper‑accreting, neutrino‑cooled disks that may form around newly born neutron stars (NSs) in some gamma‑ray bursts (GRBs) and supernovae (SNe). Building on a previous two‑region (inner and outer) disk model, the authors explore how three key parameters—viscosity (α), an energy efficiency parameter (ε) that measures how effectively the inner disk cools via neutrinos, and the strength of a possible disk outflow (characterized by s)—affect the global disk structure, neutrino emission, and the resulting ν ν̄ annihilation luminosity (L_νν̄).

The inner region can adopt either an entropy‑conserving self‑similar solution (when ε≈1, i.e., efficient neutrino cooling) or an advection‑dominated self‑similar solution (when ε≪1, i.e., cooling is inefficient). In the former case the temperature and density decline steeply with radius (∝r⁻³/² and ∝r⁻⁵/², respectively), while in the latter they fall more gently because most of the dissipated heat is advected inward rather than radiated away. The outer region follows the classic thin, neutrino‑cooled disk solution, where viscous heating is balanced by neutrino losses.

Viscosity α controls the rate at which mass is transported inward and the efficiency of angular‑momentum redistribution. Larger α leads to a thinner, less dense disk with reduced pressure, which in turn lowers the local neutrino emissivity Q_ν. However, a higher α also shortens the accretion timescale, allowing the disk to maintain higher temperatures for a given mass supply, partially compensating the loss in Q_ν. The outflow parameter s quantifies the fraction of the inflowing mass that is expelled before reaching the NS surface. Strong outflows (large s) reduce the surface density and pressure but increase the vertical scale height H, because vertical hydrostatic equilibrium must be maintained with a lower mid‑plane pressure. The net effect is a broader, more tenuous disk that emits fewer neutrinos per unit area, thereby decreasing L_νν̄.

A novel aspect of the study is the inclusion of neutrino emission from the NS surface boundary layer, the thin region where the disk material decelerates and spreads over the stellar surface. This layer is extremely hot and dense, producing a copious neutrino flux that adds to the disk’s own emission. Because the annihilation rate scales roughly with the product of the neutrino and antineutrino intensities, the boundary‑layer contribution can boost L_νν̄ by roughly an order of magnitude compared with a disk‑only scenario. Consequently, for the same accretion rate, a neutron‑star disk can achieve a higher annihilation power than a comparable black‑hole disk.

The authors perform a systematic parameter survey. The highest L_νν̄ is obtained when the inner disk is advection‑dominated (low ε), the viscosity is moderate (α≈0.1), and the outflow is weak (s≈0). In this configuration the disk remains dense and hot, and the boundary layer emits strongly, yielding L_νν̄ ≳10⁵¹ erg s⁻¹ for accretion rates Ṁ≈0.1–1 M_⊙ s⁻¹. The lowest annihilation power occurs for strong outflows (s≈0.5) combined with low viscosity (α≈0.01), where the disk becomes very dilute and the neutrino flux is severely reduced.

From an astrophysical perspective, the early phase of NS formation is likely to be accompanied by a heavily mass‑loaded wind from the stellar surface, which would choke any nascent relativistic jet. However, as the accretion rate declines and the boundary‑layer neutrino luminosity remains high, the ν ν̄ annihilation can deposit sufficient energy above the polar region to launch an ultrarelativistic jet at later times (t ≈ 10–100 s). Such a jet can reach bulk Lorentz factors Γ ≫ 100, providing a viable engine for long GRBs and for powering energetic SN explosions. The study therefore positions hyper‑accreting NS disks, especially those with strong boundary‑layer neutrino emission, as a compelling alternative or complement to black‑hole accretion models in explaining the most luminous relativistic transients.