Effect of magnetic field on neutrino annihilation efficiency in gamma-ray bursts

Neutrino annihilation process on a hyperaccreting disk is one of the leading models to explain the generation of relativistic jets of gamma-ray bursts (GRBs). However, there is still uncertainty regarding the NAE of neutron star-accretion disc (NS-disc) system because of complicated microphysics processes and effects of strong magnetic field. In this paper, we investigate the NAE by assuming that the prompt jet of GRB 070110 is driven by neutrino pair annihilation in the NS-disc system. Our calculation shows $\eta_{\nu\bar{\nu}}> 1.2 \times 10^{-3}$ under the estimated accretion rate $\dot{M}\simeq 0.04\rm M_{\odot}\cdot s^{-1}$. Independent of the detailed accretion disc models, our result shows that the magnetic field may play an important role in the neutrino annihilation process on the hyperaccreting magnetized accretion disc. Compared with the theoretical value of $\eta_{\rm \nu \bar{\nu}}$ of the nonmagnetized BH-disc system, the NAE should increase significantly in the case of the NS-disc system if the GRB is powered by magnetar-disc system.