Anisotropic neutrino effect on magnetar spin: constraint on inner toroidal field

Abstract

The ultrastrong magnetic field of magnetars modifies the neutrino cross-section due to the parity violation of the weak interaction and can induce asymmetric propagation of neutrinos. Such an anisotropic neutrino radiation transfers not only the linear momentum of a neutron star but also the angular momentum, if a strong toroidal field is embedded inside the stellar interior. As such, the hidden toroidal field implied by recent observations potentially affects the rotational spin evolution of new-born magnetars. We analytically solve the transport equation for neutrinos and evaluate the degree of anisotropy that causes the magnetar to spin-up or spin-down during the early neutrino cooling phase. Supposing that after the neutrino cooling phase the dominant process causing the magnetar spin-down is the canonical magnetic dipole radiation, we compare the solution with the observed present rotational periods of anomalous X-ray pulsars 1E 1841−045 and 1E 2259+586, whose poloidal (dipole) fields are ∼1015 and 1014 G, respectively. Combining with the supernova remnant age associated with these magnetars, the present evaluation implies a rough constraint of global (average) toroidal field strength at Bϕ ≲ 1015 G.