Reply to Comment on "Pulsar velocities and neutrino oscillations"

TL;DR

This paper discusses different approximation methods for calculating neutrino-driven pulsar velocities, comparing their predictions for magnetic fields inside neutron stars and emphasizing the uncertainties involved.

Contribution

It clarifies the impact of different approximation assumptions on neutrino oscillation models for pulsar velocities, highlighting their reasonable agreement.

Findings

Different approximation methods yield similar predictions within uncertainties.

The assumption of constant electron fraction (Ye) affects magnetic field estimates.

Uncertainties in magnetic field geometry influence model predictions.

Abstract

We have recently proposed an explanation for the birth velocities of pulsars based on neutrino oscillations (hep-ph/9606428). One of the quantities, dN/dT, was evaluated in the approximation of constant chemical potential for the electrons. An alternative approximation based on the assumption Ye=const, used by Qian (astro-ph/9705055), yields a somewhat higher prediction for the magnetic field inside a neutron star. If the same input parameters are used, the two approximations are in reasonable agreement, given the uncertainty in the geometry of the magnetic field and the simplified picture of neutrino emission that comes with the notion of a neutrinosphere.