# Neutron star dynamics under time dependent external torques

## TL;DR

This paper derives a general solution for neutron star dynamics under arbitrary time-dependent external torques, extending previous models to include nonlinear internal torques, enabling analysis of various neutron star systems with observed variability.

## Contribution

It provides the first comprehensive solution for two-component neutron star models with arbitrary external torques, including nonlinear internal effects like vortex creep.

## Key findings

- Solution applicable to radio pulsars, magnetars, and binary neutron stars.
- Allows extraction of external torque profiles from observed spin data.
- Extends modeling capabilities to variable and noisy spin-down/up rates.

## Abstract

The two component model describes neutron star dynamics incorporating the response of the superfluid interior. Conventional solutions and applications involve constant external torques, as appropriate for radio pulsars on dynamical timescales. We present the general solution of two component dynamics under arbitrary time dependent external torques, with internal torques that are linear in the rotation rates, or with the extremely non-linear internal torques due to vortex creep. The two-component model incorporating the response of linear or nonlinear internal torques can now be applied not only to radio pulsars but also to magnetars and to neutron stars in binary systems, with strong observed variability and noise in the spin-down or spin-up rates. Our results allow the extraction of the time dependent external torques from the observed spin-down (or spin-up) time series, $\dot{\Omega}(t)$. Applications are discussed.