# Relaxation by thermal conduction of a magnetically confined mountain on an accreting neutron star

## TL;DR

This study investigates how thermal conduction affects the structure and evolution of magnetically confined mountains on accreting neutron stars, revealing effects on magnetic burial, star shape, and hot spot formation.

## Contribution

It generalizes previous mountain models by including finite thermal conduction, showing its role in matter flow, magnetic field resurrection, and hot spot creation.

## Key findings

- Thermal conduction promotes matter flow towards the pole.
- It partially restores the buried magnetic field.
- Hot spots with temperatures over 10^8 K are generated near the pole.

## Abstract

A magnetically confined mountain on the surface of an accreting neutron star simultaneously reduces the global magnetic dipole moment through magnetic burial and generates a mass quadrupole moment, which emits gravitational radiation. Previous mountain models have been calculated for idealized isothermal and adiabatic equations of state. Here these models are generalised to include non-zero, finite thermal conduction. Grad-Shafranov equilibria for three representative, polytropic equations of state are evolved over many conduction time-scales with the magnetohydrodynamic solver PLUTO. It is shown that conduction facilitates the flow of matter towards the pole. Consequently the buried magnetic field is partially resurrected starting from an initially polytropic Grad-Shafranov equilibrium. The poleward mass current makes the star more prolate, marginally increasing its detectability as a gravitational wave source, though to an extent which is likely to be subordinate to other mountain physics. Thermal currents also generate filamentary hot spots $(\gtrsim 10^{8} \text{ K})$ in the mountain, especially near the pole where the heat flux is largest, with implications for type I X-ray bursts.