Gravitational-wave spin-down and stalling lower limits on the electrical resistivity of the accreted mountain in a millisecond pulsar

TL;DR

This paper derives lower limits on the electrical resistivity of accreted mountains in millisecond pulsars using gravitational-wave data, challenging theoretical models and promising future constraints from advanced detectors.

Contribution

It introduces new resistivity limits based on gravitational-wave observations, linking astrophysical data with theoretical resistivity calculations in neutron star crusts.

Findings

BRMSP spin-down limits approach theoretical electron-impurity resistivity at high temperatures.

AMSP stalling limits are below electron-phonon resistivity at temperatures above 10^8 K.

Next-generation detectors will further constrain resistivity, rivaling electromagnetic methods.

Abstract

The electrical resistivity of the accreted mountain in a millisecond pulsar is limited by the observed spin-down rate of binary radio millisecond pulsars (BRMSPs) and the spins and X-ray fluxes of accreting millisecond pulsars (AMSPs). We find $\eta \ge 10^{-28}\,\mathrm{s}\, (\tau_\mathrm{SD}/1\,\mathrm{Gyr})^{-0.8}$ (where $\tau_\mathrm{SD}$ is the spin-down age) for BRMSPs and $\eta \ge 10^{-25}\,\mathrm{s}\,(\dot{M}_\mathrm{a}/\dot{M}_\mathrm{E})^{0.6}$ (where $\dot{M}_\mathrm{a}$ and $\dot{M}_\mathrm{E}$ are the actual and Eddington accretion rates) for AMSPs. These limits are inferred assuming that the mountain attains a steady state, where matter diffuses resistively across magnetic flux surfaces but is replenished at an equal rate by infalling material. The mountain then relaxes further resistively after accretion ceases. The BRMSP spin-down limit approaches the theoretical electron-impurity resistivity at temperatures $\ga 10^5$ K for an impurity concentration of $\sim 0.1$, while the AMSP stalling limit falls two orders of magnitude below the theoretical electron-phonon resistivity for temperatures above $10^8$ K. Hence BRMSP observations are already challenging theoretical resistivity calculations in a useful way. Next-generation gravitational-wave interferometers will constrain $\eta$ at a level that will be competitive with electromagnetic observations.