2010ApJ...717..404V

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 η≥10^-28 s  (τ_SD/1 Gyr)^-0.8 (where τ_SD is the spin-down age) for BRMSPs and η≥10^-25 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 ≳10⁵ K for an impurity concentration of ∼0.1, while the AMSP stalling limit falls 2 orders of magnitude below the theoretical electron-phonon resistivity for temperatures above 10⁸ K. Hence, BRMSP observations are already challenging theoretical resistivity calculations in a useful way. Next-generation gravitational-wave interferometers will constrain η at a level that will be competitive with electromagnetic observations.