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 \geq 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 \geq 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 \gtrsim 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 .