Constraints on the steady state r-mode amplitude in neutron star transients

Recent observations suggest that neutron stars in low-mass X-ray binaries r otate within a narrow range of spin frequencies clustered around 300 Hz. A proposed explanation for this remarkable fact is that gravitational radiati on from a steady state r-mode oscillation in the neutron star's core halts the spin-up due to accretion. For the neutron star transients, balancing th e time-averaged accretion torque with gravitational wave emission from stea dy state, constant amplitude r-mode pulsations implies a quiescent luminosi ty too bright to be consistent with observations (in particular of Aql X-1) . The viscous dissipation (roughly 10 MeV per accreted nucleon for a spin o f 300 Hz) from such an r-mode makes the core sufficiently hot to power a th ermal luminosity similar to 10(34) ergs s(-1) when accretion halts. This is the minimum quiescent luminosity that the neutron star must emit when visc ous heating in the core is balanced by radiative cooling from the surface, as is the case when the core of the star is superfluid. We therefore conclu de that either the accretion torque is much less than M(GMR)(1/2) or a stea dy state r-mode does not limit the spin rate of the neutron star transients . Future observations with Chandra and XMM promise to further constrain the amount of viscous dissipation in the neutron star core.