  Detection of continuous gravitational waves from rapidly-spinning neutron
stars opens up the possibility of examining their internal physics. We develop
a framework that leverages a future continuous gravitational wave detection to
infer a neutron star's moment of inertia, equatorial ellipticity, and the
component of the magnetic dipole moment perpendicular to its rotation axis. We
assume that the neutron star loses rotational kinetic energy through both
gravitational wave and electromagnetic radiation, and that the distance to the
neutron star can be measured, but do not assume electromagnetic pulsations are
observable or a particular neutron star equation of state. We use the Fisher
information matrix and Monte Carlo simulations to estimate errors in the
inferred parameters, assuming a population of gravitational-wave-emitting
neutron stars consistent with the typical parameter domains of continuous
gravitational wave searches. After an observation time of one year, the
inferred errors for many neutron stars are limited chiefly by the error in the
distance to the star. The techniques developed here will be useful if
continuous gravitational waves are detected from a radio, X-ray, or gamma-ray
pulsar, or else from a compact object with known distance, such as a supernova
remnant.
