A new study has calculated the energy gained by a compact star, such as a neutron star, through the accretion of matter from the inner edge of a thin accretion disk. The researchers employed a controlled slow-rotation expansion based on the Hartle-Thorne metric, a model describing the gravitational field of rotating objects. This approach has yielded more precise expressions for the heating and spin-up of these stars, consistently incorporating rotational, relativistic, and nuclear effects.

The work reveals that, in non-magnetized neutron stars, leading-order rotational corrections to the metric, describing frame-dragging, are sizable. However, for magnetized neutron stars, where the accretion disk roughly extends to the co-rotation radius, even frame-dragging effects are minor. This suggests that the influence of rotation on accretion dynamics critically depends on the magnetic properties of the central star.

Based on general conservation laws, the team derived simple, equation-of-state-independent expressions for the spin-up and heating energy. These new estimates, which consistently include relevant rotational, relativistic, and nuclear effects, show that the results can strongly deviate from presently employed estimates in observed accreting millisecond sources. This implies that current interpretations of observations of these systems might require revision.

The research provides a more robust tool for understanding the evolution of compact stars accreting matter, which is crucial for the study of millisecond pulsars and other high-energy astrophysical phenomena. The improved precision of these calculations will allow for a better characterization of neutron star properties and the physical processes occurring in their extreme environments.