Spin Equilibrium of Rapidly Spinning Neutron Stars via Transient Accretion

The concept of spin equilibrium due to an interaction between the stellar magnetosphere and a thin, Keplerian accretion disk, and a well-known formula of the corresponding equilibrium spin frequency, provide a key understanding of spin evolution and the distribution of rapidly spinning neutron stars, viz., millisecond pulsars. However, this concept and formula are for stable accretion, but the mass transfer to most accreting millisecond pulsars is transient and the accretion rate evolves by orders of magnitude during an outburst. In this short and focussed review, we briefly discuss a relatively new concept of the spin equilibrium condition and a new formula for the equilibrium spin frequency for transiently accreting millisecond pulsars. We also review a new method to estimate this equilibrium spin frequency for observed transiently accreting millisecond pulsars, even when a pulsar has not yet attained the spin equilibrium. These will be crucial to probe the spin evolution and distribution of millisecond pulsars, and should also be applicable to all magnetic stars transiently accreting via a thin, Keplerian accretion disk.