Binary system of a neutron star with a black hole

[Stella.Physics]

I am reading about mergers of a neutron star with a black hole and the association with GRB. While talking about the accretion disk, the paper I am reading says about the last stable circular orbit.
Firstly I thought it was where the Roche limit lies, where mass transfer or matter ejection from the neutron star begins, but I think it must be something else.
I would appreciate some enlightenment :)

 

[PAllen]

Close to a BH, the potential is such that tiny perturbations of even a circular orbit would lead to ever more wild motion. The boundary where this starts to happen defines the innermost stable circular orbit. Here are a few references in increasing level detail:

https://en.wikipedia.org/wiki/Innermost_stable_circular_orbit
http://eagle.phys.utk.edu/guidry/astro616/lectures/lecture_ch18.pdf (see 18.1.6, page 790)
http://arxiv.org/abs/1503.07060

 

[Stella.Physics]

Close to a BH, the potential is such that tiny perturbations of even a circular orbit would lead to ever more wild motion. The boundary where this starts to happen defines the innermost stable circular orbit. Here are a few references in increasing level detail:

https://en.wikipedia.org/wiki/Innermost_stable_circular_orbit
http://eagle.phys.utk.edu/guidry/astro616/lectures/lecture_ch18.pdf (see 18.1.6, page 790)
http://arxiv.org/abs/1503.07060

Quite helpful references. Thanks!