The innermost stable cicular orbit (ISCO) of an accretion disc orbiting a
neutron star (NS) is often assumed a unique prediction of general relativity.
However, it has been argued that ISCO also appears around highly elliptic
bodies described by Newtonian theory. In this sense, the behaviour of an ISCO
around a rotating oblate neutron star is formed by the interplay between
relativistic and Newtonian effects. Here we briefly explore the consequences of
this interplay using a straightforward analytic approach as well as numerical
models that involve modern NS equations of state. We examine the ratio K
between the ISCO radius and the radius of the neutron star. We find that, with
growing NS spin, the ratio K first decreases, but then starts to increase. This
non-monotonic behaviour of K can give rise to a neutron star spin interval in
which ISCO appears for two very different ranges of NS mass. This may strongly
affect the distribution of neutron stars that have an ISCO (ISCO-NS). When
(all) neutron stars are distributed around a high mass M0, the ISCO-NS spin
distribution is roughly the same as the spin distribution corresponding to all
neutron stars. In contrast, if M0 is low, the ISCO-NS distribution can only
have a peak around a high value of spin. Finally, an intermediate value of M0
can imply an ISCO-NS distribution divided into two distinct groups of slow and
fast rotators. Our findings have immediate astrophysical applications. They can
be used for example to distinguish between different models of high-frequency
quasiperiodic oscillations observed in low-mass NS X-ray binaries.Comment: 4 pages, 2 figures, accepted by A&A Letter
