Appearance of innermost stable circular orbits of accretion discs around rotating neutron stars

Abstract

The innermost stable cicular orbit (ISCO) of an accretion disc that orbits a neutron star (NS) is often assumed to be 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 M 0 , the ISCO-NS spin distribution is roughly the same as the spin distribution corresponding to all neutron stars. In contrast, if M 0 is low, the ISCO-NS distribution can only have a peak around a high value of spin. Finally, an intermediate value of M 0 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.

Constraining Models of Twin-Peak Quasi-Periodic Oscillations With Realistic Neutron Star Equations of State

“…As emphasized by Urbanec et al (2010b), , Kluźniak & Rosińska (2013), Török et al (2014), Rosińska et al (2014) and Boshkayev et al (2015), Newtonian effects following from the influence of the quadrupole moment act on the orbital frequencies in a way opposite to that which is related to relativis- tic effects following from the increase of the angular momentum. The behaviour of the relations shown in the left panel of Figure 3 is determined by this interplay.…”

Rotating stars in relativity

“…2002 ) (see also Török et al. 2014 for a more recent study). Epicyclic frequencies for Maclaurin spheroids in Newtonian gravity have also been computed by Kluźniak and Rosińska ( 2013 ).…”

Test of the string loop oscillation model using kHz quasiperiodic oscillations in a neutron star binary

“…Since the XTE J1701-407 neutron star has to be very massive, we can conclude that the application of the Kerr geometry in the fitting procedure is justified, as for the near-maximum-mass neutron stars the exterior Hartle-Thorne geometry has to be close to the exterior Kerr geometry, giving close predictions of the physical phenomena occurring in their vicinity. Of course, we have to test in future, if application of the string loop model related to the Hartle-Thorne geometry with large values of q/a 2 > 3, when complex behaviour of the frequency relations is expected [79], could allow for fitting the data by neutron star models with intermediate or low mass, M < 2M .…”

“…We can see in Figure 3 of [82] that for the so called "canonical" neutron star mass M = 1.4M , there is q/a 2 → (3 − 7) for all of the considered realistic equations of state. In such cases, dependence of astrophysical phenomena on the neutron star parameters M, a, q can be very complex as demonstrated in [79] for the case of the position of the innermost stable circular geodesic (r ISCO ) in the Hartle-Thorne spacetime. The difference of the r ISCO in the Hartle-Thorne and Kerr spacetimes having identical parameters M and a reaches tens of percent and the dependence of r ISCO on the spacetime parameters differs even qualitatively for any value of spin a < 0.4 and for large values of the parameter q giving q/a 2 > 3.…”