Lense-Thirring precession in ULXs as a possible means to constrain the neutron star equation of state

Abstract

The presence of neutron stars in at least three ultraluminous X-ray sources is now firmly established and offers an unambiguous view of super-critical accretion. All three systems show long-timescale periods (60-80 days) in the X-rays and/or optical, two of which are known to be super-orbital in nature. Should the flow be classically super critical, i.e. the Eddington limit is reached locally in the disc (implying surface dipole fields that are submagnetar in strength), then the large scale-height flow can precess through the Lense-Thirring effect which could provide an explanation for the observed super-orbital periods. By connecting the details of the Lense-Thirring effect with the observed pulsar spin period, we are able to infer the moment-of-inertia and therefore equation-of-state of the neutron star without relying on the inclination of, or distance to the system. We apply our technique to the case of NGC 7793 P13 and demonstrate that stronger magnetic fields imply stiffer equations of state. We discuss the caveats and uncertainties, many of which can be addressed through forthcoming radiative magnetohydrodynamic (RMHD) simulations and their connection to observation.

A rapidly changing jet orientation in the stellar-mass black-hole system V404 Cygni

“…Predicted precession period. The expected Lense-Thirring precession period for an inner supercritical accretion disk rotating as a solid body is 15,22…”

M51 ULX-7: superorbital periodicity and constraints on the neutron star magnetic field

“…According to Middleton et al (2018b), the precession period depends on parameters such as the NS spin, the size of R sph and the extent of the outflows (R out ). Following Middleton et al (2018b) the precession timescale is:…”

“…Based on the observed properties of NGC300 ULX1 one can expect a timescale of precession of the order of a year, thus naturally explaining extended epochs of decreased flux due to obscuration from the outflows. We can estimate the timescale of precession for M51 ULX-7 by following Middleton et al (2018b) and invoking the same analytical relations used for NGC300 ULX1 (see eq. 13 & 14 of Vasilopoulos et al 2019).…”

NGC 300 ULX1: spin evolution, super-Eddington accretion, and outflows

“…The accretion disc around a black hole or a NS can precess due to the Lense-Thirring effect (Bardeen & Petterson 1975;Truemper et al 1986). Recently, it has been postulated that this mechanism can explain the super-orbital modulation in the observed flux of ULXPs (Middleton et al 2018). According to this scenario, the drop in the observed flux is due to changes in the geometrical configuration of the inner accretion disc and the outflow.…”

“…The observed X-ray flux (F X ) during these super-orbital phases can vary by a factor of 100, with no evidence of spectral changes expected from accretor-to-propeller transitions (Illarionov & Sunyaev 1975;Corbet 1996;Campana et al 2018). A possible scenario to explain the flux changes on super-orbital timescales is the obscuration from a precessing accretion disc (Fürst et al 2017;Middleton et al 2018). However, the latter has never been confirmed by any timing study of their pulse period evolution.…”