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Register a new userThe Lense-Thirring timing-accretion plane for ULXs
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Identifying the compact object in ultraluminous X-ray sources (ULXs) has to-date required detection of pulsations or a cyclotron resonance scattering feature (CRSF), indicating a magnetised neutron star. However, pulsations are observed to be transient and it is plausible that accretion onto the neutron star may have suppressed the surface magnetic field such that pulsations and CRSFs will be entirely absent. We may therefore lack direct means to identify neutron star systems whilst we presently lack an effective means by which to identify black hole ULXs. Here we present a possible method for separating the ULX population by assuming the X-ray, mHz quasi-periodic oscillations (QPOs) and day timescale periods/QPOs are associated with Lense-Thirring precession of the inflow and outflowing wind respectively. The precession timescales combined with the temperature of the soft X-ray component produce planes where the accretor mass enters as a free parameter. Depending on the properties of the wind, use of these planes may be robust to a range in the angular momentum (spin) and, for high accretion rates, essentially independent of the neutron stars surface dipole field strength. Our model also predicts the mHz QPO frequency and magnitude of the phase-lag imprinted due to propagation through the optically thick wind; in the case of NGC 5408 X-1 we subsequently infer a black hole mass and high spin. Finally, we note that observing secular QPO evolution over sufficient baselines may indicate a neutron star, as the precession responds to spin-up which is not readily observable for black hole primaries.
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The timing properties of X-ray binaries are still not understood, particularly the presence of quasi-periodic oscillations (QPOs) in their X-ray power spectra. The solid-body regime of Lense-Thirring precession is one prominent model invoked to explain the most common type of QPOs, Type C. However, solid-body precession requires a specific structure that has not been examined in light of constrained properties of accretion flows. We assume in this paper, as solid-body precession requires, a disk separated into two flows at a transition radius $r_t$: a cold outer flow and a hot inner flow (playing the role of the corona). We explore the physical structure of both flows using model-independent estimates of accretion parameters. We show that, in order to reproduce the observed X-ray spectra during luminous hard states, the hot flow must accrete at sonic to supersonic speeds, unreachable with typical viscous torques. As a result of this extreme accretion speed (or high $alpha$ parameter), no region of the disk during these states lies in the `wave-like regime required for solid-body precession. Furthermore, we expect the flow to align with the black hole spin axis via the Bardeen-Petterson effect inside a radius $r_{rm break}>r_t$. As a consequence, the hot inner flow cannot exhibit solid body precession -- as currently pictured in the literature -- during luminous hard states. Since Type C QPOs are prevalent in these states, we conclude that this mechanism is unlikely to be responsible for producing Type C QPOs around stellar mass black holes.
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 sub-magnetar 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.
An elementary pedagogical derivation of the Lense-Thirring precession is given based on the use of Hamilton vector. The Hamilton vector is an extra constant of motion of the Kepler/Coulomb problem related simply to the more popular Runge-Lenz vector. When a velocity-dependent Lorentz-like gravitomagnetic force is present, the Hamilton vector, as well as the canonical orbital momentum are no longer conserved and begin to precess. It is easy to calculate their precession rates, which are related to the Lense-Thirring precession of the orbit.
The geodesics of bound spherical orbits i.e. of orbits performing Lense-Thirring precession, are obtained in the case of the $Lambda$-term within gravito-electromagnetic formalism. It is shown that the presence of the $Lambda$-term in the equations of gravity leads to both relativistic and non-relativistic corrections in the equations of motion. The contribution of the $Lambda$-term in the Lense-Thirring precession is interpreted as an additional relativistic correction and the gravito-gyromagnetic ratio is defined.
The orbital Lense-Thirring precession is considered in the context of constraints for weak-field General Relativity involving the cosmological constant $Lambda$. It is shown that according to the current accuracy of satellite measurements the obtained error limits for $Lambda$ is self-consistent with cosmological observations. The corrections of $Lambda$ term are derived for the strong field Lense-Thirring precession i.e. the frame dragging effect and for the nutation. As a result, in the context of recently proposed $Lambda$-gravity we obtain constraints for $Lambda$ in both relativistic and weak-field limits. Namely, for the latter we analyze several Keplerian systems at different scales. We find that the obtained constraints for the modified gravity corrections are several orders of magnitude tighter than those available for such effects as gravitational redshift, gravitational time delay and geodetic precession in Solar System.
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