We develop a Monte-Carlo code to compute the Compton scattered X-ray flux arising from a hot inner flow which undergoes Lense-Thirring precession. The hot flow intercepts seed photons from an outer truncated thin disk. A fraction of the Comptonized photons will illuminate back the disk and the reflected/reprocessed photons will contribute to the observed spectrum. The total spectrum, including disk thermal emission, hot flow Comptonization, and disk reflection, is modelled within the framework of general relativity, taking light-bending and gravitational redshift into account. The simulations are performed in the context of the Lense-Thirring precession model for the low-frequency quasi-periodic oscillations, so the inner flow is assumed to precess, leading to periodic modulation of the emitted radiation.
In this work, we concentrate on the energy-dependent X-ray variability of the model and, in particular, on the evolution of the variability during the spectral transition from hard to soft state, which is implemented by the decrease of the truncation radius of the outer disk towards Innermost Stable Circular Orbit (ISCO). In the hard state where the Comptonizing flow is geometrically thick, the Comptonization is weakly variable with the fractional variability amplitude of $\leq$10\%; in the soft state where the Comptonizing flow is cooled down and thus becomes geometrically thin, and the fractional variability of the Comptonization is highly variable, increasing with photon energy. The fractional variability of the reflection increases with energy, and the reflection emission for low spin is counterintuitively more variable than the one for high spin.
We propose a polynomial approximation of the global Lense-Thirring rigid precession frequency to study low frequency quasi-periodic oscillations around spinning black holes. This high-performing approximation allows to determine the expected frequencies of a precessing thick accretion disc with fixed inner radius and variable outer radius around a black hole with given mass and spin. We discuss the accuracy and the applicability regions of our polynomial approximation, showing that the computational times are reduced by a factor of $\approx70$ in the range of minutes.
Relativistic Lense-Thirring precession of a tilted inner accretion disk around a compact object has been proposed as a mechanism for low-frequency (~0.01-70 Hz) quasi-periodic oscillations (QPOs) in the light curves of X-ray binaries. A substantial misalignment angle (~15-20 degrees) between the inner-disk rotation axis and the compact-object spin axis is required for the effects of this precession to produce observable modulations in the X-ray light curve. A consequence of this misalignment is that in high-inclination X-ray binaries the precessing inner disk will quasi-periodically intercept …
Very recent analysis of the radio spectral index and high energy observations have shown that the two-peak accretion/ejection microquasar model applies for LSI+61303. The fast variations of the position angle observed with MERLIN and confirmed by consecutive VLBA images must therefore be explained in the context of the microquasar scenario. We calculate what could be the precessional period for the accretion disk in LSI+61303 under tidal forces of the Be star (P_{tidal-forces}) or under the effect of frame dragging produced by the rotation of the compact object (P_{Lense-Thirring}). P_{tidal-f…
A tidal disruption event (TDE) occurs when a star wanders close enough to a black hole to be disrupted by its tidal force. The debris of a tidally disrupted star are expected to form an accretion disc around the supermassive black hole. The light curves of these events sometimes show a quasi-periodic modulation of the flux that can be associated with the precession of the accretion disc due to the Lense-Thirring ("frame-dragging") effect. Since the initial star orbit is in general inclined with respect to the black hole spin, this misalignment combined with the Lense-Thirring effect leads to a…
We model the energy dependence of a quasi periodic oscillation (QPOs) produced by Lense-Thirring precession of a hot inner flow. We use a fully 3-dimensional Monte-Carlo code to compute the Compton scattered flux produced by the hot inner flow intercepting seed photons from an outer truncated standard disc. The changing orientation of the precessing torus relative to the line of sight produces the observed modulation of the X-ray flux. We consider two scenarios of precession. First, we assume that the precession axis is perpendicular to the plane of the outer disc. In this scenario the relativ…
We study Lense-Thirring precession of inviscid and viscous misaligned $α-$discs around a black hole using a gravitomagnetic term in the momentum equation. For weak misalignments, $i \lesssim 10^{\circ}$, the discs behave like rigid bodies, undergoing the full suite of classical harmonic oscillator dynamics including, weak and critically damped motion (due to viscosity), precession (due to Lense-Thirring torque) and nutation (due to apsidal precession). For strong misalignments, $i \gtrsim 30^{\circ}$, we find sufficiently thin, $h/r \lesssim 0.05$ discs break, form a gap and the inner and oute…
An exact expression of Lense-Thirring precession rate is derived for non-extremal and extremal Plebański-Demiański spacetimes. This formula is used to find the exact Lense-Thirring precession rate in various axisymmetric spacetimes, like: Kerr, Kerr-Newman, Kerr-de Sitter etc. We also show, if the Kerr parameter vanishes in Plebański-Demiański(PD) spacetime, the Lense-Thirring precession does not vanish due to the existence of NUT charge. To derive the LT precession rate in extremal Plebański-Demiański we first derive the general extremal condition for PD spacetimes. This general result could …
Recently, repeating fast radio bursts (FRBs) with a period of $P_{\rm FRB}=16.35\pm0.18$ days from FRB 180916.J0158+65 had been reported. It still remains controversial how to give rise to such a periodicity of this FRB. In this Letter, based on an assumption of a young pulsar surrounding by a debris disk, we attempt to diagnose whether the Lense-Thirring precession of the disk on the emitter can produce the observed periodicity. Our calculations indicate that the Lense-Thirring effect of a tilted disk can result in a precession period of 16 days for a mass inflow rate of $0.5-1.5\times10^{18}…
An exact expression for the rate of dragging of inertial frames (Lense-Thirring (LT) precession) in a general stationary spacetime, is derived without invoking the weak field approximation. This expression, when used for the Kerr metric, leads to the LT precession frequency in the strong gravity regime appropriate to compact gravitating objects like rotating neutron stars and black holes. Numerical values of the precession rate are computed for a few known cases of pulsars (including a double-pulsar) and compared to the precession rates in the weaker gravity regimes of the earth and the sun.
Type-C QPOs in X-ray binaries have been often interpreted as a consequence of relativistic Lense-Thirring precession around a spinning black hole and they potentially offer a way to measure black hole spins and masses. The connection between relativistic precession and the resulting QPO has been made either in terms of a simplified model involving a single test particle producing the QPO, or in terms of a global model where a geometrically thick accretion flow precesses coherently as a rigid body. In this paper, we analyse similarities and differences between these two models, sometimes consid…
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 (play…
We consider the effects of black hole tilt on accretion disk alignment, studying three initial black hole tilts,6 degrees, 12 degrees and 24 degrees, with both magnetohydrodynamic and (inviscid) hydrodynamic evolution. In a number of ways, but not all, the dynamics are homologous in the sense that the alignment fronts resulting from different initial tilts are very similar when analyzed in terms of the fraction of the initial tilt angle. Even when the initial misalignment is 24 degrees, which, for the sound speed studied, is 4 vertical scale heights at the disk fiducial radius, the surface den…
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 ob…
The Double Pulsar system PSR J0737-3039A/B has proven to be an excellent laboratory for high precision tests of general relativity. With additional years of timing measurements and new telescopes like the Square Kilometre Array (SKA), the precision of these tests will increase and new effects like the Lense-Thirring precession of the orbit will become measurable. Here, we discuss the prospects of measuring the Lense-Thirring effect and thereby constraining the equations of state at supra-nuclear densities in neutron stars using the Double Pulsar.
It has long been recognised that quasi-periodic oscillations (QPOs) in the X-ray light curves of accreting black hole and neutron star binaries have the potential to be powerful diagnostics of strong field gravity. However, this potential cannot be fulfilled without a working theoretical model, which has remained elusive. Perhaps the most promising model associates the QPO with Lense-Thirring precession of the inner accretion flow, with the changes in viewing angle and Doppler boosting modulating the flux over the course of a precession cycle. Here, we consider the polarization signature of a …
Reprocessing of primary X-ray emission in the accretion disk of black hole X-ray binaries (BHXRBs) produces the reflection spectrum, with the characteristic Fe K$α$ fluorescence line. Strong low frequency quasi-periodic oscillations (QPOs) are observed from BHXRBs, and the dependence of QPO properties (e.g., phase-lag) on the inclination angle suggests that the observed QPO may be associated with a geometrical effect, e.g., the precession of the X-ray source due to frame-dragging near the spining black hole. Here, in the scenario of Lense-Thirring precession of the X-ray source, we use a Monte…
We make use of the absence of Lense-Thirring precession of the innermost megamaser clumps around black holes in order to place upper limits on the spin amplitude of seven black holes at the center of megamaser galaxies: NGC 4258, NGC 2273, UGC 3789, NGC 3393, NGC 5495, NGC 5765b, and UGC 6093. The constraints are derived by requiring that the associated precession time-scale be longer than the age of the megamaser clumps, in order to preserve the single-plane geometry of the megamasers.
Misalignment of the Lense-Thirring precession by an accretion torque
Indian Institute of Technology Indore（印度理工学院印多尔分校）；Northwestern University（西北大学）；Academy of Sciences（科学院）；Nicolaus Copernicus Astronomical Center（尼古拉·哥白尼天文中心）；College of Charleston（查尔斯顿学院）；Flatiron Institute（平研究所）
When a star is tidally disrupted by a supermassive black hole (SMBH), the streams of liberated gas form an accretion disk after their return to pericenter. We demonstrate that Lense-Thirring precession in the spacetime around a rotating SMBH can produce significant time evolution of the disk angular momentum vector, due to both the periodic precession of the disk and the nonperiodic, differential precession of the bound debris streams. Jet precession and periodic modulation of disk luminosity are possible consequences. The persistence of the jetted X-ray emission in the Swift J164449.3+573451 …
When matter orbits around a central mass obliquely with respect to the mass's spin axis, the Lense-Thirring effect causes it to precess at a rate declining sharply with radius. Ever since the work of Bardeen & Petterson (1975), it has been expected that when a fluid fills an orbiting disk, the orbital angular momentum at small radii should then align with the mass's spin. Nearly all previous work has studied this alignment under the assumption that a phenomenological "viscosity" isotropically degrades fluid shears in accretion disks, even though it is now understood that internal stress in fla…
Lense-Thirring precession of neutron-star accretion flows: Relativistic versus classical precession
Silesian University in Opava（奥帕瓦西里西亚大学）；Nicolaus Copernicus Astronomical Center of the Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）；Astronomical Institute of the Czech Academy of Sciences（捷克科学院天文研究所）
Exact Lense-Thirring (LT) precession in Kerr-Taub-NUT spacetime is reviewed. It is shown that the LT precession does not obey the general inverse cube law of distance at strong gravity regime in Kerr-Taub-NUT spacetime. Rather, it becomes maximum just near the horizon, falls sharply and becomes zero near the horizon. The precession rate increases again and after that it falls obeying the general inverse cube law of distance. This anomaly is maximum at the polar region of this spacetime and it vanishes after crossing a certain `critical' angle towards equator from pole. We highlight that this p…
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…
Radio pulsars in short-period eccentric binary orbits can be used to study both gravitational dynamics and binary evolution. The binary system containing PSR J1141$-$6545 includes a massive white dwarf (WD) companion that formed before the gravitationally bound young radio pulsar. We observe a temporal evolution of the orbital inclination of this pulsar that we infer is caused by a combination of a Newtonian quadrupole moment and Lense-Thirring precession of the orbit resulting from rapid rotation of the WD. Lense-Thirring precession, an effect of relativistic frame-dragging, is a prediction o…
We study the exact evolution of the orbital angular momentum of a massive particle in the gravitational field of a Kerr black hole. We show analytically that, for a wide class of orbits, the angular momentum's hodograph is always close to a circle. This applies to both bounded and unbounded orbits that do not end up in the black hole. Deviations from the circular shape do not exceed $\approx10\%$ and $\approx7\%$ for bounded and unbounded orbits, respectively. We also find that nutation provides an accurate approximation for those deviations, which fits the exact curve within $\sim 0.01\%$ for…
Recent observations of accreting black holes reveal the presence of quasi-periodic oscillations (QPO) in the optical power density spectra. The corresponding oscillation periods match those found in the X-rays, implying a common origin. Among the numerous suggested X-ray QPO mechanisms, some may also work in the optical. However, their relevance to the broadband -- optical through X-ray -- spectral properties have not been investigated. For the first time, we discuss the QPO mechanism in the context of the self-consistent spectral model. We propose that the QPOs are produced by Lense-Thirring …
Using only physical mechanisms, i.e., 3D MHD with no phenomenological viscosity, we have simulated the dynamics of a moderately thin accretion disk subject to torques whose radial scaling mimics those produced by lowest-order post-Newtonian gravitomagnetism. In this simulation, we have shown how, in the presence of MHD turbulence, a time-steady transition can be achieved between an inner disk region aligned with the equatorial plane of the central mass's spin and an outer region orbiting in a different plane. The position of the equilibrium orientation transition is determined by a balance bet…
We present a series of simulations in both pure hydrodynamics (HD) and magnetohydrodynamics (MHD) exploring the degree to which alignment of disks subjected to external precessional torques (e.g., as in the `Bardeen-Petterson' effect) is dependent upon the disk sound speed c_s. Across the range of sound speeds examined, we find that the influence of the sound speed can be encapsulated in a simple "lumped-parameter" model proposed by Sorathia et al. (2013a). In this model, alignment fronts propagate outward at a speed ~0.2 rOmega_precess(r), where Omega_precess is the local test-particle preces…
Accretion discs and black holes (BHs) have angular momenta that are generally misaligned with respect to each other, which can lead to warps in the discs and bends in any jets produced. We consider a disc that is misaligned at large radii and torqued by Lense-Thirring (LT) precession and a Blandford-Znajek (BZ) jet torque. We consider a variety of disc states that include radiatively inefficient thick discs, radiatively efficient thin discs, and super-Eddington accretion discs. The magnetic field strength of the BZ jet is chosen as either from standard equipartition arguments or from magnetica…
Black hole and neutron star X-ray binary systems routinely show quasi-periodic oscillations (QPOs) in their X-ray flux. Despite being strong, easily measurable signals, their physical origin has long remained elusive. However, recent observational and theoretical work has greatly improved our understanding. Here, we briefly review the basic phenomenology of the different varieties of QPO in both black hole and neutron star systems before focusing mainly on low frequency QPOs in black hole systems, for which much of the recent progress has been made. We describe the detailed statistical propert…
We comment on a recent study reporting evidence for the general relativistic Lense-Thirring secular precession of the inclination $I$ of the orbital plane to the plane of the sky of the tight binary system PSR J1141-6545 made of a white dwarf and an emitting radiopulsar of comparable masses. The quadrupole mass moment $Q_2^\mathrm{c}$ and the angular momentum ${\boldsymbol S}^\mathrm{c}$ of the white dwarf cause the detectable effects on $I$ with respect to the present-day accuracy in the pulsar's timing. The history-dependent and model-dependent assumptions to be made on $Q_2^\mathrm{c}$ and …
Quasiperiodic oscillations (QPOs) have been observed in the power-density spectra of some low-mass X-ray binaries(LMXB) containing a black hole. The two major groups of QPOs -- low-frequency and high-frequency -- have rather different properties. That is why they are usually studied separately. In the literature one can find a large number of models for the high-frequency QPOs but not so many for the low-frequency ones. HF QPOs have attracted significant research efforts due to their potential to provide indispensable information for the properties of the black hole, for its accretion disc and…
The Lense-Thirring effect from spinning neutron stars in double neutron star binaries contribute to the periastron advance of the orbit. This extra term involves the moment of inertia of the neutron stars. Moment of inertia, on the other hand, depends on the mass and spin of the neutron star as well as the equation of state of the matter. If at least one member of the double neutron star binary (better the faster one) is a radio pulsar, then accurate timing analysis might lead to the estimation of the contribution of the Lense-Thirring effect to the periastron advance, which will lead to the m…
We study the accretion flow from a counter-rotating torus orbiting a central Kerr black hole (BH). We characterize the flow properties at the turning point of the accreting matter flow from the orbiting torus, defined by the condition $u^ϕ= 0$ on the flow torodial velocity. The counter-rotating accretion flow and jet-like flow turning point location along BH rotational axis is given. Some properties of the counter-rotating flow thickness and counter-rotating tori energetics are studied.The maximum amount of matter swallowed by the BH from the counter-rotating tori is determined by the backgrou…
Recently, some S-stars (S4711, S62, S4714) orbiting the supermassive black hole (SMBH) in Sgr A$^\ast$ with short orbital periods ($7.6\,\mathrm{yr}\leq P_\mathrm{b}\leq 12\,\mathrm{yr}$) were discovered. It was suggested that they may be used to measure the general relativistic Lense-Thirring (LT) precessions of their longitudes of ascending node $\mathitΩ$ induced by the SMBH's angular momentum $\boldsymbol{J}_\bullet$. In fact, the proposed numerical estimates hold only in the particular case of a perfect alignment of $\boldsymbol{J}_\bullet$ with the line of sight, which does not seem to b…
After the Tidal Disruption Event (TDE) of a star around a SuperMassive Black Hole (SMBH), the bound stellar debris rapidly forms an accretion disk. If the accretion disk is not aligned with the spinning SMBH's equatorial plane, the disk will be driven into Lense-Thirring precession around the SMBH's spin axis, possibly affecting the TDE's light curve. We carry out an eigenmode analysis of such a disk to understand how the disk's warp structure, precession, and inclination evolution are influenced by the disk's and SMBH's properties. We find an oscillatory warp may develop as a result of strong…
We study the precession of accretion disks in the context of gamma-ray burst inner engines. Our aim is to quantitatively estimate the characteristics of gravitational waves produced by the precession of the transient accretion disk in gamma-ray bursts. We evaluate the possible periods of disk precession caused by the Lense-Thirring effect using an accretion disk model that allows for neutrino cooling. Assuming jet ejection perpendicular to the disk plane and a typical intrinsic time-dependence for the burst, we find gamma-ray light curves that have a temporal microstructure similar to that obs…
Almost all accreting black hole and neutron star X-ray binary systems (XRBs) exhibit prominent brightness variations on a few characteristic time-scales and their harmonics. These quasi-periodic oscillations (QPOs) are thought to be associated with the precession of a warped accretion disc, but the physical mechanism that generates the precessing warp remains uncertain. Relativistic frame dragging (Lense-Thirring precession) is one promising candidate, but a misaligned magnetic field is an alternative, especially for neutron star XRBs. Here, we report the discovery of 5 accreting white dwarf s…
