Black Hole Spin Axis Research Articles

Shock-induced Partial Alignment in Geometrically Thick Tilted Accretion Disks Around Black Holes

We carry out idealized three-dimensional general-relativistic magnetohydrodynamic simulations of prograde, weakly magnetized, and geometrically thick accretion flows where the gas distribution is misaligned from the black hole (BH) spin axis. We evolve the disk for three BH spins: a = 0.5, 0.75, and 0.9375, and we contrast them with a standard aligned disk simulation with a = 0.9375. The tilted disks achieve a warped and twisted steady-state structure, with the outer disk misaligning further away from the BH and surpassing the initial 24° misalignment. However, closer to the BH, there is evidence of partial alignment, as the inclination angle decreases with radius in this regime. Standing shocks also emerged in proximity to the BH, roughly at ∼6 gravitational radii. We show that these shocks act to partially align the inner disk with the BH spin. The rate of alignment increases with increasing BH spin magnitude, but in all cases is insufficient to fully align the gas before it accretes. Additionally, we present a toy model of orbit crowding that can predict the location of the shocks in moderate-to-fast rotating BHs, illustrating a potential physical origin for the behavior seen in simulations—with possible applications in determining the positions of shocks in real misaligned astrophysical systems.

Misaligned precessing jets are choked by the accretion disc wind

ABSTRACT We analytically and numerically study the hydrodynamic propagation of a precessing jet in the context of tidal disruption events (TDEs) where the star’s angular momentum is misaligned with the black hole spin. We assume that a geometrically thick accretion disc undergoes Lense–Thirring precession around the black hole spin axis and that the jet is aligned with the instantaneous disc angular momentum. At large spin-orbit misalignment angles $\theta _{\it LS}$, the duty cycle along a given angle that the jet sweeps across is much smaller than unity. The faster jet and slower disc wind alternately fill a given angular region, which leads to strong shock interactions between the two. We show that precessing jets can only break out of the wind confinement if $\theta _{\it LS}$ is less than a few times the jet opening angle $\theta _{\rm j}$. The very small event rate of observed jetted TDEs is then explained by the condition of double alignment: both the stellar angular momentum and the observer’s line of sight are nearly aligned with the black hole spin. In most TDEs with $\theta _{\it LS}\gg \theta _{\rm j}$, the jets are initially choked by the disc wind and may only break out later when the disc eventually aligns itself with the spin axis due to the viscous damping of the precession. Such late-time jets may produce delayed radio rebrightening as seen in many optically bright TDEs. Our model is also applicable to jets associated with (stellar mass) black hole-neutron star mergers where the black hole’s spin is misaligned with the orbital angular momentum.

An IXPE-led X-Ray Spectropolarimetric Campaign on the Soft State of Cygnus X-1: X-Ray Polarimetric Evidence for Strong Gravitational Lensing

We present the first X-ray spectropolarimetric results for Cygnus X-1 in its soft state from a campaign of five IXPE observations conducted during 2023 May–June. Companion multiwavelength data during the campaign are likewise shown. The 2–8 keV X-rays exhibit a net polarization degree PD = 1.99% ± 0.13% (68% confidence). The polarization signal is found to increase with energy across the Imaging X-ray Polarimetry Explorer’s (IXPE) 2–8 keV bandpass. The polarized X-rays exhibit an energy-independent polarization angle of PA = −25.°7 ± 1.°8 east of north (68% confidence). This is consistent with being aligned to Cyg X-1’s au-scale compact radio jet and its parsec-scale radio lobes. In comparison to earlier hard-state observations, the soft state exhibits a factor of 2 lower polarization degree but a similar trend with energy and a similar (also energy-independent) position angle. When scaling by the natural unit of the disk temperature, we find the appearance of a consistent trend line in the polarization degree between the soft and hard states. Our favored polarimetric model indicates that Cyg X-1’s spin is likely high (a * ≳ 0.96). The substantial X-ray polarization in Cyg X-1's soft state is most readily explained as resulting from a large portion of X-rays emitted from the disk returning and reflecting off the disk surface, generating a high polarization degree and a polarization direction parallel to the black hole spin axis and radio jet. In IXPE’s bandpass, the polarization signal is dominated by the returning reflection emission. This constitutes polarimetric evidence for strong gravitational lensing of X-rays close to the black hole.

Choked Precessing Jets in Tidal Disruption Events and High-energy Neutrinos

It has been suggested that relativistic jets might have been commonly formed in tidal disruption events (TDEs), but those with relatively weak power could be choked by the surrounding envelope. The discovery of high-energy neutrinos possibly associated with some normal TDEs may support this picture in the hypothesis that the neutrinos are produced by choked jets. Recently, it was noted that disrupted stars generally have misaligned orbits with respect to the supermassive black hole spin axis, and highly misaligned precessing jets are more likely to be choked. Here we revisit the jet breakout condition for misaligned precessing jets by considering that the jet could be collimated by the cocoon pressure while propagating in the disk wind envelope. The jet head opening angle decreases as the jet propagates in the envelope, but the minimum power of a successful jet remains unchanged in terms of the physical jet power. We further calculate the neutrino flux from choked precessing jets, assuming that the cocoon energy does not exceed the kinetic energy of the disk wind. We find that neutrino flux from highly misaligned choked jets is sufficient to explain the neutrinos from AT2019aalc, while it is marginal to explain the neutrinos from AT2019dsg and AT2019fdr. The latter could be produced by weakly misaligned choked jets, since the duty cycle that the jet sweeps across increases as the misaligned angle decreases. We also show that the population of choked TDE jets could contribute to ∼10% of the observed diffuse neutrino flux measured by IceCube.

Wind-fed GRMHD simulations of Sagittarius A*: tilt and alignment of jets and accretion discs, electron thermodynamics, and multiscale modelling of the rotation measure

ABSTRACTWind-fed models offer a unique way to form predictive models of the accretion flow surrounding Sagittarius A*. We present 3D wind-fed magnetohydrodynamic (MHD) and general relativistic magnetohydrodynamic (GRMHD) simulations spanning the entire dynamic range of accretion from parsec scales to the event horizon. We expand on previous work by including non-zero black hole spin and dynamically evolved electron thermodynamics. Initial conditions for these simulations are generated from simulations of the observed Wolf–Rayet stellar winds in the Galactic Centre. The resulting flow tends to be highly magnetized (β ≈ 2) with an ∼r−1 density profile independent of the strength of magnetic fields in the winds. Our simulations reach the magnetically arrested disc (MAD) state for some, but not all cases. In tilted flows, standard and normal evolution (SANE) jets tend to align with the angular momentum of the gas at large scales, even if that direction is perpendicular to the black hole spin axis. Conversely, MAD jets tend to align with the black hole spin axis. The gas angular momentum shows similar behaviour: SANE flows tend to only partially align while MAD flows tend to fully align. With a limited number of dynamical free parameters, our models can produce accretion rates, 230 GHz flux, and unresolved linear polarization fractions roughly consistent with observations for several choices of electron heating fraction. Absent another source of large-scale magnetic field, winds with a higher degree of magnetization (e.g. where the magnetic pressure is 1/100 of the ram pressure in the winds) may be required to get a sufficiently large rotation measure with consistent sign.

Radiation Transport Two-temperature GRMHD Simulations of Warped Accretion Disks

In many black hole (BH) systems, the accretion disk is expected to be misaligned with respect to the BH spin axis. If the scale height of the disk is much smaller than the misalignment angle, the spin of the BH can tear the disk into multiple, independently precessing “sub-disks.” This is most likely to happen during outbursts in black hole X-Ray binaries (BHXRBs) and in active galactic nuclei (AGNs) accreting above a few percent of the Eddington limit, because the disk becomes razor-thin. Disk tearing has the potential to explain variability phenomena including quasi-periodic oscillations in BHXRBs and changing-look phenomena in AGNs. Here, we present the first radiative two-temperature general relativistic magnetohydrodynamic (GRMHD) simulation of a strongly tilted (65°) accretion disk around an M BH = 10 M ⊙ BH, which tears and precesses. This leads to luminosity swings between a few percent and 50% of the Eddington limit on sub-viscous timescales. Surprisingly, even where the disk is radiation-pressure-dominated, the accretion disk is thermally stable over t ≳ 14,000 r g /c. This suggests warps play an important role in stabilizing the disk against thermal collapse. The disk forms two nozzle shocks perpendicular to the line of nodes where the scale height of the disk decreases tenfold and the electron temperature reaches T e ∼ 108–109 K. In addition, optically thin gas crossing the tear between the inner and outer disk gets heated to T e ∼ 108 K. This suggests that warped disks may emit a Comptonized spectrum that deviates substantially from idealized models.

Effect of geometrically thin discs on precessing, thick flows: relevance to type-C QPOs

ABSTRACT Type-C quasi-periodic oscillations (QPOs) are the low-frequency QPOs most commonly observed during the hard spectral state of X-ray binary systems. The leading model for these QPOs is the Lense-Thirring precession of a hot geometrically thick accretion flow that is misaligned with respect to the black hole spin axis. However, none of the work done to date has accounted for the effects of a surrounding geometrically thin disc on this precession, as would be the case in the truncated disc picture of the hard state. To address this, we perform a set of general relativistic magnetohydrodynamics simulations of truncated discs misaligned with the spin axes of their central black holes. Our results confirm that the inner-hot flow still undergoes precession, though at a rate that is only 5 per cent of what is predicted for an isolated precessing torus. We find that the exchange of angular momentum between the outer thin and the inner thick disc causes this slow-down in the precession rate and discuss its relevance to type-C QPOs.

Disc tearing leads to low and high frequency quasi-periodic oscillations in a GRMHD simulation of a thin accretion disc

ABSTRACT Black hole X-ray binaries (BHXRBs) display a wide range of variability phenomena, from long duration spectral state changes to short-term broad-band variability and quasi-periodic oscillations (QPOs). A particularly puzzling aspect is the production of QPOs, which – if properly understood – could be used as a powerful diagnostic tool of black hole accretion and evolution. In this work, we analyse a high-resolution 3D general relativistic magnetohydrodynamic simulation of a geometrically thin accretion disc, which is tilted by 65° with respect to the black hole spin axis. We find that the Lense–Thirring torque from the rapidly spinning 10 M⊙ black hole causes several sub-discs to tear off within ∼10–20 gravitational radii. Tearing occurs in cycles on time-scales of seconds. During each tearing cycle, the inner sub-disc precesses for 1–5 periods before it falls into the black hole. We find a precession frequency of $\sim 3\rm Hz$, consistent with observed low-frequency QPOs. In addition, we find a high frequency QPO (HFQPO) with centroid frequency of ∼55 Hz in the power spectra of the mass-weighted radius of the inner disc and the radial mass flux. This signal is caused by radial epicyclic oscillations of a dense ring of gas at the tearing radius, which suggests a corresponding modulation of the X-ray light curve and may thus explain some of the observed HFQPOs.

Electromagnetic emission from a binary black hole merger remnant in plasma: Field alignment and plasma temperature

Comparable-mass black-hole mergers generically result in moderate to highly spinning holes, whose spacetime curvature will significantly affect nearby matter in observable ways. We investigate how the moderate spin of a post-merger Kerr black hole immersed in a plasma with initially uniform density and uniform magnetic field affects potentially observable accretion rates and energy fluxes. Varying the initial specific internal energy of the plasma over two decades, we find very little change in steady-state mass accretion rate or Poynting luminosity, except at the lowest internal energies, where fluxes do not exhibit steady-state behavior during the simulation timescale. Fixing the internal energy and varying the initial fixed magnetic-field amplitude and orientation, we find that the steady-state Poynting luminosity depends strongly on the initial field angle with respect to the black hole spin axis, while the matter accretion rate is more stable until the field angle exceeds $\sim 45\degree$. The proto-jet formed along the black hole spin-axis conforms to a thin, elongated cylinder near the hole, while aligning with the asymptotic magnetic field at large distances.

Disk Tearing: Implications for Black Hole Accretion and AGN Variability

Abstract Accretion disks around black holes power some of the most luminous objects in the universe. Disks that are misaligned to the black hole spin can become warped over time by Lense–Thirring precession. Recent work has shown that strongly warped disks can become unstable, causing the disk to break into discrete rings producing a more dynamic and variable accretion flow. In a companion paper, we present numerical simulations of this instability and the resulting dynamics. In this paper, we discuss the implications of this dynamics for accreting black hole systems, with particular focus on the variability of active galactic nuclei (AGN). We discuss the timescales on which variability might manifest, as well as the impact of the observer orientation with respect to the black hole spin axis. When the disk warp is unstable near the inner edge of the disk, we find quasi-periodic behavior of the inner disk, which may explain the recent quasi-periodic eruptions observed in, for example, the Seyfert 2 galaxy GSN 069 and in the galactic nucleus of RX J1301.9+2747. These eruptions are thought to be similar to the “heartbeat” modes observed in some X-ray binaries (e.g., GRS 1915+105 and IGR J17091-3624). When the instability manifests at larger radii in the disk, we find that the central accretion rate can vary on timescales that may be commensurate with, e.g., changing-look AGN. We therefore suggest that some of the variability properties of accreting black hole systems may be explained by the disk being significantly warped, leading to disk tearing.

Can Lense–Thirring Precession Produce QPOs in Supersonic Accretion Flows?

Abstract 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 α 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 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.

Silhouettes of invisible black holes

In general relativity, isolated black holes are invisible due to the infinitely large redshift of photons propagating from the event horizon to a remote observer. However, the dark shadow (silhouette) of a black hole can be visible on the background of matter radiation lensed by the gravitational field of the black hole. The black hole shadow is the celestial sphere projection of the cross section of photon capture by the black hole. If the illuminating background is far behind the black hole (at a distance much greater than the event horizon radius), a classic black hole shadow of a maximal size can also be observed. A minimal-size shadow can be observed if the same black hole is illuminated by the inner part of the accretion disk adjacent to the event horizon. In this case, the shadow of an accreting black hole is a lensed image of the northern or southern hemisphere of the event horizon, depending on the orientation of the black hole spin axis. A dark silhouette of the southern hemisphere of the event horizon is seen in the first image of the supermassive black hole M87* presented by the Event Horizon Telescope. The brightness of accretion matter is much higher than the corresponding one of the usual astrophysical stationary background in the form of numerous stars or extensive hot gas clouds. For this reason, it is improbable that a black hole shadow can be observed in the presence of very luminous accretion matter.

Origin of spin–orbit misalignments: the microblazar V4641 Sgr

ABSTRACT Of the known microquasars, V4641 Sgr boasts the most severe lower limit (>52°) on the misalignment angle between the relativistic jet axis and the binary orbital angular momentum. Assuming the jet and black hole spin axes coincide, we attempt to explain the origin of this extreme spin–orbit misalignment with a natal kick model, whereby an aligned binary system becomes misaligned by a supernova kick imparted to the newborn black hole. The model inputs are the kick velocity distribution, which we measure customized to V4641 Sgr, and the immediate pre/post-supernova binary system parameters. Using a grid of binary stellar evolution models, we determine post-supernova configurations that evolve to become consistent with V4641 Sgr today and obtain the corresponding pre-supernova configurations by using standard prescriptions for common envelope evolution. Using each of these potential progenitor system parameter sets as inputs, we find that a natal kick struggles to explain the origin of the V4641 Sgr spin–orbit misalignment. Consequently, we conclude that evolutionary pathways involving a standard common envelope phase followed by a supernova kick are highly unlikely for V4641 Sgr. An alternative interpretation is that the jet axis does not reliably trace the black hole spin axis. Our results raise concerns about compact object merger statistics gleaned from binary population synthesis models, which rely on unverified prescriptions for common envelope evolution and natal kicks. We also challenge the spin–orbit alignment assumption routinely invoked to measure black hole spin magnitudes.

Orientation of the crescent image of M 87*

The first image of the black hole (BH) M 87* obtained by the Event Horizon Telescope (EHT) has the shape of a crescent extending from the E to WSW position angles, while the observed direction of the large-scale jet is WNW. Images based on numerical simulations of BH accretion flows suggest that on average the projected BH spin axis should be oriented SSW. We explore highly simplified toy models for geometric distribution and kinematics of emitting regions in the Kerr metric, perform ray tracing to calculate the corresponding images, and simulate their observation by the EHT to calculate the corresponding visibilities and closure phases. We strictly assume that (1) the BH spin vector is fixed to the jet axis, (2) the emitting regions are stationary and symmetric with respect to the BH spin, and that (3) the emissivities are isotropic in the local rest frames. Emission from the crescent sector between SSE and WSW can be readily explained in terms of an equatorial ring with either circular or plunging geodesic flows, regardless of the value of BH spin. In the case of plane-symmetric polar caps with plunging geodesic flows, the dominant image of the cap located behind the BH is sensitive to the angular momentum of the emitter. Within the constraints of our model, we have not found a viable explanation for the observed brightness of the ESE sector. Most likely, the ESE “hotspot” has been produced by a non-stationary localised perturbation in the inner accretion flow. Alternatively, it could result from locally anisotropic synchrotron emissivities. Multi-epoch and polarimetric results from the EHT will be essential to verify the theoretically expected alignment of the BH spin with the large-scale jet.

Exciting black hole modes via misaligned coalescences. I. Inspiral, transition, and plunge trajectories using a generalized Ori-Thorne procedure

The last gravitational waves emitted in the coalescence of two black holes are quasi-normal ringing modes of the merged remnant. In general relativity, the mass and the spin of the remnant black hole uniquely determine the frequency and damping time of each radiated mode. The amplitudes of these modes are determined by the mass ratio of the system and the geometry of the coalescence. This paper is part I of an analysis that aims to compute the "excitation factors" associated with misaligned binary black hole coalescence. To simplify the analysis, we consider a large mass ratio system consisting of a non-spinning body of mass $\mu$ that inspirals on a quasi-circular trajectory into a Kerr black hole of mass $M$ and spin parameter $a$, with $\mu/M \ll 1$. Our goal is to understand how different modes are excited as a function of the black hole spin $a$ and an angle $I$ which characterizes the misalignment of the orbit with the black hole's spin axis. Though the large mass ratio limit does not describe the binaries that are being observed by gravitational-wave detectors today, this limit makes it possible to quickly and easily explore the binary parameter space, and to develop insight into how the system's late ringing waves depend on the binary's geometry. In this first analysis, we develop the worldline which the small body follows as it inspirals and then plunges into the large black hole. Our analysis generalizes earlier work by Ori and Thorne to describe how a non-equatorial circular inspiral transitions into a plunging trajectory that falls into the black hole. The worldlines which we develop here are used in part II as input to a time-domain black hole perturbation solver. This solver computes the gravitational waves generated by such inspirals and plunges, making it possible to characterize the modes which the coalescence excites.

Exciting black hole modes via misaligned coalescences. II. The mode content of late-time coalescence waveforms

Using inspiral and plunge trajectories we construct with a generalized Ori-Thorne algorithm, we use a time-domain black hole perturbation theory code to compute the corresponding gravitational waves. The last cycles of these waveforms are a superposition of Kerr quasinormal modes. In this paper, we examine how the modes' excitations vary as a function of source parameters, such as the larger black hole's spin and the geometry of the smaller body's inspiral and plunge. We find that the mixture of quasinormal modes that characterize the final gravitational waves from a coalescence is entirely determined by the spin $a$ of the larger black hole, an angle $I$ which characterizes the misalignment of the orbital plane from the black hole's spin axis, a second angle $\theta_{\rm fin}$ which describes the location at which the small body crosses the black hole's event horizon, and the direction sgn$(\dot\theta_{\rm fin})$ of the body's final motion. If these large-mass-ratio results hold at less extreme mass ratios, then measuring multiple ringdown modes of binary black hole coalescence gravitational waves may provide important information about the source's binary properties, such as the misalignment of the orbit's angular momentum with black hole spin. This may be particularly useful for large mass binaries, for which the early inspiral waves are out of the detectors' most sensitive band.

Black Hole and Neutron Star Binary Mergers in Triple Systems. II. Merger Eccentricity and Spin–Orbit Misalignment

Abstract We study the dynamical signatures of black hole (BH) and neutron star (NS) binary mergers via Lidov–Kozai oscillations induced by tertiary companions in hierarchical triple systems. For each type of binary (BH–BH and BH–NS), we explore a wide range of binary/triple parameters that lead to binary mergers and determine the distributions of merger time T m, eccentricity (e m), and spin–orbit misalignment angle ( ) when the binary enters the LIGO/VIRGO band (10 Hz). We use the double-averaged (over both orbits) and single-averaged (over the inner orbit) secular equations, as well as N-body integration, to evolve systems with different hierarchy levels, including the leading-order post-Newtonian effect, de Sitter spin–orbit coupling, and gravitational radiation. We find that for merging BH–BH binaries with comparable masses, about 7% have e m > 0.1 and 0.7% have e m > 0.9. The majority of the mergers have significant eccentricities in the LISA band. The BH spin evolution and the final spin–orbit misalignment are correlated with the orbital evolution and e m. Mergers with negligible e m (≲10−3) have a distribution of that peaks around 90° (and thus favoring a projected binary spin parameter χ eff ∼ 0), while mergers with larger e m have more isotropic spin–orbit misalignments. For typical BH–NS binaries, strong octupole effects lead to more mergers with nonnegligible e m (with ∼18% of the mergers having e m > 0.1 and 2.5% having e m > 0.9), and the final BH spin axis tends to be randomly oriented. Measurements or constraints on eccentric mergers and from LIGO/VIRGO and LISA would provide useful diagnostics on the dynamical formation of merging BH or NS binaries in triples. The recently detected BH merger events may implicate such dynamical formation channel.

Tilted Disks around Black Holes: A Numerical Parameter Survey for Spin and Inclination Angle

Abstract We conduct a systematic study of the properties of tilted accretion flows around spinning black holes, covering a range of tilt angles and black hole spins, using the general-relativistic magnetohydrodynamics code Athena++. The same initial magnetized torus is evolved around black holes with spins ranging from 0 to 0.9, with inclinations ranging from 0° to 24°. The tilted disks quickly reach a warped and twisted shape that rigidly precesses about the black hole spin axis with deformations in shape large enough to hinder the application of linear bending wave theory. Magnetized polar outflows form, oriented along the disk rotation axes. At sufficiently high inclinations a pair of standing shocks develops in the disks. These shocks dramatically affect the flow at small radii, driving angular momentum transport. At high spins they redirect material more effectively than they heat it, reducing the dissipation rate relative to the mass accretion rate and lowering the heating efficiency of the flow.

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

Powerful relativistic jets are one of the main ways in which accreting black holes provide kinetic feedback to their surroundings. Jets launched from or redirected by the accretion flow that powers them are expected to be affected by the dynamics of the flow, which for accreting stellar-mass black holes has shown evidence for precession1 due to frame-dragging effects that occur when the black-hole spin axis is misaligned with the orbital plane of its companion star2. Recently, theoretical simulations have suggested that the jets can exert an additional torque on the accretion flow3, although the interplay between the dynamics of the accretion flow and the launching of the jets is not yet understood. Here we report a rapidly changing jet orientation-on a time scale of minutes to hours-in the black-hole X-ray binary V404 Cygni, detected with very-long-baseline interferometry during the peak of its 2015 outburst. We show that this changing jet orientation can be modelled as the Lense-Thirring precession of a vertically extended slim disk that arises from the super-Eddington accretion rate4. Our findings suggest that the dynamics of the precessing inner accretion disk could play a role in either directly launching or redirecting the jets within the inner few hundred gravitational radii. Similar dynamics should be expected in any strongly accreting black hole whose spin is misaligned with the inflowing gas, both affecting the observational characteristics of the jets and distributing the black-hole feedback more uniformly over the surrounding environment5,6.

A Study of a Tilted Thin Inner Accretion Disk around a Spinning Black Hole

Abstract The inner part of a thin accretion disk around a Kerr black hole can serve as an important tool to study the physics of the strong gravity regime. A tilt in such a disk with respect to the black hole spin axis is particularly useful for this purpose, as such a tilt can have a significant effect on the observed X-ray spectral and timing features via Lense–Thirring precession. However, the inner disk has been predicted to become aligned with the spin direction of the black hole by the well-known Bardeen–Petterson effect. Here we calculate, both analytically and numerically, the radial profile of the thin accretion disk tilt angle in the viscous regime (i.e., α is the Shakura–Sunyaev viscosity parameter, H is the disk thickness, and R is the radial distance). We show that the inner disk may not be aligned at all for certain reasonable ranges of parameter values. This makes the inner accretion disk particularly promising to probe the black hole parameters, and the accretion process in the strong gravity region.