Tilted, truncated accretion flows
Quasi-periodic oscillations (QPOs) are one of the most fascinating features observed in the X-ray light curves of accreting black hole and neutron star X-ray binary systems. They are identified by the broad peaks of power in the power spectrum, caused by the modulation of QPO frequency with time. It is thought that the origin of the QPOs is closely related to the compact object and its physical environment; therefore understanding the origin of these QPOs helps us probe the nature of the compact object and its surroundings. Based on the frequencies, they are broadly classified into high-frequency (> 60 Hz) and low-frequency (< 30 Hz) QPOs. High-frequency QPOs (HFQPOs) may be associated with the orbital/epicyclic frequencies at characteristic radii, or other gravity/inertial pressure modes in the accretion disc. Low-frequency QPOs (LFQPOs) are further classified into type-A, B & C, of which the type-C QPOs are commonly observed and are thought to originate from the Lense-Thirring precession of the accretion flow. The Type-C QPOs are first observed in the hard spectral state of BHXRBs during which the accretion flow has truncated-disc geometry; a standard-thin disc truncated well outside the last stable orbit, and the corona as a geometrically thick, radiatively inefficient accretion flow filling in the inner gap. However, the key assumption of this QPO model is that the inner, hot, geometrically thick accretion flow can precess as a rigid body, independent of the surrounding thin disc and none of the numerical studies performed so far consider the full truncated-disc geometry to study the effect of the outer thin disc.
​
Using advanced numerical techniques, we performed general relativistic magnetohydrodynamic (GRMHD) simulations of a truncated disc misaligned with the spin axis of the black hole. These simulations are the very first to investigate the effect of the outer, thin disc on the Lense-Thirring precession of inner, hot accretion flow, and thus add much-needed realism to the usual simulations.
Initial setup of the simulation; Pseudocolor plot of gas density overlaid with the magnetic field contours
The accretion flow around black holes is more complicated with two-components: inner, hot precessing corona (in red) surrounded by the cool, thin disc (in blue). The corona precesses around the black hole spin axis (marked in the image from our simulation), but the thin disc remains relatively unchanged throughout the simulation; playing a role in slowing down the precession rate of the corona.
Black hole accretion discs may dance around more slowly than previously thought
Bollimpalli et. al 2023
The key finding of our simulations is that the presence of an outer-thin disc decreases the precession rate of the inner torus by nearly 95 per cent. The slowdown in the precession rate is caused by the exchange of the angular momentum between the outer, thin and inner, thick discs.
With this effect, the model now requires a much smaller inner, precessing thick disc to be able to match the typically observed range of type-C QPO frequencies (0.1-10 Hz). Some recent observations have already suggested that the precessing flow needs to be smaller than the estimated size from the Lense-Thirring model for an isolated torus. Thus, our new results help relieve some of the remaining tensions between the model and observations.
Time evolution of the cumulative precession angle of the inner, hot accretion flow around a black hole with spin parameter 0.9. The precession rate is given by the slope of these curves. The precession rate computed from our two-component accretion flow simulations (in the solid curve) is significantly lower than the estimated rate for an isolated torus, i.e., not surrounded by an outer, thin disc (in the dashed line). When we include the angular momentum flux terms, in addition to the Lense-Thirring torque term, we find remarkable agreement between the simulation results and the analytical estimate shown by the dotted curve.
High-resolution simulationss
misaligned simulation, spin = 0.5
misaligned simulation, spin = 0.9
Low-resolution simulationss
misaligned simulation, spin = 0.9
aligned simulation, spin = 0.9
The misalignment also excites prominent vertical oscillations (relevant to HFQPOs) in the inner-hot flow, which is otherwise absent in the aligned discs (Bollimpalli et. al 2024). Such variability is likely caused by the radial and vertical pressure gradients present in the tilted, precessing discs.
Power-spectral densities for four different simulations computed for the density-weighted average of the polar velocity. The solid, dashed, and dotted curves correspond to the Keplerian, radial, and vertical epicyclic frequencies, respectively. Note the power along or between the epicyclic frequencies in all simulations, as well as horizontal (QPO-like) features present only in the tilted simulations.