Tilted, warped, and eccentric disks

Abstract

We review some of the interesting consequences that tilts, warps, and eccentricities can introduce into the dynamics, thermodynamics, and observational appearance of accreting systems, with an emphasis on disks around black holes and compact stars. We begin with a review of the two types of precession that are associated with eccentric and tilted orbits in general relativity and Newtonian gravity. We then discuss the types of accretion systems that may manifest tilted or eccentric disks. In separate sections we discuss first tilted and then eccentric disks, each section covering relevant and interesting observational, theoretical, and numerical results. Next, we explore potential connections between the phenomenology of quasi-periodic oscillations and either tilted or eccentric disks. Finally, we present some concluding thoughts and discuss future directions this research might take.

Figures (10)

• Figure 1: Example of a low frequency QPO observed from the black hole XRB H 1743-322 by XMM-Newton. Left: A 100 s segment of the $4-10$ keV light curve. Right: the power spectrum of the light curve, averaged over a 70 ks interval. The $\sim 4$ s modulation visible in the light curve (left) appears as two narrow, harmonically related peaks in the power spectrum (right). Image reproduced by permission from Ingram2016 (Figure 2), copyright by RAS.
• Figure 2: Schematic illustrations of three possible geometries of tilted accretion disks around a spinning black hole. Left: Smooth, monotonic warp with BP alignment at small radius. Centre: Smooth, oscillatory warp. Right: Broken warp with a torn inner disk. The arrows represent the spin axis of the black hole.
• Figure 3: Left: Geometry of a truncated, tilted disk, with $a = 0.9$, $\beta_0 = 15^\circ$, and a truncation radius of $15\,GM/c^2$. The black-hole $L_\mathrm{BH}$, thin disk $L_\mathrm{disk}$, and torus $L$ angular momenta are indicated. The inner torus precesses about $L_\mathrm{BH}$. Right: Space-time plot of the cumulative precession angle, $\gamma$ (measured in degrees) as a function of radius. The dashed curve represents the instantaneous position of a bending wave propagating outward through the disk at half the sound speed. The consistent, growing precession angle between 5 and $20\,GM/c^2$ confirms that this region is undergoing rigid-body precession. Images reproduced by permission from Bollimpalli25 and Bollimpalli23 (Figure 1), copyright by ESO and RAS.
• Figure 4: Pseudocolor plot of density for a thin ($H/r = 0.03$), tilted disk, showing that only the innermost part of the disk ($r \lesssim 5\,GM/c^2$) has aligned with the black hole symmetry plane (horizontal in this image). Image reproduced by permission from Liska19 (Figure 1), copyright by RAS.
• Figure 5: Left: Schematic diagram of the inner region of the tilted accretion disk, showing the pattern of epicyclic motion, the standing shock, and the plunging streams. Right: Constant density surface (green) together with selected fluid element trajectories (blue curves) for a $15^\circ$ tilted thick disk simulation. Images reproduced by permission from Fragile08 (Figure 14) and Generozov14 (Figure 4), copyright by AAS.