Warped Accretion Disk Research Articles

Hydrodynamic simulations of propagating warps and bending waves in accretion discs

We present the results of a study of propagating warp or bending waves in accretion discs. Three dimensional hydrodynamic simulations were performed using SPH, and the results of these are compared with calculations based on the linear theory of warped discs. We consider primarily the physical regime in which the dimensionless viscosity parameter `alpha' H/r, where the warps are expected to behave diffusively. Small amplitude perturbations are studied in both Keplerian and slightly non Keplerian discs, and we find that the SPH results can be reasonably well fitted by those of the linear theory. The main results of these calculations are: (1) the warp in Keplerian discs when `alpha' H/r, (3) the non Keplerian discs exhibit a substantially more dispersive behaviour of the warps. Initially imposed higher amplitude nonlinear warping disturbances were studied in Keplerian discs. The results indicate that nonlinear warps can lead to the formation of shocks, and that the evolution of the warp becomes less wave-like and more diffusive in character. This work is relevant to the study of the warped accretion discs that may occur around Kerr black holes or in misaligned binary systems. The results indicate that SPH can accurately model the hydrodynamics of warped discs, even when using rather modest numbers of particles.

Warped discs and the directional stability of jets in active galactic nuclei

Warped accretion discs in active galactic nuclei (AGN) exert a torque on the black hole that tends to align the rotation axis with the angular momentum of the outer disc. We compute the magnitude of this torque by solving numerically for the steady-state shape of the warped disc, and verify that the analytic solution of Scheuer & Feiler provides an excellent approximation. We generalize these results for discs with strong warps and arbitrary surface density profiles, and calculate the time-scale over which the black hole becomes aligned with the angular momentum in the outer disc. For massive black holes and accretion rates of the order of the Eddington limit, the alignment time-scale is always short (≲106 yr), so that jets accelerated from the inner disc region provide a prompt tracer of the angular momentum of gas at large radii in the disc. Longer time-scales are predicted for low-luminosity systems, depending on the degree of anisotropy in the hydrodynamic response of the disc to shear and warp, and for the final decay of modest warps at large radii in the disc that are potentially observable via very-long-baseline interferometry (VLBI). We discuss the implications of this for the inferred accretion history of those AGN with jet directions that appear to be stable over long time-scales. The large energy deposition rate at modest disc radii during rapid realignment episodes should make such objects transiently bright at optical and infrared wavelengths.

The non-linear fluid dynamics of a warped accretion disc

The dynamics of a viscous accretion disc subject to a slowly varying warp of large amplitude is considered. Attention is restricted to discs in which self-gravitation is negligible, and to the generic case in which the resonant wave propagation found in inviscid Keplerian discs does not occur. The equations of fluid dynamics are derived in a coordinate system that follows the principal warping motion of the disc. They are reduced using asymptotic methods for thin discs, and solved to extract the equation governing the warp. In general, this is a wave equation of parabolic type with non-linear dispersion and diffusion, which describes fully non-linear bending waves. This method generalizes the linear theory of Papaloizou & Pringle (1983) to allow for an arbitrary rotation law, and extends it into the non-linear domain, where it connects with a generalized version of the theory of Pringle (1992). The astrophysical implications of this analysis are discussed briefly.

On the Enigmatic X‐Ray Source V1408 Aquilae (=4U 1957+11)

Models for the characteristically soft X-ray spectrum of the compact X-ray source V1498 Aql (=4U 1957+11) have ranged from optically thick Comptonization to multicolor accretion disk models. We critically examine the X-ray spectrum of V1408 Aql via archival Advanced Satellite for Cosmology and Astrophysics (ASCA) data, archival Roentgensatellit (ROSAT) data, and recent Rossi X-Ray Timing Explorer (RXTE) data. Although we are able to fit a variety of X-ray spectral models to these data, we favor an interpretation of the X-ray spectrum as being due to an accretion disk viewed at large inclination angles. Evidence for this hypothesis includes long term (117 day, 235 day, 352 day) periodicities seen by the RXTE All Sky Monitor (ASM), which we interpret as being due to a warped precessing disk, and a 1 keV feature in the ASCA data, which we interpret as being the blend of L fluorescence features from a disk atmosphere or wind. We also present timing analysis of the RXTE data and find upper limits of 4% for the root mean square (rms) variability between f=0.001-16 Hz. The situation of whether the compact object is a black hole or neutron star is still ambiguous; however, it now seems more likely that an X-ray emitting, warped accretion disk is an important component of this system.

X-ray spectroscopy of the broad-line radio galaxy 3C 111

We present an ASCA observation of the broad-line radio galaxy 3C 111. The X-ray spectrum is well described by a model consisting of a photoelectrically absorbed power-law form. The inferred absorbing column density is significantly greater than expected on the basis of 21-cm measurements of Galactic H I. Whilst this may be the result of intrinsic absorption from a circumnuclear torus or highly warped accretion disc, inhomogeneities and molecular gas within the foreground giant molecular cloud may also be responsible for some of this excess absorption. We also claim a marginal detection of a broad iron Kα line which is well explained as being a fluorescent line originating from the central regions of a radiatively efficient accretion disc. This line appears weak in comparison to those found in (radio-quiet) Seyfert nuclei. We briefly discuss the implications of this fact.

A Geometrical Relationship between Broad-Line Clouds and an Accretion Disk around Active Galactic Nuclei

Recent hard X-ray spectroscopy of active galactic nuclei has strongly suggested that double-peaked, very broad Fe K emission arises from an accretion disk around the central engine. Model fitting of the observed Fe K emission line profile makes it possible to estimate a probable inclination angle of the accretion disk. In order to study the geometrical relationship between the accretion disk and broad emission-line regions (BLRs), we investigate the correlation between the inclination angle of the accretion disk and the velocity width of BLRs for 18 type-1 Seyfert galaxies. We found that there may be a negative correlation between them, i.e., Seyfert nuclei with a more face-on accretion disk tend to have larger BLR velocity widths, suggesting that the BLRs are not coplanar with respect to the accretion disk. The most probable interpretation may be that the BLRs arise from outer parts (r ∼ 0.01 pc) of a warped accretion disk illuminated by the central engine.

Probing Accretion Disks in AGN with Water Masers

AbstractExtremely luminous extragalactic water masers – the so-called “megamasers”, with isotropic luminosities of tens to hundreds of solar luminosities – appear to be uniquely associated with active galactic nuclei. The recent survey of Braatz et al. indicates that 20% of Seyfert 2 galaxies have detectable water maser emission. Although originally suggested to arise in shocks, it now seems likely that the masers arise from the irradiation of high-pressure molecular gas by X-rays from the AGN. Quantitative modelling shows that the observed megamaser luminosities can plausibly be produced in this fashion. Both observational limits on the size scales and the high gas pressures required indicate that the water maser emission arises on very small scales, either in a circumnuclear “torus” or the accretion disk itself. In the best-studied case, NCG 4258, the masers are produced in a geometrically thin, warped accretion disk. The maser models can be used to derive quantitative information about the physical conditions in the disk, namely, the mass accretion rate, and therefore the radiative efficiency. I discuss the implications of water maser observations and models for the study of accretion disks and circumnuclear tori in AGN.

Radiation-Driven Warping: The Origin of Warps and Precession in Accretion Disks

AbstractA geometrically thin, optically thick, warped accretion disk with a central source of luminosity is subject to non-axisymmetric forces due to radiation pressure; the resulting torque acts to modify the warp. Initially planar accretion disks are unstable to warping driven by radiation torque, as shown in a local analysis by Pringle (1996) and a global analysis of the stable and unstable modes by Maloney, Begelman, & Pringle (1996). In general, the warp also precesses.We discuss the nature of this instability, and its possible implications for accretion disks in X-ray binaries and active galactic nuclei. Specifically, we argue that this effect provides a plausible explanation for the misalignment and precession of the accretion disks in X-ray binaries such as SS 433 and Her X–l; the same mechanism explains why the maser disk in NGC 4258 is warped.

Water megamasers as a probe of a circumnuclear accretion disk in an active galaxy

In the past three years, observations of extragalactic water masers have demonstrated the extraordinary power of spectral line radio interferometry to probe the inner regions of active galaxies on subparsec scales. In the case of the active galaxy NGC 4258, the observations of Miyoshi et al. (1995) have established the presence of a thin, slightly warped, and Keplerian circumnuclear accretion disk that orbits a central object of mass 3.6 × 107M⊙. In addition to their immense value as kinematic probes, extragalactic water masers also provide valuable constraints upon the physical and chemical conditions in the masing circumnuclear gas, yielding an estimate of the mass accretion rate through the circumnuclear disk of NGC 4258. These recent observational and theoretical developments are reviewed here.

Radiation‐Driven Warping: The Origin of Warps and Precession in Accretion Disks

A geometrically thin, optically thick, warped accretion disk with a central source of luminosity is subject to non-axisymmetric forces due to radiation pressure; the resulting torque acts to modify the warp. In a recent paper, \cite{pri96} used a local analysis to show that initially planar accretion disks are unstable to warping driven by radiation torque. Here we extend this work with a global analysis of the stable and unstable modes. We confirm Pringle's conclusion that thin centrally-illuminated accretion disks are generically unstable to warping via this mechanism; we discuss the time-evolution and likely steady-state of such systems and show specifically that this mechanism can explain the warping of the disk of water masers in NGC 4258 and the 164-day precession period of the accretion disk in SS 433. Radiation-driven warping and precession provides a robust mechanism for producing warped, precessing accretion disks in active galactic nuclei and X-ray binary systems.

Self-induced warping of accretion discs

A warped accretion disc with a central radiation source is subject to non-axisymmetric radiation pressure forces, which in turn modify the warp. We show here, with a simple analytic approach, that even an initially flat disc is unstable to warping through this effect. We give estimates of the radii at which such self-induced warping takes place, and discuss applications to discs in binary X-ray sources and in active galactic nuclei.

The 35 Day Cycle of Her X-1

AbstractThe 35 d period in the observed X-ray and optical light curves of Her X-1 can be understood in terms of a warped accretion disk precessing in the tidal field of the companion. We propose that repulsive forces of the X-ray driven coronal wind acting on the disk causes and maintains the warp of the disk (Fig. 1). The resulting shape of the precessing disk reproduces the main features of the observed X-ray light curve [1]. Based on the calculated disk shape we model the dip structure in the X-ray observations as caused by the interaction between the accretion stream and the warped disk.

0n the dynamics of warped accretion disks

We present some analyses of warping modes in inviscid near Keplerian disks taking the three-dimensional structure fully into account. The results of this investigation verify the validity of a vertical averaging approximation for thin disks when the radial wavelength is significantly longer than the disk thickness. They also indicate that long wavelength disturbances may persist for long times. Shorter wavelength disturbances in non-self gravitating disks are found to propagate with little dispersion at a speed related to the sound speed. When self-gravity becomes important, fast and slow waves are found which also propagate with little dispersion. When a small viscosity is included, the evolution of the disturbances becomes more diffusive in character.

The Stability of a Warped Accretion Disc

AbstractAn accretion disc becomes warped when subjected to a torque which is misaligned with the disc plane. Such torques may be caused by Lense-Thirring precession near a spinning compact object, or the quadrupole field of a binary star. Here the flow in an adiabatic warped disc is modelled as a two-dimensional shear layer with linear velocity profile and free surface boundary conditions, and is investigated by means of a linear stability analysis.The flow is found to be unstable whenever it contains a critical layer, i.e., a level at which the shear velocity is equal to the phase velocity. The instability occurs over a broad wavenumber range and has a typical dimensionless growth rate ≈ 0.1 for both the compressible and incompressible cases. These waves grow with a time-scale of about one orbital period, and are likely to have a major effect on the disc viscosity.