Radiation-driven Warping Research Articles

Correction to: Radiation-driven warping of accretion discs due to X-ray bursts

Correction to: Radiation-driven warping of accretion discs due to X-ray bursts

Radiation-driven warping of accretion discs due to X-ray bursts

ABSTRACT The outpouring of radiation during an X-ray burst can affect the properties of accretion discs around neutron stars: the corona can cool and collapse, the inner regions can be bled away due to enhanced accretion, and the additional heating will lead to changes in the disc height. In this paper, we investigate whether radiation from bursts can cause the disc to distort through a warping instability. Working in the limit of isotropic viscosity and linear growth, we find that bursts are more likely to drive disc warps when they have larger luminosities and longer durations. Therefore, warps will be most probable during intermediate-duration bursts (IMDBs) and superbursts with evidence for photospheric radius expansion. Further, the development of warps depends on the disc viscosity with larger values of α increasing the likelihood of warp growth. We perform time-dependent evolution calculations of the development of warps during type I bursts and IMDBs. Depending on the initial warp prior to the burst, we find that the burst produces warps at r ≲ 50rg that rapidly grow and decay on second-long time-scales, or ones that grow more slowly and cover a large fraction of the disc. The pulsations of warp at small radii appear to have the properties needed to explain the achromatic fluctuations that have been observed during the tails of some IMDBs. The large-scale, slowly growing warps could account for the large reflection strengths and absorbing column densities inferred late in the 4U 1820-30 and 4U 1636-53 superbursts.

RADIATION-DRIVEN WARPING OF CIRCUMBINARY DISKS AROUND ECCENTRIC YOUNG STAR BINARIES

We study a warping instability of a geometrically thin, non-self-gravitating, circumbinary disk around young binary stars on an eccentric orbit. Such a disk is subject to both the tidal torques due to a time-dependent binary potential and the radiative torques due to radiation emitted from each star. The tilt angle between the circumbinary disk plane and the binary orbital plane is assumed to be very small. We find that there is a radius within/beyond which the circumbinary disk is unstable to radiation-driven warping, depending on the disk density and temperature gradient indices. This marginally stable warping radius is very sensitive to viscosity parameters, a fiducial disk radius and the temperature measured there, the stellar luminosity, and the disk surface density at a radius where the disk changes from the optically thick to thin for the irradiation from the central stars. On the other hand, it is insensitive to the orbital eccentricity and binary irradiation parameter, which is a function of the binary mass ratio and luminosity of each star. Since the tidal torques can suppress the warping in the inner part of the circumbinary disk, the disk starts to be warped in the outer part. While the circumbinary disks are most likely to be subject to the radiation-driven warping on a AU to kilo-AU scale for binaries with young massive stars more luminous than 10^4Lsun, the radiation driven warping does not work for those around young binaries with the luminosity comparable to the solar luminosity.

WARPED CIRCUMBINARY DISKS IN ACTIVE GALACTIC NUCLEI

We study a warping instability of a geometrically thin, non-self-gravitating disk surrounding binary supermassive black holes on a circular orbit. Such a circumbinary disk is subject to not only tidal torques due to the binary gravitational potential but also radiative torques due to radiation emitted from an accretion disk around each black hole. We find that a circumbinary disk initially aligned with the binary orbital plane is unstable to radiation-driven warping beyond the marginally stable warping radius, which is sensitive to both the ratio of vertical to horizontal shear viscosities and the mass-to-energy conversion efficiency. As expected, the tidal torques give no contribution to the growth of warping modes but tend to align the circumbinary disk with the orbital plane. Since the tidal torques can suppress the warping modes in the inner part of circumbinary disk, the circumbinary disk starts to be warped at radii larger than the marginally stable warping radius. If the warping radius is of the order of 0.1 pc, a resultant semi-major axis is estimated to be of the order of 10^-2 pc to 10^-4 pc for 10^7 Msun black hole. We also discuss the possibility that the central objects of observed warped maser disks in active galactic nuclei are binary supermassive black holes with a triple disk: two accretion disks around the individual black holes and one circumbinary disk surrounding them.

Three-dimensional smoothed particle hydrodynamics simulations of radiation-driven warped accretion discs

We present three-dimensional smoothed particle hydrodynamics calculations of warped accretion discs in X-ray binary systems. Geometrically thin, optically thick accretion discs are illuminated by a central radiation source. This illumination exerts a non-axisymmetric radiation pressure on the surface of the disc, resulting in a torque that acts on the disc to induce a twist or warp. Initially planar discs are unstable to warping driven by the radiation torque and, in general, the warps also precess in a retrograde direction relative to the orbital flow. We simulate a number of X-ray binary systems which have different mass ratios, using a number of different luminosities for each. Radiation-driven warping occurs for all systems simulated. For mass ratios q∼ 0.1 a moderate warp occurs in the inner disc while the outer disc remains in the orbital plane (cf. X 1916-053). For less extreme mass ratios, the entire disc tilts out of the orbital plane (cf. Her X-1). For discs that are tilted out of the orbital plane in which the outer edge material of the disc is precessing in a prograde direction, we obtain both positive and negative superhumps simultaneously in the dissipation light curve (cf. V603 Aql).

Long-term periodicities in X-ray binaries

A significant number of X-ray binaries are now known to exhibit long-term periodicities on timescales of ∼10 - 100 days. Several physical mechanisms have been proposed that give rise to such periodicities, one of which is radiation-driven warping and precession of the accretion disk. Recent theoretical work predicts the stability to disk warping as a function of the mass ratio, binary radius, viscosity and accretion efficiency, and we confront this theory with observed longterm behaviour of a sample of neutron star X-ray Binaries. We find good agreement, establishing this mechanism observationally for the high-luminosity systems studied here.

Fine-Tuning the Accretion Disk Clock in Hercules X-1

RXTE ASM count rates from the X-ray pulsar Her X-1 began falling consistently during the late months of 2003. The source is undergoing another state transition similar to the anomalous low state of 1999. This new event has triggered observations from both space- and ground-based observatories. In order to aid data interpretation and telescope scheduling, and to facilitate the phase-connection of cycles before and after the state transition, we have re-calculated the precession ephemeris using cycles over the last 3.5 years. We report that the source has displayed a different precession period since the last anomalous event. Additional archival data from CGRO suggests that each low state is accompanied by a change in precession period and that the subsequent period is correlated with accretion flux. Consequently our analysis reveals long-term accretion disk behaviour which is predicted by theoretical models of radiation-driven warping.

Warped Accretion Disks and Longterm X-Ray Periodicities

AbstractA significant number of X-ray binaries are now known to exhibit long-term periodicities on timescales of ~10 - 100 days. Several physical mechanisms have been proposed that give rise to such periodicities, one of which is radiation-driven warping and precession of the accretion disk. Recent theoretical work predicts the stability to disk warping as a, function of the mass ratio, binary radius, viscosity and accretion efficiency. We investigate the stability of the superorbital periodicities in the neutron star X-ray binaries Cyg X-2, LMC X-4, SMC X-l and Her X-l, and thereby confront stability predictions with observation. We find that the period and nature of the superorbital variations in these sources is consistent with the predictions of warping theory.

Long-term properties of accretion discs in X-ray binaries -- II. Stability of radiation-driven warping

A significant number of X-ray binaries (XRBs) are now known to exhibit long-term 'superorbital' periodicities on time-scales of ∼10-100 d. Several physical mechanisms have been proposed that give rise to such periodicities, in particular warping and/or precession of the accretion disc. Recent theoretical work predicts the stability to disc warping of XRBs as a function of the mass ratio, binary radius, viscosity and accretion efficiency, and here we examine the constraints that can be placed on such models by current observations. In Paper I we used a dynamic power spectrum (DPS) analysis of long-term X-ray data sets (Compton Gamma Ray Observatory, Rossi X-Ray Timing Explorer), focusing on the remarkable, smooth variations in the superorbital period exhibited by SMC X-1. Here we use a similar DPS analysis to investigate the stability of the superorbital periodicities in the neutron star XRBs Cyg X-2, LMC X-4 and Her X-1, and thereby confront stability predictions with observation. We find that the period and nature of superorbital variations in these sources are consistent with the predictions of warping theory. We also use a dynamic light-curve analysis to examine the behaviour of Her X-1 as it enters and leaves the 1999 anomalous low state (ALS). This reveals a significant phase shift some 15 cycles before the ALS, which indicates a change in the disc structure or profile leading into the ALS.

Long-term properties of accretion discs in X-ray binaries -- I. The variable third period in SMC X-1

Long-term X-ray monitoring data from the Rossi X-Ray Timing Explorer (RXTE) All-Sky Monitor (ASM) and the Compton Gamma Ray Observatory (CGRO) Burst And Transient Source Experiment (BATSE) reveal that the third (superorbital) period in SMC X-1 is not constant, but varies between 40 and 60 d. A dynamic power spectrum analysis indicates that the third period has been present continuously throughout the five years of ASM observations. This period changed smoothly from 60 to 45 d and then returned to its former value, on a time-scale of approximately 1600 d. During the nearly 4 yr of overlap between the CGRO and RXTE missions, the simultaneous BATSE hard X-ray data confirm and extend this variation in SMC X-1. Our discovery of such an instability in the superorbital period of SMC X-1 is interpreted in the context of recent theoretical studies of warped, precessing accretion discs. We find that the behaviour of SMC X-1 is consistent with a radiation-driven warping model.

Precessing warped accretion discs in X-ray binaries

We study the radiation-driven warping of accretion discs in the context of X-ray binaries. The latest evolutionary equations are adopted, which extend the classical alpha theory to time-dependent thin discs with non-linear warps. We also develop accurate, analytical expressions for the tidal torque and the radiation torque, including self-shadowing. We investigate the possible non-linear dynamics of the system within the framework of bifurcation theory. First, we re-examine the stability of an initially flat disc to the Pringle instability. Then we compute directly the branches of non-linear solutions representing steadily precessing discs. Finally, we determine the stability of the non-linear solutions. Each problem involves only ordinary differential equations, allowing a rapid, accurate and well resolved solution. We find that radiation-driven warping is probably not a common occurrence in low-mass X-ray binaries. We also find that stable, steadily precessing discs exist for a narrow range of parameters close to the stability limit. This could explain why so few systems show clear, repeatable `super-orbital' variations. The best examples of such systems, Her X-1, SS 433 and LMC X-4, all lie close to the stability limit for a reasonable choice of parameters. Systems far from the stability limit, including Cyg X-2, Cen X-3 and SMC X-1, probably experience quasi-periodic or chaotic variability as first noticed by Wijers & Pringle. We show that radiation-driven warping provides a coherent and persuasive framework but that it does not provide a generic explanation for the long-term variabilities in all X-ray binaries.

Radiation‐driven Warping. II. Nonisothermal Disks

Recent work by Pringle and by Maloney, Begelman, & Pringle has shown that geometrically thin, optically thick, accretion disks are unstable to warping driven by radiation torque from the central source. This work was confined to isothermal (i.e., surface density Σ ∝ R-3/2) disks. In this paper we generalize the study of radiation-driven warping to include general power-law surface density distributions, Σ ∝ R-δ. We consider the range from δ = 3/2 (the isothermal case) to δ = -3/2, which corresponds to a radiation-pressure-supported disk; this spans the range of surface density distributions likely to be found in real astrophysical disks. In all cases there are an infinite number of zero-crossing solutions (i.e., solutions that cross the equator), which are the physically relevant modes if the outer boundary of the disk is required to lie in a specified plane. However, unlike the isothermal disk, which is the degenerate case, the frequency eigenvalues for δ ≠ 3/2 are all distinct. In all cases the location of the zero moves outward from the steady state (pure precession) value with increasing growth rate; thus, there is a critical minimum size for unstable disks. Modes with zeros at smaller radii are damped. The critical radius and the steady state precession rate depend only weakly on δ. An additional analytic solution has been found for δ = 1. The case δ = 1 divides the solutions into two qualitatively different regimes. For δ ≥ 1, the fastest growing modes have maximum warp amplitude, βmax, close to the disk outer edge, and the ratio of βmax to the warp amplitude at the disk inner edge, β0, is 1. For δ < 1, βmax/β0 1, and the warp maximum steadily approaches the origin as δ decreases. This implies that nonlinear effects must be important if the warp extends to the disk inner edge for δ ≥ 1, but for δ < 1 nonlinearity will be important only if the warp amplitude is large at the origin. Because of this qualitative difference in the shapes of the warps, the effects of shadowing of the central source by the warp will also be very different in the two regimes of δ. This has important implications for radiation-driven warping in X-ray binaries, for which the value of δ characterizing the disk is likely to be less than unity. In real accretion disks the outer boundary condition is likely to be different from the zero-crossing condition that we have assumed. In accretion disks around massive black holes in active galactic nuclei, the disk will probably become optically thin before the outer disk boundary is reached, whereas in X-ray binaries there will be an outer disk region (outside the circularization radius) in which the inflow velocity is zero but angular momentum is still transported. We show that in both these cases the solutions are similar to the zero-crossing eigenfunctions.

The Origin of Warped, Precessing Accretion Disks in X-Ray Binaries

The radiation-driven warping instability discovered by Pringle holds considerable promise as the mechanism responsible for producing warped, precessing accretion disks in X-ray binaries. This instability is an inherently global mode of the disk, thereby avoiding the difficulties with earlier models for the precession. Here we follow up on earlier work to study the linear behavior of the instability in the specific context of a binary system. We treat the influence of the companion as an orbit-averaged quadrupole torque on the disk. The presence of this external torque allows the existence of solutions in which the direction of precession of the warp is retrograde with respect to disk rotation, in addition to the prograde solutions that exist in the absence of external torques.

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, &amp; 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.

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.