Viscous Accretion Disk Research Articles

ON THE HIGH-FREQUENCY QUASI-PERIODIC OSCILLATIONS FROM BLACK HOLES

We apply the global mode analysis, which has been recently developed for the modeling of kHz quasi-periodic oscillations (QPOs) from neutron stars, to the inner region of an accretion disk around a rotating black hole. Within a pseudo-Newtonian approach that keeps the ratio of the radial epicyclic frequency $\kappa$ to the orbital frequency $\Omega$ the same as the corresponding ratio for a Kerr black hole we determine the innermost disk region where the hydrodynamic modes grow in amplitude. We find that the radiation flux emerging from the inner disk has the highest values within the same region. Using the flux weighted averages of the frequency bands over this region we identify the growing modes with highest frequency branches $\Omega +\kappa $ and $\Omega $ to be the plausible candidates for the high-frequency QPO pairs observed in black hole systems. The observed frequency ratio around 1.5 can therefore be understood naturally in terms of the global free oscillations in the innermost region of a viscous accretion disk around a black hole without invoking a particular resonance to produce black hole QPOs. Although the frequency ratio $<\Omega +\kappa>/<\Omega>$ is found to be not sensitive to the black hole's spin which is good for explaining the high-frequency QPOs it may work as a limited diagnostic of the spin parameter to distinguish black holes with very large spin from the slowly rotating ones. Within our model we estimate the frequency ratio of a high-frequency QPO pair to be greater than 1.5 if the black hole is a slow rotator. For fast rotating black holes, we expect the same ratio to be less than 1.5.

RESOLVING THE CIRCUMSTELLAR DISK OF HL TAURI AT MILLIMETER WAVELENGTHS

We present results of high-resolution imaging toward HL Tau by the Combined Array for Research in Millimeter-wave Astronomy (CARMA). We have obtained 1.3 and 2.7 mm dust continua with an angular resolution down to 0.13 arc second. Through model fitting to the two wavelength data simultaneously in Bayesian inference using a flared viscous accretion disk model, we estimate the physical properties of HL Tau, such as density distribution, dust opacity spectral index, disk mass, disk size, inclination angle, position angle, and disk thickness. HL Tau has a circumstellar disk mass of 0.13 solar mass, a characteristic radius of 79 AU, an inclination of 40 degree, and a position angle of 136 degree. Although a thin disk model is preferred by our two wavelength data, a thick disk model is needed to explain the high mid- and far-infrared emission of the HL Tau spectral energy distribution. This could imply large dust grains settled down on the mid plane with fine dust grains mixed with gas. The HL Tau disk is likely gravitationally unstable and can be fragmented between 50 and 100 AU of radius. However, we did not detect dust thermal continuum supporting the protoplanet candidate claimed by a previous study using observations of the Very Large Array at 1.3 cm.

Angular momentum transport by thermal emission in black hole accretion disks

AbstractWe calculate the amount of angular momentum that thermal photons carry out of a viscous black hole accretion disk, due to the strong Doppler shift imparted to them by the high orbital velocity of the radiating disk material. While thermal emission can not drive accretion on its own, we show that along with disk heating it does nonetheless result in a loss of specific angular momentum, thereby contributing to an otherwise viscosity‐driven accretion flow. In particular, we show that the fraction of the angular momentum that is lost to thermal emission at a radius r in a standard, multi‐color disk is ∼0.4rs/r, where rs is the Schwarzschild radius of the black hole. We briefly highlight the key similarties between this effect and the closely related Poynting‐Robertson effect (© 2011 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Variation of the gas and radiation content in the sub-Keplerian accretion disk around black holes and its impact to the solutions

We investigate the variation of the gas and the radiation pressure in accretion disks during the infall of matter to the black hole and its effect to the flow. While the flow far away from the black hole might be non-relativistic, in the vicinity of the black hole it is expected to be relativistic behaving more like radiation. Therefore, the ratio of gas pressure to total pressure ( β) and the underlying polytropic index ( γ) should not be constant throughout the flow. We obtain that accretion flows exhibit significant variation of β and then γ, which affects solutions described in the standard literature based on constant β. Certain solutions for a particular set of initial parameters with a constant β do not exist when the variation of β is incorporated appropriately. We model the viscous sub-Keplerian accretion disk with a nonzero component of advection and pressure gradient around black holes by preserving the conservations of mass, momentum, energy, supplemented by the evolution of β. By solving the set of five coupled differential equations, we obtain the thermo-hydrodynamical properties of the flow. We show that during infall, β of the flow could vary up to ∼300%, while γ up to ∼20%. This might have a significant impact to the disk solutions in explaining observed data, e.g. super-luminal jets from disks, luminosity, and then extracting fundamental properties from them. Hence any conclusion based on constant γ and β should be taken with caution and corrected.

The role of the initial surface density profiles of the disc on giant planet formation: comparing with observations

In order to explain the main characteristics of the observed population of extrasolar planets and the giant planets in the Solar System, we need to get a clear understanding of which are the initial conditions that allowed their formation. To this end we develop a semi-analytical model for computing planetary systems formation based on the core instability model for the gas accretion of the embryos and the oligarchic growth regime for the accretion of the solid cores. With this model we explore not only different initial discs profiles motivated by similarity solutions for viscous accretion discs, but we also consider different initial conditions to generate a variety of planetary systems assuming a large range of discs masses and sizes according to the last results in protoplanetary discs observations. We form a large population of planetary systems in order to explore the effects in the formation of assuming different discs and also the effects of type I and II regimes of planetary migration, which were found to play fundamental role in reproducing the distribution of observed exoplanets. Our results show that the observed population of exoplanets and the giant planets in the Solar System are well represented when considering a surface density profile with a power law in the inner part characterized by an exponent of -1, which represents a softer profile when compared with the case most similar to the MMSN model case.

PROTOPLANETARY DISK STRUCTURES IN OPHIUCHUS. II. EXTENSION TO FAINTER SOURCES

We present new results from a significant extension of our previous high angular resolution (0.3" = 40 AU) Submillimeter Array survey of the 880 um continuum emission from dusty circumstellar disks in the ~1 Myr-old Ophiuchus star-forming region. An expanded sample is constructed to probe disk structures that emit significantly lower millimeter luminosities (hence dust masses), down to the median value for T Tauri stars. Using a Monte Carlo radiative transfer code, the millimeter visibilities and broadband spectral energy distribution for each disk are simultaneously reproduced with a two-dimensional parametric model for a viscous accretion disk. We find wide ranges of characteristic radii (14-198 AU) and disk masses (0.004-0.143 M_sun), but a narrow distribution of surface density gradients (0.4-1.1) that is consistent with a uniform value $\gamma$ = 0.9 +/- 0.2 and independent of mass (or millimeter luminosity). In this sample, we find a correlation between the disk luminosity/mass and characteristic radius, such that fainter disks are both smaller and less massive. We suggest that this relationship is an imprint of the initial conditions inherited by the disks at their formation epoch, compare their angular momenta with those of molecular cloud cores, and speculate on how future observations can help constrain the distribution of viscous evolution timescales. No other correlations between disk and star properties are found. The inferred disk structures are briefly compared with theoretical models for giant planet formation, although resolution limitations do not permit us to directly comment on material inside R = 20 AU. However, there is some compelling evidence for dust evolution in the planet formation region: 4/17 disks in the sample show resolved regions of significantly reduced optical depths within ~20-40 AU of their central stars.

An approach to solving the boundary free edge difficulties in SPH modelling: application to a viscous accretion disc in close binaries

In this work, we propose a SPH interpolating Kernel reformulation suitable also to treat free edge boundaries in the computational domain. Application to both inviscid and viscous stationary low compressibility accretion disc models in Close Binaries (CB) are shown. The investigation carried out in this paper is a consequence of the fact that a low compressibility modelling is crucial to check numerical reliability. Results show that physical viscosity supports a well-bound accretion disc formation, despite the low gas compressibility, when a Gaussian-derived Kernel (from the Error Function) is assumed, in extended particle range - whose Half Width at Half Maximum (HWHM) is fixed to a constant $h$ value - without any spatial restrictions on its radial interaction (hereinafter GASPHER). At the same time, GASPHER ensures adequate particle interpolations at the boundary free edges. Both SPH and adaptive SPH (hereinafter ASPH) methods lack accuracy if there are not constraints on the boundary conditions, in particular at the edge of the particle envelope: Free Edge (FE) conditions. In SPH, an inefficient particle interpolation involves a few neighbour particles; instead, in the second case, non-physical effects involve both the boundary layer particles themselves and the radial transport. Either in a regime where FE conditions involve the computational domain, or in a viscous fluid dynamics, or both, a GASPHER scheme can be rightly adopted in such troublesome physical regimes. Despite the applied low compressibiity condition, viscous GASPHER model shows clear spiral pattern profiles demonstrating the better quality of results compared to SPH viscous ones. Moreover a successful comparison of results concerning GASPHER 1D inviscid shock tube with analytical solution is also reported.

On the diffusive propagation of warps in thin accretion discs

In this paper we revisit the issue of the propagation of warps in thin and viscous accretion discs. In this regime warps are know to propagate diffusively, with a diffusion coefficient approximately inversely proportional to the disc viscosity. Previous numerical investigations of this problem (Lodato & Pringle 2007) did not find a good agreement between the numerical results and the predictions of the analytic theories of warp propagation, both in the linear and in the non-linear case. Here, we take advantage of a new, low-memory and highly efficient SPH code to run a large set of very high resolution simulations (up to 20 million SPH particles) of warp propagation, implementing an isotropic disc viscosity in different ways, to investigate the origin of the discrepancy between the theory and the numerical results. Our new and improved analysis now shows a remarkable agreement with the analytic theory both in the linear and in the non-linear regime, in terms of warp diffusion coefficient and precession rate. It is worth noting that the resulting diffusion coefficient is inversely proportional to the disc viscosity only for small amplitude warps and small values of the disc $\alpha$ coefficient ($\alpha < 0.1$). For non-linear warps, the diffusion coefficient is a function of both radius and time, and is significantly smaller than the standard value. Warped accretion discs are present in many contexts, from protostellar discs to accretion discs around supermassive black holes. In all such cases, the exact value of the warp diffusion coefficient may strongly affect the evolution of the system and therefore its careful evaluation is critical in order to correctly estimate the system dynamics (abridged).

Large scale magnetic fields in viscous resistive accretion disks

<i>Aims. <i/>Cold steady-state disk wind theory from near Keplerian accretion disks requires a large scale magnetic field at near equipartition strength. However the minimum magnetization has never been tested with time dependent simulations. We investigate the time evolution of a Shakura-Sunyaev accretion disk threaded by a weak vertical magnetic field. The strength of the field is such that the disk magnetization falls off rapidly with radius.<i>Methods. <i/>Four 2.5D numerical simulations of viscous resistive accretion disk are performed using the magnetohydrodynamic code PLUTO. In these simulations, a mean field approach is used and turbulence is assumed to give rise to anomalous transport coefficients (alpha prescription). <i>Results. <i/>The large scale magnetic field introduces only a small perturbation to the disk structure, with accretion driven by the dominant viscous torque. However, a super fast magnetosonic jet is observed to be launched from the innermost regions and remains stationary over more than 953 Keplerian orbits. This is the longest accretion-ejection simulation ever carried out. The self-confined jet is launched from a finite radial zone in the disk which remains constant over time. Ejection is made possible because the magnetization reaches unity at the disk surface, due to the steep density decrease. However, no ejection is reported when the midplane magnetization becomes too small. The asymptotic jet velocity remains nevertheless too low to explain observed jets. This is because of the negligible power carried away by the jet.<i>Conclusions. <i/>Astrophysical disks with superheated surface layers could drive analogous outflows even if their midplane magnetization is low. Sufficient angular momentum would be extracted by the turbulent viscosity to allow the accretion process to continue. The magnetized outflows would be no more than byproducts, rather than a fundamental driver of accretion. However, if the midplane magnetization increases towards the center, a natural transition to an inner jet dominated disk could be achieved.

Rayleigh adjustment of narrow barriers in protoplanetary discs

Sharp density features in protoplanetary discs, for instance at the edge of a magnetically dead zone, have recently been proposed as effective barriers to slow down or even stop the problematically fast migration of planetary cores into their central star. Density features on a radial scale approaching the disc vertical scale height might not exist, however, since they could be Rayleigh (or more generally Solberg-Hoiland) unstable. Stability must be checked explicitly in one-dimensional viscous accretion disc models because these instabilities are artificially eliminated in the process of reducing the full set of axisymmetric equations. The disc thermodynamics, via the entropy stratification, and its vertical structure also influence stability when sharp density features are present. We propose the concept of Rayleigh adjustment for viscous disc models: any density feature that violates Rayleigh stability (or its generalization) should be diffused radially by hydrodynamical turbulence on a dynamical time-scale, approaching marginal stability in a quasi-continuous manner.

MHD simulations of accretion onto a dipolar magnetosphere

Aims. We investigate the accretion process from an accretion disk onto a magnetized rotating star with a purely dipolar magnetic field. Our main aim is to study the mechanisms that regulate the stellar angular momentum. In this work, we consider two effects that can contrast with the spin-up torque normally associated with accretion: (1) the spin-down torque exerted by an extended magnetosphere connected to the disk beyond the corotation radius; (2) the spin-down torque determined by a stellar wind flowing along the opened magnetospheric field lines. Methods. Our study is based on time-dependent axisymmetric magnetohydrodynamic numerical simulations of the interaction between a viscous and resistive accretion disk with the dipolar magnetosphere of a rotating star. We present the first example of a numerical experiment able to model at the same time the formation of accretion curtains, the effects of an extended stellar magnetosphere and the launching of a stellar wind. Results. In the examples presented, the spin-down torque related to the star-disk interaction can extract only ∼10% of the accretion torque, due to the weakness of the extended connection. Not even the spin-down torque exerted by a stellar wind is strong enough (∼20%): despite a huge lever arm (RA ≈ 19 R� ), the mass-loss rate ( u Mwind ≈ 1% u Macc) is too low to provide an efficient torque.

Young pre-low-mass X-ray binaries in the propeller phase

<i>Context. <i/>Discovery of the 6.7-h periodicity in the X-ray source 1E 161348-5055 in RCW 103 has led to investigations of the nature of this periodicity.<i>Aims. <i/>To explore a model for 1E 161348-5055 wherein a fast-spinning neutron star with a magnetic field ~10<sup>12<sup/> G in a young pre-low-mass X-ray Binary (pre-LMXB) with an eccentric orbit of period 6.7 h operates in the “propeller” phase.<i>Methods. <i/>The 6.7-h light curve of 1E 161348-5055 is modeled in terms of orbitally-modulated mass transfer through a viscous accretion disk and subsequent propeller emission. Formation of eccentric binaries in supernovae and their subsequent tidal evolution are studied.<i>Results. <i/>The light curve of 1E 161348-5055 can be quantitatively accounted for by models of propeller torques of both Illarionov-Sunyaev type and Romanova-Lovelace et al. type, and spectral and other properties are also in agreement. Formation and evolution of model systems are shown to be in accordance both with standard theories and with X-ray observations of 1E 161348-5055.<i>Conclusions. <i/>The pre-LMXB model for 1E 161348-5055 and similar sources agrees with observation. Distinguishing features between this model and the recently-proposed magnetar model need to be explored.

PROTOPLANETARY DISK STRUCTURES IN OPHIUCHUS

We present a high angular resolution (0.3 = 40 AU) SMA survey of the 870 micron thermal continuum emission from 9 of the brightest, and therefore most massive, circumstellar disks in the ~1 Myr-old Ophiuchus star-forming region. Using 2-D radiative transfer calculations, we simultaneously fit the observed continuum visibilities and broadband spectral energy distribution for each disk with a parametric structure model. Compared to previous millimeter studies, this survey includes significant upgrades in modeling, data quality, and angular resolution that provide improved constraints on key structure parameters, particularly those that characterize the spatial distribution of mass in the disks. In the context of a surface density profile motivated by similarity solutions for viscous accretion disks, the best-fit models for the sample disks have characteristic radii R_c = 20-200 AU, high disk masses M_d = 0.005-0.14 M_sun, and a narrow range of radial surface density gradients around a median $\gamma$ = 0.9. These density structures are used in conjunction with accretion rate estimates from the literature to help characterize the viscous evolution of the disk material. Using the standard prescription for disk viscosities, those combined constraints indicate that $\alpha$ = 0.0005-0.08. Three of the sample disks show large (R = 20-40 AU) central cavities in their continuum emission morphologies, marking extensive zones where dust has been physically removed and/or has significantly diminished opacities. Based on the current requirements of planet formation models, these emission cavities and the structure constraints for the sample as a whole suggest that these young disks may eventually produce planetary systems, and have perhaps already started. (abridged)

Global transient dynamics of three-dimensional hydrodynamical disturbances in a thin viscous accretion disk

Thin viscous Keplerian accretion disks are considered asymptotically stable, even though they can show significant dynamic activity on short time scales. In this paper the dynamics of nonaxisymmetric hydrodynamical disturbances of disks are investigated analytically, building upon the steady state three-dimensional structure and evolution of axisymmetric perturbations explored in previous work. Assuming a polytropic equation of state, solutions are found by means of an asymptotic expansion in the small parameter measuring the ratio of the disk thickness to characteristic radius. In-depth analysis shows that every perturbation that disturbs the radial velocity induces significant transient growth in the (acoustic) energy of the evolving disturbance. This effect is most evident in the density and vertical velocity. The transient growth observed is tied to the nonseparable nature of the solutions where, in particular, pattern evolution is controlled by a similarity variable composed of the radial coordinate and time. This leads to growing winding perturbations that display successive radial peaks and troughs. We argue that these transient nonaxisymmetric structures may precipitate secondary instabilities which, consequently, may be a critical element for a new alternative picture of turbulence arousal in nonmagnetized astrophysical disks.

Quasi‐Periodic Oscillations as Global Hydrodynamic Modes in the Boundary Layers of Viscous Accretion Disks

The observational characteristics of quasi-periodic oscillations (QPOs) from accreting neutron stars strongly indicate the oscillatory modes in the innermost regions of accretion disks as a likely source of the QPOs. The inner regions of accretion disks around neutron stars can harbor very high frequency modes related to the radial epicyclic frequency κ. The degeneracy of κ with the orbital frequency Ω is removed in a non-Keplerian boundary or transition zone near the magnetopause between the disk and the compact object. We show, by analyzing the global hydrodynamic modes of long wavelength in the boundary layers of viscous accretion disks, that the fastest growing mode frequencies are associated with frequency bands around κ and κ ± Ω . The maximum growth rates are achieved near the radius where the orbital frequency Ω is maximum. The global hydrodynamic parameters such as the surface density profile and the radial drift velocity determine which modes of free oscillations will grow at a given particular radius in the boundary layer. In accordance with the peak separation between kHz QPOs observed in neutron star sources, the difference frequency between two consecutive bands of the fastest growing modes is always related to the spin frequency of the neutron star. This is a natural outcome of the boundary condition imposed by the rotating magnetosphere on the boundary region of the inner disk.

Axisymmetric magneto-rotational instability in viscous accretion disks

AbstractAxisymmetric MRI in viscous accretion disks is investigated. The linear growth of the viscous MRI is characterized by the Reynolds number RMRI ≡ v2A/νΩ, where vA is the Alfvén velocity, ν is the kinematic viscosity, and Ω is the angular velocity of the disk. Although the linear growth of the MRI is suppressed as the Reynolds number decreases, its nonlinear behavior is found to be almost independent of RMRI. At the nonlinear stage, the channel flow grows and the Maxwell stress increases even though RMRI is much smaller than unity. Nonlinear behavior of the MRI in the viscous regime can be explained by the characteristics of the linear dispersion relation. Applying our results to the case with both viscosity and resistivity, it is anticipated that the critical value of the Lundquist number SMRI ≡ v2A/ηΩ for active turbulence would depend on the magnetic Prandtl number Pm ≡ ν/η, where η is the magnetic diffusivity.

THE ENGINE OF OUTFLOWS IN AGN: THE ROLE OF PHYSICAL TURBULENT VISCOSITY

Adopting the smoothed particle hydrodynamics (SPH) numerical method, we performed a grid of evolving models of a 3D, axially symmetric, physically viscous accretion disc around a black hole (BH) in an AGN. In such disc models, the role of the specific angular momentum λ and of the physical turbulent viscosity parameter α, according to the Shakura and Sunyaev prescription, are examined. One or two shock fronts develop in the radial inviscid flow, according to the assigned initial kinematic and thermodynamic conditions. Couples of (α, λ) values determine radial periodical oscillations in the shock front. An outflow can develop from the subsonic post shock region, close to the black hole, in some cases. This provides evidence for a link between the accretion disc and the fueling of a jet, through the presence of shock fronts in an accretion disc close to the centrifugal barrier.

Axisymmetric Magnetorotational Instability in Viscous Accretion Disks

Axisymmetric magnetorotational instability (MRI) in viscous accretion disks is investigated by linear analysis and two-dimensional nonlinear simulations. The linear growth of the viscous MRI is characterized by the Reynolds number defined as -->RMRI ≡ v2A/ν Ω , where -->vA is the Alfven velocity, ν is the kinematic viscosity, and Ω is the angular velocity of the disk. Although the linear growth rate is suppressed considerably as the Reynolds number decreases, the nonlinear behavior is found to be almost independent of -->RMRI. At the nonlinear evolutionary stage, a two-channel flow continues growing and the Maxwell stress increases until the end of calculations even though the Reynolds number is much smaller than unity. A large portion of the injected energy to the system is converted to the magnetic energy. The gain rate of the thermal energy, on the other hand, is found to be much larger than the viscous heating rate. Nonlinear behavior of the MRI in the viscous regime and its difference from that in the highly resistive regime can be explained schematically by using the characteristics of the linear dispersion relation. Applying our results to the case with both the viscosity and resistivity, it is anticipated that the critical value of the Lundquist number -->SMRI ≡ v2A/η Ω for active turbulence depends on the magnetic Prandtl number -->SMRI ,c Pm1/2 in the regime of -->Pm 1 and remains constant when -->Pm 1, where -->Pm ≡ SMRI/RMRI = ν/η and η is the magnetic diffusivity.

Particle Acceleration and the Formation of Relativistic Outflows in Viscous Accretion Disks with Shocks

In this Letter, we present a new self-consistent theory for the production of the relativistic outflows observed from radio-loud black hole candidates and active galaxies as a result of particle acceleration in hot, viscous accretion disks containing standing, centrifugally-supported isothermal shocks. This is the first work to obtain the structure of such disks for a relatively large value of the Shakura-Sunyaev viscosity parameter ($\alpha=0.1$), and to consider the implications of the shock for the acceleration of relativistic particles in viscous disks. In our approach, the hydrodynamics and the particle acceleration are coupled and the solutions are obtained self-consistently based on a rigorous mathematical method. We find that particle acceleration in the vicinity of the shock can provide enough energy to power the observed relativistic jet in M87.

Computation of mass loss from viscous accretion disc in presence of cooling

Rotating accretion flow may undergo centrifugal pressure mediated shock transition even in presence of various dissipative processes, such as viscosity and cooling mechanism. The extra thermal gradient force along the vertical direction in the post-shock flow drives a part of the accreting matter as bipolar outflows which are believed to be the precursor of relativistic jets. We compute mass loss rates from a viscous accretion disc in presence of synchrotron cooling in terms of the inflow parameters. We show cooling significantly affects the mass outflow rate, to the extent that, jets may be generated from flows with higher viscosity. We discuss that our formalism may be employed to explain observed jet power for a couple of black hole candidates. We also indicate that using our formalism, it is possible to connect the spectral properties of the disc with the rate of mass loss.