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1
MUKHOPADHYAY, BANIBRATA. "ESTIMATE OF THE SHAKURA–SUNYAEV VISCOSITY PARAMETER IN THE KEPLERIAN ACCRETION DISK FROM HYDRODYNAMIC TURBULENCE." International Journal of Modern Physics D 17, no. 03n04 (March 2008): 467–73. http://dx.doi.org/10.1142/s0218271808012139.
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Recently, in a series of papers, Mukhopadhyay and his collaborators have argued for possible pure hydrodynamic turbulence in a Keplerian accretion disk. This is essentially important to solving the puzzle of the transport mechanism in cold accretion disk systems where the temperature could be lower than 5000 K, where magnetorotational instability seems not to be working to trigger turbulence. Here we quantify the corresponding instability and turbulence in terms of turbulent viscosity and obtain the famous Shakura–Shunyaev viscosity parameter, α. It is exciting that the range of α obtained from our analysis is 0.1 ≳ α ≳ 0.0001 for a realistic parameter region. This range also suggests that once the hydrodynamic instability described by Mukhopadhyay and his collaborators leads to turbulence — an effect which should exist in systems independent of being hot or cold — the effect may compete with the magnetohydrodynamic effect even in hot accretion disks and thus may be effective in transporting matter in hot gas systems as well.
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CASSARO, P., F. SCHILLIRÓ, V. COSTA, G. BELVEDERE, R. A. ZAPPALÁ, and G. LANZAFAME. "THE ENGINE OF OUTFLOWS IN AGN: THE ROLE OF PHYSICAL TURBULENT VISCOSITY." International Journal of Modern Physics D 17, no. 09 (September 2008): 1635–40. http://dx.doi.org/10.1142/s0218271808013248.
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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.
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Chen, Yi-Xian, Yan-Fei Jiang, Jeremy Goodman, and Eve C. Ostriker. "3D Radiation Hydrodynamic Simulations of Gravitational Instability in AGN Accretion Disks: Effects of Radiation Pressure." Astrophysical Journal 948, no. 2 (May 1, 2023): 120. http://dx.doi.org/10.3847/1538-4357/acc023.
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Abstract We perform 3D radiation hydrodynamic local shearing-box simulations to study the outcome of gravitational instability (GI) in optically thick active galactic nuclei (AGNs) accretion disks. GI develops when the Toomre parameter Q T ≲ 1, and may lead to turbulent heating that balances radiative cooling. However, when radiative cooling is too efficient, the disk may undergo runaway gravitational fragmentation. In the fully gas-pressure-dominated case, we confirm the classical result that such a thermal balance holds when the Shakura–Sunyaev viscosity parameter (α) due to the gravitationally driven turbulence is ≲0.2, corresponding to dimensionless cooling times Ωt cool ≳ 5. As the fraction of support by radiation pressure increases, the disk becomes more prone to fragmentation, with a reduced (increased) critical value of α (Ωt cool). The effect is already significant when the radiation pressure exceeds 10% of the gas pressure, while fully radiation-pressure-dominated disks fragment at t cool ≲ 50 Ω−1. The latter translates to a maximum turbulence level α ≲ 0.02, comparable to that generated by magnetorotational instability. Our results suggest that gravitationally unstable (Q T ∼ 1) outer regions of AGN disks with significant radiation pressure (likely for high/near-Eddington accretion rates) should always fragment into stars, and perhaps black holes.
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Bi, Jiaqing, and Jeffrey Fung. "Dust Dynamics in Transitional Disks: Clumping and Disk Recession." Astrophysical Journal 928, no. 1 (March 1, 2022): 74. http://dx.doi.org/10.3847/1538-4357/ac53ac.
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Abstract The role of radiation pressure in dust migration and the opening of inner cavities in transitional disks is revisited in this paper. Dust dynamics including radiation pressure is often studied in axisymmetric models, but in this work, we show that highly non-axisymmetric features can arise from an instability at the inner disk edge. Dust grains clump into high density features there, allowing radiation to leak around them and penetrate deeper into the disk, changing the course of dust migration. Our proof-of-concept, two-dimensional, vertically averaged simulations show that the combination of radiation pressure, shadowing, and gas drag can produce a net outward migration, or recession, of the dust component of the disk. The recession speed of the inner disk edge is on the order of 10−5 times Keplerian speed in our parameter space, which is faster than the background viscous flow, assuming a Shakura–Sunyaev viscosity α ≲ 10−3. This speed, if sustained over the lifetime of the disk, can result in a dust cavity as large as tens of astronomical units.
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Sellek, Andrew D., Richard A. Booth, and Cathie J. Clarke. "The evolution of dust in discs influenced by external photoevaporation." Monthly Notices of the Royal Astronomical Society 492, no. 1 (December 18, 2019): 1279–94. http://dx.doi.org/10.1093/mnras/stz3528.
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ABSTRACT Protoplanetary discs form and evolve in a wide variety of stellar environments and are accordingly exposed to a wide range of ambient far-ultraviolet (FUV) field strengths. Strong FUV fields are known to drive vigorous gaseous flows from the outer disc. In this paper we conduct the first systematic exploration of the evolution of the solid component of discs subject to external photoevaporation. We find that the main effect of photoevaporation is to reduce the reservoir of dust at large radii and this leads to more efficient subsequent depletion of the disc dust due to radial drift. Efficient radial drift means that photoevaporation causes no significant increase of the dust-to-gas ratio in the disc. We show that the disc lifetime in both dust and gas is strongly dependent on the level of the FUV background and that the relationship between these two lifetimes just depends on the Shakura–Sunyaev α parameter, with the similar lifetimes observed for gas and dust in discs pointing to higher α values (∼10−2). On the other hand, the distribution of observed discs in the plane of disc size versus flux at 850 μm is better reproduced by lower α (∼10−3). We find that photoevaporation does not assist rocky planet formation but need not inhibit mechanisms (such as pebble accretion at the water snow line) which can be effective sufficiently early in the disc’s lifetime (i.e. well within a Myr).
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Trapman, Leon, Benoît Tabone, Giovanni Rosotti, and Ke Zhang. "Effect of MHD Wind-driven Disk Evolution on the Observed Sizes of Protoplanetary Disks." Astrophysical Journal 926, no. 1 (February 1, 2022): 61. http://dx.doi.org/10.3847/1538-4357/ac3ed5.
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Abstract It is still unclear whether the evolution of protoplanetary disks, a key ingredient in the theory of planet formation, is driven by viscous turbulence or magnetic disk winds. As viscously evolving disks expand outward over time, the evolution of disk sizes is a discriminant test for studying disk evolution. However, it is unclear how the observed disk size changes over time if disk evolution is driven by magnetic disk winds. Combining the thermo-chemical code DALI with the analytical wind-driven disk-evolution model presented in Tabone et al., we study the time evolution of the observed gas outer radius as measured from CO rotational emission (R CO,90%). The evolution of R CO,90% is driven by the evolution of the disk mass, as the physical radius stays constant over time. For a constant α DW , an extension of the α Shakura–Sunyaev parameter to wind-driven accretion, R CO,90% decreases linearly with time. Its initial size is set by the disk mass and the characteristic radius R c,0, but only R c,0 affects the evolution of R CO,90%, with a larger R c,0 resulting in a steeper decrease of R CO,90%. For a time-dependent α DW , R CO,90% stays approximately constant during most of the disk lifetime until R CO,90% rapidly shrinks as the disk dissipates. The constant α DW models are able to reproduce the observed gas disk sizes in the ∼1–3 Myr old Lupus and ∼5–11 Myr old Upper Sco star-forming regions. However, they likely overpredict the gas disk size of younger (⪅0.7 Myr) disks.
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Proga, Daniel, Janet E. Drew, and James M. Stone. "Radiation driven winds from CV accretion disks." International Astronomical Union Colloquium 163 (1997): 782. http://dx.doi.org/10.1017/s0252921100043967.
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AbstractWe present some initial results of our numerical, 2D hydrodynamical models of line driven flows from the accretion disk in cataclysmic variables. We assume the disk radiation pressure pushes out the isothermal material from a flat, geometrically thin, Keplerian disk.We calculate the disk radiation field using the surface brightness of a standard “α disk” (Shakura & Sunyaev 1973). We do not include a bright boundary layer in the calculations. We approximate the total radiative line acceleration, adopting the formalism due to Castor, Abbott, & Klein (1975). We use our generalized 2D version of their force multiplier. The multiplier is still described by two parameters representing the number of lines and the ratio of optically thin to optically thick lines. The main modification of the original CAK force multiplier is in the depth parameter, which is now a function of the gradients of two velocity components instead of the single velocity gradient as in the ID case.We investigate how the disk structure and mass loss rate depend on the disk and central star luminosity, and boundary conditions such as the disk density.We find that transonic flows from disks do not relax toward steady states. However, their time averaged properties become constant after some time. Our models show that most of mass loss originates from close to the central star – a few stellar radii. Models without a central star radiation field produce flows more vertical than models in which one is present. However, other global, time averaged properties of flows such as the total wind mass, the wind mass loss rate, and velocity are similar. The ratio between the wind mass loss and disk accretion rate increases rapidly with the accrection rate.
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Delage, Timmy N., Satoshi Okuzumi, Mario Flock, Paola Pinilla, and Natalia Dzyurkevich. "Steady-state accretion in magnetized protoplanetary disks." Astronomy & Astrophysics 658 (February 2022): A97. http://dx.doi.org/10.1051/0004-6361/202141689.
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Context. The transition between magnetorotational instability (MRI)-active and magnetically dead regions corresponds to a sharp change in the disk turbulence level, where pressure maxima may form, hence potentially trapping dust particles and explaining some of the observed disk substructures. Aims. We aim to provide the first building blocks toward a self-consistent approach to assess the dead zone outer edge as a viable location for dust trapping, under the framework of viscously driven accretion. Methods. We present a 1+1D global magnetically driven disk accretion model that captures the essence of the MRI-driven accretion, without resorting to 3D global nonideal magnetohydrodynamic (MHD) simulations. The gas dynamics is assumed to be solely controlled by the MRI and hydrodynamic instabilities. For given stellar and disk parameters, the Shakura–Sunyaev viscosity parameter, α, is determined self-consistently under the adopted framework from detailed considerations of the MRI with nonideal MHD effects (Ohmic resistivity and ambipolar diffusion), accounting for disk heating by stellar irradiation, nonthermal sources of ionization, and dust effects on the ionization chemistry. Additionally, the magnetic field strength is numerically constrained to maximize the MRI activity. Results. We demonstrate the use of our framework by investigating steady-state MRI-driven accretion in a fiducial protoplanetary disk model around a solar-type star. We find that the equilibrium solution displays no pressure maximum at the dead zone outer edge, except if a sufficient amount of dust particles has accumulated there before the disk reaches a steady-state accretion regime. Furthermore, the steady-state accretion solution describes a disk that displays a spatially extended long-lived inner disk gas reservoir (the dead zone) that accretes a few times 10−9 M⊙ yr−1. By conducting a detailed parameter study, we find that the extent to which the MRI can drive efficient accretion is primarily determined by the total disk gas mass, the representative grain size, the vertically integrated dust-to-gas mass ratio, and the stellar X-ray luminosity. Conclusions. A self-consistent time-dependent coupling between gas, dust, stellar evolution models, and our general framework on million-year timescales is required to fully understand the formation of dead zones and their potential to trap dust particles.
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Granada, A., C. E. Jones, and T. A. A. Sigut. "The Viscosity Parameter for Late-type Stable Be Stars." Astrophysical Journal 922, no. 2 (November 26, 2021): 148. http://dx.doi.org/10.3847/1538-4357/ac222f.
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Abstract Using hydrodynamic principles we investigate the nature of the disk viscosity following the parameterization by Shakura & Sunyaev adopted for the viscous decretion model in classical Be stars. We consider a radial viscosity distribution including a constant value, a radially variable α assuming a power-law density distribution, and isothermal disks, for a late-B central star. We also extend our analysis by determining a self-consistent temperature disk distribution to model the late-type Be star 1 Delphini, which is thought to have a nonvariable, stable disk as evidenced by Hα emission profiles that have remained relatively unchanged for decades. Using standard angular momentum loss rates given by Granada et al., we find values of α of approximately 0.3. Adopting lower values of angular momentum loss rates, i.e., smaller mass loss rates, leads to smaller values of α. The values for α vary smoothly over the Hα emitting region and exhibit the biggest variations nearest the central star within about five stellar radii for the late-type, stable Be stars.
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Ma, Zhen Guo, and Xi Zhen Zhang. "Prediction of the Black-Hole Mass in 3C 273 by Multiband Observations." Symposium - International Astronomical Union 214 (2003): 281–86. http://dx.doi.org/10.1017/s0074180900194574.
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With the determined black-hole (BH) spin of 3C 273 by data-fitting to the detected iron Kα line emission in the soft X-ray band, the BH mass of the galaxy is predicted by formulations of both the observed disk-luminosity in the optical-UV band and the observed jet-precession in the radio band. The multiband synthesis suggests that the BH is supermassive, 2.4 × 109M⊙. Simultaneously, other physical parameters are self-consistently obtained at the precessing radius of 230.2rg: the accretion rate of the disk is 74.9M⊙ yr−1, the Shakura-Sunyaev viscosity α is 0.134, and the radial & orbital velocities of fluid elements are 4.3 × 10−8 and 6.6 × 10−2, respectively.
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Mao, Shunyuan, Ruobing Dong, Lu Lu, Kwang Moo Yi, Sifan Wang, and Paris Perdikaris. "PPDONet: Deep Operator Networks for Fast Prediction of Steady-state Solutions in Disk–Planet Systems." Astrophysical Journal Letters 950, no. 2 (June 1, 2023): L12. http://dx.doi.org/10.3847/2041-8213/acd77f.
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Abstract We develop a tool, which we name Protoplanetary Disk Operator Network (PPDONet), that can predict the solution of disk–planet interactions in protoplanetary disks in real time. We base our tool on Deep Operator Networks, a class of neural networks capable of learning nonlinear operators to represent deterministic and stochastic differential equations. With PPDONet we map three scalar parameters in a disk–planet system—the Shakura–Sunyaev viscosity α, the disk aspect ratio h 0, and the planet–star mass ratio q—to steady-state solutions of the disk surface density, radial velocity, and azimuthal velocity. We demonstrate the accuracy of the PPDONet solutions using a comprehensive set of tests. Our tool is able to predict the outcome of disk–planet interaction for one system in less than a second on a laptop. A public implementation of PPDONet is available at https://github.com/smao-astro/PPDONet.
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Gurzadyan, Vahagn G. "General Discussion of Accretion Disks." Symposium - International Astronomical Union 194 (1999): 321–22. http://dx.doi.org/10.1017/s0074180900162205.
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Even 25 years after the Shakura-Sunyaev seminal paper on the α-disk, we cannot claim that we have a reliable theory of accretion disks in galactic nuclei. Why? Because the problem is extremely complicated, it is essentially nonlinear and contains a number of parameters (i.e. is many-dimensional). The key point is whether it is possible to determine the magneto-hydrodynamical viscosity self-consistently, i.e. as a function of parameters of the disk - the temperature, matter and radiation densities, magnetic field, radius, etc., both in the radiation dominated and matter dominated regions. Another class of fundamental problems concerns the stability of the disk; Krolik mentioned only one instability - in the radiation dominated region, but there are many other types of instabilities which are quite sensitive to the physical conditions in the disk, for example, to the anisotropy of the ion pressure in the outer regions and possible electron-positron pair production near the inner edge of the disk. The other problems include those of the radiative transfer within the disk in various conditions, Comptonization of the outgoing radiation, radiation reflections by the desk, etc. Therefore it is not suprising that one can ‘explain' almost whatever he wants - spectra, variability, jets, wind, etc., by proper fit of the ‘free’ (which are never free) parameters and ignoring the instabilities and so on.
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Riffert, H., T. Dörrer, R. Staubert, and H. Ruder. "The Vertical Structures of Accretion Disks in AGN." Symposium - International Astronomical Union 159 (1994): 478. http://dx.doi.org/10.1017/s0074180900176557.
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Radiation emitted from an accretion disk around a central black hole is the widely accepted model for the observed optical to UV emission from AGN. We have calculated the properties of a standard α-accretion disk (Shakura and Sunyaev, 1973). We present a fully self-consistent model of the structure and the spectrum of such a disk, i.e. the internal vertical density and temperature profiles are calculated simultaneously with the local spectra. Constant density models have been presented by (Ross et al., 1992). The central object is assumed to be a Kerr black hole (BH); relativistic corrections are included. The local energy production is assumed to be entirely due to turbulence. The radiative transfer equation is solved using the Eddington approximation. Inelastic Compton scattering is treated approximately by the Kompaneets equation, and the absorption cross section contains free-free and bound-free processes for hydrogen. The energy transport includes radiation and convection, and the convective flux is calculated in the mixing length theory, taking into account the heating and cooling of the rising elements. Although the convective flux is energetically negligible it has a strong influence on the vertical density structure. We performed several calculations for different parameters such as Ṁ and α. In regions, where the surface radiation flux is large, we get a strong density inversion because the radiation force per unit mass overcomes the gravitational force. Such a density profile, however, is unstable against convection. Including the convective flux then leads to a monotonic density profile. Figures 1 and 2 show the structure and integrated spectrum for two different disk models.
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Shende, Mayur B., Prashali Chauhan, and Prasad Subramanian. "X-ray Dips in AGN and Microquasars – Collapse Timescales of Inner Accretion Disc." Monthly Notices of the Royal Astronomical Society, December 12, 2020. http://dx.doi.org/10.1093/mnras/staa3838.
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Abstract The temporal behaviour of X-rays from some AGN and microquasars is thought to arise from the rapid collapse of the hot, inner parts of their accretion discs. The collapse can occur over the radial infall timescale of the inner accretion disc. However, estimates of this timescale are hindered by a lack of knowledge of the operative viscosity in the collisionless plasma comprising the inner disc. We use published simulation results for cosmic ray diffusion through turbulent magnetic fields to arrive at a viscosity prescription appropriate to hot accretion discs. We construct simplified disc models using this viscosity prescription and estimate disc collapse timescales for 3C 120, 3C 111, and GRS 1915+105. The Shakura-Sunyaev α parameter resulting from our model ranges from 0.02 to 0.08. Our inner disc collapse timescale estimates agree well with those of the observed X-ray dips. We find that the collapse timescale is most sensitive to the outer radius of the hot accretion disc.
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Sánchez-Salcedo, F. J., R. O. Chametla, and O. Chrenko. "Estimating the depth of gaps opened by planets in eccentric orbit." Monthly Notices of the Royal Astronomical Society, October 6, 2022. http://dx.doi.org/10.1093/mnras/stac2856.
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Abstract Planets can carve gaps in the surface density of protoplanetary discs. The formation of these gaps can reduce the corotation torques acting on the planets. In addition, gaps can halt the accretion of solids onto the planets as dust and pebbles can be trapped at the edge of the gap. This accumulation of dust could explain the origin of the ring-like dust structures observed using high-resolution interferometry. In this work we provide an empirical scaling relation for the depth of the gap cleared by a planet on an eccentric orbit as a function of the planet-to-star mass ratio q, the disc aspect ratio h, Shakura-Sunyaev viscosity parameter α, and planetary eccentricity e. We construct the scaling relation using a heuristic approach: we calibrate a toy model based on the impulse approximation with 2D hydrodynamical simulations. The scaling reproduces the gap depth for moderate eccentricities (e ≤ 4h) and when the surface density contrast outside and inside the gap is ≤102. Our framework can be used as the basis of more sophisticated models aiming to predict the radial gap profile for eccentric planets.