Dissipative Disk Research Articles

Dynamics of Planetary Systems within Star Clusters: Aspects of the Solar System’s Early Evolution

Abstract Most planetary systems—including our own—are born within stellar clusters, where interactions with neighboring stars can help shape the system architecture. This paper develops an orbit-averaged formalism to characterize the cluster’s mean-field effects, as well as the physics of long-period stellar encounters. Our secular approach allows for an analytic description of the dynamical consequences of the cluster environment on its constituent planetary systems. We analyze special cases of the resulting Hamiltonian, corresponding to eccentricity evolution driven by planar encounters, as well as hyperbolic perturbations upon dissipative disks. We subsequently apply our results to the early evolution of our solar system, where the cluster’s collective potential perturbs the solar system’s plane, and stellar encounters act to increase the velocity dispersion of the Kuiper Belt. Our results are twofold. First, we find that cluster effects can alter the mean plane of the solar system by ≲1° and are thus insufficient to explain the ψ ≈ 6° obliquity of the Sun. Second, we delineate the extent to which stellar flybys excite the orbital dispersion of the cold classical Kuiper Belt and show that while stellar flybys may grow the cold belt’s inclination by the observed amount, the resulting distribution is incompatible with the data. Correspondingly, our calculations place an upper limit on the product of the stellar number density and residence time of the Sun in its birth cluster, η τ ≲ 2 × 104 Myr pc−3.

Quadratic dissipation effect on the moonpool resonance

This paper adopted a semi-analytical method based on eigenfunction matching to solve the problem of sharp resonance of cylindrical structures with a moonpool that has a restricted entrance. To eliminate the sharp resonance and to measure the viscous effect, a quadratic dissipation is introduced by assuming an additional dissipative disk at the moonpool entrance. The fluid domain is divided into five cylindrical subdomains, and the velocity potential in each subdomain is obtained by meeting the Laplace equation as well as the boundary conditions. The free-surface elevation at the center of the moonpool, along with the pressure and velocity at the restricted entrance for first-order wave are evaluated. By choosing appropriate dissipation coefficients, the free-surface elevation calculated at the center of the moonpool is in coincidence with the measurements in model tests both at the peak period and amplitude at resonance. It is shown that the sharp resonance in the potential flow theory can be eliminated and the viscous effect can be estimated with a simple method in some provided hydrodynamic models.

Warm and optically thick dissipative coronae above accretion disks

In the past years, several observations of AGN and X-ray binaries have suggested the existence of a warm T around 0.5-1 keV and optically thick, \tau ~ 10-20, corona covering the inner parts of the accretion disk. These properties are directly derived from spectral fitting in UV to soft-X-rays using Comptonization models. However, whether such a medium can be both in radiative and hydrostatic equilibrium with an accretion disk is still uncertain. We investigate the properties of such warm, optically thick coronae and put constraints on their existence. We solve the radiative transfer equation for grey atmosphere analytically in a pure scattering medium, including local dissipation as an additional heating term in the warm corona. The temperature profile of the warm corona is calculated assuming it is cooled by Compton scattering, with the underlying dissipative disk providing photons to the corona. Our analytic calculations show that a dissipative thick, (\tau_{cor} ~ 10-12) corona on the top of a standard accretion disk can reach temperatures of the order of 0.5-1 keV in its upper layers provided that the disk is passive. But, in absence of strong magnetic fields, the requirement of a Compton cooled corona in hydrostatic equilibrium in the vertical direction sets an upper limit on the Thomson optical depth \tau_{cor} < 5 . We show this value cannot be exceeded independently of the accretion disk parameters. However, magnetic pressure can extend this result to larger optical depths. Namely, a dissipative corona might have an optical depth up to ~ 20 when the magnetic pressure is 100 times higher that the gas pressure. The observation of warm coronae with Thomson depth larger than ~ 5 puts tights constraints on the physics of the accretion disk/corona systems and requires either strong magnetic fields or vertical outflows to stabilize the system.

THE UNUSUAL QUADRUPLE SYSTEM HD 91962 WITH A “PLANETARY” ARCHITECTURE

The young nearby solar-type star HD 91962 is a rare quadruple system where three companions revolve around the main component with periods of 170.3 days, 8.85 years, and 205 years. The two outer orbits are nearly co-planar, and all orbits have small eccentricities. We refine the visual orbit of the outer pair, determine the combined spectro-interferometric orbit of the middle 8.8-yr pair and the spectroscopic orbit of the inner binary. The middle and inner orbits are likely locked in a 1:19 resonance, the ratio of the outer and middle periods is ~23. The masses of all components are estimated (inside-out: 1.14, 0.32, 0.64, 0.64 solar mass), the dynamical parallax is 27.4+-0.6 mas. We speculate that this multiple system originated from collapse of an isolated core and that the companions migrated in a dissipative disk. Other multiple systems with similar features (coplanarity, small eccentricity, and period ratio around 20) are known.

Mean-Motion Resonances of High Order in Extrasolar Planetary Systems

Many multi-planet systems have been discovered in recent years. Some of them are in mean-motion resonances (MMR). Planet formation theory was successful in explaining the formation of 2:1, 3:1 and other low resonances as a result of convergent migration. However, higher order resonances require high initial orbital eccentricities in order to be formed by this process and these are in general unexpected in a dissipative disk. We present a way of generating large initial eccentricities using additional planets. This procedure allows us to form high order MMRs and predict new planets using a genetic N-body code.

Global Magnetorotational Instability with Inflow. II. The Nonlinear Development of Axisymmetric Wall Modes

We investigate numerically the global, nonlinear behavior of magnetorotational instabilities in accretion disks by considering our previously formulated model of a cylindrical, dissipative disk with permeable boundaries. We extend the linear theory to follow the development of unstable, axisymmetric, magnetorotational modes into the nonlinear regime to determine the saturation mechanism. In each case parameters are chosen so that the most unstable mode is localized close to the inner boundary. We conduct an extensive parameter survey and find that the nonlinear behavior is mediated by the formation of a coherent radial jet that transports vertical magnetic flux within the disk. The mechanism for saturation depends critically on the strength of this jet. Different scenarios for saturation are explored in detail. The instability can either saturate in a nonlinear steady or oscillatory, non-Keplerian state, or relax back to a Keplerian state via the removal of flux from the disk by the jet.

Rheophysics of dense granular materials: Discrete simulation of plane shear flows

We study the plane shear flow of a dense assembly of dissipative disks using discrete simulation and prescribing the pressure and the shear rate. Those shear states are steady and uniform, and become intermittent in the quasistatic regime. In the limit of rigid grains, the shear state is determined by a single dimensionless number, called the inertial number I , which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasistatic critical state of soil mechanics, while large values of I correspond to the fully collisional regime of kinetic theory. When I increases in the intermediate dense flow regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. The mechanical characteristics of the grains (restitution, friction, and elasticity) have a small influence in the dense flow regime. Finally, we show that the evolution of the relative velocity fluctuations and of the contact force anisotropy as a function of I provides a simple explanation of the friction law.

Granular Flows: Boundary Conditions for Slightly Bumpy Walls

An approximate analytical solution of the boundary conditions of Pasquarell and Ackermann is presented for the simple shear Couette flow of identical, smooth, slightly inelastic disks in the limit where a parametric measure of the wall form roughness is small. Excellent agreement is shown between the approximate solution and a numerical solution of the original integral equations. The solution predicts that simple shear Couette flow only occurs for unique combinations of wall and particle properties. As the wall form roughness decreases, so must the wall elasticity in order to sustain simple shear. The theory is applied to previous experimental work in which shear cells were used to study granular flows. Experimental observations comparing soft to hard walls and bumpy to smooth walls are explained in the context of the theory. It is shown that the accuracy of such experimental results is greatly increased when the walls in the shear cells are nearly elastic and roughened with closely spaced elements of dimensions on the same order or larger than the diameter of the sheared particles. These boundary conditions may be employed in problems involving more dissipative disks than those considered herein.