The Global Baroclinic Instability in Accretion Disks. II: Local Linear Analysis

This paper contains a local linear stability analysis for accretion disks under the influence of a global radial entropy gradient beta = - d log T / d log r for constant surface density. Numerical simulations suggested the existence of an instability in two- and three-dimensional models of the solar nebula. The present paper tries to clarify, quantify, and explain such a global baroclinic instability for two-dimensional flat accretion disk models. As a result linear theory predicts a transient linear instability that will amplify perturbations only for a limited time or up to a certain finite amplification. This can be understood as a result of the growth time of the instability being longer than the shear time which destroys the modes which are able to grow. So only non-linear effects can lead to a relevant amplification. Nevertheless, a lower limit on the entropy gradient ~beta = 0.22 for the transient linear instability is derived, which can be tested in future non-linear simulations. This would help to explain the observed instability in numerical simulations as an ultimate result of the transient linear instability, i.e. the Global Baroclinic Instability.Comment: 35 pages, 11 figures; ApJ in pres

An Exact, Three-Dimensional, Time-Dependent Wave Solution in Local Keplerian Flow

We present an exact three-dimensional wave solution to the shearing sheet equations of motion. The existence of this solution argues against transient amplification as a route to turbulence in unmagnetized disks. Moreover, because the solution covers an extensive dynamical range in wavenumber space, it is an excellent test of the dissipative properties of numerical codes.Comment: 22 pages, 4 figures. To appear Apj Dec 1 200

Gravity-modes in ZZ Ceti Stars. II. Effects of Turbulent Dissipation

We investigate dynamical interactions between turbulent convection and g-mode pulsations in ZZ Ceti variables (DAVs). Since our understanding of turbulence is rudimentary, we are compelled to settle for order of magnitude results. A key feature of these interactions is that convective response times are much shorter than pulsation periods. Thus the dynamical interactions enforce near uniform horizontal velocity inside the convection zone. They also give rise to a narrow shear layer in the region of convective overshoot at the top of the radiative interior. Turbulent damping inside the convection zone is negligible for all modes, but that in the region of convective overshoot may be significant for a few long period modes near the red edge of the instability strip. These conclusions are in accord with those reached earlier by Brickhill. Our major new result concerns nonlinear damping arising from the Kelvin-Helmholtz instability of the aforementioned shear layer. Amplitudes of overstable modes saturate where dissipation due to this instability balances excitation by convective driving. This mechanism of amplitude saturation is most effective for long period modes, and it may play an important role in defining the red edge of the instability strip.Comment: 7 pages, including 2 figures. Used emulateapj.sty and apjfonts.sty obtained from http://hea-www.harvard.edu/~alexey/emulateapj

Spectral Methods for Time-Dependent Studies of Accretion Flows. II. Two-Dimensional Hydrodynamic Disks with Self-Gravity

Spectral methods are well suited for solving hydrodynamic problems in which the self-gravity of the flow needs to be considered. Because Poisson's equation is linear, the numerical solution for the gravitational potential for each individual mode of the density can be pre-computed, thus reducing substantially the computational cost of the method. In this second paper, we describe two different approaches to computing the gravitational field of a two-dimensional flow with pseudo-spectral methods. For situations in which the density profile is independent of the third coordinate (i.e., an infinite cylinder), we use a standard Poisson solver in spectral space. On the other hand, for situations in which the density profile is a delta function along the third coordinate (i.e., an infinitesimally thin disk), or any other function known a priori, we perform a direct integration of Poisson's equation using a Green's functions approach. We devise a number of test problems to verify the implementations of these two methods. Finally, we use our method to study the stability of polytropic, self-gravitating disks. We find that, when the polytropic index Gamma is <= 4/3, Toomre's criterion correctly describes the stability of the disk. However, when Gamma > 4/3 and for large values of the polytropic constant K, the numerical solutions are always stable, even when the linear criterion predicts the contrary. We show that, in the latter case, the minimum wavelength of the unstable modes is larger than the extent of the unstable region and hence the local linear analysis is inapplicable.Comment: 13 pages, 9 figures. To appear in the ApJ. High resolution plots and animations of the simulations are available at http://www.physics.arizona.edu/~chan/research/astro-ph/0512448/index.htm

Spectral Energy Distributions of Passive T Tauri Disks: Inclination

We compute spectral energy distributions (SEDs) for passive T Tauri disks viewed at arbitrary inclinations. Semi-analytic models of disks in radiative and hydrostatic equilibrium are employed. Over viewing angles for which the flared disk does not occult the central star, the SED varies negligibly with inclination. For such aspects, the SED shortward of ~80 microns is particularly insensitive to orientation, since short wavelength disk emission is dominated by superheated surface layers which are optically thin. The SED of a nearly edge-on disk is that of a class I source. The outer disk occults inner disk regions, and emission shortward of ~30 microns is dramatically extinguished. Spectral features from dust grains may appear in absorption. However, millimeter wavelength fluxes decrease by at most a factor of 2 from face-on to edge-on orientations. We present illustrative applications of our SED models. The class I source 04108+2803B is considered a T Tauri star hidden from view by an inclined circumstellar disk. Fits to its observed SED yield model-dependent values for the disk mass of ~0.015 solar masses and a disk inclination of ~65 degrees relative to face-on. The class II source GM Aur represents a T Tauri star unobscured by its circumstellar disk. Fitted parameters include a disk mass of \~0.050 solar masses and an inclination of ~60 degrees.Comment: Accepted to ApJ, 20 pages, 7 figures, aaspp4.st

Research at Palomar Observatory in planetary astronomy

A wide range of observational studies are carried out to improve our understanding of the bodies of the outer solar system. Using the 200-inch Hale telescope, near-infrared observations are made of Uranus, Neptune, and the Pluto-Charon system. High time resolution occultation observations of the Uranus Ring system are used to study in detail the dynamics of this system. Occultation studies of Neptune are probing this intriguing ring-arc system. Occulation observations of the Pluto-Charon system probe the surface properties of these distant bodies. In addition, the plate material of the PSSII servey is being used to search for new comets and asteroids. Researchers observed one Neptune stellar occultation in July 1987 and completed the analysis of a series of seven separate Neptune occultation observations in conjunction with Nicholson et al., of Cornell. The analysis has shown that minimum of three ring arcs, at radii ranging from 54,000 km - 67,000 km are required to account for the high quality ring events. Current theoretical models can account for these data. Of two observations scheduled of Pluto-Charon mutual occulations scheduled for the 200-inch, the Charon eclipse event was successfully observed (the other was clouded out)

Compressible MHD Turbulence in Interstellar Plasmas

Radio-wave scintillation observations reveal a nearly Kolmogorov spectrum of density fluctuations in the ionized interstellar medium. Although this density spectrum is suggestive of turbulence, no theory relevant to its interpretation exists. We calculate the density spectrum in turbulent magnetized plasmas by extending the theory of incompressible MHD turbulence given by Goldreich & Sridhar to include the effects of compressibility and particle transport. Our most important results are as follows. (1) Density fluctuations are due to the slow mode and the entropy mode. Both modes are passively mixed by the cascade of shear Alfven waves. Since the shear Alfven waves have a Kolmogorov spectrum, so do the density fluctuations. (2) Observed density fluctuation amplitudes imply either that the magnetic and gas pressures are comparable, or that the outer scale of the turbulence is very small. (3) A high degree of ionization is required for the cascade to survive damping by neutrals and thereby to extend to small lengthscales. Regions that are insufficiently ionized produce density fluctuations only on lengthscales larger than the neutral damping scale. These regions may account for the excess of power that is found on large scales. (4) Both the entropy mode and the slow mode are damped on lengthscales below that at which protons can diffuse across an eddy during the eddy's turnover time. Consequently, eddies whose extents along the magnetic field are smaller than the proton collisional mean free path do not contribute to the density spectrum. However, in MHD turbulence eddies are highly elongated along the magnetic field. From an observational perspective, the relevant lengthscale is that transverse to the magnetic field. Thus the cut-off lengthscale for density fluctuations is significantly smaller than the proton mean free path.Comment: 19 pages, 2 figures, submitted to Ap

Neutron starquakes and the nature of gamma-ray bursts

The possibility that gamma-ray bursts originate from quakes deep in the solid crust of a neutron star is investigated. Seismic waves are radiated if shear stress is relieved by brittle fracture. However they cannot propagate directly to the surface but are temporarily trapped below a reflecting layer. The shaking of the stellar surface couples the seismic waves to Alfven waves which propagate out into the magnetosphere. The crust-magnetosphere transmission coefficient strongly increases with wave frequency and magnetic field strength. Alfven wave luminosities sufficient to power galactic gamma-ray bursts are possible if magnetic fields greater than 100 billion G cover at least part of the stellar surface. As the Alfven waves propagate out into the low density magnetosphere, they become increasingly charge starved, thereby accelerating particles to relativistic energies

Resonant capture by inward migrating planets

We investigate resonant capture of small bodies by planets that migrate inwards, using analytic arguments and three-body integrations. If the orbits of the planet and the small body are initially circular and coplanar, the small body is captured when it crosses the 2:1 resonance with the planet. As the orbit shrinks it becomes more eccentric, until by the time its semimajor axis has shrunk by a factor of four, its eccentricity reaches nearly unity (1-e<<10^{-4}). In typical planetary systems, bodies in this high-eccentricity phase are likely to be consumed by the central star. If they can avoid this fate, as migration continues the inclination flips from 0 to i=180 degrees; thereafter the eccentricity declines until the semimajor axis is a factor of nine smaller than at capture, at which point the small body is released from the 2:1 resonance on a nearly circular retrograde orbit. Small bodies captured into resonance from initially inclined or eccentric orbits can also be ejected from the system, or released from the resonance on highly eccentric polar orbits (i\simeq 90 degrees) that are stabilized by a secular resonance. We conclude that migration can drive much of the inner planetesimal disk into the star, and that post-migration multi-planet systems may not be coplanar.Comment: 12 pages, 5 figures, submitted to Astronomical Journa

Honest Verifier Statistical Zero-Knowledge Equals General Statistical Zero-Knowledge

We show how to transform any interactive proof system which is statistical zero-knowledge with respect to the honest-verifier, into a proof system which is statistical zero-knowledge with respect to any verifier. This is done by limiting the behavior of potentially cheating verifiers, without using computational assumptions or even referring to the complexity of such verifier strategies. (Previous transformations have either relied on computational assumptions or were applicable only to constant-round public-coin proof systems.) Our transformation also applies to public-coin (aka Arthur-Merlin) computational zero-knowledge proofs: We transform any Arthur-Merlin proof system which is computational zero-knowledge with respect to the honest-verifier, into an Arthur-Merlin proof system which is computational zero-knowledge with respect to any probabilistic polynomial-time verifier. A crucial ingredient in our analysis is a new lemma regarding 2-universal hashing functions.Engineering and Applied Science