Studies of heat source driven natural convection

Natural convection energy transport in a horizontal layer of internally heated fluid with a zero heat flux lower boundary, and an isothermal upper boundary, has been studied. Quantitative information on the time-mean temperature distribution and the fluctuating component of temperature about the mean temperature in steady turbulent convection are obtained from a small thermocouple inserted into the layer through the upper bounding plate. Data are also presented on the development of temperature at several vertical positions when the layer is subject to both a sudden increase and to a sudden decrease in power input. For changes of power input from zero to a value corresponding to a Rayleigh number much greater than the critical linear stability theory value, a slight hysteresis in temperature profiles near the upper boundary is observed between the heat-up and cool-down modes

The viscosity of Miranda

Voyager 2 images of Miranda revealed a significant history of geological activity. Overlying an apparently ancient cratered terrain are assemblages of concentric ridges, scarps, and dark banded material. The problems that evolutionary thermal and structural modes of Miranda must face, to provide a convincing explanation for such topographic complexity, are examined

Protostellar disks and the primitive solar nebula

The objective is to obtain quantitative information on the turbulent transport of mass, angular momentum, and energy under the conditions that characterize the solar nebula, by direct numerical calculations. These calculations were made possible by research conducted on supercomputers (Cray XMP and Cray 2) by the Ames Computational Fluid Dynamics Branch. Techniques were developed that permitted the accurate representation of turbulent flows over the full range of important eddy sizes. So far, these techniques were applied (and verified) primarily in mundane laboratory situations, but they have a strong potential for astrophysical applications. A sequence of numerical experiments were conducted to evaluate the Reynold's stress tensor, turbulent heat transfer rate, turbulent dissipation rate, and turbulent kinetic energy spectrum, as functions of position, for conditions relevant to the solar nebula. Emphasis is placed on the variation of these properties with appropriate nondimensional quantities, so that relations can be derived that will be useful for disk modeling under a variety of hypotheses and initial conditions

The potential for tidally heated icy and temperate moons around exoplanets

Moons of giant planets may represent an alternative to the classical picture of habitable worlds. They may exist within the circumstellar habitable zone of a parent star, and through tidal energy dissipation they may also offer alternative habitable zones, where stellar insolation plays a secondary, or complementary, role. We investigate the potential extent of stable satellite orbits around a set of 74 known extrasolar giant planets located beyond 0.6 AU from their parent stars - where moons should be long-lived with respect to removal by stellar tides. Approximately 60% of these giant planets can sustain satellites or moons in bands up to $\sim 0.04$ AU in width. For comparison, the Galiean satellites extend to $\sim 0.013$ AU. We investigate the stellar insolation that moons would experience for these exoplanet systems, and the implications for sublimation loss of volatiles. We find that between 15 and 27% of {\em all} known exoplanets may be capable of harboring small, icy, moons. In addition, some 22-28% of all known exoplanets could harbor moons within a ``sublimation zone'', with insolation temperatures between 273 K and 170 K. A simplified energy balance model is applied to the situation of temperate moons, maintained by a combination of stellar insolation and tidal heat flow. We demonstrate that large moons ($>0.1$M$_{\oplus}$), at orbital radii commensurate with those of the Galilean satellites, could maintain temperate, or habitable, surface conditions during episodes of tidal heat dissipation of the order 1-100 times that currently seen on Io. (Abridged).Comment: 28 pages, 8 Figures, AASTex, Accepted for publication in the Astrophysical Journa

Nonlinear Outcome of Gravitational Instability in Disks with Realistic Cooling

We consider the nonlinear outcome of gravitational instability in optically thick disks with a realistic cooling function. We use a numerical model that is local, razor-thin, and unmagnetized. External illumination is ignored. Cooling is calculated from a one-zone model using analytic fits to low temperature Rosseland mean opacities. The model has two parameters: the initial surface density Sigma_0 and the rotation frequency Omega. We survey the parameter space and find: (1) The disk fragments when t_c,eff Omega = 1, where t_c,eff is an effective cooling time defined as the average internal energy of the model divided by the average cooling rate. This is consistent with earlier results that used a simplified cooling function. (2) The initial cooling time t_c0 or a uniform disk with Q = 1 can differ by orders of magnitude from t_c,eff in the nonlinear outcome. The difference is caused by sharp variations in the opacity with temperature. The condition t_c0 Omega = 1 therefore does not necessarily indicate where fragmentation will occur. (3) The largest difference between t_c,eff and t_c0 is near the opacity gap, where dust is absent and hydrogen is largely molecular. (4) In the limit of strong illumination the disk is isothermal; we find that an isothermal version of our model fragments for Q < 1.4. Finally, we discuss some physical processes not included in our model, and find that most are likely to make disks more susceptible to fragmentation. We conclude that disks with t_c,eff Omega < 1 do not exist.Comment: 30 pages, 12 figure

Selected Papers on Protoplanetary Disks

Three papers present studies of thermal balances, dynamics, and electromagnetic spectra of protoplanetary disks, which comprise gas and dust orbiting young stars. One paper addresses the reprocessing, in a disk, of photons that originate in the disk itself in addition to photons that originate in the stellar object at the center. The shape of the disk is found to strongly affect the redistribution of energy. Another of the three papers reviews an increase in the optical luminosity of the young star FU Orionis. The increase began in the year 1936 and similar increases have since been observed in other stars. The paper summarizes astronomical, meteoric, and theoretical evidence that these increases are caused by increases in mass fluxes through the inner portions of the protoplanetary disks of these stars. The remaining paper presents a mathematical-modeling study of the structures of protostellar accretion disks, with emphasis on limits on disk flaring. Among the conclusions reached in the study are that (1) the radius at which a disk becomes shadowed from its central stellar object depends on radial mass flow and (2) most planet formation has occurred in environments unheated by stellar radiation

Protostellar collapse: rotation and disk formation

We present some important conclusions from recent calculations pertaining to the collapse of rotating molecular cloud cores with axial symmetry, corresponding to evolution of young stellar objects through classes 0 and begin of class I. Three main issues have been addressed: (1) The typical timescale for building up a preplanetary disk - once more it turned out that it is of the order of one free-fall time which is decisively shorter than the widely assumed timescale related to the so-called 'inside-out collapse'; (2) Redistribution of angular momentum and the accompanying dissipation of kinetic (rotational) energy - together these processes govern the mechanical and thermal evolution of the protostellar core to a large extent; (3) The origin of calcium-aluminium-rich inclusions (CAIs) - due to the specific pattern of the accretion flow, material that has undergone substantial chemical and mineralogical modifications in the hot (exceeding 900 K) interior of the protostellar core may have a good chance to be advectively transported outward into the cooler remote parts (beyond 4 AU, say) of the growing disk and to survive there until it is incorporated into a meteoritic body.Comment: 4 pages, 4 figure

Vertically Self-Gravitating ADAFs in the Presence of Toroidal Magnetic Field

Force due to the self-gravity of the disc in the vertical direction is considered to study its possible effects on the structure of a magnetized advection-dominated accretion disc. We present steady-sate self similar solutions for the dynamical structure of such a type of the accretion flows. Our solutions imply reduced thickness of the disc because of the self-gravity. It also imply that the thickness of the disc will increase by adding the magnetic field strength.Comment: Accepted for publication in Astrophysics and Space Science

Accretion of low angular momentum material onto black holes: 2D hydrodynamical inviscid case

We report on the first phase of our study of slightly rotating accretion flows onto black holes. We consider inviscid accretion flows with a spherically symmetric density distribution at the outer boundary, but with spherical symmetry broken by the introduction of a small, latitude-dependent angular momentum. We study accretion flows by means of numerical 2D, axisymmetric, hydrodynamical simulations. Our main result is that the properties of the accretion flow do not depend as much on the outer boundary conditions (i.e., the amount as well as distribution of the angular momentum) as on the geometry of the non-accreting matter. The material that has too much angular momentum to be accreted forms a thick torus near the equator. Consequently, the geometry of the polar region, where material is accreted (the funnel), and the mass accretion rate through it are constrained by the size and shape of the torus. Our results show one way in which the mass accretion rate of slightly rotating gas can be significantly reduced compared to the accretion of non-rotating gas (i.e., the Bondi rate), and set the stage for calculations that will take into account the transport of angular momentum and energy.Comment: LaTeX,to appear in Ap

Substellar companions and isolated planetary mass objects from protostellar disc fragmentation

Self-gravitating protostellar discs are unstable to fragmentation if the gas can cool on a time scale that is short compared to the orbital period. We use a combination of hydrodynamic simulations and N-body orbit integrations to study the long term evolution of a fragmenting disc with an initial mass ratio to the star of M_disc/M_star = 0.1. For a disc which is initially unstable across a range of radii, a combination of collapse and subsequent accretion yields substellar objects with a spectrum of masses extending (for a Solar mass star) up to ~0.01 M_sun. Subsequent gravitational evolution ejects most of the lower mass objects within a few million years, leaving a small number of very massive planets or brown dwarfs in eccentric orbits at moderately small radii. Based on these results, systems such as HD 168443 -- in which the companions are close to or beyond the deuterium burning limit -- appear to be the best candidates to have formed via gravitational instability. If massive substellar companions originate from disc fragmentation, while lower-mass planetary companions originate from core accretion, the metallicity distribution of stars which host massive substellar companions at radii of ~1 au should differ from that of stars with lower mass planetary companions.Comment: 5 pages, accepted for publication in MNRA