Hydrostatic equilibrium

About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.

Multi-dimensional radiative transfer in circumstellar disks

Abstract: In this thesis a radiative transfer model for the simulation of protoplanetary disks was developed. As a basis served the general stellar atmosphere package PHOENIX (Hauschildt et al. 1999). Substantial modifications accounting for accretion disk properties have been implemented. The disk is divided into rings and the vertical structure is calculated for each one. A summation of all rings gives a so-called 1+1D disk structure description. The models have been tested and were confronted with high-resolution infrared spectra of the inner disk of T Tauri stars which display rich molecular emission line spectra. The models can reproduce the observational data nicely identifying the properties of the gas in the disk. Furthermore, the simulation of the radiative transfer was extended to 3 dimensions providing a more realistical treatment of the problem. Two major projects were followed with this method. On the one hand, the influence of disk asymmetries, caused e.g. by planets, on the line profile were investigated by means of a 2-level model atom. Second, the influence of the radial radiative transfer of the disk structure was simulated using an iterative method employing both the 1D code for the determination of the hydrostatic equilibrium and the calculation of the opacities as well as the 3D code for the radiative transfer and the temperature correction. The former simulation showed that line asymmetries caused by density waves in the inner disks can be detected in some cases. The latter demonstrated that the disk is heated by radial diffusion leading to a measurable vertical blow-up.

FROM: Large-scale Earth Structure from Analyses of Free Oscillation Splitting and Coupling

Abstract: Since departures from spherical symmetry are small (particularly in the deep Earth), it is useful to consider an approximate Earth model which is spherically symmetric, non-rotating, and elastically isotropic. Departures from this state (anelasticity, anisotropy, rotation and three-dimensional structure) are supposed sufficiently small that they can be treated by perturbation theory. The model is assumed to be initially quiescent and in a state of hydrostatic equilibrium. The equations governing the small oscillations of such a body are given by:

Radiation-Dominated Disks Are Thermally Stable

Abstract: When the accretion rate is more than a small fraction of Eddington, the inner regions of accretion disks around black holes are expected to be radiation-dominated. However, in the alpha-model, these regions are also expected to be thermally unstable. In this paper, we report two 3-d radiation MHD simulations of a vertically-stratified shearing box in which the ratio of radiation to gas pressure is ~ 10, and yet no thermal runaway occurs over a timespan ~ 40 cooling times. Where the time-averaged dissipation rate is greater than the critical dissipation rate that creates hydrostatic equilibrium by diffusive radiation flux, the time-averaged radiation flux is held to the critical value, with the excess dissipated energy transported by radiative advection. Although the stress and total pressure are well-correlated as predicted by the alpha-model, we show that stress fluctuations precede pressure fluctuations, contrary to the usual supposition that the pressure controls the saturation level of the magnetic energy. This fact explains the thermal stability. Using a simple toy-model, we show that independently-generated magnetic fluctuations can drive radiation pressure fluctuations, creating a correlation between the two while maintaining thermal stability.

3-Dimensional numerical simulations of the dynamics of the Venusian mesosphere and thermosphere

Abstract: We present the first results from a new 3‐dimensional numerical simulation of the steady state dynamics of the Venusian mesosphere and thermosphere (60‐300 km). We have adapted the dynamical core of the Titan thermosphere global circulation model (GCM) [1] to a steady state background atmosphere. Our background atmosphere is derived from a hydrostatic combination of the VTS3 [2] and Venus International Reference Atmosphere (VIRA) [3] empirical models, which are otherwise discontinuous at their 100 km interface. We use 4 th order polynomials to link the VTS3 and VIRA thermal profiles and employ hydrostatic balance to derive a consistent density profile. We also present comparisons of our background atmosphere to data from the ESA Venus Express Mission. The thermal structure of the Venusian mesosphere is relatively well documented; however, direct measurements of wind speeds are limited. Venus’ slow rotation results in a negligible Coriolis force. This suggests that the zonal circulation should arise from cyclostrophic balance; where the equatorward component of the centrifugal force balances poleward meridional pressure gradients [4]. The sparseness of direct and in-situ measurements has resulted in the application of cyclostrophic balance to measured thermal profiles to derive wind speeds [5] [6] [7] [8]. However, cyclostrophic balance is only strictly valid at mid latitudes ( 30‐75 ) and its applicability to the Venusian mesosphere has not been conclusively demonstrated. Our simulations, by solving the full Navier‐Stokes momentum equation, will enable us assess the validity of cyclostrophic balance as a description of mesospheric dynamics. This work is part of an ongoing project to develop the first GCM to encompass the atmosphere from the cloud tops into the thermosphere. When complete, this model will enable self-consistent calculations of the dynamics, energy and composition of the atmosphere. It will thus provide a framework to address many of the outstanding problems in Venus atmosphere science. References