Topic
Hydrostatic equilibrium
About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.
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TL;DR: Explicit 2-d axisymmetric solutions are found to the hydrostatic equilibrium, energy balance, and photon diffusion equations within obscuring tori around active galactic nuclei.
Abstract: Explicit 2-d axisymmetric solutions are found to the hydrostatic equilibrium, energy balance, and photon diffusion equations within obscuring tori around active galactic nuclei. These solutions demonstrate that infrared radiation pressure can support geometrically thick structures in AGN environments subject to certain constraints: the bolometric luminosity must be roughly 0.03--1 times the Eddington luminosity; and the Compton optical depth of matter in the equatorial plane should be order unity, with a tolerance of about an order of magnitude up or down. Both of these constraints are at least roughly consistent with observations. In addition, angular momentum must be redistributed so that the fractional rotational support against gravity rises from the inner edge of the torus to the outer in a manner specific to the detailed shape of the gravitational potential. This model also predicts that the column densities observed in obscured AGN should range from about 10^{22} to about 10^{24} cm^{-2}.
5 citations
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TL;DR: In this paper, the authors showed that an ad hoc correction is undesirable, and an analysis that shows such a correction is unnecessary is presented, provided the multiplicative inverse of the first vertical derivative of the vertical...
Abstract: Attempts to represent the vertical structure in primitive equation models of the atmosphere with the spectral method have been unsuccessful to date. The linear stability analysis of Francis showed that small time steps were required for computational stability near the upper boundary with a vertical spectral method using Laguerre polynomials. Machenhauer and Daley used Legendre polynomials in their vertical spectral representation and found it necessary to use an artificial constraint to force temperature to zero when pressure was zero to control the upper-level horizontal velocities. This ad hoc correction is undesirable, and an analysis that shows such a correction is unnecessary is presented. By formulating the model in terms of velocity and geopotential and then using the hydrostatic equation to calculate temperature from geopotential, temperature is necessarily zero when pressure is zero. This strategy works provided the multiplicative inverse of the first vertical derivative of the vertical...
5 citations
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01 Jan 1985TL;DR: In this paper, a numerical code has been written which is designed to calculate radiation transport and atmospheric structure under the constraints of statistical equilibrium in atomic transitions and radiative and hydrostatic equilibrium in the medium.
Abstract: A numerical code has been written which is designed to calculate radiation transport and atmospheric structure under the constraints of statistical equilibrium in atomic transitions and radiative and hydrostatic equilibrium in the medium In addition to the complete linearization and variable Eddington factor techniques of Auer and Mihalas, it uses a multi-frequency / multi-grey algorithm which admits the inclusion of many spectral lines in full statistical equilibrium The program can comfortably accept up to about 300 specific lines arising from about 30 lower states and any number of continua Cleverly constructed artificial model atoms can extend the number of lines to 3000 or more, where opacity sampling techniques can begin to approximate the blanketing accomplished by Kurucz in LTE By way of example, I present a model of a stellar atmosphere with effective temperature 35,000 K and surface gravity 104 cm s-2 The calculation includes 98 bound-free transitions and 93 bound-bound transitions (57 with radiative rates) between 91 states in 36 ions of 9 cosmically abundant species
5 citations
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TL;DR: In this paper, it is argued that this must be caused by convection in the solid interior rather than an initial distortion retained by the finite strength of the interior, and the presence of an iron core in Mercury poses an interesting question as to why a second degree harmonic convection pattern in the silicate mantle is present.
5 citations