Hydrostatic equilibrium

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

Hydrostatic equilibrium and gravitational collapse of relativistic charged fluid balls.

Abstract: We obtain the metric corresponding to an arbitrary spherically symmetric distribution of charged perfect fluid without restricting consideration to the static case, and we show that it joins onto the standard Reissner-Nordstr\"om exterior solution of Einstein's equations. We also generalize the Oppenheimer-Volkoff equations of hydrostatic equilibrium to the charged case, and we discuss their applicability. Using our formalism, we then rederive a formula of Christodoulou which splits the mass of a charged black hole into an irreducible part and a reducible electrical part. Finally, we derive the equations for the gravitational collapse of a charged fluid ball, and we draw some general conclusions from them.

Tides for a convective Earth

Abstract: In this paper we give values of the tidal gravimetric factor as well as of the Love numbers for the tidal surface displacement and for the tidal mass redistribution potential that are consistent with the presently adopted definitions. We present analytical expressions for these quantities and compute numerical values for two rotating, nonspherical Earth models. In the first model the Earth is everywhere in hydrostatic equilibrium, and the inner core and mantle are both elastic. In the second model the Earth is ellipsoidal with an inelastic mantle and with a nonhydrostatic initial state for which the effects of mantle convection and its associated boundary deformations are considered. This latter model is constrained to reproduce the observed free core nutation period and global Earth dynamical flattening.

Variation of Elastic Constants and Static Strains with Hydrostatic Pressure: A Method for Calculation from Ultrasonic Measurements

Abstract: The elastic constants and static strains of a solid subjected to large hydrostatic pressures can be deduced from measurements of resonant frequencies (or transit times) for ultrasonic waves in specimens of suitable crystallographic orientations. The pressure changes the specimen's size, shape, and density as well as the elastic constants, and all of the effects influence the resonant frequencies. An algorithm for separating out the effects due to variations in elastic constants from the effects due to static strains is presented and applied to cubic crystals and hexagonal crystals, these structures being of immediate interest to investigators concerned with the properties of metals. The results apply also to isotropic and transversely isotropic solids. The only measurements needed while the specimen is under hydrostatic pressure are resonant frequencies (or transit times). Also required are the size and density at zero pressure, or the elastic constants at zero pressure.

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 α-model, these regions are also expected to be thermally unstable. In this paper, we report two three-dimensional radiation magnetohydrodynamic 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 α-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.

The Stagger-grid: A grid of 3D stellar atmosphere models - I. Methods and general properties

Abstract: Aims. We present the Stagger-grid, a comprehensive grid of time-dependent, three-dimensional (3D), hydrodynamic model atmospheres for late-type stars with realistic treatment of radiative transfer, covering a wide range in stellar parameters. This grid of 3D models is intended for various applications besides studies of stellar convection and atmospheres per se, including stellar parameter determination, stellar spectroscopy and abundance analysis, asteroseismology, calibration of stellar evolution models, interferometry, and extrasolar planet search. In this introductory paper, we describe the methods we applied for the computation of the grid and discuss the general properties of the 3D models as well as of their temporal and spatial averages (here denoted ⟨3D⟩ models).Methods. All our models were generated with the Stagger-code, using realistic input physics for the equation of state (EOS) and for continuous and line opacities. Our ~ 220 grid models range in effective temperature, T eff , from 4000 to 7000 K in steps of 500 K, in surface gravity, log g , from 1.5 to 5.0 in steps of 0.5 dex, and metallicity, [Fe/H], from − 4.0 to + 0.5 in steps of 0.5 and 1.0 dex.Results. We find a tight scaling relation between the vertical velocity and the surface entropy jump, which itself correlates with the constant entropy value of the adiabatic convection zone. The range in intensity contrast is enhanced at lower metallicity. The granule size correlates closely with the pressure scale height sampled at the depth of maximum velocity. We compare the ⟨3D⟩ models with currently widely applied one-dimensional (1D) atmosphere models, as well as with theoretical 1D hydrostatic models generated with the same EOS and opacity tables as the 3D models, in order to isolate the effects of using self-consistent and hydrodynamic modeling of convection, rather than the classical mixing length theory approach. For the first time, we are able to quantify systematically over a broad range of stellar parameters the uncertainties of 1D models arising from the simplified treatment of physics, in particular convective energy transport. In agreement with previous findings, we find that the differences can be rather significant, especially for metal-poor stars.