Hydrostatic equilibrium

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

Density Structure and Star Formation in Dense Cores with Thermal and Nonthermal Motions

Abstract: An equilibrium model of a spherically symmetric dense core which incorporates both thermal and nonthermal motions is presented. This model use the spatial structure of the thermal and non-thermal motions to specify the core density structure in hydrostatic equilibrium. The thermal motions are spatially uniform, and the nonthermal motions increase with radius r as a power law, as indicated by observations

Gas density and X-ray surface brightness profiles of clusters of galaxies from dark matter halo potentials: beyond the isothermal beta model

Abstract: We describe a theoretical framework to compute the cluster gas distribution in hydrostatic equilibrium embedded in a class of spherical dark matter halo potentials. Unlike the conventional isothermal $\beta$-model, the present method provides a physical basis to directly probe the shape of dark matter halo from the observed X-ray surface brightness and temperature profiles of clusters of galaxies. Specifically, we examine the extent to which the resulting gas density and X-ray surface brightness profiles are sensitive to the inner slope of the dark matter halo density and other more realistic effects including the self-gravity of the gas and the polytropic equation of state. We also discuss a practical strategy to apply the present methodology to the actual cluster profiles from future X-ray observations.

Effect of Enceladus's rapid synchronous spin on interpretation of Cassini gravity

Abstract: Enceladus's degree 2 gravity, determined by Cassini, is nominally nonhydrostatic to 3σ (J2/C22 = 3.38–3.63, as opposed to 10/3). Iess et al. (2014) interpret this in terms of a hydrostatic interior (core) and isostatic (not hydrostatic) floating ice shell. Enceladus's rapid (1.37 d) synchronous spin and tide distorts its shape substantially, though, enough that the predicted hydrostatic J2/C22 is not 10/3 but closer to 3.25. This leads to the following revision to the internal picture of Enceladus, compared with Iess et al.: (1) the satellite's core is somewhat smaller and slightly denser (190 km radius and 2450 kg/m3); (2) the compensation depth (shell thickness) of the global (degree 2) ice shell is ≈ 50 km, rather close to the base of the modeled ice + water layer; and (3) the compensation depth (shell thickness) beneath the South Polar Terrain (from J3) remains shallower (thinner) at ≈ 30 km, independent of but influenced by the degree 2 solution.

Hot jupiter magnetospheres

Abstract: The upper atmospheres of close-in gas giant exoplanets (hot Jupiters) are subjected to intense heating and tidal forces from their parent stars. The atomic (H) and ionized (H+) hydrogen layers are sufficiently rarefied that magnetic pressure may dominate gas pressure for expected planetary magnetic field strength. We examine the structure of the magnetosphere using a 3D isothermal magnetohydrodynamic model that includes a static dead zone near the magnetic equator containing gas confined by the magnetic field, a wind zone outside the magnetic equator in which thermal pressure gradients and the magneto-centrifugal-tidal effect give rise to a transonic outflow, and a region near the poles where sufficiently strong tidal forces may suppress transonic outflow. Using dipole field geometry, we estimate the size of the dead zone to be several to tens of planetary radii for a range of parameters. Tides decrease the size of the dead zone, while allowing the gas density to increase outward where the effective gravity is outward. In the wind zone, the rapid decrease of density beyond the sonic point leads to smaller densities relative to the neighboring dead zone, which is in hydrostatic equilibrium. To understand the appropriate base conditions for the 3D isothermal model, we compute a simple 1D thermal model in which photoelectric heating from the stellar Lyman continuum is balanced by collisionally excited Lyα cooling. This 1D model exhibits a H layer with temperature T 5000-10,000 K down to a pressure P ~ 10-100 nbar. Using the 3D isothermal model, we compute maps of the H column density as well as the Lyα transmission spectra for parameters appropriate for HD 209458b. Line-integrated transit depths 5%-10% can be achieved for the above base conditions, in agreement with the results of Koskinen et al. A deep, warm H layer results in a higher mass-loss rate relative to that for a more shallow layer, roughly in proportion to the base pressure. Strong magnetic fields have the effect of increasing the transit signal while decreasing the mass loss, due to higher covering fraction and density of the dead zone. Absorption due to bulk fluid velocity is negligible at linewidths 100 km s-1 from line center. In our model, most of the transit signal arises from magnetically confined gas, some of which may be outside the L1 equipotential. Hence, the presence of gas outside the L1 equipotential does not directly imply mass loss. We verify a posteriori that particle mean free paths and ion-neutral drift are small in the region of interest in the atmosphere, and that flux freezing is a good approximation. We suggest that resonant scattering of Lyα by the magnetosphere may be observable due to the Doppler shift from the planet's orbital motion, and may provide a complementary probe of the magnetosphere. Lastly, we discuss the domain of applicability for the magnetic wind model described in this paper as well as the Roche-lobe overflow model.

Shear strain in carbon nanotubes under hydrostatic pressure

Abstract: We investigated the hydrostatic and shear strain components introduced in the graphite hexagons by applying hydrostatic pressure to single-walled carbon nanotubes. The vibrational modes are expected to show different pressure derivatives depending on the polarization of the eigenvector with respect to the nanotube axis, but independent of chirality. A comparison with tight-binding calculations allows us to estimate the Gr\"uneisen parameter (1.24) and the shear phonon deformation potentials (0.41); they compare favorably with experimental results on nanotubes.