Hydrostatic equilibrium

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

Quasi-hydrostatic intracluster gas under radiative cooling

Abstract: Quasi-hydrostatic cooling of the intracluster gas is studied. In the quasi-hydrostatic model, work done by gravity on the inflow gas with dP ¬= 0, where P is the gas pressure, is taken into account in the thermal balance. The gas flows in from the outer part so as to compensate the pressure loss of the gas undergoing radiative cooling, but the mass flow is so moderate and smooth that the gas is considered to be quasi-hydrostatic. The temperature of the cooling gas decreases toward the cluster center, but, unlike cooling flows with dP = 0, approaches a constant temperature of ∼1/3 the temperature of the non-cooling ambient gas. This does not mean that gravitational work cancels out radiative cooling, but means that the temperature of the cooling gas appears to approach a constant value toward the cluster center if the gas maintains the quasi-hydrostatic balance. We discuss the mass flow in quasi-hydrostatic cooling, and compare it with the standard isobaric cooling flow model. We also discuss the implication of M for the standard cooling flow model.

Hydrostatic and non-hydrostatic simulations of moist convection: Review and further study

Abstract: Quantitatively comparative experiments of moist convection using hydrostatic and non-hydrostatic models are reviewed and a further study is made of the suitability of the hydrostatic approximation for a high-resolution model when the grid size falls below 20 km. Idealized moist convection is treated, and then the torrential rain that occurred on 6 August 1993 in Kagoshima, southern Kyushu, Japan is simulated by each model. An explicit warm-rain process predicting cloud water and rainwater and the scheme of moist convective adjustment are individually or conjunctively employed in the model. The effect of hydrostatic water loading is also examined in detall.

The Effect of Contraction in the Cooling by Conduction of a Gravitating Sphere, with Special Reference to the Earth

Abstract: Summary When a hot gravitating sphere cools, gravitational potential energy is lost in contraction. We consider a sphere that can be taken as in continual hydrostatic equilibrium for slow changes of state, and, assuming radial symmetry, set up the modified Fourier equation for heat conduction. This contains two extra terms, one contributed by the heating effect of contraction, and another from the change of temperature gradients with shrinkage. This equation is checked by integration through time and through the sphere to give a comprehensive energy equation. For an initial parabolic temperature distribution in the Earth, the heating effect of contraction is small, and more than counteracted by the extra cooling provided by increased temperature gradients. Moreover, it is probable that the modifications to the first (uniform rigid sphere) approximation which are needed to allow for departures from uniformity in density, specific heat, and thermal conductivity in the Earth are greater than those which allow for contraction.

Experimental investigation of the liquid interface reorientation upon step reduction in gravity.

Abstract: Experiments have been carried out to investigate the settling behavior of a free liquid/gas interface in a partly filled right circular cylinder upon step reduction in gravity. Microgravity conditions were obtained within milliseconds after the release of a drop capsule in the drop tower facility in Bremen. In the experiments the cylinder radius was varied from 10 mm to 20mm with static contact angles of 2 degrees to 60 degrees. In addition to a series of silicone fluids, two different test liquids with a refractive index matched with the value of the cylinder material were used for experiments. The use of a digital high-speed recording system with a recording frequency of up to 500 fps allowed both an observation of the entire free liquid interface and a detail view on the moving contact line. Digital image processing techniques were applied to detect the contour of the free surface. For the initial condition the system is dominated by hydrostatic forces. In this case the equilibrium of the free liquid surface is characterized by a high Bond number yielding a flat surface and a small liquid ascent at the cylinder wall depending on the static contact angle. After transition to reduced gravity with a very low Bond number, capillary forces govern the flow and a capillary driven reorientation of the liquid to the new equilibrium position is established in a damped oscillation. The particular interest of this study is the investigation of the initial behavior of the free surface reorientation. It was found that the initial rise velocity of the contact point is determined by the Morton number and the static contact angle. Experimental results are presented that show an increasing rise velocity for decreasing Morton numbers. Further results characterize the initial behavior of the free surface at the center point as a function of characteristic time scales.

Does space-time torsion determine the minimum mass of gravitating particles?

Abstract: We derive upper and lower limits for the mass–radius ratio of spin-fluid spheres in Einstein–Cartan theory, with matter satisfying a linear barotropic equation of state, and in the presence of a cosmological constant. Adopting a spherically symmetric interior geometry, we obtain the generalized continuity and Tolman–Oppenheimer–Volkoff equations for a Weyssenhoff spin fluid in hydrostatic equilibrium, expressed in terms of the effective mass, density and pressure, all of which contain additional contributions from the spin. The generalized Buchdahl inequality, which remains valid at any point in the interior, is obtained, and general theoretical limits for the maximum and minimum mass–radius ratios are derived. As an application of our results we obtain gravitational red shift bounds for compact spin-fluid objects, which may (in principle) be used for observational tests of Einstein–Cartan theory in an astrophysical context. We also briefly consider applications of the torsion-induced minimum mass to the spin-generalized strong gravity model for baryons/mesons, and show that the existence of quantum spin imposes a lower bound for spinning particles, which almost exactly reproduces the electron mass.