Hydrostatic equilibrium

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

Evaporation of dark matter from celestial bodies

Abstract: Scatterings of galactic dark matter (DM) particles with the constituents of celestial bodies could result in their accumulation within these objects. Nevertheless, the finite temperature of the medium sets a minimum mass, the evaporation mass, that DM particles must have in order to remain trapped. DM particles below this mass are very likely to scatter to speeds higher than the escape velocity, so they would be kicked out of the capturing object and escape. Here, we compute the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium, spanning the mass range $[10^{-10} - 10^2]~M_\odot$. We illustrate the critical importance of the exponential tail of the evaporation rate, which has not always been appreciated in recent literature, and obtain a robust result: for the geometric value of the scattering cross section and for interactions with nucleons, the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium is approximately given by $E_c/T_\chi \sim 30$, where $E_c$ is the escape energy of DM particles at the core of the object and $T_\chi$ is the DM temperature. The minimum value of the DM evaporation mass is obtained for super-Jupiters and brown dwarfs, $m_{\rm evap} \simeq 0.7$ GeV. For other values of the scattering cross section, the DM evaporation mass only varies by a factor of two or less within the range $10^{-41}~\textrm{cm}^2 \leq \sigma_p \leq 10^{-31}~\textrm{cm}^2$, where $\sigma_p$ is the spin-independent DM-nucleon scattering cross section. Its dependence on parameters such as the local galactic DM density and velocity, or the scattering and annihilation cross sections is only logarithmic.

How first hydrostatic cores, tidal forces, and gravoturbulent fluctuations set the characteristic mass of stars

Abstract: The stellar initial mass function (IMF) is playing a critical role in the history of our universe. We propose a theory that is based solely on local processes, namely the dust opacity limit, the tidal forces and the properties of the collapsing gas envelope. The idea is that the final mass of the central object is determined by the location of the nearest fragments, which accrete the gas located further away, preventing it to fall onto the central object. To estimate the relevant statistics in the neighbourhood of an accreting protostar, we perform high resolution numerical simulations. We also use these simulations to further test the idea that fragmentation in the vicinity of an existing protostar is determinant in setting the peak of the stellar mass spectrum. We develop an analytical model, which is based on a statistical counting of the turbulent density fluctuations, generated during the collapse, that are at least equal to the mass of the first hydrostatic core, and sufficiently important to supersede tidal and pressure forces to be self-gravitating. The analytical mass function presents a peak located at roughly 10 times the mass of the first hydrostatic core in good agreement with the numerical simulations. Since the physical processes involved are all local, i.e. occurs at scales of a few 100 AU or below, and do not depend on the gas distribution at large scale and global properties such as the mean Jeans mass, the mass spectrum is expected to be relatively universal.

Hydrostatic and Geostrophic Adjustment in a Compressible Atmosphere: Initial Response and Final Equilibrium to an Instantaneous Localized Heating

Abstract: The initial and steady-state response of a compressible atmosphere to an instantaneous, localized heat source is investigated analytically. Potential vorticity conservation removes geostrophic and hydrostatic degeneracy and provides a direct method for obtaining the steady-state solution. The heat source produces a vertical potential vorticity dipole that induces a hydrostatically and geostrophically balanced cyclone–anticyclone structure in the final state. For a typical deep mesoscale heating, the net displacements required for the adjustment to the final steady state include a small, O(100 m) ascent of the core of the heated air with weak far-field descent and a large, O(10 km) outward/inward lateral displacement at the top/base of the heating. The heating initially generates available elastic and potential energy. The energy is then exchanged between kinetic, elastic, potential, and acoustic and gravity wave energy. In the final state, after the acoustic and gravity wave energy has dispersed,...

Modeling of Gas Thermal Effect Based on Energy Equipartition Principle

Abstract: In the present article, a gas thermal effect is modeled based on the energy equipartition principle. Two new independent state equations for an ideal gas are developed that provide a new way to analyze thermal effects in gas lubrication. Furthermore, the energy equation is derived for gas lubrication and the analysis of thermal effects is carried out on a gas spiral thrust bearing and a gas hydrostatic journal bearing. The results show that gas temperature increases significantly in the lubricated region at high speed for both the thrust and hydrostatic journal bearings, and the thermal effect positively influences the load capacity of the thrust bearing. The gas expansion effect makes the gas temperature decrease in the hydrostatic journal bearing, and the gas temperature decreases with an increase in the inlet pressure.