Hydrostatic equilibrium

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

On the influence of non-thermal pressure on the mass determination of galaxy clusters

Abstract: Aims. Given that in most cases just thermal pressure is taken into account in the hydrostatic equilibrium equation to estimate galaxy cluster mass, the main purpose of this paper is to consider the contribution of all three non-thermal components to total mass measurements. The non-thermal pressure is composed by cosmic rays, turbulence and magnetic pressures. Methods. To estimate the thermal pressure we used public XMM-Newton archival data of five Abell clusters to derive temperature and density profiles. To describe the magnetic pressure, we assume a radial distribution for the magnetic field, B(r) ∝ ρ α . To seek generality we assume α within the range of 0.5 to 0.9, as indicated by observations and numerical simulations. Turbulent motions and bulk velocities add a turbulent pressure, which is considered using an estimate from numerical simulations. For this component, we assume an isotropic pressure, Pturb = 1 ρg(σ 2 + σ 2 ). We also consider the contribution of cosmic ray pressure, Pcr ∝ r −0.5 . Thus, besides the gas (thermal) pressure, we include these three non-thermal components in the magnetohydrostatic equilibrium equation and compare the total mass estimates with the values obtained without them. Results. A consistent description for the non-thermal component could yield a variation in mass estimates that extends from 10% to ∼30%. We verified that in the inner parts of cool core clusters the cosmic ray component is comparable to the magnetic pressure, while in non-cool core clusters the cosmic ray component is dominant. For cool core clusters the magnetic pressure is the dominant component, contributing more than 50% of the total mass variation due to non-thermal pressure components. However, for non-cool core clusters, the major influence comes from the cosmic ray pressure that accounts for more than 80% of the total mass variation due to non-thermal pressure effects. For our sample, the maximum influence of the turbulent component to the total mass variation can be almost 20%. Although all of the assumptions agree with previous works, it is important to notice that our results rely on the specific parametrization adopted in this work. We show that this analysis can be regarded as a starting point for a more detailed and refined exploration of the influence of non-thermal pressure in the intra-cluster medium (ICM).

Mathematical Justification of a Shallow Water Model

Abstract: The shallow water equations are widely used to model the flow of a thin layer of fluid submitted to gravity forces. They are usually formally derived from the full incompressible Navier-Stokes equations with free surface under the modeling hypothesis that the pressure is hydrostatic, the flow is laminar, gradually varied and the characteristic fluid height is small relative to the characteristics flow length. This paper deals with the mathematical justification of such asymptotic process assuming a non zero surface tension coefficient and some constraints on the data. We also discuss relation between lubrication models and shallow water systems with no surface tension coefficient necessity.

The hydromagnetic interior of a solar quiescent prominence. ii. magnetic discontinuities and cross-field mass transport

Abstract: This second paper of the series investigates the transverse response of a magnetic field to the independent relaxation of its flux tubes of fluid seeking hydrostatic and energy balance, under the frozen-in condition and suppression of cross-field thermal conduction. The temperature, density, and pressure naturally develop discontinuities across the magnetic flux surfaces separating the tubes, requiring the finite pressure jumps to be compensated by magnetic-pressure jumps in cross-field force balance. The tangentially discontinuous fields are due to discrete currents in these surfaces, δ-function singularities in the current density that are fully admissible under the rigorous frozen-in condition but must dissipate resistively if the electrical conductivity is high but finite. The magnetic field and fluid must thus endlessly evolve by this spontaneous formation and resistive dissipation of discrete currents taking place intermittently in spacetime, even in a low-β environment. This is a multi-dimensional effect in which the field plays a central role suppressed in the one-dimensional (1D) slab model of the first paper. The study begins with an order-of-magnitude demonstration that of the weak resistive and cross-field thermal diffusivities in the corona, the latter is significantly weaker for small β. This case for spontaneous discrete currents, as an important example of the general theory of Parker, is illustrated with an analysis of singularity formation in three families of two-dimensional generalizations of the 1D slab model. The physical picture emerging completes the hypothesis formulated in Paper I that this intermittent process is the origin of the dynamic interiors of a class of quiescent prominences revealed by recent Hinode/SOT and SDO/AIA high-resolution observations.