Hydrostatic equilibrium

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

Direct Measurements of Gas Bulk Flows in the Intracluster Medium of the Centaurus Cluster with the Chandra Satellite

Abstract: We present the analysis of the velocity structure of the intracluster gas near the core of Abell 3526 obtained with two off-center Chandra observations, specifically designed to eliminate errors due to spatial variations of the instrumental gain. We detected a significant velocity gradient along the northeast-southwest direction, roughly perpendicular to the direction of the incoming subgroup Cen 45, in agreement with previous ASCA SIS measurements. The presence of gas bulk velocities is observed both with and without the inclusion of the Fe K line complex in the spectral fittings. The configuration and magnitude of the velocity gradient is consistent with near transonic circulatory motion, either bulk or eddylike. The velocity difference obtained using the best calibrated central regions of ACIS-S3 is found to be (2.4 ± 1.0) × 103 km s-1 for rectangular regions 24 × 3' roughly diametrically opposed around the cluster's core. There are also indications of a high-velocity zone toward the southern region with similar magnitudes. The detection of velocity gradients is significant at >99.4% confidence, and simulations show that intrachip gain fluctuations >1800 km s-1 are required to explain the velocity gradient by chance. The measurements suggest that >1% of the total merger energy can still be bulk kinetic 0.4 Gyr after the merging event. This is the first direct confirmation of velocity gradients in the intracluster gas with independent instruments and indicates that strong departure from hydrostatic equilibrium is possible even for cool clusters that do not show obvious signs of merging.

Hydrostatic Adjustment: Lamb's Problem.

Abstract: The prototype problem of hydrostatic adjustment for large-scale atmospheric motions is Presented. When a horizontally infinite layer of compressible fluid, initially at rest, is instantaneously heated, the fluid is no longer in hydrostatic balance since its temperature and pressure in the layer have increased while its density remains unchanged. The subsequent adjustment of the fluid is described in detail for an isothermal base-state atmosphere. The initial imbalance generates acoustic wave fronts with trailing wakes of dispersive acoustic gravity waves. There are two characteristic timescales of the adjustment. The first is the transit time it takes an acoustic front to travel from the source region to a particular location. The second timescale, the acoustic cutoff frequency, is associated with the trailing wake. The characteristic depth scale of the adjustment is the density scale height. If the depth of the heating is small compared with the scale height, the final pressure perturbation tend...

Gravitational Collapse of Filamentary Magnetized Molecular Clouds

Abstract: We develop models for the self-similar collapse of magnetized isothermal cylinders. We find solutions for the case of a fluid with a constant toroidal flux-to-mass ratio (Γ = constant) and the case of a fluid with a constant gas to magnetic pressure ratio (β = constant). In both cases, we find that a low magnetization results in density profiles that behave as ρ ∝ r-4 at large radii, and at high magnetization we find density profiles that behave as ρ ∝ r-2. This density behavior is the same as for hydrostatic filamentary structures, suggesting that density measurements alone cannot distinguish between hydrostatic and collapsing filaments—velocity measurements are required. Our solutions show that the self-similar radial velocity behaves as vr ∝ r during the collapse phase, and that unlike collapsing self-similar spheres, there is no subsequent accretion (i.e., expansion-wave) phase. We also examine the fragmentation properties of these cylinders and find that in both cases, the presence of a toroidal field acts to strengthen the cylinder against fragmentation. Finally, the collapse timescales in our models are shorter than the fragmentation timescales. Thus, we anticipate that highly collapsed filaments can form before they are broken into pieces by gravitational fragmentation.

The CO Fundamental Vibration-Rotation Lines in the Solar Spectrum. II. Non-LTE Transfer Modeling in Static and Dynamic Atmospheres

Abstract: We present a numerical method for solving radiative transfer in molecular vibration-rotation bands that allows for departures from local thermodynamic equilibrium (LTE) while accurately including a large number of lines. The method is applied to the formation of the CO fundamental vibration-rotation bands in several plane-parallel hydrostatic models and in a sequence of 20 snapshots from a radiation-hydrodynamics simulation of chromospheric dynamics. Calculations for the hydrostatic models performed with different values of the collisional coupling between different vibrational states confirm earlier results in the literature showing that the CO lines have LTE source functions in the solar atmosphere, so emergent CO intensities reflect actual temperatures therein. Only if the canonical collisional strengths are too large by more than 2 orders of magnitude would it be possible to explain the low temperatures derived from CO line core intensities at the solar limb by scattering in an atmosphere with much higher temperatures, consistent with the values derived from UV line and continuum and Ca II resonance line diagnostics. An interesting feature in the wavelength structure of the CO vibration-rotation bands is pointed out, in which pairs of lines can be found in different bands but of similar strength and wavelength. In principle such pairs provide a diagnostic for departures from LTE in the CO lines. CO line core intensity variations computed from the sequence of dynamical snapshots, which represent a typical episode in the chromospheric dynamics simulation, have an amplitude that is 2.5 times higher than observed. It is shown that this large amplitude is due in part to the up and down shift of the CO line formation region during the evolution of the atmosphere and is related to the assumption of instantaneous chemical equilibrium that was assumed to calculate CO concentrations. This suggests that the CO concentration is not in equilibrium, may be lower than would be expected on the basis of chemical equilibrium at the time-averaged mean temperature of the atmosphere, and may have reduced variations compared to instantaneous chemical equilibrium values at the local temperatures.

The Quasi-Hydrostatic Approximation

Abstract: Second-order expansion of the aspect ratio gives rise to simple equations with a quasi-hydrostatic approximation that perform far better than the classical hydrostatic system in the simulation of moist convection in a mesoscale model. It also suggests that a simple modification to this system may extend the validity of schemes for aspect ratios larger than 1.