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 Uncertainty in X-Ray Cluster Mass Estimates from the Equation of Hydrostatic Equilibrium

Abstract: We study the uncertainty in galaxy cluster mass estimates derived from X-ray data, assuming hydrostatic equilibrium for the intracluster gas. Using a Monte Carlo procedure, we generate a general class of mass models allowing very massive clusters. We then compute the corresponding temperature profiles through the equation of hydrostatic equilibrium and compare them to observational data for some clusters. We find several massive clusters that pass the observational constraints, with integrated masses varying over quite a wide range. The resulting accuracy of the mass estimates is rather poor, the uncertainties larger than what is generally claimed. Despite the fact that the mass profile can be exactly determined mathematically from the temperature and surface brightness profiles, we find that very accurate measurements of both quantities are required to determine the actual mass with moderate accuracy. We argue that the tight constraints on cluster masses previously obtained arise from the fact that a too restricted class of mass density profiles has been investigated so far, without serious physical justification. Applying our procedure to the Perseus and then to the Coma clusters, we find that an improvement of the observational constraints results in a quite modest improvement in the accuracy of the mass estimate. For Coma, using the best current available data, we end up with an uncertainty of a factor of 2 for the mass within the Abell radius. This uncertainty rapidly increases at further radius.

On the numerical resolution of the bottom layer in simulations of oceanic gravity currents

Abstract: . The role of an increased numerical vertical resolution, leading to an explicit resolution of the bottom Ekman layer dynamics, is investigated. Using the hydrostatic ocean model NEMO-OPA9, we demonstrate that the dynamics of an idealised gravity current (on an inclined plane), is well captured when a few (around five) sigma-coordinate levels are added near the ocean floor. Such resolution allows to considerably improve the representation of the descent and transport of the gravity current and the Ekman dynamics near the ocean floor, including the important effect of Ekman veering, which is usually neglected in today's simulations of the ocean dynamics. Results from high resolution simulations (with σ and z-coordinates) are compared to simulations with a vertical resolution commonly employed in today's ocean models. The latter show a downslope transport that is reduced by almost an order of magnitude and the decrease in the along slope transport is reduced six-fold. We strongly advocate for an increase of the numerical resolution at the ocean floor, similar to the way it is done at the ocean surface and at the lower boundary in atmospheric models.

Comparing analytical and numerical solution of nonlinear two and three‐dimensional hydrostatic flows

Abstract: New test cases for frictionless, three-dimensional hydrostatic flows have been derived from some known analytical solutions of the two-dimensional shallow water equations. The flow domain is a paraboloid of revolution and the flow is determined by the initial conditions, the nonlinear advective terms, the Coriolis acceleration and by the hydrostatic pressure. Wetting and drying is also included. Some specific properties of the exact solutions are discussed under different hypothesis and relative importance of the forcing terms. These solutions are proposed for testing the stability, the accuracy and the efficiency of numerical models to be used for simulating environmental hydrostatic flows. The computed solutions obtained with a semi-implicit finite difference-finite volume algorithm on unstructured grid are compared with the corresponding analytical solutions in both two and three space dimension. Excellent agreement are obtained for the velocity and for the resulting water surface elevation. Comparison of the computed inundation area also shows a good agreement with the analytical solution with degrading accuracy observed when the inundation area becomes relatively large and for long simulation time.

Characterizing hydrostatic mass bias with Mock-X

Abstract: Surveys in the next decade will deliver large samples of galaxy clusters that transform our understanding of their formation. Cluster astrophysics and cosmology studies will become systematics limited with samples of this magnitude. With known properties, hydrodynamical simulations of clusters provide a vital resource for investigating potential systematics. However, this is only realized if we compare simulations to observations in the correct way. Here we introduce the \textsc{Mock-X} analysis framework, a multiwavelength tool that generates synthetic images from cosmological simulations and derives halo properties via observational methods. We detail our methods for generating optical, Compton-$y$ and X-ray images. Outlining our synthetic X-ray image analysis method, we demonstrate the capabilities of the framework by exploring hydrostatic mass bias for the IllustrisTNG, BAHAMAS and MACSIS simulations. Using simulation derived profiles we find an approximately constant bias $b\approx0.13$ with cluster mass, independent of hydrodynamical method or subgrid physics. However, the hydrostatic bias derived from synthetic observations is mass-dependent, increasing to $b=0.3$ for the most massive clusters. This result is driven by a single temperature fit to a spectrum produced by gas with a wide temperature distribution in quasi-pressure equilibrium. The spectroscopic temperature and mass estimate are biased low by cooler gas dominating the emission, due to its quadratic density dependence. The bias and the scatter in estimated mass remain independent of the numerical method and subgrid physics. Our results are consistent with current observations and future surveys will contain sufficient samples of massive clusters to confirm the mass dependence of the hydrostatic bias.