Hydrostatic equilibrium

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

The Three Hundred Project: correcting for the hydrostatic-equilibrium mass bias in X-ray and SZ surveys

Abstract: Accurate and precise measurements of masses of galaxy clusters are key to derive robust constraints on cosmological parameters. Rising evidence from observations, however, confirms that X-ray masses, obtained under the assumption of hydrostatic equilibrium, might be underestimated, as previously predicted by cosmological simulations. We analyse more than 300 simulated massive clusters, from `The Three Hundred Project', and investigate the connection between mass bias and several diagnostics extracted from synthetic X-ray images of these simulated clusters. We find that the azimuthal scatter measured in 12 sectors of the X-ray flux maps is a statistically significant indication of the presence of an intrinsic (i.e. 3D) clumpy gas distribution. We verify that a robust correction to the hydrostatic mass bias can be inferred when estimates of the gas inhomogeneity from X-ray maps (such as the azimuthal scatter or the gas ellipticity) are combined with the asymptotic external slope of the gas density or pressure profiles, which can be respectively derived from X-ray and millimetric (Sunyaev-Zeldovich effect) observations. We also obtain that mass measurements based on either gas density and temperature or gas density and pressure result in similar distributions of the mass bias. In both cases, we provide corrections that help reduce both the dispersion and skewness of the mass bias distribution. These are effective even when irregular clusters are included leading to interesting implications for the modelling and correction of hydrostatic mass bias in cosmological analyses of current and future X-ray and SZ cluster surveys.

Interior solutions of relativistic stars with anisotropic matter in scale-dependent gravity

Abstract: We obtain well behaved interior solutions describing hydrostatic equilibrium of anisotropic relativistic stars in scale-dependent gravity, where Newton’s constant is allowed to vary with the radial coordinate throughout the star. Assuming (1) a linear equation-of-state in the MIT bag model for quark matter, and (2) a certain profile for the energy density, we integrate numerically the generalized structure equations, and we compute the basic properties of the strange quark stars, such as mass, radius and compactness. Finally, we demonstrate that stability criteria as well as the energy conditions are fulfilled. Our results show that a decreasing Newton’s constant throughout the objects leads to slightly more massive and more compact stars.

Non-isothermal filaments in equilibrium

Abstract: The physical properties of the so-called Ostriker isothermal filament (Ostriker 1964) have been classically used as benchmark to interpret the stability of the filaments observed in nearby clouds. However, recent continuum studies have shown that the internal structure of the filaments depart from the isothermality, typically exhibiting radially increasing temperature gradients. The presence of internal temperature gradients within filaments suggests that the equilibrium configuration of these objects should be therefore revisited. The main goal of this work is to theoretically explore how the equilibrium structure of a filament changes in a non-isothermal configuration. We solve the hydrostatic equilibrium equation assuming temperature gradients similar to those derived from observations. We obtain a new set of equilibrium solutions for non-isothermal filaments with both linear and asymptotically constant temperature gradients. Our results show that, for sufficiently large internal temperature gradients, a non-isothermal filament could present significantly larger masses per unit length and shallower density profiles than the isothermal filament without collapsing by its own gravity. We conclude that filaments can reach an equilibrium configuration under non-isothermal conditions. Detailed studies of both the internal mass distribution and temperature gradients within filaments are then needed in order to judge the physical state of filaments.

The equilibrium form of a rotating earth with an elastic shell

Abstract: SUMMARY The equilibrium form of the Earth is generally computed using a hydrostatic theory that assumes a rotating, inviscid planet. We compute the perturbation to this equilibrium form due to the presence of a thin elastic lithospheric shell using viscoelastic Love number theory. The thin shell acts to reduce the flattening of the equilibrium form relative to the value obtained from the traditional hydrostatic calculation. Our results indicate that current estimates of the excess non-hydrostatic flattening of the Earth, defined as the discrepancy between the observed and hydrostatic forms, may therefore be underestimating the actual departure of the observed form from its equilibrium state. This conclusion may be important for viscous flow models of mantle convection, which are commonly constrained to fit the non-hydrostatic flattening. For completeness, we also adopt the Love number formulation to estimate the excess flattening associated with the gradual slowing of the Earth's rotation. Our predictions of the fossil rotational bulge confirm the widespread view that this effect is small for reasonable mantle viscosity profiles.