Hydrostatic equilibrium

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

Retrieval of the Fluid Love Number k 2 in Exoplanetary Transit Curves

Abstract: We are witness to a great and increasing interest in internal structure, composition, and evolution of exoplanets. However, direct measurements of exoplanetary mass and radius cannot be uniquely interpreted in terms of interior structure, justifying the need for an additional observable. The second degree fluid Love number, k 2, is proportional to the concentration of mass toward the body’s center, hence providing valuable additional information about the internal structure. When hydrostatic equilibrium is assumed for the planetary interior, k 2 is a direct function of the planetary shape. Previous attempts were made to link the observed tidally and rotationally induced planetary oblateness in photometric light curves to k 2 using ellipsoidal shape models. Here, we construct an analytical 3D shape model function of the true planetary mean radius that properly accounts for tidal and rotational deformations. Measuring the true planetary mean radius is critical when one wishes to compare the measured k 2 to interior theoretical expectations. We illustrate the feasibility of our method and show, by applying a Differential Evolution Markov Chain to synthetic data of WASP-121b, that a precision ≤65 ppm/\sqrt{2 {minutes}} is required to reliably retrieve k 2 with present understanding of stellar limb darkening (LD), therefore improving recent results based on ellipsoidal shape models. Any improvement on stellar LD would increase such performance.

Transport model of buoyant metamorphic fluid by hydrofracturing in leaky rock

Abstract: Aqueous fluid released in metamorphism is transported upwards from depth to the Earth's surface. I propose a hydrofracturing model for the fluid transport. In the model, fluid is transported by the upward propagation of a two-dimensional vertical fluid-filled crack from a fluid reservoir (e.g. overpressured compartment under a seal) at depth to the Earth's surface; fluid is injected consecutively from the reservoir into the crack at a given (but not necessarily constant) injection rate; some of the injected fluid is lost by infiltration from the crack walls into the surrounding permeable rock. An approximate solution of the crack propagation is obtained using fluid dynamics for turbulent film flow and linear elastic fracture mechanics. The solution shows the transition from a regime in which the excess pressure of the fluid in the reservoir drives the propagation to a regime in which the buoyancy of the fluid in the crack drives the propagation. For example, if the net injection rate of H2O is 1 m2/s, the regime transition occurs when the vertical crack length becomes 280 m; after the transition, the propagation velocity and average aperture are constant: 21 m/s and 4.8 cm. If the injection rate is lower than a critical value, hydrofracturing cannot be an effective mode for the fluid transport because of the significant fluid loss by infiltration from the crack walls into the surrounding permeable rock. Assuming a fluid-saturated crust with hydrostatic pore fluid pressure, a lower limit can be estimated for the injection rate required to transport H2O by hydrofracturing without significant fluid loss. For example, the lower limit for transport from a depth of 15 km to the Earth's surface is estimated at 0.2 m2/s if the crustal permeability is 10-17 m2. The lower limit decreases with decreasing crustal permeability.

Dilatonic Equation of Hydrostatic Equilibrium and Neutron Star Structure

Abstract: In this paper, we present a new hydrostatic equilibrium equation related to dilaton gravity. We consider a spherical symmetric metric to obtain the hydrostatic equilibrium equation of stars in $4$-dimensions, and generalize TOV equation to the case of regarding a dilaton field. Then, we calculate the structure properties of neutron star using our obtained hydrostatic equilibrium equation employing the modern equations of state of neutron star matter derived from microscopic calculations. We show that the maximum mass of neutron star depends on the parameters of dilaton field and cosmological constant. In other words, by setting the parameters of new hydrostatic equilibrium equation, we calculate the maximum mass of neutron star.

Equilibrium configurations of anisotropic polytropes in f(R, T) gravity

Abstract: This paper explores the anisotropic stellar configurations governed by polytopic equation of state in f (R , T ) theory (where R denotes the Ricci scalar and T is the trace of energy-momentum tensor). For this purpose, we numerically solve the system of differential equations obtained from the field equations and hydrostatic equilibrium equation. We investigate physical characteristics of polytropic stars and examine their stability using both causality condition as well as the adiabatic index. It is concluded that stellar configurations are stable and the value of mass function lies within the Chandrasekhar limit.

The Role of Non-ionizing Radiation Pressure in Star Formation: The Stability of Cores and Filaments

Abstract: Stars form when filaments and dense cores in molecular clouds fragment and collapse due to self-gravity. In the most basic analyses of gravitational stability, the competition between self-gravity and thermal pressure sets the critical (i.e. maximum stable) mass of spheres and the critical line density of cylinders. Previous work has considered additional support from magnetic fields and turbulence. Here, we consider the effects of non-ionizing radiation, specifically the inward radiation pressure force that acts on dense structures embedded in an isotropic radiation field. Using hydrostatic, isothermal models, we find that irradiation lowers the critical mass and line density for gravitational collapse, and can thus act as a trigger for star formation. For structures with moderate central densities, $\sim10^3$ cm$^{-3}$, the interstellar radiation field in the Solar vicinity has an order unity effect on stability thresholds. For more evolved objects with higher central densities, a significant lowering of stability thresholds requires stronger irradiation, as can be found closer to the Galactic center or near stellar associations. Even when strong sources of ionizing radiation are absent or extincted, our study shows that interstellar irradiation can significantly influence the star formation process.