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Hydrostatic equilibrium

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


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TL;DR: In this article, the authors present models with temperatures set by the balance between starlight heating and radiative cooling, that are also in vertical hydrostatic equilibrium, and show that even small features on the disk's surface cast shadows, because the starlight grazing the surface.
Abstract: Many protostellar disks show central cavities, rings, or spiral arms likely caused by low-mass stellar or planetary companions, yet few such features are conclusively tied to bodies embedded in the disks. We note that even small features on the disk's surface cast shadows, because the starlight grazes the surface. We therefore focus on accurately computing the disk's thickness, which depends on its temperature. We present models with temperatures set by the balance between starlight heating and radiative cooling, that are also in vertical hydrostatic equilibrium. The planet has 20, 100, or 1000~M$_\oplus$, ranging from barely enough to perturb the disk significantly, to clearing a deep tidal gap. The hydrostatic balance strikingly alters the model disk's appearance. The planet-carved gap's outer wall puffs up under starlight heating, throwing a shadow across the disk beyond. The shadow appears in scattered light as a dark ring that could be mistaken for a gap opened by another more distant planet. The surface brightness contrast between outer wall and shadow for the 1000-M$_\oplus$ planet is an order of magnitude greater than a model neglecting the temperature disturbances. The shadow is so deep it largely hides the planet-launched spiral wave's outer arm. Temperature gradients are such that outer low-mass planets undergoing orbital migration will converge within the shadow. Furthermore the temperature perturbations affect the shape, size, and contrast of features at millimeter and centimeter wavelengths. Thus radiative heating and cooling are key to the appearance of protostellar disks with embedded planets.

44 citations

Journal ArticleDOI
TL;DR: In this paper, the authors improved on previous work on the subject by self-consistently calculating the temperature and density structures under the assumption of hydrostatic equilibrium and taking the full three-dimensional shape of the disk into account rather than assuming a plane-parallel disk.
Abstract: Planets embedded in optically thick passive accretion disks are expected to produce perturbations in the density and temperature structure of the disk. We calculate the magnitudes of these perturbations for a range of planet masses and distances. The model predicts the formation of a shadow at the position of the planet paired with a brightening just beyond the shadow. We improve on previous work on the subject by self-consistently calculating the temperature and density structures under the assumption of hydrostatic equilibrium and taking the full three-dimensional shape of the disk into account rather than assuming a plane-parallel disk. While the excursion in temperatures is less than in previous models, the spatial size of the perturbation is larger. We demonstrate that a self-consistent calculation of the density and temperature structure of the disk has a large effect on the disk model. In addition, the temperature structure in the disk is highly sensitive to the angle of incidence of stellar irradiation at the surface, so accurately calculating the shape of the disk surface is crucial for modeling the thermal structure of the disk.

43 citations

Journal ArticleDOI
TL;DR: In this article, the results of magnetohydrodynamic (MHD) modeling of winds from luminous late-type stars using a 2.5-dimensional, nonlinear MHD computer code are presented.
Abstract: We present the results of magnetohydrodynamic (MHD) modeling of winds from luminous late-type stars using a 2.5-dimensional, nonlinear MHD computer code. We assume that the wind is generated within an initially hydrostatic atmosphere and is driven by torsional Alfven waves generated at the stellar surface. Two cases of atmospheric topology are considered: case I has longitudinally uniform density distribution and isotropic radial magnetic field over the stellar surface, and case II has an isotropic, radial magnetic field with a transverse density gradient, which we refer to as an "atmospheric hole." We use the same set of boundary conditions for both models.The calculations are designed to model a cool luminous star, for which we assume an initial hydrostatic pressure scale height of 0.072 R*, an Alfven wave speed of 92 km s-1 at the surface, and a wave period of 76 days, which roughly corresponds with the convective turnover time. For case I the calculations produce a wind with terminal velocity of ~22 km s-1 and a mass loss rate comparable to the expected value of 10-6 M☉ yr-1. For case II we predict a two-component wind: a fast (25 km s-1) and relatively dense wind outside of the atmospheric hole and a slow (15 km s-1), rarefied wind inside of the hole.

43 citations

Journal ArticleDOI
TL;DR: The dependence of Tc for MgB2 on purely hydrostatic or nearly hydrostatic pressure has been determined to 23 GPa for single-crystalline and to 32 GPA for polycrystallized samples, and found to be in good agreement.
Abstract: The dependence of Tc for MgB2 on purely hydrostatic or nearly hydrostatic pressure has been determined to 23 GPa for single-crystalline and to 32 GPa for polycrystalline samples, and found to be in good agreement. Tc decreases from 39 K at ambient pressure to 15 K at 32 GPa with an initial slope dTc/dP = -1.11(2) K/GPa. Evidence is presented that the differing values of dTc/dP reported in the literature result primarily from shear-stress effects in nonhydrostatic pressure media and not differences in the samples. Although comparison of these results with theory supports phonon-mediated superconductivity, a critical test of theory must await volume-dependent calculations based on the solution of the anisotropic Eliashberg equations.

43 citations

Journal ArticleDOI
TL;DR: In this paper, a penumbra model in hydrostatic equilibrium is presented, which accounts for the continuum observations as well as the observations of Fraunhofer lines in the Penumbra.
Abstract: A penumbra model in hydrostatic equilibrium is presented. The model accounts for the continuum observations as well as the observations of Fraunhofer lines in the penumbra. The uncertainty in the model in deeper layers is discussed. It is shown that the penumbra is probably not in strict radiative equilibrium.

43 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023282
2022708
202167
202089
201998
201893