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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 paper, the authors study the evolution of an embedded protoplanet in a circumstellar disk using the 3D-Radiation Hydro code TRAMP, and treat the thermodynamics of the gas properly in three dimensions.
Abstract: We study the evolution of an embedded protoplanet in a circumstellar disk using the 3D-Radiation Hydro code TRAMP, and treat the thermodynamics of the gas properly in three dimensions. The primary interest of this work lies in the demonstration and testing of the numerical method. We show how far numerical parameters can influence the simulalions of gap opening. We study a standard reference model under various numerical approximations. Then we compare the commonly used locally isothermal approximation to the radialion hydro simulation using an equation for the internal energy. Models with different treatments of the mass accretion process are compared. Often mass accumulates in the Roche lobe of the planet creating a hydrostatic atmosphere around the planet. The gravitational torques induced by the spiral pattern of the disk onto the planet are not strongly affected in the average magnitude, but the short time scale fluctuations are stronger in the radiation hydro models. An interesting result of this work lies in the analysis of the temperature structure around the planet. The most striking effect of treating the thermodynamics properly is the formation of a hot pressure-supported bubble around the planet with a pressure scale height of H/R 0.5 rather than a thin Keplerian circumplanetary accretion disk.

134 citations

Journal ArticleDOI
TL;DR: In this article, a series of 3D global, radiative hydrodynamical simulations reveal a steady-state gas flow, which enters through the poles and exits in the disk midplane.
Abstract: A large fraction of giant planets have gaseous envelopes that are limited to about 10% of their total mass budget. Such planets are present in the solar system (Uranus, Neptune) and are frequently observed in short periods around other stars (the so-called super-Earths). In contrast to these observations, theoretical calculations based on the evolution of hydrostatic envelopes argue that such low-mass envelopes cannot be maintained around cores exceeding five Earth masses. Instead, under nominal disk conditions, these planets would acquire massive envelopes through runaway gas accretion within the lifetime of the protoplanetary disk. In this work we show that planetary envelopes are not in hydrostatic balance, which slows down envelope growth. A series of 3D global, radiative hydrodynamical simulations reveal a steady-state gas flow, which enters through the poles and exits in the disk midplane. Gas is pushed through the outer envelope in about ten orbital timescales. In regions of the disk that are not significantly dust-depleted, envelope accretion onto cores of about five Earth masses can get stalled as the gas flow enters the deep interior. Accreted solids sublimate deep in the convective interior, but small opacity-providing grains are trapped in the flow and do not settle, which further prevents rapid envelope accretion. The transition to runaway gas accretion can however be reached when cores grow larger than typical super-Earths, beyond 15 Earth masses, and preferably when disk opacities are below κ = 1 cm2 /g. These findings offer an explanation for the typical low-mass envelopes around the cores of super-Earths.

134 citations

Journal ArticleDOI
TL;DR: In this paper, the level of hydrostatic equilibrium (HE) in the intracluster medium of simulated galaxy clusters, extracted from state-of-the-art cosmological hydrodynamical simulations performed with the Smoothed-Particle-Hydrodynamic code GADGET-3.
Abstract: In this paper, we investigate the level of hydrostatic equilibrium (HE) in the intracluster medium of simulated galaxy clusters, extracted from state-of-the-art cosmological hydrodynamical simulations performed with the Smoothed-Particle-Hydrodynamic code GADGET-3. These simulations include several physical processes, among which are. stellar and active galactic nucleus feedback, and have been performed with an improved version of the code that allows for a better description of hydrodynamical instabilities and gas mixing processes. Evaluating the radial balance between the gravitational and hydrodynamical forces. via the gas accelerations generated, we effectively examine the level of HE in every object of the sample and. its dependence on the radial distance from the center and on the classification of the cluster in terms of either cool-coreness or dynamical state. We find an average deviation of 10%-20% out to the virial radius, with no evident distinction between cool-core and non-cool-core clusters. Instead, we observe a clear separation between regular and disturbed systems, with a more significant deviation from HE for the disturbed objects. The investigation of the bias between the hydrostatic estimate and the total gravitating mass indicates that, on average, this traces the deviation from HE. very well, even though individual cases show a more complex picture. Typically, in the radial ranges where mass bias and deviation from HE are substantially different, the gas is characterized by a significant amount of random motions (greater than or similar to 30%), relative to thermal ones. As a general result, the HE-deviation and mass bias, at a. given distance from the cluster center, are not very sensitive to the temperature inhomogeneities in the gas.

132 citations

Journal ArticleDOI
TL;DR: In this paper, column density profiles of "cores" in three-dimensional smoothed particle hydrodynamics (SPH) numerical simulations of turbulent molecular clouds were discussed, and it was shown that 65% of the cores can be matched to Bonnor-Ebert (BE) profiles, and 47% correspond to stable equilibrium configurations with ξmax < 6.5.
Abstract: We discuss the column density profiles of "cores" in three-dimensional smoothed particle hydrodynamics (SPH) numerical simulations of turbulent molecular clouds. The SPH scheme allows us to perform a high spatial resolution analysis of the density maxima (cores) at scales between ~0.003 and 0.3 pc. We analyze simulations in three different physical conditions: large-scale driving (LSD), small-scale driving (SSD), and random Gaussian initial conditions without driving (GC), each one at two different time steps: just before self-gravity is turned on (t0) and when gravity has been operating such that 5% of the total mass in the box has been accreted into cores (t1). For this data set, we perform Bonnor-Ebert fits to the column density profiles of cores found by a clump-finding algorithm. We find that, for the particular fitting procedure we use, 65% of the cores can be matched to Bonnor-Ebert (BE) profiles, and of these, 47% correspond to stable equilibrium configurations with ξmax < 6.5, even though the cores analyzed in the simulations are not in equilibrium but instead are dynamically evolving. The temperatures obtained with the fitting procedure vary between 5 and 60 K (in spite of the simulations being isothermal, with T = 11.3 K), with the peak of the distribution being at T = 11 K and most clumps having fitted temperatures between 5 and 30 K. Central densities obtained with the BE fit tend to be smaller than the actual central densities of the cores. We also find that for the LSD and GC cases, there are more BE-like cores at t0 than at t1 with ξmax ≤ 20, while in the case of SSD, there are more such cores at t1 than at t0. We interpret this as a consequence of the stronger turbulence present in the cores of run SSD, which prevents good BE fits in the absence of gravity, and delays collapse in its presence. Finally, in some cases we find substantial superposition effects when we analyze the projection of the density structures, even though the scales over which we project are small (0.18 pc). As a consequence, different projections of the same core may give very different values of the BE fits. Finally, we briefly discuss recent results claiming that Bok globule B68 is in hydrostatic equilibrium, stressing that they imply that this core is unstable by a wide margin. We conclude that fitting BE profiles to observed cores is not an unambiguous test of hydrostatic equilibrium and that fit-estimated parameters such as mass, central density, density contrast, temperature, or radial profile of the BE sphere may differ significantly from the actual values in the cores.

132 citations

Journal ArticleDOI
01 Oct 1974-Icarus
TL;DR: In this paper, the moment of inertia and the hydrostatic value of the second degree harmonic coefficient of Mercury's gravity field are found for the differentiated and undifferentiated models, respectively.

131 citations


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