Hydrostatic equilibrium

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

Evolution of the Merger Induced Hydrostatic Mass Bias in Galaxy Clusters

Abstract: In this work, we examine the effects of mergers on the hydrostatic mass estimate of galaxy clusters using high-resolution Eulerian cosmological simulations. We utilize merger trees to isolate the last merger for each cluster in our sample and follow the time evolution of the hydrostatic mass bias as the systems relax. We find that during a merger, a shock propagates outward from the parent cluster, resulting in an overestimate in the hydrostatic mass bias. After the merger, as a cluster relaxes, the bias in hydrostatic mass estimate decreases but remains at a level of -5-10% with 15-20% scatter within r500. We also investigate the post-merger evolution of the pressure support from bulk motions, a dominant cause of this residual mass bias. At r500, the contribution from random motions peaks at 30% of the total pressure during the merger and quickly decays to \sim 10-15% as a cluster relaxes. Additionally, we use a measure of the random motion pressure to correct the hydrostatic mass estimate. We discover that 4 Gyr after mergers, the direct effects of the merger event on the hydrostatic mass bias have become negligible. Thereafter, the mass bias is primarily due to residual bulk motions in the gas which are not accounted for in the hydrostatic equilibrium equation. We present a hydrostatic mass bias correction method that can recover the unbiased cluster mass for relaxed clusters with 9% scatter at r500 and 11% scatter in the outskirts, within r200.

Transport of Magnetic Fields in Convective, Accreting Supernova Cores

Abstract: We consider the amplification and transport of a magnetic field in the collapsed core of a massive star, including both the region between the neutrinosphere and the shock, and the central, opaque core. An analytical argument explains why rapid convective overturns persist within a newly formed neutron star for roughly 10 s (>103 overturns), consistent with recent numerical models. A dynamical balance between turbulent and magnetic stresses within this convective layer corresponds to flux densities in excess of 1015 G. Material accreting onto the core is heated by neutrinos and also becomes strongly convective. We compare the expected magnetic stresses in this convective "gain layer" with those deep inside the neutron core. Buoyant motions of magnetized fluid are greatly aided by the intense neutrino flux. We calculate the transport rate through a medium containing free neutrons, protons, and electrons, in the limiting cases of degenerate or nondegenerate nucleons. Fields stronger than ~1013 G are able to rise through the outer degenerate layers of the neutron core during the last stages of Kelvin-Helmholtz cooling (up to 10 s postcollapse), even though these layers have become stable to convection. We also find the equilibrium shape of a thin magnetic flux rope in the dense hydrostatic atmosphere of the neutron star, along with the critical separation of the footpoints above which the rope undergoes unlimited expansion against gravity. The implications of these results for pulsar magnetism are summarized, and applied to the case of late fallback over the first 103-104 s of the life of a neutron star.

Rotational stability of dynamic planets with elastic lithospheres

Abstract: Received 13 April 2005; revised 21 October 2005; accepted 3 November 2005; published 14 February 2006. [1] We revisit the classic problem of the secular rotational stability of planets in response to loading using the fluid limit of viscoelastic Love number theory. Gold (1955) and Goldreich and Toomre (1969) considered the stability of a hydrostatic planet subject to an uncompensated surface mass load and concluded that a mass of any size would drive true polar wander (TPW) that ultimately reorients the load to the equator. Willemann (1984) treated the more self-consistent problem where the presence of a lithosphere leads to both imperfect load compensation and a remnant rotational bulge. Willemann considered axisymmetric loads and concluded that the equilibrium pole location was governed by a balance, independent of elastic lithospheric thickness, between the loadinduced TPW and stabilization by the remnant bulge. Our new analysis demonstrates that the equilibrium pole position is a function of the lithospheric strength, with a convergence to Willemann’s results evident at high values of elastic thickness (>400 km for an application to Mars), and significantly larger predicted TPW for planets with thin lithospheres. Furthermore, we demonstrate that nonaxisymmetric surface mass loads and internal (convective) heterogeneity, even when these are small relative to axisymmetric contributions, can profoundly influence the rotational stability. Indeed, we derive the relatively permissive conditions under which nonaxisymmetric forcing initiates an inertial interchange TPW event (i.e., a 90� pole shift). Finally, Willemann’s analysis is often cited to argue for a small (<18� ) TPW of Mars driven by the development of a Tharsissized load. We show that even in the absence of the destabilizing effects of load asymmetry, the equations governing rotational stability permit higher excursions of the Martian rotation vector than has previously been appreciated.

Heating and Cooling Protostellar Disks

Abstract: We examine heating and cooling in protostellar disks using 3-D radiation-MHD calculations of a patch of the Solar nebula at 1 AU, employing the shearing-box and flux-limited radiation diffusion approximations. The disk atmosphere is ionized by stellar X-rays, well-coupled to magnetic fields, and sustains a turbulent accretion flow driven by magneto-rotational instability, while the interior is resistive and magnetically dead. The turbulent layers heat by absorbing the light from the central star and by dissipating the magnetic fields. They are optically-thin to their own radiation and cool inefficiently. The optically-thick interior in contrast is heated only weakly, by re-emission from the atmosphere. The interior is colder than a classical viscous model, and isothermal. The magnetic fields support an extended atmosphere that absorbs the starlight 1.5 times higher than the hydrostatic viscous model. The disk thickness thus measures not the internal temperature, but the magnetic field strength. Fluctuations in the fields move the starlight-absorbing surface up and down. The height ranges between 13% and 24% of the radius over timescales of several orbits, with implications for infrared variability. The fields are buoyant, so the accretion heating occurs higher in the atmosphere than the stresses. The heating is localized around current sheets, caused by magneto-rotational instability at lower elevations and by Parker instability at higher elevations. Gas in the sheets is heated above the stellar irradiation temperature, even though accretion is much less than irradiation power when volume-averaged. The hot optically-thin current sheets might be detectable through their line emission.

Hydrostatic Gas Constraints on Supermassive Black Hole Masses: Implications for Hydrostatic Equilibrium and Dynamical Modelling in a Sample of Early-Type Galaxies

Abstract: We present new mass measurements for the supermassive black holes (SMBHs) in the centres of three early-type galaxies. The gas pressure in the surrounding, hot interstellar medium (ISM) is measured through spatially resolved spectroscopy with the Chandra X-ray observatory, allowing the SMBH mass (Mbh) to be inferred directly under the hydrostatic approximation. This technique does not require calibration against other SMBH measurement methods and its accuracy depends only on the ISM being close to hydrostatic, which is supported by the smooth X-ray isophotes of the galaxies. Combined with results from our recent study of the elliptical galaxy NGC4649, this brings to four the number of galaxies with SMBHs measured in this way. Of these, three already have mass determinations from the kinematics of either the stars or a central gas disc, and hence join only a handful of galaxies with Mbh measured by more than one technique. We find good agreement between the different methods, providing support for the assumptions implicit in both the hydrostatic and the dynamical models. The stellar mass-to-light ratios for each galaxy inferred by our technique are in agreement with the predictions of stellar population synthesis models assuming a Kroupa initial mass function (IMF). This concurrence implies that no more than ~10-20% of the ISM pressure is nonthermal, unless there is a conspiracy between the shape of the IMF and nonthermal pressure. Finally, we compute Bondi accretion rates, finding that the two galaxies with the highest rates exhibit little evidence of X-ray cavities, suggesting that the correlation with the AGN jet power takes time to be established.