Evaporation and condensation of spherical interstellar clouds. Self-consistent models with saturated heat conduction and cooling

Shortened version: The fate of IS clouds embedded in a hot tenuous medium depends on whether the clouds suffer from evaporation or whether material condensates onto them. Analytical solutions for the rate of evaporative mass loss from an isolated spherical cloud embedded in a hot tenuous gas are deduced by Cowie & McKee (1977). In order to test the validity of the analytical results for more realistic IS conditions the full hydrodynamical equations must be treated. Therefore, 2D numerical simulations of the evolution of IS clouds %are performed with different internal density structures and surrounded by a hot plasma reservoir. Self-gravity, interstellar heating and cooling effects and heat conduction by electrons are added. Classical thermal conductivity of a fully ionized hydrogen plasma and saturated heat flux are considered. Using pure hydrodynamics and classical heat flux we can reproduce the analytical results. Heat flux saturation reduces the evaporation rate by one order of magnitude below the analytical value. The evolution changes totally for more realistic conditions when interstellar heating and cooling effects stabilize the self-gravity. Evaporation then turns into condensation, because the additional energy by heat conduction can be transported away from the interface and radiated off efficiently from the cloud's inner parts. I.e. that the saturated heat flux consideration is inevitable for IS clouds embedded in hot tenuous gas. Various consequences are discussed in the paper.Comment: 16 pages, 24 figures, accepted in Astronomy and Astrophysic

On the Divergence-Free Condition in Godunov-Type Schemes for Ideal Magnetohydrodynamics: the Upwind Constrained Transport Method

We present a general framework to design Godunov-type schemes for multidimensional ideal magnetohydrodynamic (MHD) systems, having the divergence-free relation and the related properties of the magnetic field B as built-in conditions. Our approach mostly relies on the 'Constrained Transport' (CT) discretization technique for the magnetic field components, originally developed for the linear induction equation, which assures div(B)=0 and its preservation in time to within machine accuracy in a finite-volume setting. We show that the CT formalism, when fully exploited, can be used as a general guideline to design the reconstruction procedures of the B vector field, to adapt standard upwind procedures for the momentum and energy equations, avoiding the onset of numerical monopoles of O(1) size, and to formulate approximate Riemann solvers for the induction equation. This general framework will be named here 'Upwind Constrained Transport' (UCT). To demonstrate the versatility of our method, we apply it to a variety of schemes, which are finally validated numerically and compared: a novel implementation for the MHD case of the second order Roe-type positive scheme by Liu and Lax (J. Comp. Fluid Dynam. 5, 133, 1996), and both the second and third order versions of a central-type MHD scheme presented by Londrillo and Del Zanna (Astrophys. J. 530, 508, 2000), where the basic UCT strategies have been first outlined

On the evolution of eccentric and inclined protoplanets embedded in protoplanetary disks

Young planets embedded in their protoplanetary disk interact gravitationally with it leading to energy and angular momentum exchange. This interaction determines the evolution of the planet through changes to the orbital parameters. We investigate changes in the orbital elements of a 20 Earth--mass planet due to the torques from the disk. We focus on the non-linear evolution of initially non-vanishing eccentricity $e$ and/or inclination $i$. We treat the disk as a two- or three-dimensional viscous fluid and perform hydrodynamical simulations with an embedded planet. We find rapid exponential decay of the planet orbital eccentricity and inclination for small initial values of $e$ and $i$, in agreement with linear theory. For larger values of $e > 0.1$ the decay time increases and the decay rate scales as $\dot{e} \propto e^{-2}$, consistent with existing theoretical models. For large inclinations ($i$ > 6 deg) the inclination decay rate shows an identical scaling $di/dt \propto i^{-2}$. We find an interesting dependence of the migration on the eccentricity. In a disk with aspect ratio $H/r=0.05$ the migration rate is enhanced for small non-zero eccentricities ($e < 0.1$), while for larger values we see a significant reduction by a factor of $\sim 4$. We find no indication for a reversal of the migration for large $e$, although the torque experienced by the planet becomes positive when $e \simeq 0.3$. This inward migration is caused by the persisting energy loss of the planet. For non gap forming planets, eccentricity and inclination damping occurs on a time scale that is very much shorter than the migration time scale. The results of non linear hydrodynamic simulations are in very good agreement with linear theory for small $e$ and $i$.Comment: accepted for Astronomy & Astrophysics, 16 pages, 16 figures, animations under: http://www.tat.physik.uni-tuebingen.de/~kley/publ/paper/eccp.htm

The growth of supermassive black holes fed by accretion disks

Supermassive black holes are probably present in the centre of the majority of the galaxies. There is a consensus that these exotic objects are formed by the growth of seeds either by accreting mass from a circumnuclear disk and/or by coalescences during merger episodes. The mass fraction of the disk captured by the central object and the related timescale are still open questions, as well as how these quantities depend on parameters like the initial mass of the disk or the seed or on the angular momentum transport mechanism. This paper is addressed to these particular aspects of the accretion disk evolution and of the growth of seeds. The time-dependent hydrodynamic equations were solved numerically for an axi-symmetric disk in which the gravitational potential includes contributions both from the central object and from the disk itself. The numerical code is based on a Eulerian formalism, using a finite difference method of second-order, according to the Van Leer upwind algorithm on a staggered mesh. The present simulations indicate that seeds capture about a half of the initial disk mass, a result weakly dependent on model parameters. The timescales required for accreting 50% of the disk mass are in the range 130-540 Myr, depending on the adopted parameters. These timescales permit to explain the presence of bright quasars at z ~ 6.5. Moreover, at the end of the disk evolution, a "torus-like" geometry develops, offering a natural explanation for the presence of these structures in the central regions of AGNs, representing an additional support to the unified model.Comment: 10 pages, 7 figures. Accepted for publication by Astronomy and Astrophysic

Shaping point- and mirror-symmetric proto-planetary nebulae by the orbital motion of the central binary system

We present 3D hydrodynamical simulations of a jet launched from the secondary star of a binary system inside a proto-planetary nebula. The secondary star moves around the primary in a close eccentric orbit. From the gasdynamic simulations we compute synthetic [NII] 6583 emission maps. Different jet axis inclinations with respect to the orbital plane, as well as different orientations of the flow with respect to the observer are considered. For some parameter combinations, we obtain structures that show point- or mirror-symmetric morphologies depending on the orientation of the flow with respect to the observer. Furthermore, our models can explain some of the emission distribution asymmetries that are summarized in the classification given by Soker & hadar (2002).Comment: 15 pages, 3 figures, 2 tables, Accepted in Apj Letter

The structure of self-gravitating clouds

To study the interaction of star-formation and turbulent molecular cloud structuring, we analyse numerical models and observations of self-gravitating clouds using the Delta-variance as statistical measure for structural characteristics. In the models we resolve the transition from purely hydrodynamic turbulence to gravitational collapse associated with the formation and mass growth of protostellar cores. We compare models of driven and freely decaying turbulence with and without magnetic fields. Self-gravitating supersonic turbulence always produces a density structure that contains most power on the smallest scales provided by collapsed cores as soon as local collapse sets in. This is in contrast to non-self-gravitating hydrodynamic turbulence where the Delta-variance is dominated by large scale structures. To detect this effect in star-forming regions observations have to resolve the high density contrast of protostellar cores with respect to their ambient molecular cloud. Using the 3mm continuum map of a star-forming cluster in Serpens we show that the dust emission traces the full density evolution. On the contrary, the density range accessible by molecular line observations is insufficient for this analysis. Only dust emission and dust extinction observations are able to to determine the structural parameters of star-forming clouds following the density evolution during the gravitational collapse.Comment: 12 pages, 9 figures, A&A in pres

SWASHES: a compilation of Shallow Water Analytic Solutions for Hydraulic and Environmental Studies

Numerous codes are being developed to solve Shallow Water equations. Because there are used in hydraulic and environmental studies, their capability to simulate properly flow dynamics is critical to guarantee infrastructure and human safety. While validating these codes is an important issue, code validations are currently restricted because analytic solutions to the Shallow Water equations are rare and have been published on an individual basis over a period of more than five decades. This article aims at making analytic solutions to the Shallow Water equations easily available to code developers and users. It compiles a significant number of analytic solutions to the Shallow Water equations that are currently scattered through the literature of various scientific disciplines. The analytic solutions are described in a unified formalism to make a consistent set of test cases. These analytic solutions encompass a wide variety of flow conditions (supercritical, subcritical, shock, etc.), in 1 or 2 space dimensions, with or without rain and soil friction, for transitory flow or steady state. The corresponding source codes are made available to the community (http://www.univ-orleans.fr/mapmo/soft/SWASHES), so that users of Shallow Water-based models can easily find an adaptable benchmark library to validate their numerical methods.Comment: 40 pages There are some errors in the published version. This is a corrected versio

The evolution of interstellar clouds in a streaming hot plasma including heat conduction

To examine the evolution of giant molecular clouds in the stream of a hot plasma we performed two-dimensional hydrodynamical simulations that take full account of self-gravity, heating and cooling effects and heat conduction by electrons. We use the thermal conductivity of a fully ionized hydrogen plasma proposed by Spitzer and a saturated heat flux according to Cowie & McKee in regions where the mean free path of the electrons is large compared to the temperature scaleheight. Significant structural and evolutionary differences occur between simulations with and without heat conduction. Dense clouds in pure dynamical models experience dynamical destruction by Kelvin-Helmholtz (KH) instability. In static models heat conduction leads to evaporation of such clouds. Heat conduction acting on clouds in a gas stream smooths out steep temperature and density gradients at the edge of the cloud because the conduction timescale is shorter than the cooling timescale. This diminishes the velocity gradient between the streaming plasma and the cloud, so that the timescale for the onset of KH instabilities increases, and the surface of the cloud becomes less susceptible to KH instabilities. The stabilisation effect of heat conduction against KH instability is more pronounced for smaller and less massive clouds. As in the static case more realistic cloud conditions allow heat conduction to transfer hot material onto the cloud's surface and to mix the accreted gas deeper into the cloud.Comment: 19 pages, 12 figures, accepted in Astronomy and Astrophysic