Self-gravity driven instabilities of interfaces in the interstellar medium

In order to understand star formation it is important to understand the dynamics of atomic and molecular clouds in the interstellar medium (ISM). Non-linear hydrodynamic flows are a key component to the ISM. One route by which non-linear flows arise is the onset and evolution of interfacial instabilities. Interfacial instabilities act to modify the interface between gas components at different densities and temperatures. Such an interface may be subject to a host of instabilities, including the Rayleigh–Taylor, Kelvin–Helmholtz, and Richtmyer–Meshkov instabilities. Recently, a new density interface instability was identified. This self-gravity interfacial instability (SGI) causes any displacement of the interface to grow on roughly a free-fall time-scale, even when the perturbation wavelength is much less than the Jeans length. In previous work, we used numerical simulations to confirm the expectations of linear theory and examine the non-linear evolution of the SGI. We now continue our study by generalizing our initial conditions to allow the acceleration due to self-gravity to be non-zero across the interface. We also consider the behaviour of the SGI for perturbation wavelengths near the Jeans wavelength. We conclude that the action of self-gravity across a density interface may play a significant role in the ISM either by fuelling the growth of new instabilities or modifying the evolution of existing instabilities.     

Numerical simulations of protostellar encounters — I. Star–disc encounters

It appears that most stars are born in clusters, and that at birth most stars have circumstellar discs which are comparable in size to the separations between the stars. Interactions between neighbouring stars and discs are therefore likely to play a key role in determining disc lifetimes, stellar masses, and the separations and eccentricities of binary orbits. Such interactions may also cause fragmentation of the discs, thereby triggering the formation of additional stars.   We have carried out a series of simulations of star–disc interactions using an SPH code which treats self-gravity, hydrodynamic and viscous forces. We find that interactions between discs and stars provide a mechanism for removing energy from, or adding energy to, the orbits of the stars, and for truncating the discs. However, capture during such encounters is unlikely to be an important binary formation mechanism.   A more significant consequence of such encounters is that they can trigger fragmentation of the disc, via tidally and compressionally induced gravitational instabilities, leading to the formation of additional stars and substellar objects. When the disc spins and stellar orbits are randomly oriented, encounters lead to the formation of new companions to the original star in 20 per cent of encounters. If most encounters are prograde and coplanar, as suggested by simulations of dynamically triggered star formation, then new companions are formed in approximately 50 per cent of encounters.     

An optimal method for the power spectrum measurement

An aliasing effect brought up by mass assignment onto Fast Fourier Transformation (FFT) grids may bias measurement of the power spectrum of large scale structures. In this paper, based on the Beylkin's unequally spaced FFT technique, we propose a new precise method to extract the true power spectrum of a large discrete data set. We compare the traditional mass assignment schemes with the new method using the Daub6 and the 3rd-order B-spline scaling functions. Our measurement of Poisson samples and samples of N-body simulations shows that the B-spline scaling function is an optimal choice for mass assignment in the sense that (1) it has a compact support in real space and thus yields an efficient algorithm (2) without any extra corrections. The Fourier space behavior of the 3rd-order B-spline scaling function enables it to be able to accurately recover the true power spectrum with errors less than 5% up to k ＜ kN. It is expected that such a method can be applied to higher order statistics in Fourier space and will enable us to have a precision capture of the non-Gaussian features in the large scale structure of the universe.     

On X-ray variability in narrow-line and broad-line active galactic nuclei

We propose a novel mathematical method to construct an exact polytropic sphere in self-gravitating hydrostatic equilibrium, improving the non-linear Poisson equation. The central boundary condition for the present equation requires a ratio of gas pressure to total one at the centre, which is uniquely identified by the whole mass and molecular weight of the system. The special solution derived from the Lane–Emden equation can be reproduced. This scheme is now available for modelling the molecular cloud cores in interstellar media. The mass–radius relation of the first core is found to be consistent with the recent results of radiation hydrodynamic simulations.     

Axisymmetric smoothed particle hydrodynamics with self-gravity

The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation of a Sun-like star), gas dynamics (wall heating problem, collision of two streams of gas) and inertial confinement fusion (ablative implosion of a small capsule). New material concerning the standard SPH formalism is given. That includes the numerical handling of those mass points which move close to the singularity axis, more accurate expressions for the artificial viscosity and the heat conduction term and an easy way to incorporate self-gravity in the simulations. The algorithm developed to compute gravity does not rely in any sort of grid, leading to a numerical scheme totally compatible with the Lagrangian nature of the SPH equations.     

Hypersonic Swizzle Sticks: Protostellar Turbulence, Outflows and Fossil Outflow Cavities

The expected lifetimes for molecular clouds has become a topic of considerable debate as numerical simulations have shown that MHD turbulence, the nominal means of support for clouds against self-gravity, will decay on short timescales. Thus it appears that either molecular clouds are transient features or they are resupplied with turbulent energy through some means. Jets and molecular outflows are recognized as a ubiquitous phenomena associated with star formation. Stars however form not isolation but in clusters of different density and composion. The ubiquity and high density of outflows from young stars in clusters make them an intriguing candidate for the source of turbulence energy in molecular clouds. In this contribution we present new studies, both observational and theoretical, which address the issue of jet/outflow interactions and their abilityto drive turbulent flows in molecular clouds. Our studies focus on scales associated with young star forming clusters. In particular we first show that direct collisions between active outflows are not effective at stirring the ambient medium. We then show that fossil cavities from “extinct” outflows may provide the missing link in terms of transferring momentum and energy to the cloud.     

Numerical simulations of type III planetary migration – I. Disc model and convergence tests

We investigate the fast (type III) migration regime of high-mass protoplanets orbiting in protoplanetary discs. This type of migration is dominated by corotational torques. We study the details of flow structure in the planet's vicinity, the dependence of migration rate on the adopted disc model and the numerical convergence of models (independence of certain numerical parameters such as gravitational softening).
We use two-dimensional hydrodynamical simulations with adaptive mesh refinement, based on the flash code with improved time-stepping scheme. We perform global disc simulations with sufficient resolution close to the planet, which is allowed to freely move throughout the grid. We employ a new type of equation of state in which the gas temperature depends on both the distance to the star and planet, and a simplified correction for self-gravity of the circumplanetary gas.
We find that the migration rate in the type III migration regime depends strongly on the gas dynamics inside the Hill sphere (Roche lobe of the planet) which, in turn, is sensitive to the aspect ratio of the circumplanetary disc. Furthermore, corrections due to the gas self-gravity are necessary to reduce numerical artefacts that act against rapid planet migration. Reliable numerical studies of type III migration thus require consideration of both the thermal and the self-gravity corrections, as well as a sufficient spatial resolution and the calculation of disc–planet attraction both inside and outside the Hill sphere. With this proviso, we find type III migration to be a robust mode of migration, astrophysically promising because of a speed much faster than in the previously studied modes of migration.     

Measuring the three-dimensional shear from simulation data, with applications to weak gravitational lensing

We have developed a new three-dimensional algorithm, based on the standard P³M method, for computing deflections resulting from weak gravitational lensing. We compare the results of this method with those of the two-dimensional planar approach, and rigorously outline the conditions under which the two approaches are equivalent. Our new algorithm uses a Fast Fourier Transform convolution method for speed, and has a variable softening feature to provide a realistic interpretation of the large-scale structure in a simulation. The output values of the code are compared with those from the Ewald summation method, which we describe and develop in detail. With an optimal choice of the high-frequency filtering in the Fourier convolution, the maximum errors, when using only a single particle, are about 7 per cent, with an rms error less than 2 per cent. For ensembles of particles, used in typical N -body simulations, the rms errors are typically 0.3 per cent. We describe how the output from the algorithm can be used to generate distributions of magnification, source ellipticity, shear and convergence for large-scale structure.     

Dynamic Monte Carlo radiation transfer in SPH: radiation pressure force implementation

We present a new framework for radiation hydrodynamics simulations. Gas dynamics is modelled by smoothed particle hydrodynamics (SPH), whereas radiation transfer is simulated via a time-dependent Monte Carlo approach that traces photon packets. As a first step in the development of the method, in this paper we consider the momentum transfer between radiation field and gas, which is important for systems where radiation pressure is high. There is no fundamental limitation on the number of radiation sources, the geometry or the optical depth of the problems that can be studied with the method. However, as expected for any Monte Carlo transfer scheme, stochastic noise presents a serious limitation. We present a number of tests that show that the errors of the method can be estimated accurately by considering Poisson noise fluctuations in the number of photon packets that SPH particles interact with per dynamical time. It is found that, for a reasonable accuracy, the momentum carried by photon packets must be much smaller than the typical momentum of SPH particles. We discuss numerical limitations of the code, and future steps that can be taken to improve performance and applicability of the method.     

The runaway instability of thick discs around black holes I. The constant angular momentum case

We present results from a numerical study of the runaway instability of thick discs around black holes. This instability is an important issue for most models of cosmic gamma-ray bursts, where the central engine responsible for the initial energy release is such a system consisting of a thick disc surrounding a black hole. We have carried out a comprehensive number of time-dependent simulations aimed at exploring the appearance of the instability. Our study has been performed using a fully relativistic hydrodynamics code. The general relativistic hydrodynamic equations are formulated as a hyperbolic flux-conservative system and solved using a suitable Godunov-type scheme. We build a series of constant angular momentum discs around a Schwarzschild black hole. Furthermore, the self-gravity of the disc is neglected and the evolution of the central black hole is assumed to be that of a sequence of exact Schwarzschild black holes of varying mass. The black hole mass increase is thus determined by the mass accretion rate across the event horizon. In agreement with previous studies based on stationary models, we find that by allowing the mass of the black hole to grow the disc becomes unstable. Our hydrodynamical simulations show that for all disc-to-hole mass ratios considered (between 1 and 0.05), the runaway instability appears very fast on a dynamical time-scale of a few orbital periods, typically a few 10 ms and never exceeding 1 s for our particular choice of the mass of the black hole (2.5 M) and a large range of mass fluxes  ( m 10^-3 M s^-1)  . The implications of our results in the context of gamma-ray bursts are briefly discussed.     

Using spherical wavelets to search for magnetically-induced alignment in the arrival directions of ultra-high energy cosmic rays

Due to the action of the intervening cosmic magnetic fields, ultra-high energy cosmic rays (UHECRs) can be deflected in such a way as to create clustered energy-ordered filamentary structures in the arrival direction of these particles, the so-called multiplets. In this work we propose a new method based on the spherical wavelet transform to identify multiplets in sky maps containing arrival directions of UHECRs. The method is illustrated in simulations with a multiplet embedded in isotropic backgrounds with different numbers of events. The efficiency of the algorithm is assessed through the calculation of Type I and II errors.     

The runaway instability of self-gravitating tori with non-constant specific angular momentum around black holes

We discuss the runaway instability of axisymmetric tori with non-constant specific angular momentum around black holes, taking into account self-gravity of the tori. The distribution of specific angular momentum of the tori is assumed to be a positive power law with respect to the distance from the rotational axis. By employing the pseudo-Newtonian potential for the gravity of the spherical black hole, we have found that self-gravity of the tori causes a runaway instability if the amount of the mass which is transferred from the torus to the black hole exceeds a critical value, i.e. 3 per cent of the mass of the torus. This has been shown by two different approaches: (1) by using equilibrium models and (2) by dynamical simulations. In particular, dynamical simulations using an SPH code have been carried out for both self-gravitating and non-self-gravitating tori. For non-self-gravitating models, all tori are runaway stable. Therefore we come to the conclusion that self-gravity of the tori has a stronger destabilizing effect than the stabilizing effect of the positive power-law distribution of the angular momentum.     

Chemodynamical evolution of interacting galaxies

We have undertaken numerical simulations of galaxy interactions and mergers, coupling the dynamics with the star formation history and the chemical evolution. The self-gravity of stars and gas is taken into account through a tree-code algorithm, the gas hydrodynamics through SPH, and an empirical law such as a local Schmidt law is used to compute star formation. The gas and stellar metallicity is computed at each position, according to assumed yields, and the dust amount is monitored. At each step the spectra of galaxies are computed, according to simple radiative transfer and dust models. Initial conditions for these simulations will be taken from a large-scale cosmological frame-work. The aim is to build a statistically significant library of merger histories. The first results of the project will be discussed, in particular on predictions about galaxy surveys at high redshift. This revised version was published online in September 2006 with corrections to the Cover Date.     

Models of Jupiter's growth incorporating thermal and hydrodynamic constraints

We model the growth of Jupiter via core nucleated accretion, applying constraints from hydrodynamical processes that result from the disk-planet interaction. We compute the planet's internal structure using a well tested planetary formation code that is based upon a Henyey-type stellar evolution code. The planet's interactions with the protoplanetary disk are calculated using 3-D hydrodynamic simulations. Previous models of Jupiter's growth have taken the radius of the planet to be approximately one Hill sphere radius, RH. However, 3-D hydrodynamic simulations show that only gas within ∼0.25RH remains bound to the planet, with the more distant gas eventually participating in the shear flow of the protoplanetary disk. Therefore in our new simulations, the planet's outer boundary is placed at the location where gas has the thermal energy to reach the portion of the flow not bound to the planet. We find that the smaller radius increases the time required for planetary growth by ∼5%. Thermal pressure limits the rate at which a planet less than a few dozen times as massive as Earth can accumulate gas from the protoplanetary disk, whereas hydrodynamics regulates the growth rate for more massive planets. Within a moderately viscous disk, the accretion rate peaks when the planet's mass is about equal to the mass of Saturn. In a less viscous disk hydrodynamical limits to accretion are smaller, and the accretion rate peaks at lower mass. Observations suggest that the typical lifetime of massive disks around young stellar objects is ∼3 Myr. To account for the dissipation of such disks, we perform some of our simulations of Jupiter's growth within a disk whose surface gas density decreases on this timescale. In all of the cases that we simulate, the planet's effective radiating temperature rises to well above 1000 K soon after hydrodynamic limits begin to control the rate of gas accretion and the planet's distended envelope begins to contract. According to our simulations, proto-Jupiter's distended and thermally-supported envelope was too small to capture the planet's current retinue of irregular satellites as advocated by Pollack et al. [Pollack, J.B., Burns, J.A., Tauber, M.E., 1979. Icarus 37, 587-611].     

Interfacial instabilities driven by self-gravity: first numerical results

The evolution of the interstellar medium (ISM) is driven by a variety of phenomena, including turbulence, shearing flows, magnetic fields and the thermal properties of the gas. Among the most important forces at work is self-gravity, which ultimately drives protostellar collapse. As part of an ongoing study of instabilities in the ISM, Hunter, Whitaker & Lovelace have discovered another process driven by self-gravity: the instability of an interface of discontinuous density. Theory predicts that this self-gravity driven interfacial instability persists in the static limit and in the absence of a constant background acceleration. Disturbances to a density interface are found to grow on a time-scale of the order of the free-fall time, even when the perturbation wavelength is much less than the Jeans length. Here we present the first numerical simulations of this instability. The theoretical growth rate is confirmed and the non-linear morphology displayed. The self-gravity interfacial instability is shown to be fundamentally different from the Rayleigh–Taylor instability, although both exhibit similar morphologies under the condition of a high density contrast, such as is commonly found in the ISM. Such instabilities are a possible mechanism by which observed features, such as the pillars of gas seen near the boundaries of interstellar clouds, are formed.     

Star formation in a multi-phase interstellar medium

This contribution reports on our first efforts to simulate a multiphase interstellar medium on a kiloparsec scale in three dimensions with the stars and gas modeled self-consistently. Starting from inhomogenous initial conditions, our closed box simulations follow the gas as it cools and collapses under its own self-gravity to form stars which eventually return material and energy back through supernovae explosions and winds. This revised version was published online in August 2006 with corrections to the Cover Date.     

New self-similar solutions of polytropic gas dynamics

We explore semicomplete self-similar solutions for the polytropic gas dynamics involving self-gravity under spherical symmetry, examine behaviours of the sonic critical curve and present new asymptotic collapse solutions that describe 'quasi-static' asymptotic behaviours at small radii and large times. These new 'quasi-static' solutions with divergent mass density approaching the core can have self-similar oscillations. Earlier known solutions are summarized. Various semicomplete self-similar solutions involving such novel asymptotic solutions are constructed, either with or without a shock. In contexts of stellar core collapse and supernova explosion, a hydrodynamic model of a rebound shock initiated around the stellar degenerate core of a massive progenitor star is presented. With this dynamic model framework, we attempt to relate progenitor stars and the corresponding remnant compact stars: neutron stars, black holes and white dwarfs.     

Double-Pulse Laser-Driven Jets on OMEGA

A double-pulse laser drive is used to create episodic supersonic plasma jets that propagate into a low density ambient medium. These are among the first laser experiments to generate pulsed outflow. The temporal laser-intensity profile consists of two 1-ns square pulses separated by 9.6 ns. The laser is focused on a truncated conical plug made of medium Z material inserted into a high-Z washer. Unloading material from the plug is collimated within the cylindrical washer hole, then propagates into the low-Z foam medium. The resulting jet is denser than the ambient medium. Double-pulse jet evolution is compared to that driven by a single laser pulse. The total drive energy is the same for both jets, as if a source with fixed energy generated a jet from either one or two bursts. Radiographs taken at 100 ns show that a single-pulse jet was broader than the double-pulse jet, as predicted by hydrodynamic simulations. Since the initial shock creating the jet is stronger when all the energy arrives in a single pulse, the jet material impacts the ambient medium with higher initial velocity. Detailed comparisons between single- and double-pulsed jet rheology and shock structure are presented. 2-D hydrodynamic simulations are compared to the experimental radiographs. PACS: 52.30.−q 41.75.Jv 42.62.−b 42.68.Sq 47.40.−x 47.56.+r     

Cepheid Limb Darkening Models for the VLTI

We present a new method to compute wavelength- and phase-dependent limb darkening corrections for classical Cepheids. These corrections are derived from hydrodynamic simulations and radiative transfer modeling with a full set of atomic and molecular opacities. Comparison with hydrostatic models having the same stellar parameters show a larger limb darkening for most phases in our models, and temporal variations related to the hydrodynamics of the stellar pulsation. Weassess the implications of our results with respect to the geometric Baade-Wesselink method, which uses interferometric measurements of Cepheid angular diameters to determine their distances and radii. The relevance of the hydrodynamic effects predicted by our model on the limb darkening of pulsating Cepheids is finally discussed in terms of the predicted capabilities of the VLTI. This revised version was published online in July 2006 with corrections to the Cover Date.