We revisit the modeling of ion-neutral (or ambipolar) diffusion with two fluid smoothed particle hydrodynamics, as discussed by Hosking & Whitworth. Some parts of the technique are optimized to testify the pioneer works on behavior of the ambipolar diffusion in an isothermal self-gravitating layer. The frictional heating by ambipolar diffusion is examined, and its effect on fragmentation of the layer is studied. The results are compared to the thermal phases of instability as obtained by Nejad-Asghar.
We describe and demonstrate a method for increasing the resolution locally in a Smoothed Particle Hydrodynamic (SPH) simulation, by splitting particles. We show that in simulations of self-gravitating collapse (of the sort which are presumed to occur in star formation) the method is stable, and affords great savings in computer time and memory. When applied to the standard Boss & Bodenheimer test -- which has been shown to depend critically on fulfilment of the Jeans Condition -- the results are comparable both with those obtained using Adaptive Mesh Refinement, and with those obtained using a…
The issue of fragmentation in self-gravitating gaseous accretion discs has implications both for the formation of stars in discs in the nuclei of active galaxies, and for the formation of gaseous planets or brown dwarfs in circumstellar discs. It is now well established that fragmentation occurs if the disc is cooled on a timescale smaller than the local dynamical timescale, while for longer cooling times the disc reaches a quasi-steady state in thermal equilibrium, with the cooling rate balanced by the heating due to gravitational stresses. We investigate here how the fragmentation boundary d…
The heating of the ion-neutral (or ambipolar) diffusion may affect the thermal phases of the molecular clouds. We present an investigation on the effect of this heating mechanism in the thermal instability of the molecular clouds. A weakly ionized one dimensional slab geometry, which is allowed for self-gravity and ambipolar diffusion, is chosen to study its thermal phases. We use the thermodynamic evolution of the slab to obtain the regions where slab cloud becomes thermally unstable. We investigate this evolution using the model of ambipolar diffusion with two-fluid smoothed particle hydrody…
We consider the effects of eccentricity on the fragmentation of gravitationally unstable accretion disks, using numerical hydrodynamics. We find that eccentricity does not affect the overall stability of the disk against fragmentation, but significantly alters the manner in which such fragments accrete gas. Variable tidal forces around an eccentric orbit slow the accretion process, and suppress the formation of weakly-bound clumps. The "stellar" mass function resulting from the fragmentation of an eccentric disk is found to have a significantly higher characteristic mass than that from a corre…
An unsolved issue in the standard core accretion model for gaseous planet formation is how kilometre-sized planetesimals form from, initially, micron-sized dust grains. Solid growth beyond metre sizes can be difficult both because the sticking efficiency becomes very small, and because these particles should rapidly migrate into the central star. We consider here how metre-sized particles evolve in self-gravitating accretion discs using simulations in which the gravitational influence of the solid particles is also included. Metre-sized particles become strongly concentrated in the spiral stru…
Numerical solutions of the isothermal Lane-Emden equation are presented, corresponding to self-gravitating gaseous cores embedded within a finite density envelope of overall cylindrical symmetry. These structures may be members of a fragmentation hierarchy proceeding from sheets, to filaments, to elongated, prolate clumps. The embedded solutions are the first of their kind, and as such represent a significant improvement upon the isolated cloud paradigm used almost exclusively by previous authors. The properties of the equilibria are in reasonable agreement with observations of dense molecular…
Gravity is scale free. Thus gravity may form similar structures in self-gravitating systems on different scales. Indeed, observations of the interstellar medium, spiral disks and cosmic structures, reveal similar characteristics. The structures in these systems are very lumpy and inhomogeneous. Moreover some of these structures do not seem to be of random nature, but obey certain power laws. Models of slightly dissipative self-gravitating disks show how such inhomogeneous structures can be maintained on the kpc-scale. The basic physical processes in these models are self-gravity, dissipation a…
A number of previous studies of the fragmentation of self-gravitating protostellar discs have modeled radiative cooling with a cooling timescale (t_{cool}) parameterised as a simple multiple (beta_{cool}) of the local dynamical timescale. Such studies have delineated the `fragmentation boundary' in terms of a critical value of beta_{cool} (beta_{crit}), where the disc fragments if beta_{cool} < beta_{crit}. Such an approach however begs the question of how in reality a disc could ever be assembled with beta_{cool} < beta_{crit}. Here we adopt the more realistic approach of gradually reducing b…
The self-gravitating thermal gas (non-relativistic particles of mass m at temperature T) is exactly equivalent to a field theory with a single scalar field phi(x) and exponential self-interaction. We build up perturbation theory around a space dependent stationary point phi_0(r) in a finite size domain delta \leq r \leq R ,(delta << R), which is relevant for astrophysical applica- tions (interstellar medium,galaxy distributions).We compute the correlations of the gravitational potential (phi) and of the density and find that they scale; the latter scales as 1/r^2. A rich structure emerges in t…
I review recent progresses in the dynamics and the evolution of self-gravitating accretion discs. Accretion discs are a fundamental component of several astrophysical systems on very diverse scales, and can be found around supermassive black holes in Active Galactic Nuclei (AGN), and also in our Galaxy around stellar mass compact objects and around young stars. Notwithstanding the specific differences arising from such diversity in physical extent, all these systems share a common feature where a central object is fed from the accretion disc, due to the effect of turbulence and disc instabilit…
(highly abridged) We define three requirements for accurate simulations that attempt to model circumstellar disks and the formation of collapsed objects (e.g. planets) within them. First, we define a resolution requirement based on the wavelength for neutral stability of self gravitating waves in the disk. For particle based or grid based simulations, this criterion takes the form, respectively, of a minimum number of particles per critical (`Toomre') mass or maximum value of a `Toomre number', $T= δx/λ_T$, where the wavelength, $λ_T$, is the wavelength for neutral stability for waves in disks…
It has already been shown, using a local model, that accretion discs with cooling times t_cool <= 3 Omega^-1 fragment into gravitationally bound objects, while those with cooling times t_cool > 3 Omega^-1 evolve into a quasi-steady state. We present results of three-dimensional simulations that test if the local result still holds globally. We find that the fragmentation boundary is close to that determined using the local model, but that fragmentation may occur for longer cooling times when the disc is more massive or when the mass is distributed in such a way as to make a particular region o…
Using a local model Gammie (2001) has shown that accretion discs with cooling times t_cool <= 3/Omega fragment into gravitationally bound objects, while those with cooling times t_cool > 3/Omega evolve into a quasi-steady state. We use three-dimensional smoothed particle hydrodynamic simulations of protoplanetary accretion discs to test if the local results hold globally. We find that for disc masses appropriate for T Tauri discs, the fragmentation boundary still occurs at a cooling time close to t_cool = 3/Omega. For more massive discs, which are likely to be present at an earlier stage of th…
Using smoothed particle hydrodynamics in combination with the special-purpose hardware device GRAPE, we follow the fragmentation process and dynamical evolution in the interior of molecular clouds until most of the gas is converted to form a cluster of protostellar cores. The properties of this protostellar cluster are compared to observational data from star forming regions.
We present an investigation on effect of the ion-neutral (or ambipolar) diffusion heating rate on thermal phases of a molecular cloud. We use the modeling of ambipolar diffusion with two-fluid smoothed particle hydrodynamics, as discussed by Nejad-Asghar & Molteni. We take into account the ambipolar drift heating rate on the net cooling function of the molecular clouds, and we investigate the thermal phases in a self-gravitating magnetized one dimensional slab. The results show that the isobaric thermal instability criterion is satisfied in the outer parts of the cloud, thus, these regions are…
In this paper we study the process of the subsequent (runaway) fragmentation of the rotating isothermal Giant Molecular Cloud (GMC) complex. Our own developed Smoothed Particle Hydrodynamics (SPH) gas-dynamical model successfully reproduce the observed Cloud Mass-distribution Function (CMF) in our Galaxy (even the differences between the inner and outer parts of our Galaxy). The steady state CMF is established during the collapse within a free-fall timescale of the GMC. We show that one of the key parameters, which defines the observed slope of the present day CMF, is the initial ratio of the …
The interstellar medium is observed in a hierarchical fractal structure over several orders of magnitude in scale. Aiming to understand the origin of this structure, we carry out numerical simulations of molecular cloud fragmentation, taking into account self-gravity, dissipation and energy input. Self-gravity is computed through a tree code, with fully or quasi periodic boundary conditions. Energy dissipation is introduced through cloud-cloud ineslatic collisions. Several schemes are tested for the energy input. It appears that energy input from galactic shear allows to achieve a stationary c…
We investigate the orbital evolution of planetesimals in a self-gravitating circumstellar disc in the size regime ($\sim 1-5000$ km) where the planetesimals behave approximately as test particles in the disc's non-axisymmetric potential. We find that the particles respond to the stochastic, regenerative spiral features in the disc by executing large random excursions (up to a factor of two in radius in $\sim 1000$ years), although typical random orbital velocities are of order one tenth of the Keplerian speed. The limited time frame and small number of planetesimals modeled does not permit us …
We performed simulations of self-gravitating hydrodynamic turbulence to model the formation of filaments, clumps and cores in molecular clouds. We find that when the mass on the initial computational grid is comparable to the Jeans mass, turbulent pressure is able to prevent gravitational collapse. When the turbulence has damped away sufficiently, gravitational collapse can occur, and the resulting structure closely resembles the pre-singularity collapse of an isothermal sphere of Penston (1969). If several Jeans masses are initially placed on the grid, turbulence may not be sufficient to prev…
In Paper I (Fiege & Pudritz, 1999), we constructed models of filamentary molecular clouds that are truncated by a realistic external pressure and contain a rather general helical magnetic field. We address the stability of our models to gravitational fragmentation and axisymmetric MHD-driven instabilities. By calculating the dominant modes of axisymmetric instability, we determine the dominant length scales and growth rates for fragmentation. We find that the role of pressure truncation is to decrease the growth rate of gravitational instabilities by decreasing the self-gravitating mass per un…
We use ZEUS-MP to perform high resolution, three-dimensional, super-Alfvenic turbulent simulations in order to investigate the role of magnetic fields in self-gravitating core formation within turbulent molecular clouds. Statistical properties of our super-Alfvenic model without gravity agree with previous similar studies. Including self-gravity, our models give the following results. They are consistent with the turbulent fragmentation prediction of the core mass distribution of Padoan & Nordlund. They also confirm that local gravitational collapse is not prevented by magnetohydrodynamic wave…
Jeans showed analytically that, in an infinite uniform-density isothermal gas, plane-wave perturbations collapse to dense sheets if their wavelength, $λ$, satisfies $λ> λ_{_{\rm JEANS}} = (πa^2 / G ρ_{_0})^{1/2}$ (where $a$ is the isothermal sound speed and $ρ_{_0}$ is the unperturbed density); in contrast, perturbations with smaller $λ$ oscillate about the uniform density state. Here we show that Smoothed Particle Hydrodynamics reproduces these results well, even when the diameters of the SPH particles are twice the wavelength of the perturbation. Our simulations are performed in 3-D with ini…
Intermediate-scale spurs are common in spiral galaxies, but perhaps most distinctively evident in a recent HST image of M51 (Scoville & Rector 2001). We investigate, using time-dependent numerical MHD simulations, how such spurs could form (and subsequently fragment) from the interaction of a gaseous ISM with a stellar spiral arm. We model the gaseous medium as a self-gravitating, magnetized, differentially-rotating, razor-thin disk. The basic flow shocks and compresses as it passes through a local segment of a tightly-wound, trailing stellar spiral arm, modeled as a rigidly-rotating gravitati…
Isolated low-mass stars are formed, in the standard picture, from the collapse of dense cores condensed out of strongly magnetized molecular clouds. The dynamically collapsing inflow traps nearly half of the critical magnetic flux needed for the core support and deposits it in a small region surrounding the protostar. It has been argued previously that the deposited flux can slow down the inflow, allowing matter to pile up and settle along field lines into a magnetically supported, circumstellar disk. Here we show that the disk typically contains $\sim 10%$ of the stellar mass, and that it cou…
Star formation is intimately linked to the dynamical evolution of molecular clouds. Turbulent fragmentation determines where and when protostellar cores form, and how they contract and grow in mass via accretion from the surrounding cloud material. Using numerical models of self-gravitating supersonic turbulence, efficiency, spatial distribution and timescale of star formation in turbulent interstellar clouds are estimated. Turbulence that is not continuously replenished or that is driven on large scales leads to a rapid formation of stars in a clustered mode, whereas interstellar turbulence t…
A method of adapting smoothed particle hydrodynamics (SPH) with periodic boundary conditions for use with the special purpose device GRAPE is presented. GRAPE (GRAvity PipE) solves the Poisson and force equations for an N-body system by direct summation on a specially designed chip and in addition returns the neighbour list for each particle. Due to its design, GRAPE cannot treat periodic particle distributions directly. This limitation of GRAPESPH can be overcome by computing a correction force for each particle due to periodicity (Ewald correction) on the host computer using a PM-like method…
In this paper, we extend our previous analysis (Lodato & Rice 2004) of the transport properties induced by gravitational instabilities in cooling, gaseous accretion discs to the case where the disc mass is comparable to the central object. In order to do so, we have performed global, three-dimensional smoothed particle hydrodynamics simulations of massive discs. These new simulations show a much more complex temporal evolution with respect to the less massive case. Whereas in the low disc mass case a self-regulated, marginally stable state (characterized by an approximately constant radial pro…
A method for following fragmentation simulations further in time using smoothed particle hydrodynamics (SPH) is presented. In a normal SPH simulation of the collapse and fragmentation of a molecular cloud, high-density regions of gas that form protostars are represented by many particles with small separations. These high-density regions require small time steps, limiting the time for which the simulation can be followed. Thus, the end result of the fragmentation can never be definitively ascertained, and comparisons between cloud fragmentation calculations and the observed characteristics of …
We use high resolution numerical simulations to study whether gravitational instabilities within circumstellar discs can produce astrometrically detectable motion of the central star. For discs with masses of M_disc = 0.1 M_star, which are permanantly stable against fragmentation, we find that the magnitude of the astrometric signal depends upon the efficiency of disc cooling. Short cooling times produce prominent filamentary spiral structures in the disc, and lead to stellar motions that are potentially observable with future high precision astrometric experiments. For a disc that is marginal…
We study the linear evolution of small perturbations in self-gravitating fluid systems with magnetic fields. We consider wave-like perturbations to nonuniform filamentary and sheet-like hydrostatic equilibria in the presence of a uniform parallel magnetic field. Motivated by observations of molecular clouds that suggest substantial nonthermal (turbulent) pressure, we adopt equations of state that are softer than isothermal. We numerically determine the dispersion relation and the form of the perturbations in the regime of instability. The form of the dispersion relation is the same for all equ…
Turbulent fragmentation determines where and when protostellar cores form, and how they contract and grow in mass from the surrounding cloud material. This process is investigated, using numerical models of self-gravitating molecular cloud dynamics. Molecular cloud regions without turbulent driving sources, or where turbulence is driven on large scales, exhibit rapid and efficient star formation in a clustered mode, whereas interstellar turbulence that carries most energy on small scales results in isolated star formation with low efficiency. The clump mass spectrum of shock-generated density …
We investigate the evolution of angular momentum in SPH simulations of galaxy formation, paying particular attention to artificial numerical effects. We find that a cold gas disc forming in an ambient hot gas halo receives a strong hydrodynamic torque from the hot gas. By splitting the hydrodynamic force into artificial viscosity and pressure gradients, we find that the angular momentum transport is caused not by the artificial viscosity but by the pressure gradients. Using simple test simulations of shear flows, we conclude that the pressure gradient-based viscosity can be divided into two co…
The dynamical instability of a self-gravitating magnetized filamentary cloud was investigated while taking account of rotation around its axis. The filamentary cloud of our model is supported against self-gravity in part by both a magnetic field and rotation. The density distribution in equilibrium was assumed to be a function of the radial distance from the axis, $ ρ_0 (r) \, = \, ρ_{\rm c} \, ( 1 \, + \, r ^2 / 8 H ^2 ) ^{-2} $, where $ ρ_{\rm c} $ and $ H $ are model parameters specifying the density on the axis and the length scale, respectively; the magnetic filed was assumed to have both…
We demonstrate that the formation of collapsing cores in subcritical clouds is accelerated by nonlinear flows, by performing three-dimensional non-ideal MHD simulations. An initial random supersonic (and trans-Alfvenic) turbulent-like flow is input into a self-gravitating gas layer that is threaded by a uniform magnetic field (perpendicular to the layer) such that the initial mass-to-flux ratio is subcritical. Magnetic ambipolar diffusion occurs very rapidly initially due to the sharp gradients introduced by the turbulent flow. It subsequently occurs more slowly in the traditional near-quasist…
We have performed magnetohydrodynamic (MHD) simulations of the collapse and fragmentation of molecular cloud cores using a new algorithm for MHD within the smoothed particle hydrodynamics (SPH) method, that enforces the zero magnetic divergence constraint. We find that the support provided by magnetic fields over thermal pressure alone has several important effects on fragmentation and the formation of binary and multiple systems, and on the properties of massive circumstellar discs. The extra support suppresses the tendency of molecular cloud cores to fragment due to either initial density pe…
We discuss the fragmentation of a filamentary cloud on the basis of a 1-dimensional hydrodynamical simulation of a self-gravitating gas cloud. The simulation shows that dense cores are produced with a semi-regular interval in space and time from one edge to the other. At the initial stage the gas near one of the edges is attracted inwards by gravity and the accumulation of the gas makes a dense core near the edge. When the dense core grows in mass up to a certain amount, it gathers gas from the other direction. Accordingly the dense core becomes isolated from the main cloud and the parent fila…
The frictional heating by ion-neutral drift is calculated and its effect on isobaric thermal instability is carried out. Ambipolar drift heating of one-dimensional self-gravitating magnetized molecular slab is used under the assumptions of quasi-magnetohydrostatic and local ionization equilibrium. We see that ambipolar drift heating is inversely proportional to density and its value in some regions of the slab can be significantly larger than the average heating rates of cosmic rays and turbulent motions. The results show that the isobaric thermal instability can occur in some regions of the s…
The microcanonical properties of a two dimensional system of N classical particles interacting via a smoothed Newtonian potential as a function of the total energy E and the total angular momentum L are discussed. In order to estimate suitable observables a numerical method based on an importance sampling algorithm is presented. The entropy surface shows a negative specific heat region at fixed L for all L. Observables probing the average mass distribution are used to understand the link between thermostatistical properties and the spatial distribution of particles. In order to define a phase …
