The existence of substellar cold H2 globules in planetary nebulae and the mere existence of comets suggest that the physics of cold interstellar gas might be much richer than usually envisioned.
We study the case of a cold gaseous medium in ISM conditions which is subject to a gas-liquid/solid phase transition.
First the equilibrium of general non-ideal fluids is studied using the virial theorem and linear stability analysis. Then the non-linear dynamics is studied by using simulations to characterize the expected formation of solid bodies analogous to comets. The simulations are run with a state of the art molecular dynamics code (LAMMPS). The long-range gravitational forces can be taken into account with short-range molecular forces with finite limited computational resources by using super-molecules, provided the right scaling is followed.
The concept of super-molecule is tested with simulations, allowing us to correctly satisfy the Jeans instability criterion for one-phase fluids. The simulations show that fluids presenting a phase transition are gravitationally unstable as well, independent of the strength of the gravitational potential, producing two distinct kinds of sub-stellar bodies, those dominated by gravity ("planetoids") and those dominated by molecular attractive force ("comets").
Observations, formal analysis and computer simulations suggest the possibility of the formation of substellar H2 clumps in cold molecular clouds due to the combination of phase transition and gravity. Fluids presenting a phase transition are gravitationally unstable, independent of the strength of the gravitational potential. Arbitrarily small H2 clumps may form even at relatively high temperatures up to 400 - 600K, according to virial analysis. The combination of phase transition and gravity may be relevant for a wider range of astrophysical situations, such as proto-planetary disks.
In this work, we derive the stellar initial mass function (IMF) from the superposition of mass distributions of dense cores, generated through gravoturbulent fragmentation of unstable clumps in molecular clouds (MCs) and growing through competitive accretion. MCs are formed by the turbulent cascade in the interstellar medium at scales L from 100 down to ~0.1 pc. Their internal turbulence is essentially supersonic and creates clumps with a lognormal distribution of densities n. Our model is based on the assumption of a power-law relationship between clump mass and clump density: n~m^x, where x …
Context. It is still an open issue whether a self-gravitating accretion disk fragments. There are many different physical and numerical explanations for fragmentation, but simulations often show a non-convergent behavior for ever better resolution. Aims. We investigate the influence of different numerical limiters in Godunov type schemes on the fragmentation boundary in self- gravitating disks. Methods. We compare the linear and non-linear outcome in two-dimensional shearingsheet simulations using the VANLEER and the SUPERBEE limiter. Results. We show that choosing inappropriate limiting funct…
We investigate the role of magnetic fields in the fragmentation of self-gravitating discs using 3D global ideal magnetohydrodynamic simulations performed with the "phantom" smoothed particle hydrodynamics code. For initially toroidal fields, we find two regimes. In the first, where the cooling time is greater than five times the dynamical time, magnetic fields reduce spiral density wave amplitudes, which in turn suppresses fragmentation. This is the case even if the magnetic pressure is only a tenth of the thermal pressure. The second regime occurs when the cooling time is sufficiently short t…
We carry out three dimensional radiation hydrodynamical simulations of gravitationally unstable discs to explore the movement of mass in a disc following its initial fragmentation. We find that the radial velocity of the gas in some parts of the disc increases by up to a factor of approximately 10 after the disc fragments, compared to before. While the movement of mass occurs in both the inward and outward directions, the inwards movement can cause the inner spirals of a self-gravitating disc to become sufficiently dense such that they can potentially fragment. This suggests that the dynamical…
We carry out a resolution study on the fragmentation boundary of self-gravitating discs. We perform three-dimensional Smoothed Particle Hydrodynamics simulations of discs to determine whether the critical value of the cooling timescale in units of the orbital timescale, beta_{crit}, converges with increasing resolution. Using particle numbers ranging from 31,250 to 16 million (the highest resolution simulations to date) we do not find convergence. Instead, fragmentation occurs for longer cooling timescales as the resolution is increased. These results suggest that at the very least, the critic…
We carry out a resolution study on the fragmentation boundary of self-gravitating discs. We perform three-dimensional Smoothed Particle Hydrodynamics (SPH) simulations of discs to determine whether the critical value of the cooling timescale in units of the orbital timescale, beta_{crit}, converges with increasing resolution. Using particle numbers ranging from 31,250 to 16 million (the highest resolution simulations to date) we do not find convergence. Instead, fragmentation occurs for longer cooling timescales as the resolution is increased. These results certainly suggest that beta_{crit} i…
We investigate the fragmentation criterion in massive self-gravitating discs. We present new analysis of the fragmentation conditions which we test by carrying out global three-dimensional numerical simulations. Whilst previous work has placed emphasis on the cooling timescale in units of the orbital timescale, β, we find that at a given radius the surface mass density (i.e. disc mass and profile) and star mass also play a crucial role in determining whether a disc fragments or not as well as where in the disc fragments form. We find that for shallow surface mass density profiles (p<2, where Σ…
It has recently been suggested that in the presence of driven turbulence discs may be much less stable against gravitational collapse than their non turbulent analogs, due to stochastic density fluctuations in turbulent flows. This mode of fragmentation would be especially important for gas giant planet formation. Here we argue, however, that stochastic density fluctuations due to turbulence do not enhance gravitational instability and disc fragmentation in the long cooling time limit appropriate for planet forming discs. These fluctuations evolve adiabatically and dissipate away by decompress…
Self-gravity becomes competitive as an angular momentum transport process in accretion discs at large radii, where the temperature is low enough that external irradiation likely contributes to the thermal balance. Irradiation is known to weaken the strength of disc self-gravity, and can suppress it entirely if the disc is maintained above the threshold for linear instability. However, its impact on the susceptibility of the disc to fragmentation is less clear. We use two-dimensional numerical simulations to investigate the evolution of self-gravitating discs as a function of the local cooling …
We carry out simulations of gravitationally unstable discs using a Smoothed Particle Hydrodynamics (SPH) code and a grid-based hydrodynamics code, FARGO, to understand the previous non-convergent results reported by Meru & Bate (2011a). We obtain evidence that convergence with increasing resolution occurs with both SPH and FARGO and in both cases we find that the critical cooling timescale is larger than previously thought. We show that SPH has a first-order convergence rate while FARGO converges with a second-order rate. We show that the convergence of the critical cooling timescale for fragm…
Self-gravitating discs are believed to play an important role in astrophysics in particular regarding the star and planet formation process. In this context, discs subject to an idealized cooling process, characterized by a cooling timescale $β$ expressed in unit of orbital timescale, have been extensively studied. We take advantage of the Riemann solver and the 3D Godunov scheme implemented in the code Ramses to perform high resolution simulations, complementing previous studies that have used smoothed particle hydrodynamics (SPH) or 2D grid codes. We observe that the critical value of $β$ fo…
Gravitational instability is a key process that may lead to fragmentation of gaseous structures (sheets, filaments, haloes) in astrophysics and cosmology. We introduce here a method to derive analytic expressions for the growth rate of gravitational instability in a plane stratified medium. We consider a pressure-confined, static, self-gravitating fluid of arbitrary polytropic exponent, with both free and rigid boundary conditions. The method we detail here can naturally be generalised to analyse the stability of more complex systems. Our analytical results are in excellent agreement with nume…
We investigate, using 3D hydrodynamic simulations, the fragmentation of pressure-confined, vertically stratified, self-gravitating gaseous layers. The confining pressure is either thermal pressure acting on both surfaces, or thermal pressure acting on one surface and ram-pressure on the other. In the linear regime of fragmentation, the dispersion relation we obtain agrees well with that derived by Elmegreen & Elmegreen (1978), and consequently deviates from the dispersion relations based on the thin shell approximation (Vishniac 1983) or pressure assisted gravitational instability (Wünsch et a…
Star formation in molecular clouds is intimately linked to their internal mass distribution. We present an unprecedentedly detailed analysis of the column density structure of a high-mass, filamentary molecular cloud, namely IRDC G11.11-0.12 (G11). We use two novel column density mapping techniques: high-resolution (FWHM=2", or ~0.035 pc) dust extinction mapping in near- and mid-infrared, and dust emission mapping with the Herschel satellite. These two completely independent techniques yield a strikingly good agreement, highlighting their complementarity and robustness. We first analyze the de…
Recent high-resolution simulations demonstrate that disks around primordial protostars easily fragment in the accretion phase before the protostars accrete less than a solar mass. To understand why the gravitational instability generally causes the fragmentation so early, we develop a one-dimensional (1D) non-steady model of the circumstellar disk that takes the mass supply from an accretion envelope into account. We also compare the model results to a three-dimensional (3D) numerical simulation performed with a code employing the adaptive mesh refinement. Our model shows that the self-gravita…
A popular theory of star formation is gravito-turbulent fragmentation, in which self-gravitating structures are created by turbulence-driven density fluctuations. Simple theories of isothermal fragmentation successfully reproduce the core mass function (CMF) which has a very similar shape to the initial mass function (IMF) of stars. However, numerical simulations of isothermal turbulent fragmentation thus far have not succeeded in identifying a fragment mass scale that is independent of the simulation resolution. Moreover, the fluid equations for magnetized, self-gravitating, isothermal turbul…
There have been several recent detections of candidate Keplerian discs around massive young protostars. Given the relatively large disc-to-star mass ratios in these systems, and their young ages, it is worth investigating their propensity to becoming self-gravitating. To this end, we compute self-consistent, semi-analytic models of putative self-gravitating discs for five candidate disc systems. Our aim is not to fit exactly the observations, but to demonstrate that the expected dust continuum emission from marginally unstable self-gravitating discs can be quite weak, due to high optical depth…
Recent observations of the Class 0 protostar L1527 IRS have revealed a rotationally supported disc with an outer radius of at least 100 au. Measurements of the integrated flux at 870 microns suggest a disc mass that is too low for gravitational instability to govern angular momentum transport. However, if parts of the disc are optically thick at sub-mm wavelengths, the sub-mm fluxes will underestimate the disc mass, and the disc's actual mass may be substantially larger, potentially sufficient to be self-gravitating. We investigate this possibility using simple self-gravitating disc models. To…
It has been shown that fragmentation within self-gravitating, turbulent molecular clouds ("turbulent fragmentation") can naturally explain the observed properties of protostellar cores, including the core mass function (CMF). Here, we extend recently-developed analytic models for turbulent fragmentation to follow the time-dependent hierarchical fragmentation of self-gravitating cores, until they reach effectively infinite density (and form stars). We show that turbulent fragmentation robustly predicts two key features of the IMF. First, a high-mass power-law scaling very close to the Salpeter …
Cosmic metallicity evolution possibly creates the diversity of star formation modes at different epochs. Gravitational fragmentation of circumstellar discs provides an important formation channel of multiple star systems, including close binaries. We here study the nature of disc fragmentation, systematically performing a suite of two-dimensional radiation-hydrodynamic simulations, in a broad range of metallicities, from the primordial to the solar values. In particular, we follow relatively long-term disc evolution over 15 kyr after the disc formation, incorporating the effect of heating by t…
The disk fragmentation is a possible process leading to the formation of Population III stellar binary systems. However, numerical simulations show diverse fates of the fragments; some evolve into stable binaries and others merge away with a central star. To clarify the physics behind such diversity, we perform a series of three dimensional hydrodynamics simulations in a controlled manner. We insert a point particle mimicking a fragment in a self-gravitating disk, where the initial mass and position are free parameters, and follow the orbital evolution for several tens of orbits. The results s…
The long-term evolution of a circumstellar disk starting from its formation and ending in the T Tauri phase was simulated numerically with the purpose of studying the evolution of dust in the disk with distinct values of viscous α-parameter and dust fragmentation velocity v_frag. We solved numerical hydrodynamics equations in the thin-disk limit, which are modified to include a dust component consisting of two parts: sub-micron-sized dust and grown dust with a maximum radius a_r. The former is strictly coupled to the gas, while the latter interacts with the gas via friction. The conversion of …
In the early stages of a protoplanetary disk, when its mass is a significant fraction of its star's, turbulence generated by gravitational instability (GI) should feature significantly in the disk's evolution. At the same time, the disk may be sufficiently ionised for magnetic fields to play some role in the dynamics. Though usually neglected, the impact of magnetism on the GI may be critical, with consequences for several processes: the efficiency of accretion, spiral structure formation, fragmentation, and the dynamics of solids. In this paper, we report on global three-dimensional magnetohy…
In recent years, there were studies on the omnipresence and structures of filaments in star-forming regions, and the role of their fragmentation in the process of star formation. However, only a few studies analysed the evolution of filaments and their distribution with the Galactic disk where filaments form self-consistently as part of large-scale molecular cloud evolution. In this thesis, I perform dust radiative transfer calculations to study the effect of inclination on dust observations of filaments to evaluate whether the variations enable the identification of more filaments within dust…
Aims. Our goal is to find a converged cooling limit for fragmentation in self-gravitating disks. This is especially interesting for the formation of planets, brown dwarfs or stars and the growth of black holes. While investigating the limit, we want to give a clear criterion for the state of convergence. Methods. We run two-dimensional shearingsheet simulations with the hydrodynamic package Fosite at high resolutions. Thereby resolution and limiters are altered. Subsequently, we investigate the spectra of important physical quantities at the length scales where fragmentation occurs. In order t…
The dominant mechanism leading to the formation of brown dwarfs (BDs) remains uncertain. The most direct keys to formation, which are obtained from younger objects (pre-BD cores and proto-BDs), are limited by the very low number statistics available. We aim to identify and characterize a set of pre- and proto-BDs as well as Class II BDs in the Lupus 1 and 3 molecular clouds to test their formation mechanism. We performed ALMA band 6 (1.3 mm) continuum observations of a selection of 64 cores previously identified from AzTEC/ASTE data (1.1 mm), along with previously known Class II BDs in the Lup…
