Non-linear Thin Shell Instability Research Articles

Cooling and instabilities in colliding flows

ABSTRACT Collisional self-interactions occurring in protostellar jets give rise to strong shocks, the structure of which can be affected by radiative cooling within the flow. To study such colliding flows, we use the AstroBEAR AMR code to conduct hydrodynamic simulations in both one and three dimensions with a power-law cooling function. The characteristic length and time-scales for cooling are temperature dependent and thus may vary as shocked gas cools. When the cooling length decreases sufficiently and rapidly, the system becomes unstable to the radiative shock instability, which produces oscillations in the position of the shock front; these oscillations can be seen in both the one- and three-dimensional cases. Our simulations show no evidence of the density clumping characteristic of a thermal instability, even when the cooling function meets the expected criteria. In the three-dimensional case, the nonlinear thin shell instability (NTSI) is found to dominate when the cooling length is sufficiently small. When the flows are subjected to the radiative shock instability, oscillations in the size of the cooling region allow NTSI to occur at larger cooling lengths, though larger cooling lengths delay the onset of NTSI by increasing the oscillation period.

Massive core/star formation triggered by cloud–cloud collision: Effect of magnetic field

Abstract We study the effect of magnetic field on massive dense core formation in colliding unequal molecular clouds by performing magnetohydrodynamic simulations with sub-parsec resolution (0.015 pc) that can resolve the molecular cores. Initial clouds with the typical gas density of the molecular clouds are immersed in various uniform magnetic fields. The turbulent magnetic fields in the clouds consistent with the observation by Crutcher et al. (2010, ApJ, 725, 466) are generated by the internal turbulent gas motion before the collision, if the uniform magnetic field strength is 4.0 μG. The collision speed of 10 km s−1 is adopted, which is much larger than the sound speeds and the Alfvén speeds of the clouds. We identify gas clumps with gas densities greater than 5 × 10−20 g cm−3 as the dense cores and trace them throughout the simulations to investigate their mass evolution and gravitational boundness. We show that a greater number of massive, gravitationally bound cores are formed in the strong magnetic field (4.0 μG) models than the weak magnetic field (0.1 μG) models. This is partly because the strong magnetic field suppresses the spatial shifts of the shocked layer that should be caused by the nonlinear thin shell instability. The spatial shifts promote the formation of low-mass dense cores in the weak magnetic field models. The strong magnetic fields also support low-mass dense cores against gravitational collapse. We show that the numbers of massive, gravitationally bound cores formed in the strong magnetic field models are much larger than in the isolated, non-colliding cloud models, which are simulated for comparison. We discuss the implications of our numerical results on massive star formation.

Shape morphing in molecular cloud-cloud collision affected by coherent instabilities

This paper presents the results of numerical simulation of Molecular Cloud-Cloud Collision in the under the head-on and glancing impacts. The calculations are performed according to different colliding scenarios between two dissimilar (by size, displacement and inner distribution of matter) spherical clouds. The aim is to study the matter compression in clumps and filaments formed, the generation of vortex coherent structures in new formations imbalanced after the collision and to analyze the influence of emergent instabilities on clouds morphing. In-house Eulerian code is used to perform a numerical experiment on high-performance computers. Nebula shaping and the compression oscillations in a shock core depend on initial impulse of colliding molecular clouds. The article gives a morphological analysis of gas redistribution by density under local compression in a bow-shock layer and filaments which are generated. The mechanism of perturbations to matter turbulization, fragmentation and disruption of new formations is revealed. Strong shock compression pulsations generated in the gas core and waved rarefactions in the interstellar medium are interpreted as possible Nonlinear Thin Shell Instability and Kelvin–Helmholtz Instability aftereffect.

Three-dimensional simulations of clump formation in stellar wind collisions

ABSTRACT The inner parsec of our Galaxy contains tens of Wolf–Rayet stars whose powerful outflows are constantly interacting while filling the region with hot, diffuse plasma. Theoretical models have shown that, in some cases, the collision of stellar winds can generate cold, dense material in the form of clumps. However, their formation process and properties are not well understood yet. In this work, we present, for the first time, a statistical study of the clump formation process in unstable wind collisions. We study systems with dense outflows (${\sim }10^{-5}\rm \ M_{\odot }\ yr^{-1}$), wind speeds of 500–$1500\rm \ km\ s^{-1}$, and stellar separations of ∼20–$200\rm \ au$. We develop three-dimensional high-resolution hydrodynamical simulations of stellar wind collisions with the adaptive-mesh refinement grid-based code ramses. We aim at characterizing the initial properties of clumps that form through hydrodynamic instabilities, mostly via the non-linear thin-shell instability (NTSI). Our results confirm that more massive clumps are formed in systems whose winds are close to the transition between the radiative and adiabatic regimes. Increasing either the wind speed or the degree of asymmetry increases the dispersion of the clump mass and ejection speed distributions. Nevertheless, the most massive clumps are very light (∼10−3–$10^{-2}\rm \ M_{\oplus }$), about three orders of magnitude less massive than theoretical upper limits. Applying these results to the Galactic Centre, we find that clumps formed through the NTSI should not be heavy enough either to affect the thermodynamic state of the region or to survive for long enough to fall on to the central supermassive black hole.

Magnetic suppression of turbulence and the star formation activity of molecular clouds

We present magnetohydrodynamic simulations aimed at studying the effect of the magnetic suppression of turbulence (generated through various instabilities during the formation of molecular clouds by converging) on the subsequent star formation (SF) activity. We study four magnetically supercritical models with magnetic field strengths $B= 0$, 1, 2, and 3 $\mu$G (corresponding to mass--to--flux ratios of $\infty$, 4.76, 2.38, and 1.59 times the critical value), with the magnetic field, initially being aligned with the flows. We find that, for increasing magnetic field strength, the clouds formed tend to be more massive, denser, less turbulent, and with higher SF activity. This causes the onset of star formation activity in the non--magnetic or more weakly magnetized cases to be delayed by a few Myr in comparison to the more strongly magnetized cases. We attribute this behavior to the suppression of the nonlinear thin shell instability (NTSI) by the magnetic field, previously found by Heitsch and coworkers. This result is contrary to the standard notion that the magnetic field provides support to the clouds, thus reducing their star formation rate (SFR). However, our result is a completely nonlinear one, and could not be foreseen from simple linear considerations.

Electrostatic shock waves in the laboratory and astrophysics: similarities and differences

Contemporary lasers allow us to create shocks in the laboratory that propagate at a speed that matches that of energetic astrophysical shocks like those that ensheath supernova blast shells. The rapid growth time of the shocks and the spatio-temporal resolution, with which they can be sampled, allow us to identify the processes that are involved in their formation and evolution. Some laser-generated unmagnetized shocks are mediated by collective electrostatic forces and effects caused by binary collisions between particles can be neglected. Hydrodynamic models, which are valid for many large-scale astrophysical shocks, assume that collisions enforce a local thermodynamic equilibrium in the medium; laser-generated shocks are thus not always representative for astrophysical shocks. Laboratory studies of shocks can improve the understanding of their astrophysical counterparts if we can identify processes that affect electrostatic shocks and hydrodynamic shocks alike. An example is the nonlinear thin-shell instability (NTSI). We show that the NTSI destabilises collisionless and collisional shocks by the same physical mechanism.

The Shock Dynamics of Heterogeneous YSO Jets:3D Simulations Meet Multi-epoch Observations

Abstract High-resolution observations of young stellar object (YSO) jets show them to be composed of many small-scale knots or clumps. In this paper, we report results of 3D numerical simulations designed to study how such clumps interact and create morphologies and kinematic patterns seen in emission line observations. Our simulations focus on clump scale dynamics by imposing velocity differences between spherical, over-dense regions, which then lead to the formation of bow shocks as faster clumps overtake slower material. We show that much of the spatial structure apparent in emission line images of jets arises from the dynamics and interactions of these bow shocks. Our simulations show a variety of time-dependent features, including bright knots associated with Mach stems where the shocks intersect, a “frothy” emission structure that arises from the presence of the Nonlinear Thin Shell Instability along the surfaces of the bow shocks, and the merging and fragmentation of clumps. Our simulations use a new non-equilibrium cooling method to produce synthetic emission maps in Hα and [S ii]. These are directly compared to multi-epoch Hubble Space Telescope observations of Herbig–Haro jets. We find excellent agreement between features seen in the simulations and the observations in terms of both proper motion and morphologies. Thus we conclude that YSO jets may be dominated by heterogeneous structures and that interactions between these structures and the shocks they produce can account for many details of YSO jet evolution.

Experimental Observation of Thin-shell Instability in a Collisionless Plasma

Abstract We report on the experimental observation of the instability of a plasma shell, which formed during the expansion of a laser-ablated plasma into a rarefied ambient medium. By means of a proton radiography technique, the evolution of the instability is temporally and spatially resolved on a timescale much shorter than the hydrodynamic one. The density of the thin shell exceeds that of the surrounding plasma, which lets electrons diffuse outward. An ambipolar electric field grows on both sides of the thin shell that is antiparallel to the density gradient. Ripples in the thin shell result in a spatially varying balance between the thermal pressure force mediated by this field and the ram pressure force that is exerted on it by the inflowing plasma. This mismatch amplifies the ripples by the same mechanism that drives the hydrodynamic nonlinear thin-shell instability (NTSI). Our results thus constitute the first experimental verification that the NTSI can develop in colliding flows.

On the impact of the magnitude of Interstellar pressure on physical properties of Molecular Cloud

Recently reported variations in the typical physical properties of Galactic and extra-Galactic molecular clouds (MCs), and in their ability to form stars have been attributed to local variations in the magnitude of interstellar pressure. Inferences from these surveys have called into question two long-standing beliefs that the MCs : 1 are Virialised entities and (2) have approximately constant surface density i.e., the validity of the Larson's third law. In this work we invoke the framework of cloud-formation via collisions between warm gas flows. Post-collision clouds forming in these realisations cool rapidly and evolve primarily via the interplay between the Non-linear Thin Shell Instability (NTSI), and the self-gravity. Over the course of these simulations we traced the temporal evolution of the surface density of the assembled clouds, the fraction of dense gas, the distribution of gas column density (NPDF), and the Virial nature of the assembled clouds. We conclude, these physical properties of MCs not only exhibit temporal variation, but their respective peak-magnitude also increases in proportion with the magnitude of external pressure, $P_{ext}$. The velocity dispersion in assembled clouds appears to follow the power-law, $\sigma_{gas}\propto P_{ext}^{0.23}$. Also, the power-law tail at higher densities becomes shallower with increasing magnitude of external pressure, for magnitudes, $P_{ext}/k_{B}\lesssim 10^{7}$ K cm$^{-3}$, at higher magnitudes such as those typically found in the Galactic CMZ ($P_{ext}/k_{B} > 10^{7}$ K cm$^{-3}$), the power-law shows significant steepening. Thus while our results are broadly consistent with inferences from various recent observational surveys, it appears, MCs hardly exhibit a unique set of properties, but rather a wide variety, that can be reconciled with a range of magnitudes of pressure between 10$^{4}$ K cm$^{-3}$ - 10$^{8}$ K cm$^{-3}$.

The interplay of the collisionless non-linear thin-shell instability with the ion acoustic instability

The nonlinear thin-shell instability (NTSI) may explain some of the turbulent hydrodynamic structures that are observed close to the collision boundary of energetic astrophysical outflows. It develops in nonplanar shells that are bounded on either side by a hydrodynamic shock, provided that the amplitude of the seed oscillations is sufficiently large. The hydrodynamic NTSI has a microscopic counterpart in collisionless plasma. A sinusoidal displacement of a thin shell, which is formed by the collision of two clouds of unmagnetized electrons and protons, grows and saturates on timescales of the order of the inverse proton plasma frequency. Here we increase the wavelength of the seed perturbation by a factor 4 compared to that in a previous study. Like in the case of the hydrodynamic NTSI, the increase in the wavelength reduces the growth rate of the microscopic NTSI. The prolonged growth time of the microscopic NTSI allows the waves, which are driven by the competing ion acoustic instability, to grow to a large amplitude before the NTSI saturates and they disrupt the latter. The ion acoustic instability thus imposes a limit on the largest wavelength that can be destabilized by the NTSI in collisionless plasma. The limit can be overcome by binary collisions. We bring forward evidence for an overstability of the collisionless NTSI.

Accretion at the periastron passage of Eta Carinae

We present high resolution numerical simulations of the colliding wind system $\eta$ Carinae, showing accretion onto the secondary star close to periastron passage. Our hydrodynamical simulations include self gravity and radiative cooling. The smooth stellar winds collide and develop instabilities, mainly the non-linear thin shell instability, and form filaments and clumps. We find that a few days before periastron passage the dense filaments and clumps flow towards the secondary as a result of its gravitational attraction, and reach the zone where we inject the secondary wind. We run our simulations for the conventional stellar masses, $M_1=120 ~\rm{M_\odot}$ and $M_2=30 ~\rm{M_\odot}$, and for a high mass model, $M_1=170 ~\rm{M_\odot}$ and $M_2=80 ~\rm{M_\odot}$, that was proposed to better fit the history of giant eruptions. As expected, the simulations results show that the accretion processes is more pronounced for a more massive secondary star.

On physical and numerical instabilities arising in simulations of non-stationary radiatively cooling shocks

We describe our modelling of the radiatively cooling shocks and their thin shells with various numerical tools in different physical and calculational setups. We inspect structure of the dense shell, its formation and evolution, pointing out physical and numerical factors that sustain its shape and also may lead to instabilities. We have found that under certain physical conditions, the circular shaped shells show a strong bending instability and successive fragmentation on Cartesian grids soon after their formation, while remain almost unperturbed when simulated on polar meshes. We explain this by physical Rayleigh--Taylor like instabilities triggered by corrugation of the dense shell surfaces by numerical noise. Conditions for these instabilities follow from both the shell structure itself and from episodes of transient acceleration during re-establishing of dynamical pressure balance after sudden radiative cooling onset. They are also easily excited by physical perturbations of the ambient medium. The widely mentioned Non-linear Thin Shell Instability, in contrast, in tests with physical perturbations is shown to have only limited chances to develop in real radiative shocks, as it seems to require a special spatial arrangement of fluctuations to be excited efficiently. The described phenomena also set new requirements on further simulations of the radiatively cooling shocks in order to be physically correct and free of numerical artefacts.

Clump formation through colliding stellar winds in the Galactic Centre

The gas cloud G2 is currently being tidally disrupted by the Galactic Centre super-massive black hole, Sgr A*. The region around the black hole is populated by $\sim 30$ Wolf-Rayet stars, which produce strong outflows. We explore the possibility that gas clumps, such as G2, originate from the collision of stellar winds via the non-linear thin shell instability. Following an analytical approach, we study the thermal evolution of slabs formed in the symmetric collision of winds, evaluating whether instabilities occur, and estimating possible clump masses. We find that the collision of relatively slow ($< 750$ km s$^{-1}$) and strong ($\sim 10^{-5}$ Msun yr$^{-1}$) stellar winds from stars at short separations ($<10$ mpc) is a process that indeed could produce clumps of G2's mass and above. Such short separation encounters of single stars along their known orbits are not common in the Galactic Centre, making this process a possible but unlikely origin for G2. We also discuss clump formation in close binaries such as IRS 16SW and in asymmetric encounters as promising alternatives that deserve further numerical study.

Convergence of AMR and SPH simulations – I. Hydrodynamical resolution and convergence tests

We compare the results for a set of hydrodynamical tests performed with the adaptive mesh refinement finite volume code, mg, and the smoothed particle hydrodynamics (SPH) code, seren. The test suite includes shock tube tests, with and without cooling, the non-linear thin-shell instability and the Kelvin–Helmholtz instability. The main conclusions are the following. (i) The two methods converge in the limit of high resolution and accuracy in most cases. All tests show good agreement when numerical effects (e.g. discontinuities in SPH) are properly treated. (ii) Both methods can capture adiabatic shocks and well-resolved cooling shocks perfectly well with standard prescriptions. However, they both have problems when dealing with under-resolved cooling shocks, or strictly isothermal shocks, at high Mach numbers. The finite volume code only works well at first order and even then requires some additional artificial viscosity. SPH requires either a larger value of the artificial viscosity parameter, αAV, or a modified form of the standard artificial viscosity term using the harmonic mean of the density, rather than the arithmetic mean. (iii) Some SPH simulations require larger kernels to increase neighbour number and reduce particle noise in order to achieve agreement with finite volume simulations (e.g. the Kelvin–Helmholtz instability). However, this is partly due to the need to reduce noise that can corrupt the growth of small-scale perturbations (e.g. the Kelvin–Helmholtz instability). In contrast, instabilities seeded from large-scale perturbations (e.g. the non-linear thin shell instability) do not require more neighbours and hence work well with standard SPH formulations and converge with the finite volume simulations. (iv) For purely hydrodynamical problems, SPH simulations take an order of magnitude longer to run than finite volume simulations when running at equivalent resolutions, i.e. when they both resolve the underlying physics to the same degree. This requires about two to three times as many particles as the number of cells.

Simulations of the non-linear thin shell instability

We use three-dimensional smoothed particle hydrodynamics simulations to study the non-linear thin shell instability (NTSI) in supersonic colliding flows. We show that for flows with monochromatic perturbations and for flows with white-noise perturbations, growth speeds approximate quite well to the analytic predictions of Vishniac. For flows with subsonic turbulence, growth speeds match Vishniac's predictions only at short wavelengths where the turbulence is weaker. We find that supersonic turbulence, of a lower Mach number than the colliding flows, completely suppresses the NTSI. Our results provide a diagnostic for identifying the presence of the NTSI in colliding flows with turbulence.

High-resolution numerical simulations of unstable colliding stellar winds

We investigate the hydrodynamics of the interaction of two supersonic winds in binary systems. The collision of the winds creates two shocks separated by a contact discontinuity. The overall structure depends on the momentum flux ratio eta of the winds. We use the code RAMSES with adaptive mesh refinement to study the shock structure up to smaller values of eta, higher spatial resolution and greater spatial scales than have been previously achieved. 2D and 3D simulations, neglecting orbital motion, are compared to widely-used analytic results and their applicability is discussed. In the adiabatic limit, velocity shear at the contact discontinuity triggers the Kelvin-Helmholtz instability. We quantify the amplitude of the resulting fluctuations and find that they can be significant even with a modest initial shear. Using an isothermal equation of state leads to the development of thin shell instabilities. The initial evolution and growth rates enables us to formally identify the non-linear thin shell instability (NTSI) close to the binary axis. Some analogue of the transverse acceleration instability is present further away. The NTSI produces large amplitude fluctuations and dominates the long-term behaviour. We point out the computational cost of properly following these instabilities. Our study provides a basic framework to which the results of more complex simulations, including additional physical effects, can be compared.

Convergence of SPH and AMR simulations

AbstractWe present the first results of a large suite of convergence tests between Adaptive Mesh Refinement (AMR) Finite Difference Hydrodynamics and Smoothed Particle Hydrodynamics (SPH) simulations of the non-linear thin shell instability and the Kelvin-Helmholtz instability. We find that the two methods converge in the limit of high resolution and accuracy. AMR and SPH simulations of the non-linear thin shell instability converge with each other with standard algorithms and parameters. The Kelvin-Helmholtz instability in SPH requires both an artificial conductivity term and a kernel with larger compact support and more neighbours (e.g. the quintic kernel) in order converge with AMR. For purely hydrodynamical problems, SPH simulations take an order of magnitude longer than the grid code when converged.

Collisions of supersonic clouds

AbstractWe present simulations of supersonic collisions between molecular clouds of mass 500 M⊙ and radius 2.24 pc. The simulations are performed with the SEREN SPH code. The code treats the energy equation and the associated transport of heating and cooling radiation. The formation of protostars is captured by introducing sink particles. Low velocity collisions form a shock-compressed layer which fragments to form stars. For high-velocity collisions, υrel ⪆ 5 km s−1, the non-linear thin shell instability strongly disrupts the shock-compressed layer, and may inhibit the formation of stars.

Magnetized Nonlinear Thin‐Shell Instability: Numerical Studies in Two Dimensions

We revisit the analysis of the Non-linear Thin Shell Instability (NTSI) numerically, including magnetic fields. The magnetic tension force is expected to work against the main driver of the NTSI -- namely transverse momentum transport. However, depending on the field strength and orientation, the instability may grow. For fields aligned with the inflow, we find that the NTSI is suppressed only when the Alfv\'en speed surpasses the (supersonic) velocities generated along the collision interface. Even for fields perpendicular to the inflow, which are the most effective at preventing the NTSI from developing, internal structures form within the expanding slab interface, probably leading to fragmentation in the presence of self-gravity or thermal instabilities. High Reynolds numbers result in local turbulence within the perturbed slab, which in turn triggers reconnection and dissipation of the excess magnetic flux. We find that when the magnetic field is initially aligned with the flow, there exists a (weak) correlation between field strength and gas density. However, for transverse fields, this correlation essentially vanishes. In light of these results, our general conclusion is that instabilities are unlikely to be erased unless the magnetic energy in clouds is much larger than the turbulent energy. Finally, while our study is motivated by the scenario of molecular cloud formation in colliding flows, our results span a larger range of applicability, from supernovae shells to colliding stellar winds.

Magnetized nonlinear thin-shell instability: Numerical studies in two dimensions

Magnetized nonlinear thin-shell instability: Numerical studies in two dimensions