Isolated regions of higher density populate the ISM on all scales -from molecular clouds, to the star-forming regions known as cores, to heterogeneous ejecta found near planetary nebulae and supernova remnants. These clumps interact with winds and shocks from nearby energetic sources. Understanding the interactions of shocked clumps is vital to our understanding of the composition, morphology, and evolution of the ISM. The evolution of shocked clumps are wellunderstood in the limiting "adiabatic" case where physical processes such as self-gravity, heat conduction, radiative cooling, and magnetic fields are ignored. In this paper we address the issue of evolution and convergence when one of these processes -radiative cooling -is included.Numeric convergence studies demonstrate that the evolution of an adiabatic clump is wellcaptured by roughly 100 cells per clump radius. The presence of radiative cooling, however, imposes limits on the problem due to the removal of thermal energy. Numerical studies which include radiative cooling typically adopt the 100-200 cells per clump radius resolution. In this paper we present the results of a convergence study for radiatively cooling clumps undertaken over a broad range of resolutions, from 12 to 1,536 cells per clump radius, employing adaptive mesh refinement (AMR) in a 2D axisymmetric geometry (2.5D). We also provide a fully 3D simulation, at 192 cells per clump radius, which supports our 2.5D results. We find no appreciable self-convergence at ∼100 cells per clump radius as small-scale differences owing to increasingly resolving the cooling length have global effects. We therefore conclude that self-convergence is an insufficient criterion to apply on its own when addressing the question of sufficient resolution for radiatively cooled shocked clump simulations. We suggest the adoption of alternate criteria to support a statement of sufficient resolution, such as the demonstration of adequate resolution of the cooling layers behind shocks. We discuss an associated refinement criteria for AMR codes.
Herbig-Haro jets are commonly thought of as homogeneous beams of plasma traveling at hypersonic velocities. Structure within jet beams is often attributed to periodic or "pulsed" variations of conditions at the jet source. Simulations based on this scenario result in knots extending across the jet diameter. Observations and recent high energy density laboratory experiments shed new light on structures below this scale and indicate they may be important for understanding the fundamentals of jet dynamics. In this paper, we offer an alternative to "pulsed" models of protostellar jets. Using direct numerical simulations we explore the possibility that jets are chains of subradial clumps propagating through a moving interclump medium. Our models explore an idealization of this scenario by injecting small (r < r jet ), dense (ρ > ρ jet ) spheres embedded in an otherwise smooth interclump jet flow. The spheres are initialized with velocities differing from the jet velocity by ∼15%. We find that the consequences of shifting from homogeneous to heterogeneous flows are significant as clumps interact with each other and with the interclump medium in a variety of ways. Structures which mimic what is expected from pulsed-jet models can form, as can be previously unseen, "subradial" behaviors including backward facing bow shocks and off-axis working surfaces. While these small-scale structures have not been seen before in simulation studies, they are found in high-resolution jet observations. We discuss implications of our simulations for the interpretation of protostellar jets with regard to characterization of knots by a "lifetime" or "velocity history" approach as well as linking observed structures with central engines which produce the jets.
Supersonic outflows from objects as varied as stellar jets, massive stars and novae often exhibit multiple shock waves that overlap one another. When the intersection angle between two shock waves exceeds a critical value, the system reconfigures its geometry to create a normal shock known as a Mach stem where the shocks meet. Mach stems are important for interpreting emission-line images of shocked gas because a normal shock produces higher postshock temperatures and therefore a higher-excitation spectrum than an oblique one does. In this paper we summarize the results of a series of numerical simulations and laboratory experiments designed to quantify how Mach stems behave in supersonic plasmas that are the norm in astrophysical flows. The experiments test analytical predictions for critical angles where Mach stems should form, and quantify how Mach stems grow and decay as intersection angles between the incident shock and a surface change. While small Mach stems are destroyed by surface irregularities and subcritical angles, larger ones persist in these situations, and can regrow if the intersection angle changes to become more favorable. The experimental and numerical results show that although Mach stems occur only over a limited range of intersection angles and size scales, within these ranges they are relatively robust, and hence are a viable explanation for variable bright knots observed in HST images at the intersections of some bow shocks in stellar jets.
We have performed 2D hydrodynamic simulations of a pulsed astrophysical jet propagating through a medium that is populated with spherical inhomogeneities, or "clumps," which are smaller than the jet radius. The clumps are seen to affect the jet in several ways, such as impeding jet propagation and deflecting the jet off-axis. While there has been some debate as to the prevalence of these types of condensations in the ISM or in molecular clouds, the exploration of this region of parameter space nonetheless both shows the potential for these clumps to disrupt astrophysical jets and yields results which recover aspects of recent observations of Herbig-Haro objects. We find that the propagation of the jet and the vorticity induced in the clump/ambient medium correlate well with a "dynamic filling function" f d across all the simulations.
We investigate the role discrete clumps embedded in an astrophysical jet play on the jet's morphology and line emission characteristics. By varying clumps' size, density, position, and velocity, we cover a range of parameter space motivated by observations of objects such as the Herbig Haro object HH 34. We here extend the results presented in Yirak et al. (2009), including how analysis of individual observations may lead to spurious sinusoidal variation whose parameters vary widely over time, owing chiefly to interacts between clumps. The goodness of the fits, while poor in all simulations, are best when clump-clump collisions are minimal. Our results indicate that a large velocity dispersion leads to a clump-clump collision-dominated flow which disrupts the jet beam. Finally, we present synthetic emission images of H-α and [SII] and note an excess of [SII] emission along the jet length as compared to observations. This suggests that observed beams undergo earlier processing, if they are present at all.
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