S. A. E. G. Falle

On the inadmissibility of non-evolutionary shocks

In recent years, numerical solutions of the equations of compressible magnetohydrodynamic (MHD) flows have been found to contain intermediate shocks for certain kinds of problems. Since these results would seem to be in conflict with the classical theory of MHD shocks, they have stimulated attempts to reexamine various aspects of this theory, in particular the role of dissipation. In this paper, we study the general relationship between the evolutionary conditions for discontinuous solutions of the dissipation-free system and the existence and uniqueness of steady dissipative shock structures for systems of quasilinear conservation laws with a concave entropy function. Our results confirm the classical theory. We also show that the appearance of intermediate shocks in numerical simulations can be understood in terms of the properties of the equations of planar MHD, for which some of these shocks turn out to be evolutionary. Finally, we discuss ways in which numerical schemes can be modified in order to avoid the appearance of intermediate shocks in simulations with such symmetry.

Dynamical and pressure structures in winds with multiple embedded evaporating clumps—I. Two-dimensional numerical simulations

Because of its key role in feedback in star formation and galaxy formation, we examine the nature of the interaction of a flow with discrete sources of mass injection. We show the results of two-dimensional numerical simulations in which we explore a range of configurations for the mass sources and study the effects of their proximity on the downstream flow. The mass sources act effectively as a single source of mass injection if they are so close together that the ratio of their combined mass injection rate is comparable to or exceeds the mass flux of the incident flow into the volume that they occupy. The simulations are relevant to many diffuse sources, such as planetary nebulae and starburst superwinds, in which a global flow interacts with material evaporating or being ablated from the surface of globules of cool, dense gas.

The turbulent destruction of clouds – I. A k–ε treatment of turbulence in 2D models of adiabatic shock–cloud interactions

The interaction of a shock with a cloud has been extensively studied in the literature, where the effects of magnetic fields, radiative cooling and thermal conduction have been considered. In many cases, the formation of fully developed turbulence has been prevented by the artificial viscosity inherent in hydrodynamical simulations. This problem is particularly severe in some recent simulations designed to investigate the interaction of a flow with multiple clouds, where the resolution of individual clouds is necessarily poor. Furthermore, the shocked flow interacting with the cloud has been assumed to be completely uniform in all previous single-cloud studies. In reality, the flow behind the shock is also likely to be turbulent, with non-uniform density, pressure and velocity structure created as the shock sweeps over inhomogeneities upstream of the cloud (as seen in recent multiple cloud simulations). To address these twin issues we use a subgrid compressible k–� turbulence model to estimate the properties of the turbulence generated in shock–cloud interactions and the resulting increase in the transport coefficients that the turbulence brings. A detailed comparison with the output from an inviscid hydrodynamical code puts these new results into context. Despite the above concerns, we find that cloud destruction in inviscid and k–� models occurs at roughly the same speed when the post-shock flow is smooth and when the density contrast between the cloud and intercloud medium, χ 100. However, there are increasing and significant differences as χ increases. The k–� models also demonstrate better convergence in resolution tests than inviscid models, a feature which is particularly useful for multiple-cloud simulations. Clouds which are over-run by a highly turbulent post-shock environment are destroyed significantly quicker as they are subject to strong ‘buffeting’ by the flow. The decreased lifetime and faster acceleration of the cloud material to the speed of the ambient flow leads to a reduction in the total amount of circulation (vorticity) generated in the interaction, so that the amount of vorticity may be self-limiting. Additional calculations with an inviscid code where the post-shock flow is given random, grid-scale, motions confirm the more rapid destruction of the cloud. Our results clearly show that turbulence plays an important role in shock–cloud interactions, and that environmental turbulence adds a new dimension to the parameter space which has hitherto been studied.

The turbulent destruction of clouds – II. Mach number dependence, mass-loss rates and tail formation

The turbulent destruction of a cloud subject to the passage of an adiabatic shock is studied. We find large discrepancies between the lifetime of the cloud and the analytical result of Hartquist et al. (1986). These differences appear to be due to the assumption in Hartquist et al. (1986) that mass-loss occurs largely as a result of lower pressure regions on the surface of the cloud away from the stagnation point, whereas in reality Kelvin-Helmholtz (KH) instabilities play a dominant role in the cloud destruction. We find that the true lifetime of the cloud (defined as when all of the material from the core of the cloud is well mixed with the intercloud material in the hydrodynamic cells) is about 6 × tKHD, where tKHD is the growth timescale for the most disruptive, long-wavelength, KH instabilities. These findings have wide implications for diffuse sources where there is transfer of material between hot and cool phases. The properties of the interaction as a function of Mach number and cloud density contrast are also studied. The interaction is milder at lower Mach numbers with the most marked differences occuring at low shock Mach numbers when the postshock gas is subsonic with respect to the cloud (i.e. M < 2:76). Material stripped off the cloud only forms a long “tail-like” feature if � � 10 3 .

Diffuse Matter from Star Forming Regions to Active Galaxies

John Dyson - a Biographical Sketch. Preface. Part I: Star Forming Regions. 1. Numerical Simulations of Star Formation S. A. E. G. Falle. 2. Molecular Astrophysics of Star Formation D. A. Williams. 3. Dusty Plasma Effects in Star Forming Regions T. W. Hartquist, O. Havnes. 4. Massive Star Formation M. G. Hoare, J. Franco. 5. Spectropolarimetry and the Study of Circumstellar Disks R. D. Oudmaijer. 6. How to Move Ionized Gas: An Introduction to the Dynamics of H II Regions W. J. Henney. 7. MHD Ionization Fronts R.J.R. Williams. 8. Herbig-Haro Jets from Young Stars T.P. Ray. 9. Hypersonic Molecular Shocks in Star Forming Regions P. W. J. L. Brand. Part II: The Effects of Evolved Stars on Their Environments. 10. Wind-Blown Bubbles around Evolved Stars S. J. Arthur. 11. Do Fast Winds Dominate the Dynamics of Planetary Nebulae? J. Meaburn. 12. Spectral Studies of Supernova Remnants J. C. Raymond. Part III: Multicomponent Flows and Cosmic Rays. 13. Mass-Loaded Flows J. M. Pittard. 14. The Effects of Cosmic Rays on Interstellar Dynamics T. W. Hartquist et al. 15. The Status of Observations and Speculations Concerning Ultra High-Energy Cosmic Rays A. A. Watson. Part IV: Starburst Galaxies and Active Galactic Nuclei. 16. The Messier 82 Starburst Galaxy A. Pedlar, K. A. Wills. 17. Active Galactic Nuclei S. L. Lumsden. Index.

A numerical scheme for multifluid magnetohydrodynamics

This paper describes a numerical scheme for multifluid hydrodynamics in the limit of small mass densities of the charged particles. The inertia of the charged particles can then be neglected, which makes it possible to write an evolution equation for the magnetic field that can be solved using an implicit scheme. This avoids the severe restriction on the stable timestep that would otherwise arise at high resolution, or when the Hall effect is large. Numerical tests show that the scheme can accurately model steady multifluid shock structures both with and without subshocks. Although the emphasis is on shocks in molecular clouds, a multidimensional version of this code could be applied to any astrophysical flow in which ambipolar diffusion or the Hall effect, or both, play a significant role.

Rarefaction Shocks, Shock Errors, and Low Order of Accuracy in ZEUS

We show that there are simple one-dimensional problems for which the MHD code, ZEUS, generates significant errors, whereas upwind conservative schemes perform very well on these problems.

Shock-triggered formation of magnetically-dominated clouds

Aims. Our aim is to understand the formation of a magnetically dominated molecular cloud out of an atomic cloud. Methods. A thermally stable warm atomic cloud is initially in static equilibrium with the surrounding hot ionised gas. A shock propagating through the hot medium interacts with the cloud. We follow the dynamical evolution of the cloud with a time-dependent axisymmetric magnetohydrodynamic code. Results. As a fast-mode shock propagates through the cloud, the gas behind it becomes thermally unstable. The β value of the gas also becomes much smaller than the initial value of order unity. These conditions are ideal for magnetohydrodynamic waves to produce high-density clumps embedded in a rarefied warm medium. A slow-mode shock follows the fast-mode shock. Behind this shock a dense shell forms, which subsequently fragments. This is a primary region for the formation of massive stars. Our simulations show that only weak and moderate-strength shocks can form cold clouds which have properties typical of giant molecular clouds.

A COSMIC-RAY PRECURSOR MODEL FOR A BALMER-DOMINATED SHOCK IN TYCHO'S SUPERNOVA REMNANT

We present a time-dependent cosmic-ray (CR) modified shock model for which the calculated H? emissivity profile agrees well with the H? flux increase ahead of the Balmer-dominated shock at knot g in Tychos supernova remnant (SNR), observed by Lee et al. The backreaction of the CR component on the thermal component is treated in the two-fluid approximation, and we include thermal particle injection and energy transfer due to the acoustic instability in the precursor. The transient state of our model that describes the current state of the shock at knot g occurs during the evolution from a thermal gas dominated shock to a smooth CR-dominated shock. Assuming a distance of 2.3 kpc to Tychos remnant, we obtain values for the CR diffusion coefficient, ?, the injection parameter, , and the timescale for the energy transfer, ?, of ? = 2 ? 1024 cm2 s?1, = 4.2 ? 10?3, and ? = 426 yr, respectively. We have also studied the parameter space for fast (300 km s?1 vs 3000 km s?1), time-asymptotically steady shocks and have identified a branch of solutions, for which the temperature in the CR precursor typically reaches 2 ? 104 to 6 ? 104 K and the bulk acceleration of the flow through the precursor is less than 10 km s?1. These solutions fall into the low CR acceleration efficiency regime and are relatively insensitive to shock parameters. This low CR acceleration efficiency branch of solutions may provide a natural explanation for the line broadening of the H? narrow component observed in nonradiative shocks in many SNRs.

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.