Shock Propagation Through Multiphase Media*

This paper presents two and three dimensional simulations of the interaction of shocks with media with large numbers of dense inclusions. An approximate model of the interaction of a starburst wind with the surrounding galactic ISM illustrates issues which must be addressed in global models of ISM dynamics. As a step towards developing the sub-grid model of multiphase turbulence, we define and study a form of ‘multiphase Riemann problem’. This allows us to develop macroscopic characteristics of the flows which may be compared to such subgrid models.     

The influence of the Mach number on the stability of radiative shocks

We study the stability properties of hydrodynamic shocks with finite Mach numbers. The linear analysis supplements previous analyses which took the strong shock limit. We derive the linearized equations for a general specific heat ratio as well as temperature and density power-law cooling functions, corresponding to a range of conditions relevant to interstellar atomic and molecular cooling processes. Boundary conditions corresponding to a return to the upstream temperature  ( R = 1)  and to a cold wall  ( R = 0)  are investigated. We find that for Mach number   M > 5  , the strong shock overstability limits are not significantly modified. For   M < 3  , however, shocks are considerably more stable for most cases. In general, as the shock weakens, the critical values of the temperature power-law index (below which shocks are overstable) are reduced for the overtones more than for the fundamental, which signifies a change in basic behaviour. In the   R = 0  scenario, however, we find that the overstability regime and growth rate of the fundamental mode are increased when cooling is under local thermodynamic equilibrium. We provide a possible explanation for the results in terms of a stabilizing influence provided downstream but a destabilizing effect associated with the shock front. We conclude that the regime of overstability for interstellar atomic shocks is well represented by the strong shock limit unless the upstream gas is hot. Although molecular shocks can be overstable to overtones, the magnetic field provides a significant stabilizing influence.     

Resolved shocks in clumpy media

We study the structure of shocks in clumpy media, using a multifluid formalism. As expected, shocks broaden as they weaken: for sufficiently weak shocks, no viscous subshock appears in the structure. This has significant implications for the survival of dense clouds in regions overrun by shocks in a wide range of astrophysical circumstances, from planetary nebulae to the nuclei of starburst galaxies.     

Hydrodynamic simulations of molecular outflows driven by slow-precessing protostellar jets

We present hydrodynamic simulations of molecular outflows driven by jets with a long period of precession, motivated by observations of arc-like features and S-symmetry in outflows associated with young stars. We simulate images of not only H₂ vibrational and CO rotational emission lines, but also of atomic emission. The density cross-section displays a jaw-like cavity, independent of precession rate. In molecular hydrogen, however, we find ordered chains of bow shocks and meandering streamers which contrast with the chaotic structure produced by jets in rapid precession. A feature particularly dominant in atomic emission is a stagnant point in the flow that remains near the inlet and alters shape and brightness as the jet skims by. Under the present conditions, slow jet precession yields a relatively high fraction of mass accelerated to high speeds, as also attested to in simulated CO line profiles. Many outflow structures, characterized by HH 222 (continuous ribbon), HH 240 (asymmetric chains of bow shocks) and RNO 43N (protruding cavities), are probably related to the slow-precession model.     

Hydrodynamic simulations of rotating molecular jets

Molecular outflows and the jets which may drive them can be expected to display signatures associated with rotation if they are the channels through which angular momentum is extracted from material accreting on to protostars. Here, we determine some basic signatures of rapidly rotating flows through three-dimensional numerical simulations of hydrodynamic jets with molecular cooling and chemistry. We find that these rotating jets generate a broad advancing interface which is unstable and develops into a large swarm of small bow features. In comparison to precessing jets, there is no stagnation point along the axis. The greater the rotation rate, the greater the instability. On the other hand, velocity signatures are only significant close to the jet inlet since jet expansion rapidly reduces the rotation speed. We present predictions for atomic, H₂ and CO submillimetre images and spectroscopy including velocity channel maps and position–velocity diagrams. We also include simulated images corresponding to Spitzer IRAC band images and CO emission, relevant for APEX and eventual ALMA observations. We conclude that protostellar jets often show signs of slow precession but only a few sources display properties which could indicate jet rotation.     

On the linear analysis of unstable radiative shocks

We study the stability properties of strong hydrodynamic shocks and their associated radiative cooling layers. We explore a range of conditions which covers both molecular and atomic gas impacting against a rigid wall. Through a linear analysis employing a cooling function of the form  Λ∝ρ^β T ^α  and a specific heat ratio of γ, we determine the overstability regime in the parameter space consisting of  α, β  and γ. In general, if α is sufficiently low, the fundamental mode leads to long-wavelength growing oscillations. For the fundamental mode, we find that values of γ corresponding to molecular hydrodynamics lead to a significantly restricted instability range for α in comparison with the shocks in a monatomic medium. The conditions for the growth of higher-order modes, however, are relatively unchanged. This predicts that certain molecular shocks are prone to displaying signatures of small-scale rapid variability. Dissociative shocks, however, can be subject to a large-scale overstability if subsequent molecule formation in the cooling layer abruptly increases the cooling rate. In contrast to the dynamical rippling overstability, the cooling overstability is suppressed for a sufficiently low specific heat ratio.     

Dynamical friction for accelerated motion in a gaseous medium

Dynamical friction arises from the interaction of a perturber and the gravitational wake it excites in the ambient medium. This interaction is usually derived assuming that the perturber has a constant velocity. In realistic situations, motion is accelerated as for instance by dynamical friction itself. Here, we study the effect of acceleration on the dynamical friction force. We characterize the density enhancement associated with a constantly accelerating perturber with rectilinear motion in an infinite homogeneous gaseous medium and show that dynamical friction is not a local force and that its amplitude may depend on the perturber's initial velocity. The force on an accelerating perturber is maximal between Mach 1 and Mach 2, where it is smaller than the corresponding uniform motion friction. In the limit where the perturber's size is much smaller than the distance needed to change the Mach number by unity through acceleration, a subsonic perturber feels a force similar to uniform motion friction only if its past history does not include supersonic episodes. Once an accelerating perturber reaches large supersonic speeds, accelerated motion friction is marginally stronger than uniform motion friction. The force on a decelerating supersonic perturber is weaker than uniform motion friction as the velocity decreases to a few times the sound speed. Dynamical friction on a decelerating subsonic perturber with an initial Mach number larger than 2 is much larger than uniform motion friction and tends to a finite value as the velocity vanishes in contrast to uniform motion friction.     

Radiative steady-state colliding stellar wind models: are they correct?

The properties of radiative steady-state colliding stellar winds in binary systems are studied. It is shown that the presence of a singularity at the stagnation point has a major influence on the structure of these flows. This problem is of great importance if their stability properties are considered. None of the existing models treats this mathematical problem properly, and special efforts must be undertaken in the future in order to come to a firm conclusion about the physical nature of possible instabilities. At the moment, neither numerical nor analytical models can be considered to be of acceptable accuracy in the case of highly radiative steady-state colliding stellar winds.     

An analytic solution to the hypersonic, radiative blunt body problem

We present an analytic model for the thin-shell, radiative interaction between a hypersonic, plane-parallel wind and a rigid, spherical obstacle. This problem has clear applications, e.g., to the interaction of winds from young stars and dense cloudlets, and to the interaction of the wind from a binary partner with the photosphere of the second star. We also present a comparison of the analytic model with a full, axisymmetric numerical simulation. We find only a partial agreement between the numerical simulation and the analytic model, apparently as a result of the very strong 'thin-shell' instabilities of the post-bow shock flow. Our analytic model predicts the surface density, flow velocity and the energy radiated per unit area, as well as the total luminosity of the bow shock. The model can therefore be used directly for carrying out comparisons with observations of different astrophysical objects.     

Shock strengths in clumps impacted by winds of increasing power

We have performed spherically symmetric and axisymetric hydrodynamic simulations of wind–clump interactions in order to determine the conditions under which a wind, impacting upon a clump and increasing in power with time, drives a strong shock into the clump. If the wind ram pressure and the clump thermal pressure are comparable when the impact first occurs, then the wind ram pressure must increase on a time-scale markedly smaller than the sound-crossing time of the clump if it is to drive a shock that becomes strong at any point in the clump. We comment on the possible relevance of this result for the dynamics and chemistry of hot cores in regions of high-mass star formation.     

On the formation of cold fronts in massive mergers

Using adiabatic hydrodynamical simulations, we follow the evolution of two symmetric cold fronts forming in the remnant of a violent   z = 0.3  massive cluster merger. Because the fronts develop after the first passage of the two gas cores of the merging subclusters, and because they soon move ahead of their associated dark matter cores, both the structure and the location of our simulated cold fronts may correspond to a stage that is later than that of most cold fronts observed so far. The cold fronts are preceded by a roughly spherical shock that originates in the centre of the cluster and disappears in the outer regions after 1.6 Gyr. The cold fronts last longer, until   z ∼ 0  . We follow the spatial evolution of the gas of the subcluster cores, and find that a fraction of this gas is liberated in the intracluster medium after core passage, but mainly at apocentre, and that it does not fall back onto the cluster centre. Conversely, we trace back the low-temperature gas constituting the fronts and find that it is initially associated with the two dense cores of the merging clusters. In addition, we find some evidence for discontinuity of the gas velocity field across the edge of the forming cold fronts, suggesting the presence of a contact discontinuity there. In the light of other recent work, we then speculate on the physical mechanism resulting in the cold fronts. We suggest that sloshing induced by strongly varying ram pressure along the subcluster's orbit and/or spatial segregation between the dark matter and gas components of the cores of the subclusters results in strong tidal forces on the gas, and that these forces could be responsible for the deposition of part of the cold dense gas in the surrounding hot intracluster medium. This deposited gas then expands, cools down further, and constitutes the cold fronts.