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.     

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 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.     

A new plasmon solution with centrifugal pressure

The 'plasmon' solution of De Young & Axford describes the interaction between a high-velocity clump and the surrounding medium. Even though this solution is probably too simplistic, it has proven to be most useful in the study of diverse astrophysical flows. In the present paper, we discuss a more detailed solution of the plasmon problem, which includes the centrifugal effects of the environmental material flowing around the plasmon. We derive both numerical and approximate analytic solutions of this problem, and compare them with the analytic solution of De Young & Axford.     

Temporal evolution of MHD shocks in the interstellar medium

We undertake calculations of the time-dependent structure of shock waves propagating in dark and diffuse interstellar clouds. The results of the time-dependent model are compared with those obtained by means of an independent steady-state code and found to agree well at sufficiently late times. Discontinuities in the flow of the neutral fluid are handled by introducing a pseudo-viscosity. Special procedures are adopted to correct for the associated widening of the discontinuity, in order not to distort the role of inelastic collision processes. We find that, in dark clouds, C shocks will tend to predominate, but are unlikely to have attained steady state in the cloud lifetime. On the other hand, in diffuse clouds, steady state may be reached but the discontinuity in the flow of the neutral fluid remains. We find no evidence for the existence of C* shocks, in which the neutral fluid undergoes a continuous transition from supersonic to subsonic flow (in the reference frame of the shock wave). Attention is drawn to the possible importance of these results for the interpretation of H₂ rovibrational line intensities.     

Driven waves in a two-fluid plasma

We study the physics of wave propagation in a weakly ionized plasma, as it applies to the formation of multifluid, magnetohydrodynamics (MHD) shock waves. We model the plasma as separate charged and neutral fluids which are coupled by ion–neutral friction. At times much less than the ion–neutral drag time, the fluids are decoupled and so evolve independently. At later times, the evolution is determined by the large inertial mismatch between the charged and neutral particles. The neutral flow continues to evolve independently; the charged flow is driven by and slaved to the neutral flow by friction. We calculate this driven flow analytically by considering the special but realistic case where the charged fluid obeys linearized equations of motion. We carry out an extensive analysis of linear, driven, MHD waves. The physics of driven MHD waves is embodied in certain Green functions which describe wave propagation on short time-scales, ambipolar diffusion on long time-scales and transitional behaviour at intermediate times. By way of illustration, we give an approximate solution for the formation of a multifluid shock during the collision of two identical interstellar clouds. The collision produces forward and reverse J shocks in the neutral fluid and a transient in the charged fluid. The latter rapidly evolves into a pair of magnetic precursors on the J shocks, wherein the ions undergo force-free motion and the magnetic field grows monotonically with time. The flow appears to be self-similar at the time when linear analysis ceases to be valid.     

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.     

C-type shocks in the interstellar medium: profiles of CH+ and CH absorption lines

We have computed optical absorption-line profiles of CH⁺ and CH, as predicted by a model of a C-type shock propagating in a diffuse interstellar cloud. Both these species are produced in the shock wave in the reaction sequence that is initiated by C⁺(H₂, H)CH⁺. Whilst CH⁺ flows at the ion speed, CH, which forms in the dissociative recombination reaction CH⁺₃(e⁻, H₂)CH, flows at a speed which is intermediate between those of the ions and the neutrals. The predicted velocity shift between the CH⁺ and CH line profiles is found to be no more than approximately 2 km s⁻¹, which is smaller than has previously been assumed. We also investigate OH and HCO⁺, finding that the correlation between their column densities, recently observed in the diffuse interstellar medium, can be reproduced by the model.     

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.