Shock-cloud interaction and gas-dust spatial separation

Computational simulations of microscale shock–vortex interaction using a mixed discontinuous Galerkin method

This paper addresses nonlinear effects which result from the interaction of shock waves with vortices. A series of experiments are carried out, which involve the interaction of a strong shock wave with a single plane vorticity wave and a randomly distributed wave system. These experiments are first conducted in the linear regime to obtain a mutual verification of theory and computation. They are subsequently extended into the nonlinear regime. A systematic study of the interaction of a plane shock wave and a single vortex is then conducted. Specifically, we investigate the conditions under which nonlinear effects become important, both as a function of shock Mach number, M1, and incident vortex strength (characterized by its circulation Γ). The shock Mach number is varied from 2 to 8, while the circulation of the vortex is varied from infinitesimally small values (linear theory) to unity. Budgets of vorticity, dilatation, and pressure are obtained. They indicate that nonlinear effects become more significant as both the shock Mach number and the circulation increase. For Mach numbers equal to 5 and above, the dilatation in the vortex core grows quadratically with circulation. An acoustic wave propagates radially outward from the vortex center. As circulation increases, its upstream-facing front steepens at low Mach numbers, and its downstream-facing front steepens at high Mach numbers. A high Mach number asymptotic expansion of the Rankine--Hugoniot conditions reveals that nonlinear effects dominate both the shock motion and the downstream flow for ΓM1 > 1.

Molecular clouds are regions of dense gas and dust in space where new stars and planets are born. There is a strong correlation between the distribution of dust and molecular gas in molecular clouds. The present work focuses on the three-dimensional morphological comparisons between dust and gas in 567 molecular clouds identified in a previously published catalog. We confirm a sample of 112 molecular clouds, where the cloud morphology based on CO observations and dust observations displays good overall consistency. There are up to 334 molecular clouds whose dust distribution might be related to the distribution of gas. We are unable to find gas structures that correlate with the shape of the dust distribution in 24 molecular clouds. For the 112 molecular clouds where the dust distribution correlates very well with the distribution of gas, we use CO observational data to measure the physical properties of these molecular clouds and compare them with the results derived from dust, exploring the correlation between gas and dust in the molecular clouds. We found that the gas and dust in the molecular clouds have a fairly good linear relationship, with a gas-to-dust ratio of GDR=(2.80−0.34+0.37)×1021cm−2mag−1 . The ratio varies considerably among different molecular clouds. We measured the scale height of dust-CO clouds exhibiting strong correlations, finding hZ=43.3−3.5+4.0 pc.

Shocks are ubiquitous in astrophysical environments and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration. It is believed that the CR pressure is important in the evolution of the interstellar medium of our galaxy and most of galactic CRs with energies up to eV are accelerated by supernova remnant shocks. In this contribution we have studied the CR acceleration at shocks through numerical simulation of 1D, quasi-parallel shocks for a wide range of shock Mach numbers and shock speeds. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies, and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number, and high Mach number shocks all evolve towards efficiencies , regardless of the injection rate and upstream CR pressure. We conclude that the injection rates in strong quasi-parallel shocks are sufficient to lead to significant nonlinear modifications to the shock structures, implying the importance of the CR acceleration at astrophysical shocks.

Cosmological shocks form as an inevitable consequence of gravitational collapse during the large scale structure formation and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration (DSA). We have calculated the evolution of CR modified shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of DSA in 1D quasi-parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc <TEX>$\ge$</TEX> 1), and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that <TEX>$10^{-4} - 10^{-3}$</TEX> of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The CR acceleration efficiency increases with shock Mach number, but it asymptotes to <TEX>${\~}50\%$</TEX> in high Mach number shocks, regardless of the injection rate and upstream CR pressure. On the other hand, in moderate strength shocks (<TEX>$M_s {\le} 5$</TEX>), the pre-existing CRs increase the overall CR energy. We conclude that the CR acceleration at cosmological shocks is efficient enough to lead to significant nonlinear modifications to the shock structures.

When the shock wave propagating along the straight circular tube reaches at the open end, the spherical shock wave is generated by the emission of a shock wave from an open end and the unsteady jet is formed near the open end behind the spherical shock wave. The shock strength of spherical shock wave is dependent on the shock Mach number in the tube, and it attenuates with propagation distance from the open end. In this study, the flow induced by the emission of a comparatively strong shock wave from an open end of a tube with the infinity flange is analyzed numerically by the TVD method. As a result, it is concluded that the asymptotic position and diameter of Mack disk of unsteady jet are equal to the steady jet corresponding the pressure ratio. In addition, the relationship between strength of spherical shock wave and Mach number of incident shock wave is clarified from viewpoints of the characteristics of attenuation and directivity for the spherical shock wave.

Detonation instability is a fundamental problem for understanding the microbehavior of a detonation front. With the theoretical approach of shock dynamics, detonation instability can be mathematically described as a second-order ordinary difference equation. A one-dimensional detonation wave can be modelled as a type of oscillators.There are two different physical mechanisms controlling the behaviors of a detonation. If the shock Mach number is smaller than the equilibrium Mach number, the fluid will reach the sonic speed before the end of the chemical reaction. Then, thermal chock occurs, and the leading shock becomes stronger. If the shock Mach number is larger than the equilibrium Mach number, the fluid will be subsonic at the end of the chemical reaction. Then,the downstream rarefaction waves propagate upstream, and weaken the leading shock.The above two mechanisms are the basic recovery forces toward the equilibrium state for detonation sustenance and propagation. The detonation oscillator concept is helpful for understanding the oscillating and periodic behaviors of detonation waves. The shock dynamics theory of detonation instability gives a description of the feedback regime of the chemical reaction, which causes variations of the leading shock of the detonation.

A simulation-derived surrogate model for the vaporization rate of aluminum droplets heated by a passing shock wave

Context. In recent decades, several multiwavelength studies have been dedicated to exploring the properties of the obscuring material in active galactic nuclei (AGN). Various models have been developed to describe the structure and distribution of this material and constrain its physical and geometrical parameters through spectral fitting techniques. However, questions around the way in which torus mid-infrared (mid-IR) and X-ray emission are related remain unanswered. Aims. In this work, we aim to study whether the dust continuum at mid-IR and gas reflection at X-rays have the same distribution in a sample of AGN. Methods. We carefully selected a sample of 36 nearby AGN with NuSTAR and Spitzer spectra available that satisfy the following criteria: (1) the AGN component dominates the mid-IR spectra (i.e., the stellar and interstellar medium components contribute less than 50% to the spectrum), and (2) the reflection component contributes significantly to the X-ray spectrum. Furthermore, we discarded the sources whose reflection component could be produced by ionized material in the disk. We derived the properties of the nuclear dust and gas through a spectral fitting, using models developed for mid-IR and X-ray wavelengths assuming smooth and clumpy distributions for this structure. Results. We find that a combination of smooth and clumpy distributions of gas and dust, respectively, is preferred for ∼80% of sources with good spectral fits according to the Akaike criterion. However, considering extra information about each individual source, such as the absorption variability, we find that ∼50% of our sources are best described by a clumpy distribution of both dust and gas. The remaining ∼50% of our sources can still be explained with a smooth distribution of gas and a clumpy distribution of dust. Furthermore, we explored the torus dust-to-gas ratio, finding that it is [0.01–1] times that of the interstellar medium. Conclusions. The results presented in this paper suggest that the distribution of the gas and dust in AGN is complex. We find at least six scenarios to explain the observed properties of our sample. In these scenarios, three gas–dust distribution combinations are possible: clumpy–clumpy, smooth–smooth, and smooth–clumpy. Most of them are in agreement with the notion that gas could also be located in the dust-free region, which is consistent with the dust-to-gas ratio found.

CIZA J2242.8+5301, a merging galaxy cluster at z = 0.19, hosts a double-relic system and a faint radio halo. Radio observations at frequencies ranging from a few MHz to several GHz have shown that the radio spectral index at the outer edge of the northern relic corresponds to a shock of Mach number |$4.6_{-0.9}^{+1.3}$|, under the assumptions of diffusive shock acceleration of thermal particles in the test-particle regime. Here, we present results from new Chandra observations of the cluster. The Chandra surface brightness profile across the northern relic only hints to a surface brightness discontinuity (<2σ detection). Nevertheless, our reanalysis of archival Suzaku data indicates a temperature discontinuity across the relic that is consistent with a Mach number of |$2.54_{-0.43}^{+0.64}$|, in agreement with previously published results. This confirms that the Mach number at the shock traced by the northern relic is much weaker than predicted from the radio. Puzzlingly, in the Chandra data we also identify additional inner small density discontinuities both on and off the merger axis. Temperature measurements on both sides of the discontinuities do not allow us to undoubtedly determine their nature, although a shock front interpretation seems more likely. We speculate that if the inner density discontinuities are indeed shock fronts, then they are the consequence of violent relaxation of the dark matter cores of the clusters involved in the merger.

Interplanetary shocks accelerate charged particles and have significant space weather effects. The widely accepted categorization of shocks uses the upstream plasma beta (βu), the shock angle (θBn), and the shock Mach number (M, i.e., the fast magnetosonic Mach number). In addition, two critical Mach numbers (Mc) classify shocks based on whether shock dissipation is provided by electron resistivity and conductance alone or also requires ion viscosity. The two critical Mach numbers were defined in studies by Edmiston and Kennel and by Kennel in the 1980s. The corresponding two transition points from subcritical to supercritical are referred to as critical Mach numbers Mc (EK84) and Mc(K87), respectively. In this study, we use the critical Mach numbers and magnetic overshoot as identifiers of supercritical shocks. When the ratio of M/Mc ≥ 1, and/or an overshoot presents, a shock is categorized as a supercritical shock. We found that in more than 80% of supercritical shocks (with M/Mc(K87) ≥ 1), in addition to the regular ion reflection around the magnetic foot, there is another group of ion reflections: energetic ion reflections (EIRs). Typically, regularly reflected ions range from ~1–4 keV, staying at or around the foot, while EIR ions range from ~4–25 keV (or higher), running minutes upstream of the shock, perhaps as a result of ion backstreaming and escaping. EIR is a newly discovered feature observed by Acceleration, Reconnection, Turbulence, and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) at supercritical interplanetary shocks, occurring even when θBn &gt; 60°, which is excluded by simulations due to a strong suppression of the backstreaming reflection in such circumstances. The close correlation between EIR occurrence and the critical Mach number Mc(K87) revealed that the conceptual ion viscosity in the magnetohydrodynamics (MHD)‐derived criticality has a root in kinetic microphysics.

This study numerically and experimentally examines the resulting flow field of a shock wave passing through a pipe gap. The effects of gap geometry and shock Mach number variation are investigated. Incident shock Mach numbers of 1.3, 1.4, and 1.5 and gap widths of 25 and 50 mm were used, which correspond to 0.5 and 1.0 pipe inner diameters, respectively. For both cases, the incident shock wave propagated into the downstream pipe at much reduced strength. A strong expansion propagated into the upstream pipe causing a significant pressure drop from the initial post-shock pressure. Expansion waves at the outflow resulted in supersonic speeds as the flow entered the gap for Mach 1.4 and 1.5. A notable feature was the formation of a standing shock at the inlet to the downstream pipe for the higher two Mach numbers in both cases. Decreasing the gap width moved the standing shock closer to the downstream pipe. For the lowest Mach number of 1.3, no standing shock system was set up. The propagation conditions in the downstream pipe showed that the pressure is initially unsteady, but becomes more uniform, controlled by the developed wave system in the gap. For the flanged gap case, the flow within the gap is confined for much longer and hence produces more intense and complex flow feature interactions and an earlier transition to turbulence. The induced shock strength in the downstream pipe is independent of gap geometry and separation distance examined in this paper as verified by experimental pressure traces.

Recent simulation results have revealed that energetic electron bursts are produced cyclically at the shock reformation period upstream of reforming shocks and are qualitatively very different from the continuous beam expected from time‐stationary shocks (Yuan et al., 2007a). This paper extends our previous studies by numerically investigating the dependence of electron burst events on shock parameters (the upstream plasma β and Mach number M A ). The test particle approximation is made for electrons, and the electron trajectories are traced exactly in the time‐dependent electromagnetic field profiles, generated by one‐dimensional hybrid simulation code. Simulation results indicate that the upstream incoming electrons can be reflected nonuniformly or continuously depending on the shock parameters. Bursty energetic electron events take place when the plasma beta is low ( β ≤ 0.4) and the shock Mach number is high ( M A ≥ 6). Time‐varying loss cone, beam, and ring beam features are observed in the upstream electron distribution functions. The beam density, speed, average kinetic energy, and speed spread cyclically change with time by factor of ∼2–4. In contrast, continuously reflected electrons are observed for low beta ( β ≤ 0.4), low Mach number ( M A ≤ 4) shocks, even when the shock is reforming because the changes in shock fields are relative small. The electron burst events disappear and the observed upstream electron distribution function contours are steady state. A continuous electron beam is formed, which is qualitative the same as the beam from steady‐state shocks. Increasing the plasma beta (providing the shock is still reforming) has minor effects on the upstream electron beam features.

Ion velocity space distributions measured with Los Alamos/Garching instruments on ISEE 1 and 2 across the earth's bow shock have revealed that the nearly perpendicular shock reflects some fraction of the incident solar wind ions over a wide range of Mach numbers (MA ≃ 2.0–12.4). The relative density of the reflected ions varies from 1–3% of the solar wind density at MA ≃ 2 to 15–25% at MA = 8–12, in qualitative agreement with computer simulations and with predictions that indicate that such ions are needed to provide essential dissipation at the shock. These ions gyrate about B in the plasma rest frame with a speed of ∼2 υin, where υin is the normal component of the solar wind flow, and their density increases by ∼2 orders of magnitude at the forward end of the ’foot‘ of the shock profile ∼0.7 ion gyroradii upstream from the shock ramp. This is substantial evidence that the bulk of these ions have been reflected at the shock in a nearly specular fashion. Depending on the shock geometry, some low numbers of reflected‐gyrating ions are sometimes observed a few gyroradii ahead of the outer edge of the foot. Model calculations suggest that these additional ions are produced by non‐specular reflection of a much smaller fraction of the incident solar wind. Downstream of the shock ramp, the secondary ions gyrate with a slightly higher speed, υg ≃ 2.15 υin, in the downstream rest frame. Individual groups of gyrating ions rapidly disperse in velocity space to form a high‐energy torus centered at the bulk velocity of the distributions. Downstream ion toruses are most clearly seen, sometimes persisting for many minutes, when the shock Mach number is low. Downstream of highly supercritical shocks (M ≫ 3), the distributions are more turbulent. In either case, the distributions retain some non‐Maxwellian features for a long time downstream from the ramp, in accordance with earlier observations. Reflected‐gyrating ions have also been identified in a number of crossings with more oblique field orientations (θnB ≳ 45°, i.e., for quasi‐perpendicular shocks). Specularly reflected ions play an important role in producing down‐stream ion thermalization for all θnB ≳ 45°, being relatively more important the higher is the Mach number.

A two-dimensional, linearized treatment, including real gas effects, of shock curvature in a shock tube is presented. An expression for shock shape as a function of shock Mach number and initial pressure of the test gas is presented. The results are compared with the available experimental data obtained in argon at low shock strengths and in air at high shock Mach numbers. Within the scatter of the data in the latter experiments, there is relatively good agreement with theory, while theory falls approximately 30 ± 10% above the data in argon. Some of this disagreement is attributed to application of the two-dimensional theoretical result to axisymmetric shock tubes of finite dimensions used in the experiments.