Newtonian Shock Research Articles

Anomalous coupling in radiation mediated shocks

We summarize recent attempts to unravel the role of plasma kinetic effects in radiation mediated shocks. Such shocks form in all strong stellar explosions and are responsible for the early electromagnetic emission released from these events. A key issue that has been overlooked in all previous works is the nature of the coupling between the charged leptons, that mediate the radiation force, and the ions, which are the dominant carriers of the shock energy. Our preliminary investigation indicates that in the case of relativistic shocks, as well as Newtonian shocks in multi-ion plasma, this coupling is driven by either, transverse magnetic fields of a sufficiently magnetized upstream medium, or plasma microturbulence if strong enough magnetic fields are absent. We discuss the implications for the shock breakout signal, as well as abundance evolution and kilonova emission in binary neutron star mergers.

Luminous Late-time Radio Emission from Supernovae Detected by the Karl G. Jansky Very Large Array Sky Survey (VLASS)

Abstract We present a population of 19 radio-luminous supernovae (SNe) with emission reaching L ν ∼ 1026–1029 erg s−1 Hz−1 in the first epoch of the Very Large Array Sky Survey (VLASS) at 2–4 GHz. Our sample includes one long gamma-ray burst, SN 2017iuk/GRB 171205A, and 18 core-collapse SNe detected at ≈1–60 yr after explosion. No thermonuclear explosion shows evidence for bright radio emission, and hydrogen-poor progenitors dominate the subsample of core-collapse events with spectroscopic classification at the time of explosion (79%). We interpret these findings in the context of the expected radio emission from the forward shock interaction with the circumstellar medium (CSM). We conclude that these observations require a departure from the single wind–like density profile (i.e., ρ CSM ∝ r −2) that is expected around massive stars and/or from a spherical Newtonian shock. Viable alternatives include the shock interaction with a detached, dense shell of CSM formed by a large effective progenitor mass-loss rate, M ̇ ∼ 10 − 4 – 10 − 1 M ⊙ yr−1 (for an assumed wind velocity of 1000 km s−1); emission from an off-axis relativistic jet entering our line of sight; or the emergence of emission from a newly born pulsar-wind nebula. The relativistic SN 2012ap that is detected 5.7 and 8.5 yr after explosion with L ν ∼ 1028 erg s−1 Hz−1 might constitute the first detections of an off-axis jet+cocoon system in a massive star. However, none of the VLASS SNe with archival data points are consistent with our model off-axis jet light curves. Future multiwavelength observations will distinguish among these scenarios. Our VLASS source catalogs, which were used to perform the VLASS cross-matching, are publicly available at https://doi.org/10.5281/zenodo.4895112.

Spherical Shocks in a Steep Density Gradient of Expanding Media

Abstract We study the propagation of a Newtonian shock in a spherically symmetric, homologously expanding ejecta. We focus on media with a steep power-law density profile of the form ρ ∝ t −3 v −α , with α > 5, where v is the velocity of the expanding medium and t is time. Such profiles are expected in the leading edge of supernovae ejecta and sub-relativistic outflows from binary neutron star mergers. We find that such shocks always accelerate in the lab frame and lose causal contact with the bulk of the driver gas, owing to the steep density profile. However, the prolonged shock evolution exhibits two distinct pathways: In one, the shock strength diminishes with time until the shock eventually dies out. In the other, the shock strength steadily increases, and the solution approaches the self-similar solution that a shock is a static medium. By mapping the parameter space of shock solutions, we find that the evolutionary pathways are dictated by α and by the initial ratio between the shock velocity and the local upstream velocity. We find that for α < ω c (ω c ≈ 8), the shock always decays, and that for α > ω c , the shock may decay or grow stronger depending on the initial value of the velocity ratio. These two branches bifurcate from a self-similar solution derived analytically for a constant velocity ratio. We analyze properties of the solutions that may have an impact on the observational signatures of such systems, and assess the conditions required for decaying shocks to break out from a finite medium.

Discrete self similarity in filled type I strong explosions

We present new solutions to the strong explosion problem in a non power law density profile. The unperturbed self similar solutions developed by Sedov, Taylor, and Von Neumann describe strong Newtonian shocks propagating into a cold gas with a density profile falling off as r−ω, where \documentclass[12pt]{minimal}\begin{document}$\omega \le \frac{7-\gamma }{\gamma +1}$\end{document}ω≤7−γγ+1 (filled type I solutions), and γ is the adiabatic index of the gas. The perturbations we consider are spherically symmetric and log periodic with respect to the radius. While the unperturbed solutions are continuously self similar, the log periodicity of the density perturbations leads to a discrete self similarity of the perturbations, i.e., the solution repeats itself up to a scaling at discrete time intervals. We discuss these solutions and verify them against numerical integrations of the time dependent hydrodynamic equations. This is an extension of a previous investigation on type II solutions and helps clarifying boundary conditions for perturbations to type I self similar solutions.

Relativistic and Newtonian Shock Breakouts

AbstractObservations of the first light from a stellar explosion can open a window to a wealth of information on the progenitor system and the explosion itself. Here I briefly discuss the theoretical expectation of that emission, comparing Newtonian and relativistic breakouts. The former takes place in regular core-collapse supernovae (SNe) while the latter is expected in SNe that are associated with gamma-ray bursts (GRBs), extremely energetic SNe (e.g., SN2007bi) and white dwarf explosions (e.g., type Ia and .Ia SNe, accretion induced collapse). I present the characteristic observable signatures of both types of breakouts, when spherical. Finally, I discuss Newtonian shock breakouts through wind, which produce a very luminous signal, with an X-ray component that is weak around the breakout, and becomes brighter afterwards.

Discrete self-similarity in type-II strong explosions

We present new solutions to the strong explosion problem in a nonpower law density profile. The unperturbed self-similar solutions discovered by Waxman and Shvarts describe strong Newtonian shocks propagating into a cold gas with a density profile falling off as r−ω, where ω>3 (type-II solutions). The perturbations we consider are spherically symmetric and log periodic with respect to the radius. While the unperturbed solutions are continuously self-similar, the log periodicity of the density perturbations leads to a discrete self-similarity of the perturbations, i.e., the solution repeats itself up to a scaling at discrete time intervals. We discuss these solutions and verify them against numerical integrations of the time dependent hydrodynamic equations. Finally we show that this method can be generalized to treat any small, spherically symmetric density perturbation by employing Fourier decomposition.

On the Stability of Shocks with Particle Pressure

We perform a linear stability analysis for corrugations of a Newtonian shock, with particle pressure included, for an arbitrary diffusion coefficient. We study first the dispersion relation for homogeneous media, showing that, besides the conventional pressure waves and entropy/vorticity disturbances, two new perturbation modes exist, dominated by the particles' pressure and damped by diffusion. We show that, due to particle diffusion into the upstream region, the fluid will be perturbed also upstream: we treat these perturbation in the short wavelength (WKBJ) regime. We then show how to construct a corrugational mode for the shock itself, one, that is, where the shock executes free oscillations (possibly damped or growing) and sheds perturbations away from itself: this global mode requires the new modes. Then, using the perturbed Rankine-Hugoniot conditions, we show that this leads to the determination of the corrugational eigenfrequency. We solve numerically the equations for the eigenfrequency in the WKBJ regime for the models of Amato and Blasi (2005), showing that they are stable. We then discuss the differences between our treatment and previous work.

STABILITY OF RADIATIVE RELATIVISTIC SHOCKS TO GLOBAL OSCILLATIONS

Thermally emitting, radiative, Newtonian shocks exhibit a global oscillatory instability. The luminosity variations that accompany such oscillations raise the possibility that, if relativistic shocks that emit nonthermal (synchrotron and inverse-Compton) radiation are also subject to such an instability, this could be relevant to the interpretation of certain flares observed in relativistic jet sources associated with AGNs and GRBs. A linear stability analysis, using the equations of special-relativistic MHD and accounting for both the energy and the momentum carried by the radiation, has, however, revealed no unstable modes for physically plausible parameter values. The likely explanation is that, even though synchrotron cooling gives rise to a local radiative instability, the dependence on the magnetic field amplitude is not strong enough to counter the stabilizing effect of enhanced magnetic pressure, due to cooling-induced compression, on the global behavior of the shock. Numerical simulations are under way to ascertain that this conclusion continues to hold also in the nonlinear regime.

Effects of nuclear equation of state on general relativistic stellar core collapse models

The consequences of the equation of state above nuclear density, parameterized by a compressibility and an adiabatic index, for the strength of the reflected shock wave following core bounce in stellar collapse are studied using a hydrodynamic model. Particular attention is paid to the amplification of the shock strength when bounce occurs near those critical parameters which would result in continued collapse to the black hole. Comparisons are made to models where Newtonian hydrodynamics is assumed, and the relativistic effects are contrasted with the dependence on the homologous core mass. The dependence of the collapsed core mass (and the Newtonian shock strength) on the (constant) electron fraction Y(e) is shown. 22 references.

Remarks on Unsteady Newtonian Flow Theory

SummaryUnsteady high Mach number flows past oscillating cones and oscillating wedges are studied according to Newtonian impact theory, with and without centrifugal force corrections. It is found that, contrary to existing theories, the centrifugal force contribution in unsteady flow is significant and not negligible; for example, it contributes one-half to the dynamic stability derivatives of an oscillating wedge and one-third to that of an oscillating cone. It is also shown that in both cases the dynamic stability derivatives calculated by Newtonian impact theory with centrifugal force correction agree exactly with those obtained by gas-dynamic theory in the double limit γ → 1 and M∞ → ∞, independently. These conclusions are expected to hold for more general three-dimensional unsteady Newtonian flow when the Newtonian shock layer is attached.

The Newton drag law for bodies formed by intersecting surfaces

The Newtonian shock layer theory for smooth surfaces has been developed in [1–7]. However, if a body consists of two intersecting surfaces, on each of which there is a regular shock layer, these two layers will interact at the line of intersection. Considering that the shock layer is hypersonic, we can again apply the Newton scheme to the impact of the particles with the second surface. As a result, concentrated forces arise at the line of intersection. An indication of the possibility of the appearance of such forces is given in [2]. In the following we present a method of calculating the concentrated forces and indicate the real flow of which they are the analogy.

The hypersonic viscous shock layer with mass transfer

An investigation of the effects of surface mass transfer on the viscous hypersonic shock layer of a blunt body has been performed. Cheng's theory of the Newtonian shock layer has been modified to include both suction and injection, and extensive numerical results have been obtained for the injection of air into air. These results indicate that the heat-transfer and skin-friction reductions due to injection can be adequately represented by the standard boundary-layer correlation formula for all but extreme low-density flows. As the Reynolds number decreases, however, mass transfer becomes ineffective in reducing heating rates and skin friction, especially for a very cold wall. The effect of nonzero wall temperature is to increase the shock-layer thickness dramatically, and there are also indications that the wall-temperature level determines whether the asymptotic inviscid-shock-layer thickness is approached from above or below. Une étude des effets du transport de masse superficiel sur la couche de choc hypersonique visqueuse d'un corps arrondi a été faite. La théorie de Cheng de la couche de choc Newtonienne a été modifiée pour inclure à la fois l'aspiration et l'injection, et l'on a obtenu de nombreux résultats numériques pour l'injection d'air dans l'air. Ces résultats indiquent que les diminutions de transport de chaleur et de frottement pariétal dues à l'injection peuvent être représentées d'une façon adéquate par la formule standard de corrélation de la couche limite pour tous les écoulements à basse densité sauf les cas extrêmes. Cependant lorsque le nombre de Reynolds décroît, le transport de masse devient inefficace pour réduire le flux de chaleur et le frottement pariétal, spécialement pour une paroi très froide. L'effet d'une température pariétale non-nulle est d'augmenter considérablement l'épaisseur de la couche de choc; et il semble que la valeur de la température pariétale détermine si l'épaisseur de la couche de choc non visqueuse asymptotique est approchée par au-dessus ou par en-dessous. Für die zähe Hyperschallstossschicht wurden die Einflüsse des Stoffüberganges an der Oberfläche eines stumpfen Körpers untersucht. Die Theorie einer Newtonschen Stossschicht von Cheng wurde modifiziert, um sowohl Absaugung als auch Einblasung zu umfassen. Eine Vielzahl numerischer Ergebnisse wurde für die Einblasung von Luft in Luft erhalten. Diese Ergebnisse zeigen, dass die Abnahme des Wärmeüberganges und der Oberflächenreibung infolge der Einblasung durch die üblichen Grenzschichtkorrelationsgleichungen für alle Fälle angemessen wiedergegeben werden können, mit Ausnahme von Strömungen bei extrem kleiner Dichte. Bei abnehmender Reynolds-Zahl verliert aber der Stofftransport seine Wirkung Aufheizung und Oberflächenreibung herabzusetzen. Das gilt besonders für sehr kalte Wände. Der Einfluss bei Wandtempraturen, die von null verschieden sind, geht dahin die Stossschichtdicke stark zu erhöhen. Es liegen auch Anzeichen vor, dass die Grösse der Wandtemperatur bestimmend dafür ist, ob die Annäherung an die asymptotische nichtzähe Stossschichtdicke von oben oder von unten erfolgt.

The separation of Newtonian shock layers

The separation points which occur in the Newtonian theory of hypersonic flow are treated by locally modifying the shock-layer equations. This approach leads to direct verification of the free-layer theory for separation on certain bodies with discontinuous curvature. Separation points on bodies with continuous curvature have already been treated by matching the upstream shock-layer solution to the downstream free-layer solution. The agreement that is found between these results and those of the present approach provides further confirmation of the free-layer theory.