New Publication: “Rankine–Hugoniot Relations and Magnetic Field Enhancement in Turbulent Shocks” by Michael Gedalin

In fast collisionless shocks, the density and magnetic field increase and the plasma is heated. The compression and heating are ultimately determined by the Rankine–Hugoniot relations connecting the upstream and downstream parameters. The standard Rankine–Hugoniot relations take into account only mean upstream and downstream parameters. Observations at the Earth’s bow shock show that the downstream magnetic field does not always relax to a uniform state, but large amplitude magnetic oscillations persist. Here, these Rankine–Hugoniot relations are extended to such turbulent shocks where the mean downstream magnetic field is accompanied by magnetic fluctuations. It is shown that the turbulent magnetic field pressure may substantially exceed the pressure of the mean field, while the density compression and heating may be only weakly affected. Thus, strong amplification of the rms magnetic field can be achieved at the expense of a modest reduction of plasma heating.

Left: dependence of the density compression N = ρd /ρu on the turbulent magnetic pressure $X=\left\langle {b}^{2}\right\rangle /8\pi {\rho }_{u}{V}_{u}^{2}$. Right: dependence of the normalized downstream ion temperature $T/({m}_{p}{V}_{u}^{2}/2)$ on the turbulent magnetic pressure $X=\left\langle {b}^{2}\right\rangle /8\pi {\rho }_{u}{V}_{u}^{2}$. The range of X in the figure is limited by the condition X < P.

Full Article:
Gedalin, M. (SHARP) (2023). Rankine–Hugoniot Relations and Magnetic Field Enhancement in Turbulent Shocks. The Astrophysical Journal, 958, doi: 10.3847/1538-4357/ad0461

License: CC BY 4.0

New Publication: “Scattering of Superthermal Ions at Shocks: Dependence on Energy” by Michael Gedalin et al.

Diffusive shock acceleration requires the production of backstreaming superthermal ions (injection) as a first step. Such ions can be generated in the process of scattering of ions in the superthermal tail off the shock front. Knowledge of the scattering of high-energy ions is essential for matching conditions of upstream and downstream distributions at the shock transition. Here we analyze the generation of backstreaming ions as a function of their initial energy in a model stationary shock and in a similar rippled shock. Rippling substantially enhances ion reflection and the generation of backstreaming ions for slightly and moderately superthermal energies, and thus is capable of ensuring ion injection into a further diffusive shock acceleration process. For high-energy ions, there is almost no difference in the fraction of backstreaming ions produced and the ion distributions between the planar stationary shock and the rippled shock.

Left column: the distribution of the forward-moving incident ions fu (v, v). Upper middle: the distribution of the ions far downstream of the shock fd (v, v) without rippling. Bottom middle: the distribution of the ions far downstream of the shock fd (v, v) in the rippled shock. Upper right (empty in this case): the distribution of the backstreaming ions fb (v, v) without rippling. Bottom right: the distribution of the backstreaming ions fb (v, v) in the rippled shock. The initial ion distribution is isotropic with vp = 0.5.

Full Article:
Gedalin, M. (SHARP), Ganushkina, N. (SHARP), Pogorelov, N. V., Roytershteyn, V. (2023). Scattering of Superthermal Ions at Shocks: Dependence on Energy. The Astrophysical Journal, 957, doi: 10.3847/1538-4357/ad04dd

License: CC BY 4.0

New Publication: “Jitter Radiation as an Alternative Mechanism for the Nonthermal X-Ray Emission of Cassiopeia A” by Emanuele Greco et al.

Synchrotron radiation from relativistic electrons is usually invoked as responsible for the nonthermal emission observed in supernova remnants. Diffusive shock acceleration is the most popular mechanism to explain the process of particles acceleration and within its framework a crucial role is played by the turbulent magnetic field. However, the standard models commonly used to fit X-ray synchrotron emission do not take into account the effects of turbulence in the shape of the resulting photon spectra. An alternative mechanism that properly includes such effects is the jitter radiation, which provides for an additional power law beyond the classical synchrotron cutoff. We fitted a jitter spectral model to Chandra, NuSTAR, SWIFT/BAT, and INTEGRAL/ISGRI spectra of Cassiopeia A (Cas A) and found that it describes the X-ray soft-to-hard range better than any of the standard cutoff models. The jitter radiation allows us to measure the index of the magnetic turbulence spectrum νB and the minimum scale of the turbulence ${\lambda }_{\min }$ across several regions of Cas A, with best-fit values νB ∼ 2 − 2.4 and ${\lambda }_{\min }\lesssim 100$ km.

Chandra and NuSTAR exposure/vignetting-corrected images of Cas A. Leftmost panel: Chandra/ACIS-S count-rate image in the 0.5–8 keV band with a pixel size of 1” and a square root scale. Other panels: exposure/vignetting-corrected and mosaicked NuSTAR images of Cas A in various energy bands, reported on the images in units of keV, with a square root scale.

Full Article:
Greco, E. (SHARP), Vink, J. (SHARP), Ellien, A. (SHARP) and Ferrigno, C. (2023). Jitter Radiation as an Alternative Mechanism for the Nonthermal X-Ray Emission of Cassiopeia A. The Astrophysical Journal, 956, doi: 10.3847/1538-4357/acf567

License: CC BY 4.0

New Publication: “Non-specular ion reflection at quasiperpendicular collisionless shock front” by Prachi Sharma and Michael Gedalin

The structure of a collisionless shock affects ion motion in the shock front and is affected by the formed ion distribution. In high-Mach-number shocks, a significant fraction of incident ions are reflected by the macroscopic electric and magnetic fields in the shock front. Ions are non-specularly reflected by the combined electric deceleration and magnetic deflection. Here, a first analytical description of the non-specular reflection is presented. The contribution of the increasing magnetic field is evaluated and shown to enhance reflection. The distribution of non-specularly reflected ions ahead of the ramp is calculated and their velocities at the re-entry to the shock are found numerically. Dependence on the angle between the shock normal and the upstream magnetic field vector is illustrated.

Normalized 1-D reduced distribution function f(x,vx) for non-specularly reflected ions only with M=5, s=0.5, β=0.5 and θBn=65∘; (a) A=0.75, (b) A=0.375. Ions which have positive vx, return to the shock and cross it again.

Full Article:
Sharma, P. (SHARP) and Gedalin, M. (SHARP) (2023). Non-specular ion reflection at quasiperpendicular collisionless shock front. Journal of Plasma Physics, 89(5), doi: 10.1017/S002237782300096X

License: CC BY 4.0

New Publication: “Electron heating in shocks: Statistics and comparison” by Michael Gedalin et al.

Supernova remnant (SNR) shocks are the highest Mach number non-relativistic shocks in electron-ion plasmas. These shocks are the most efficient particle accelerators in space. SNR shock parameters are inferred from measurements of electromagnetic radiation from heated and accelerated particles. Temperature of the shock heated electrons is one of the most important parameters in supernova remnant shocks. Knowledge of the downstream electron-to-ion temperature ratio or of the ratio of the downstream electron temperature to the incident ion energy is crucial for understanding physics of the very high-Mach number SNR shocks. Heliospheric shocks have substantially lower Mach numbers than SNR shocks but can be extensively studied in in situ observations with further extrapolation of the findings to higher Mach numbers. Magnetospheric Multiscale mission observations of the Earth bow shock are used to analyze dependence of the electron heating on the shock Mach number. It is found that the ratio of the downstream electron temperature to the incident ion energy decreases with the increase of the Mach number. At high Mach numbers this ratio and stabilizes at about 2.5%. The electron-to-ion temperature ratio stabilizes at about 10%. The peak electron temperature occurs at the overshoot maximum, further downstream electrons cool down. The mean ratio of the 4.5 s averages of the downstream and maximum electron temperatures is 0.85. Electron heating does not follow the thermodynamic adiabatic law. The heating and cooling behavior implies that the energy is provided by the overall cross-shock potential while small-scale electric fields rapidly isotropize the electron distribution.

Examples of two shock crossings included in the selection for the analysis. The shock crossing is zero time. The magnetic field magnitude (black line) is normalized on the maximum magnetic field inside the window of ±1,200 s around the crossing. The electron temperature is normalized on the maximum temperature in the same window

Full Article:
Gedalin, M. (SHARP), Golan, M., Vink, J. (SHARP), Ganushkina, N. (SHARP), & Balikhin, M. (2023). Electron heating in shocks: Statistics and comparison. Journal of Geophysical Research: Space Physics, 128, doi: 10.1029/2023JA0316

License: CC BY-NC-ND 4.0

SHARP Summer School on Collisionless Shocks in Space, August 21-25, 2023

In August, the SHARP consortium organised a summer school on collisionless shocks in space in Levi, Finland. In total 23 students from more than 10 different countries attended the school. The lectures covered all research areas of the SHARP project, including basic theory on collisionless shocks, heliospheric shocks and astrophysical shocks. The students also attended exercise sessions where they learned about data analysis of shocks and the computation of basic shock parameters.

The program of the summer school can be found here.

SHARP summer school participants

New Publication: “Non-locality of ion reflection at the shock front: Dependence on the shock angle” by Michael Gedalin

In typical heliospheric collisionless shocks most of the mass, momentum and energy are carried by ions. Therefore, the shock structure should be most affected by ions. With the increase of the Mach number, ion reflection becomes more and more important, and reflected ions participate in shaping the shock profile. Ion reflection at the collisionless shock is a non-local process: the reflected–transmitted ions re-enter the shock front far from the reflection point. The direction and the magnitude of this shift depend on the shock angle. The distance between the reflection point and the re-entry point is of the order of the upstream ion convective gyroradius and exceeds the shock width. The non-locality of ion reflection may have implications for shock rippling since reflected ions may carry perturbations along the shock front.

Two-dimensional cuts of the ion distribution at the red line position for θBn=75∘. (a) The reduced two-dimensional distribution function f(vx,vy,x=0). (b) The reduced two-dimensional distribution function f(vx,vz,x=0)

Full Article:
Gedalin, M. (SHARP) (2023). Non-locality of ion reflection at the shock front: Dependence on the shock angle. Journal of Plasma Physics, 89(4), doi: 10.1017/S0022377823000831

License: CC BY 4.0

New Publication: “Effect of the reflected ions on the magnetic overshoot of a collisionless shock” by Michael Gedalin and Prachi Sharma

A collisionless shock transfer of mass, momentum, and energy occurs from upstream to downstream. Most of the momentum and energy fluxes are carried by ions so the shock structure is affected mainly by ions. With the increase in the Mach number, the fraction of reflected ions increases and their influence on the shock structure becomes progressively more important. Here, we study the effect of the reflected ions on the overshoot strength. It is shown that directly transmitted ions are responsible for the overshoot formation and the interaction of the overshoot field with these ions alone might result in an unstable growth of the overshoot. On the contrary, reflected ions, at their second crossing of the shock, are accelerated along the shock normal and, thus, provide a stabilizing effect on the overshoot.

The reduced distribution function f(x,vx) (normalized on the maximum value, linear scale), for the shock crossing measured by MMS1.

Full Article:
Gedalin, M. (SHARP), Sharma, P. (SHARP) (2023). Effect of the reflected ions on the magnetic overshoot of a collisionless shock. Physics of Plasmas, 30 (7), doi: 10.1063/5.0154840

License: CC BY 4.0

New Publication: “Evidence for Thermal X-Ray Emission from the Synchrotron-dominated Shocks in Tycho’s Supernova Remnant” by Amaël Ellien et al.

Young supernova remnant (SNR) shocks are believed to be the main sites of galactic cosmic-ray production, showing X-ray synchrotron-dominated spectra in the vicinity of their shock. While a faint thermal signature left by the shocked interstellar medium (ISM) should also be found in the spectra, proofs for such an emission in Tycho’s SNR have been lacking. We perform an extended statistical analysis of the X-ray spectra of five regions behind the blast wave of Tycho’s SNR using Chandra archival data. We use Bayesian inference to perform extended parameter space exploration and sample the posterior distributions of a variety of models of interest. According to Bayes factors, spectra of all five regions of analysis are best described by composite three-component models taking nonthermal emission, ejecta emission, and shocked ISM emission into account. The shocked ISM stands out the most in the northern limb of the SNR. We performed an extended analysis of the northern limb and show that the measured synchrotron cutoff energy is not well constrained in the presence of a shocked ISM component. Such results cannot currently be further investigated by analyzing emission lines in the 0.5–1 keV range, because of the low Chandra spectral resolution in this band. We show with simulated spectra that Athena X-ray Integral Field Unit future performances will be crucial to address this point.

Left: broadband Chandra image of Tycho’s SNR. Right: schematic view of Tycho’s SNR. The five black boxes are the regions over which our shock spectra were extracted and analyzed. The contours are drawn from the contrast image computed from the normalized 1.7–1.95 keV and 4.0–6.0 keV images. Note that the contrast image has been smoothed with a 1σ Gaussian kernel before drawing the contours.

Full Article:
Ellien, A. (SHARP), Greco, E. (SHARP) and Vink, J. (SHARP) (2023). Evidence for Thermal X-Ray Emission from the Synchrotron-dominated Shocks in Tycho’s Supernova Remnant. The Astrophysical Journal, 951, doi: 10.3847/1538-4357/accc85

License: CC BY 4.0

New Publication: “Scattering of Ions at a Rippled Shock” by Michael Gedalin et al.

In a collisionless shock the energy of the directed flow is converted to heating and acceleration of charged particles, and to magnetic compression. In low-Mach number shocks the downstream ion distribution is made of directly transmitted ions. In higher-Mach number shocks ion reflection is important. With the increase of the Mach number, rippling develops, which is expected to affect ion dynamics. Using ion tracing in a model shock front, downstream distributions of ions are analyzed and compared for a planar stationary shock with an overshoot and a similar shock with ripples propagating along the shock front. It is shown that rippling results in the distributions, which are substantially broader and more diffuse in the phase space. Gyrotropization is sped up. Rippling is able to generate backstreaming ions, which are absent in the planar stationary case.

The two-dimensional surface of the magnetic field magnitude for the rippled shock. Y is in the direction or rippling propagation. The global shock normal is along x. The local shock normal is determined by the steepest gradient of the magnetic field magnitude, depends on Y, and differs from the global normal. The maximum overshoot magnetic field also depends on Y.

Full Article:
Gedalin, M. (SHARP), Pogorelov, N. V. and Roytershteyn, V. (2023). Scattering of Ions at a Rippled Shock. The Astrophysical Journal, 951, doi: 10.3847/1538-4357/acd63c

License: CC BY 4.0