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1. Investigating Particle Acceleration by Dynamic Small-scale Flux Ropes behind Interplanetary Shocks in the Inner Heliosphere

   https://doi.org/10.3847/1538-4357/ac6d5e  

   Van Eck, Keaton ; le Roux, Jakobus ; Chen, Yu ; Zhao, Ling Ling ; Thompson, Noah ( July 2022 , The Astrophysical Journal)

   We recently extended our Parker-type transport equation for energetic particle interaction with numerous dynamic small-scale magnetic flux ropes (SMFRs) to include perpendicular diffusion in addition to parallel diffusion. We present a new analytical solution to this equation assuming heliocentric spherical geometry with spherical symmetry for all SMFR acceleration mechanisms present in the transport theory. With the goal of identifying the dominant mechanism(s) through which particles are accelerated by SMFRs, a search was launched to identify events behind interplanetary shocks that could be explained by our new solution and not classical diffusive shock acceleration. Two new SMFR acceleration events were identified in situ for the first time within heliocentric distances of 1 astronomical unit (au) in Helios A data. A Metropolis–Hastings algorithm is employed to fit the new solution to the energetic proton fluxes so that the relative strength of the transport coefficients associated with each SMFR acceleration mechanism can be determined. We conclude that the second-order Fermi mechanism for particle acceleration by SMFRs is more important than first-order Fermi acceleration due to the mean compression of the SMFRs regions during these new events. Furthermore, with the aid of SMFR parameters determined via the Grad–Shafranov reconstruction method, we find thatmore »second-order Fermi SMFR acceleration is dominated by the turbulent motional electric field parallel to the guide/background field. Finally, successful reproduction of energetic proton flux data during these SMFR acceleration events also required efficient particle escape from the SMFR acceleration regions.

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2. Cosmic ray protons and electrons from supernova remnants

   https://doi.org/10.1051/0004-6361/202140448  

   Cristofari, P. ; Blasi, P. ; Caprioli, D. ( June 2021 , Astronomy & Astrophysics)

   Context. The spectrum of cosmic ray protons and electrons released by supernova remnants throughout their evolution is poorly known because of the difficulty in accounting for particle escape and confinement downstream of a shock front, where both adiabatic and radiative losses are present. Since electrons lose energy mainly through synchrotron losses, it is natural to ask whether the spectrum released into the interstellar medium may be different from that of their hadronic counterpart. Independent studies of cosmic ray transport through the Galaxy require that the source spectrum of electrons and protons be very different. Therefore, the above question acquires a phenomenological relevance. Aims. Here we calculate the spectrum of cosmic ray protons released during the evolution of supernovae of different types, accounting for the escape from the upstream region and for adiabatic losses of particles advected downstream of the shock and liberated at later times. The same calculation is carried out for electrons, where in addition to adiabatic losses we take the radiative losses suffered behind the shock into account. These electrons are dominated by synchrotron losses in the magnetic field, which most likely is self-generated by cosmic rays accelerated at the shock. Methods. We use standard temporal evolution relationsmore »for supernova shocks expanding in different types of interstellar media together with an analytic description of particle acceleration and magnetic field amplification to determine the density and spectrum of cosmic ray particles. Their evolution in time is derived by numerically solving the equation describing advection with adiabatic and radiative losses for electrons and protons. The flux from particles continuously escaping the supernova remnants is also accounted for. Results. The magnetic field in the post-shock region is calculated by using an analytic treatment of the magnetic field amplification due to nonresonant and resonant streaming instability and their saturation. The resulting field is compared with the available set of observational results concerning the dependence of the magnetic field strength upon shock velocity. We find that when the field is the result of the growth of the cosmic-ray-driven nonresonant instability alone, the spectrum of electrons and protons released by a supernova remnant are indeed different; however, such a difference becomes appreciable only at energies ≳100−1000 GeV, while observations of the electron spectrum require such a difference to be present at energies as low as ∼10 GeV. An effect at such low energies requires substantial magnetic field amplification in the late stages of supernova remnant evolution (shock velocity ≪1000 km s −1 ); this may not be due to streaming instability but rather hydrodynamical processes. We comment on the feasibility of such conditions and speculate on the possibility that the difference in spectral shape between electrons and protons may reflect either some unknown acceleration effect or additional energy losses in cocoons around the sources.« less
3. Simulation of the Solar Energetic Particle Event on 2020 May 29 Observed by Parker Solar Probe

   https://doi.org/10.3847/1538-4357/acac21  

   Cheng, Lei ; Zhang, Ming ; Lario, David ; Balmaceda, Laura A. ; Kwon, Ryun Young ; Cohen, Christina ( February 2023 , The Astrophysical Journal)

   This paper presents a stochastic three-dimensional focused transport simulation of solar energetic particles (SEPs) produced by a data-driven coronal mass ejection (CME) shock propagating through a data-driven model of coronal and heliospheric magnetic fields. The injection of SEPs at the CME shock is treated using diffusive shock acceleration of post-shock suprathermal solar wind ions. A time-backward stochastic simulation is employed to solve the transport equation to obtain the SEP time–intensity profile at any location, energy, and pitch angle. The model is applied to a SEP event on 2020 May 29, observed by STEREO-A close to ∼1 au and by Parker Solar Probe (PSP) when it was about 0.33 au away from the Sun. The SEP event was associated with a very slow CME with a plane-of-sky speed of 337 km s⁻¹at a height below 6R_Sas reported in the SOHO/LASCO CME catalog. We compute the time profiles of particle flux at PSP and STEREO-A locations, and estimate both the spectral index of the proton energy spectrum for energies between ∼2 and 16 MeV and the equivalent path length of the magnetic field lines experienced by the first arriving SEPs. We find that the simulation results are well correlated with observations.more »The SEP event could be explained by the acceleration of particles by a weak CME shock in the low solar corona that is not magnetically connected to the observers.

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4. Interaction between Multiple Current Sheets and a Shock Wave: 2D Hybrid Kinetic Simulations

   https://doi.org/10.3847/1538-4357/ac2e06  

   Nakanotani, M. ; Zank, G. P. ; Zhao, L.-L. ( December 2021 , The Astrophysical Journal)

   Abstract Particle acceleration behind a shock wave due to interactions between magnetic islands in the heliosphere has attracted attention in recent years. The downstream acceleration may yield a continuous increase of particle flux downstream of the shock wave. Although it is not obvious how the downstream magnetic islands are produced, it has been suggested that current sheets are involved in the generation of magnetic islands due to their interaction with a shock wave. We perform 2D hybrid kinetic simulations to investigate the interaction between multiple current sheets and a shock wave. In the simulation, current sheets are compressed by the shock wave and a tearing instability develops at the compressed current sheets downstream of the shock. As the result of this instability, the electromagnetic fields become turbulent and magnetic islands form well downstream of the shock wave. We find a “post-cursor” region in which the downstream flow speed normal to the shock wave in the downstream rest frame is decelerated to ∼ 1 V A immediately behind the shock wave, where V A is the upstream Alfvén speed. The flow speed then gradually decelerates to 0 accompanied by the development of the tearing instability. We also observe an efficient productionmore »of energetic particles above 100 E 0 during the development of the instability some distance downstream of the shock wave, where E 0 = m p V A 2 and m p is the proton mass. This feature corresponds to Voyager observations showing that the anomalous cosmic-ray intensity increase begins some distance downstream of the heliospheric termination shock.« less
5. Stochastic re-acceleration and magnetic-field damping in Tycho ’s supernova remnant

   https://doi.org/10.1051/0004-6361/201936079  

   Wilhelm, A. ; Telezhinsky, I. ; Dwarkadas, V. V. ; Pohl, M. ( July 2020 , Astronomy & Astrophysics)

   Context.   Tycho ’s supernova remnant (SNR) is associated with the historical supernova (SN) event SN 1572 of Type Ia. The explosion occurred in a relatively clean environment, and was visually observed, providing an age estimate. This SNR therefore represents an ideal astrophysical test-bed for the study of cosmic-ray acceleration and related phenomena. A number of studies suggest that shock acceleration with particle feedback and very efficient magnetic-field amplification combined with Alfvénic drift are needed to explain the rather soft radio spectrum and the narrow rims observed in X-rays. Aims. We show that the broadband spectrum of Tycho ’s SNR can alternatively be well explained when accounting for stochastic acceleration as a secondary process. The re-acceleration of particles in the turbulent region immediately downstream of the shock should be efficient enough to impact particle spectra over several decades in energy. The so-called Alfvénic drift and particle feedback on the shock structure are not required in this scenario. Additionally, we investigate whether synchrotron losses or magnetic-field damping play a more profound role in the formation of the non-thermal filaments. Methods. We solved the full particle transport equation in test-particle mode using hydrodynamic simulations of the SNR plasma flow. The background magneticmore »field was either computed from the induction equation or follows analytic profiles, depending on the model considered. Fast-mode waves in the downstream region provide the diffusion of particles in momentum space. Results. We show that the broadband spectrum of Tycho can be well explained if magnetic-field damping and stochastic re-acceleration of particles are taken into account. Although not as efficient as standard diffusive shock acceleration, stochastic acceleration leaves its imprint on the particle spectra, which is especially notable in the emission at radio wavelengths. We find a lower limit for the post-shock magnetic-field strength ∼330  μ G, implying efficient amplification even for the magnetic-field damping scenario. Magnetic-field damping is necessary for the formation of the filaments in the radio range, while the X-ray filaments are shaped by both the synchrotron losses and magnetic-field damping.« less