arXiv subjects

A. P. Rouillard

Publications and source records attributed to A. P. Rouillard.

At least 19 recordsLinked to original sources

arXiv2026

Catalogue and statistics of greater than 100 MeV solar proton events during solar cycles 23-25 from SOHO-ERNE observations

The SPEARHEAD (specification, analysis, and re-calibration of high-energy particle data) project, funded by the European Union Horizon Europe programme, enhances the accuracy and usability of high-energy particle measurements. It investigates particle acceleration, release, and transport during solar eruptions by refining instrument response functions and cross-calibrating datasets. We present a comprehensive catalogue of greater than 100 MeV proton events identified from May 1996 to August 2024 using SOHO-ERNE penetrating-particle rates, together with associated solar phenomena derived from multi-instrument observations. The SEP events were detected through a systematic scan of ERNE-HED counter data and cross-calibrated with SOHO-EPHIN to derive peak fluxes and fluences. Each event was associated with its likely parent eruption using X-ray (XR) (GOES-XRS, RHESSI, SolO-STIX), radio (Wind-WAVES, STEREO-WAVES, ground-based observatories), and gamma-ray (Fermi-LAT) observations, CMEs (SOHO-LASCO), and ground-level enhancements (GLEs) (neutron monitors). Timings and physical properties were systematically compared to investigate the relationships between SEP onset, flare evolution, CME kinematics, and radio signatures. Statistical analyses reveal that most SEP releases closely follow flare and CME onsets, with moderate SEP-XR-CME correlations, and a strong SEP-GLE fluence link. These results indicate that high-energy SEP events are typically associated with strong solar activity signatures, with the observed intensities and timings strongly modulated by magnetic connectivity and coronal conditions. This catalogue provides the most extensive reference to date for high-energy SEP events over solar cycles 23-25, establishing a unified framework for future investigations of extreme particle acceleration.

astro-ph.SR↗

arXiv2025

CoSEE-Cat: A Comprehensive Solar Energetic Electron event Catalogue obtained from combined in situ and remote-sensing observations from Solar Orbiter -- Catalogue description and first statistical results

(abridged) The acceleration of particles at the Sun and their propagation through interplanetary space are key topics in heliophysics. Specifically, solar energetic electrons (SEEs) measured in situ can be linked to solar flares and coronal mass ejections (CMEs), which can be observed remotely in radio, optical, UV and X-rays. Solar Orbiter, equipped with a wide range of remote-sensing and in situ detectors, provides an excellent opportunity to investigate SEEs and their solar origin from the inner heliosphere. The Comprehensive Solar Energetic Electron event Catalogue (CoSEE-Cat) provides details for all SEE events measured in situ by Solar Orbiter, as well as associated flares, CMEs, and radio bursts. The catalogue contains key parameters of the SEEs, as derived from the Energetic Particle Detector (EPD), complemented with basic parameters of associated X-ray flares provided by STIX, information on eruptive phenomena seen by EUI, characteristics of type III radio bursts observed by RPW, and indications of CME observed by Metis and SoloHI. The conditions in interplanetary space were characterised using SWA and MAG measurements. Finally, data-driven modelling with the Magnetic Connectivity Tool provided an independent estimate of the solar source position of the SEEs. The first data release contains 303 SEE events observed from November 2020 until the end of 2022. In this paper, we describe the catalogue and provide a first statistical analysis. Preliminary results support the flare-related origin of events with an impulsive ion composition and the association of gradual events with extended structures such as CME-driven shocks or erupting flux ropes. We also show that the commonly observed delays of the solar release times of the SEEs relative to the associated X-ray flares and type III radio bursts are at least partially due to propagation effects.

astro-ph.SR↗

arXiv2025

The high-energy protons of the ground level enhancement (GLE74) event on 11 May 2024

High energy solar protons were observed by particle detectors aboard spacecraft in near-Earth orbit on May 11, 2024 and produced the 74th ground level enhancement (GLE74) event registered by ground-based neutron monitors. This study involves a detailed reconstruction of the neutron monitor response, along with the identification of the solar eruption responsible for the emission of the primary particles, utilizing both in situ and remote-sensing. Observations spanning proton energies from a few MeV to around 1.64 GeV, collected from the Solar and Heliospheric Observatory (SOHO), the Geostationary Operational Environmental Satellite (GOES), the Solar Terrestrial Relations Observatory (STEREO-A), and neutron monitors, were integrated with records of the associated solar soft X-ray flare, coronal mass ejection, and radio bursts, to identify the solar origin of the GLE74. Additionally, a time-shift analysis was conducted to link the detected particles to their solar sources. Finally, a comparison of GLE74 to previous ones is carried out. GLE74 reached a maximum particle rigidity of at least 2.4 GV and was associated with a series of type III, type II, and type IV radio bursts. The release time of the primary solar energetic particles (SEPs) with an energy of 500 MeV was estimated to be around 01:21 UT. A significant SEP flux was observed from the anti-Sun direction with a relatively broad angular distribution, rather than a narrow, beam-like pattern, particularly during the main phase at the particle peak flux. Comparisons with previous GLEs suggest that GLE74 was a typical event in terms of solar eruption dynamics.

astro-ph.SR↗

arXiv2025

Generalized Two Thermal Regimes Approach : Bipoly Fluid Modeling

The isopoly bi-fluid approach assumes an isothermal evolution of the solar wind near the Sun up to the radial distance riso, followed by a polytropic evolution constrained by the observed polytropic indices. This approach provides a more accurate model of the interplanetary properties of the solar wind (u, n, Tp, Te) and their radial evolution (Dakeyo et al. 2022, 2024). In this article, we present an improvement of the isopoly approach by considering a generalized two thermal regime approach, embedding two distinct polytropic evolutions, the "bipoly" modeling. To demonstrate the capability of the approach, the models are fitted to both interplanetary and coronal observations, all classified by wind speed population in the spirit of Maksimovic et al. (2020). The set of observations used as constraints are coronal temperatures inferred from charge-state ratio observations from Solar Orbiter, and interplanetary measurements from Helios and Parker Solar Probe. The relaxation of the isothermal criteria in the near-Sun region permits to significantly improve the fast wind acceleration for low coronal temperature conditions. In summary, the new model matches closely the observational constraints: the coronal temperature and the radial evolution of the wind properties (u, n, Tp, Te) in the interplanetary medium, and this for all the wind speed populations.

astro-ph.SR↗

arXiv2024

Testing the flux tube expansion factor -- solar wind speed relation with Solar Orbiter data

The properties of the solar wind measured in-situ in the heliosphere are largely controlled by energy deposition in the solar. Previous studies have shown that long duration and large scale magnetic structures show an inverse relation between the solar wind velocity measured in situ near 1 au and the expansion factor of the magnetic flux tubes in the solar atmosphere. We exploit Solar Orbiter data in conjunction with the Potential Field Source Surface (PFSS) coronal model, and the solar wind trajectory to evaluate the flux expansion factor - speed relation at the solar "source surface" at rss. We find a statistically weak anti-correlation between the in-situ bulk velocity and the coronal expansion factor, for about 1.5 years of solar data. Classification of the data by source latitude reveals different levels of anticorrelation. We show the existence of fast solar wind that originates in strong magnetic field regions at low latitudes and undergoes large expansion factor. We provide evidence that such winds become supersonic during the super radial expansion (below rss), and are theoretically governed by a positive correlation v-f. We find that faster winds on average have a flux tube expansion at a larger radius than slower winds. An anticorrelation between solar wind speed and expansion factor is present for solar winds originating in high latitude structures in solar minimum activity, typically associated with coronal hole-like structures, but this cannot be generalized to lower latitude sources. Therefore, the value of the expansion factor alone cannot be used to predict the solar wind speed. Other parameters, such as the height at which the expansion gradient is the strongest must also be taken into account.

astro-ph.SR↗

arXiv2024

The multi-spacecraft high-energy solar particle event of 28 October 2021

Aims. We studied the first multi-spacecraft high-energy solar energetic particle (SEP) event of solar cycle 25, which triggered a ground level enhancement (GLE) on 28 October 2021, using data from multiple observers that were widely distributed throughout the heliosphere. Methods. We performed detail modelling of the shock wave and investigated the magnetic connectivity of each observer to the solar surface and examined the shock magnetic connection. We performed 3D SEP propagation simulations to investigate the role of particle transport in the distribution of SEPs to distant magnetically connected observers. Results. Observations and modelling show that a strong shock wave formed promptly in the low corona. At the SEP release time windows, we find a connection with the shock for all the observers. PSP, STA, and Solar Orbiter were connected to strong shock regions with high Mach numbers, whereas the Earth and other observers were connected to lower Mach numbers. The SEP spectral properties near Earth demonstrate two power laws, with a harder (softer) spectrum in the low-energy (high-energy) range. Composition observations from SIS (and near-Earth instruments) show no serious enhancement of flare-accelerated material. Conclusions. A possible scenario consistent with the observations and our analysis indicates that high-energy SEPs at PSP, STA, and Solar Orbiter were dominated by particle acceleration and injection by the shock, whereas high-energy SEPs that reached near-Earth space were associated with a weaker shock; it is likely that efficient transport of particles from a wide injection source contributed to the observed high-energy SEPs. Our study cannot exclude a contribution from a flare-related process; however, composition observations show no evidence of an impulsive composition of suprathermals during the event, suggestive of a non-dominant flare-related process.

astro-ph.SR↗

arXiv2023

Parker Solar Probe: Four Years of Discoveries at Solar Cycle Minimum

Launched on 12 Aug. 2018, NASA's Parker Solar Probe had completed 13 of its scheduled 24 orbits around the Sun by Nov. 2022. The mission's primary science goal is to determine the structure and dynamics of the Sun's coronal magnetic field, understand how the solar corona and wind are heated and accelerated, and determine what processes accelerate energetic particles. Parker Solar Probe returned a treasure trove of science data that far exceeded quality, significance, and quantity expectations, leading to a significant number of discoveries reported in nearly 700 peer-reviewed publications. The first four years of the 7-year primary mission duration have been mostly during solar minimum conditions with few major solar events. Starting with orbit 8 (i.e., 28 Apr. 2021), Parker flew through the magnetically dominated corona, i.e., sub-Alfvénic solar wind, which is one of the mission's primary objectives. In this paper, we present an overview of the scientific advances made mainly during the first four years of the Parker Solar Probe mission, which go well beyond the three science objectives that are: (1) Trace the flow of energy that heats and accelerates the solar corona and solar wind; (2) Determine the structure and dynamics of the plasma and magnetic fields at the sources of the solar wind; and (3) Explore mechanisms that accelerate and transport energetic particles.

astro-ph.SR↗

arXiv2022

The First Ground Level Enhancement of Solar Cycle 25 on 28 October 2021

Aims. The first relativistic solar proton event of solar cycle 25 (SC25) was detected on 28 October 2021 by neutron monitors (NMs) on the ground and particle detectors onboard spacecraft in the near-Earth space. This is the first ground level enhancement (GLE) of the current cycle. A detailed reconstruction of the NM response together with the identification of the solar eruption that generated these particles is investigated based on in-situ and remote-sensing measurements. Methods. In-situ proton observations from a few MeV to $\sim$500 MeV were combined with the detection of a solar flare in soft X-rays (SXRs), a coronal mass ejection (CME), radio bursts and extreme ultraviolet (EUV) observations to identify the solar origin of the GLE. Timing analysis was performed and a relation to the solar sources was outlined. Results. GLE73 reached a maximum particle rigidity of $\sim$2.4 GV and is associated with type III, type II, type IV radio bursts and an EUV wave. A diversity of time profiles recorded by NMs was observed. This points to an anisotropic nature of the event. The peak flux at E$>$10 MeV was only $\sim$30 pfu and remained at this level for several days. The release time of $\geq$1 GV particles was found to be $\sim$15:40 UT. GLE73 had a moderately hard rigidity spectrum at very high energies ($γ$ $\sim$5.5). Comparison of GLE73 to previous GLEs with similar solar drivers is performed

astro-ph.SR↗

arXiv2021

Flux ropes and dynamics of the heliospheric current sheet

Context. Solar Orbiter and PSP jointly observed the solar wind for the first time in June 2020, capturing data from very different solar wind streams, calm and Alfvénic wind as well as many dynamic structures. Aims. The aim here is to understand the origin and characteristics of the highly dynamic solar wind observed by the two probes, in particular in the vicinity of the heliospheric current sheet (HCS). Methods. We analyse the plasma data obtained by PSP and Solar Orbiter in situ during the month of June 2020. We use the Alfvén-wave turbulence MHD solar wind model WindPredict-AW, and perform two 3D simulations based on ADAPT solar magnetograms for this period. Results. We show that the dynamic regions measured by both spacecraft are pervaded with flux ropes close to the HCS. These flux ropes are also present in the simulations, forming at the tip of helmet streamers, i.e. at the base of the heliospheric current sheet. The formation mechanism involves a pressure driven instability followed by a fast tearing reconnection process, consistent with the picture of Réville et al. (2020a). We further characterize the 3D spatial structure of helmet streamer born flux ropes, which seems, in the simulations, to be related to the network of quasi-separatrices.

astro-ph.SR↗

arXiv2021

Magnetic reconnection as a mechanism to produce multiple protonpopulations and beams locally in the solar wind

Context. Spacecraft observations early revealed frequent multiple proton populations in the solar wind. Decades of research on their origin have focused on processes such as magnetic reconnection in the low corona and wave-particle interactions in the corona and locally in the solar wind.Aims.This study aims to highlight that multiple proton populations and beams are also produced by magnetic reconnection occurring locally in the solar wind. Methods. We use high resolution Solar Orbiter proton velocity distribution function measurements, complemented by electron and magnetic field data, to analyze the association of multiple proton populations and beams with magnetic reconnection during a period of slow Alfvénic solar wind on 16 July 2020. Results. At least 6 reconnecting current sheets with associated multiple proton populations and beams, including a case of magnetic reconnection at a switchback boundary, are found during this day. This represents 2% of the measured distribution functions. We discuss how this proportion may be underestimated, and how it may depend on solar wind type and distance from the Sun. Conclusions. Although suggesting a likely small contribution, but which remains to be quantitatively assessed, Solar Orbiter observations show that magnetic reconnection must be considered as one of the mechanisms that produce multiple proton populations and beams locally in the solar wind.

astro-ph.SR↗

arXiv2021

Solar wind rotation rate and shear at coronal hole boundaries, possible consequences for magnetic field inversions

In-situ measurements by several spacecraft have revealed that the solar wind is frequently perturbed by transient structures (magnetic folds, jets, waves, flux-ropes) that propagate rapidly away from the Sun over large distances. Parker Solar Probe has detected frequent rotations of the magnetic field vector at small heliocentric distances, accompanied by surprisingly large solar wind rotation rates. The physical origin of such magnetic field bends, the conditions for their survival across the interplanetary space, and their relation to solar wind rotation are yet to be clearly understood. We traced measured solar wind flows from the spacecraft position down to the surface of the Sun to identify their potential source regions and used a global MHD model of the corona and solar wind to relate them to the rotational state of the low solar corona. We identified regions of the solar corona for which solar wind speed and rotational shear are important and long-lived, that can be favourable to the development of magnetic deflections and to their propagation across extended heights in the solar wind. We show that coronal rotation is highly structured and that enhanced flow shear develops near the boundaries between coronal holes and streamers, around and above pseudo-streamers, even when such boundaries are aligned with the direction of solar rotation. A large fraction of the switchbacks identified by PSP map back to these regions, both in terms of instantaneous magnetic field connectivity and of the trajectories of wind streams that reach the spacecraft. These regions of strong shears are likely to leave an imprint on the solar wind over large distances and to increase the transverse speed variability in the slow solar wind. The simulations and connectivity analysis suggest they can be a source of the switchbacks and spikes observed by Parker Solar Probe.

astro-ph.SR↗

arXiv2021

Solar wind current sheets and deHoffmann-Teller analysis: First results of DC electric field measurements by Solar Orbiter

Solar Orbiter was launched on February 10, 2020 with the purpose of investigating solar and heliospheric physics using a payload of instruments designed for both remote and in-situ sensing. Similar to the recently launched Parker Solar Probe, and unlike earlier missions, Solar Orbiter carries instruments designed to measure the low frequency DC electric fields. In this paper we assess the quality of the low-frequency DC electric field measured by the Radio and Plasma Waves instrument (RPW) on Solar Orbiter. In particular we investigate the possibility of using Solar Orbiter's DC electric and magnetic field data to estimate the solar wind speed. We use deHoffmann-Teller (HT) analysis based on measurements of the electric and magnetic fields to find the velocity of solar wind current sheets which minimizes a single component of the electric field. By comparing the HT velocity to proton velocity measured by the Proton and Alpha particle Sensor (PAS) we develop a simple model for the effective antenna length, $L_\text{eff}$ of the E-field probes. We then use the HT method to estimate the speed of the solar wind. Using the HT method, we find that the observed variations in $E_y$ are often in excellent agreement with the variations in the magnetic field. The magnitude of $E_y$, however, is uncertain due to the fact that the $L_\text{eff}$ depends on the plasma environment. We derive an empirical model relating $L_\text{eff}$ to the Debye length, which we can use to improve the estimate of $E_y$ and consequently the estimated solar wind speed. The low frequency electric field provided by RPW is of high quality. Using deHoffmann-Teller analysis, Solar Orbiter's magnetic and electric field measurements can be used to estimate the solar wind speed when plasma data is unavailable.

physics.space-ph↗

arXiv2020

CMEs in the Heliosphere: III. A Statistical Analysis of the Kinematic Properties Derived from Stereoscopic Geometrical Modelling Techniques Applied to CMEs Detected in the Heliosphere from 2008 to 2014 by STEREO/HI-1

We present an analysis of coronal mass ejections (CMEs) observed by the Heliospheric Imagers (HIs) on board NASA's Solar Terrestrial Relations Observatory (STEREO) spacecraft. Between August 2008 and April 2014 we identify 273 CMEs that are observed simultaneously, by the HIs on both spacecraft. For each CME, we track the observed leading edge, as a function of time, from both vantage points, and apply the Stereoscopic Self-Similar Expansion (SSSE) technique to infer their propagation throughout the inner heliosphere. The technique is unable to accurately locate CMEs when their observed leading edge passes between the spacecraft, however, we are able to successfully apply the technique to 151, most of which occur once the spacecraft separation angle exceeds 180 degrees, during solar maximum. We find that using a small half-width to fit the CME can result in observed acceleration to unphysically high velocities and that using a larger half-width can fail to accurately locate the CMEs close to the Sun because the method does not account for CME over-expansion in this region. Observed velocities from SSSE are found to agree well with single-spacecraft (SSEF) analysis techniques applied to the same events. CME propagation directions derived from SSSE and SSEF analysis agree poorly because of known limitations present in the latter. This work was carried out as part of the EU FP7 HELCATS (Heliospheric Cataloguing, Analysis and Techniques Service) project (http://www.helcats-fp7.eu/).

astro-ph.SR↗

arXiv2019

CME -Associated Energetic Ions at 0.23 AU -- Consideration of the Auroral Pressure Cooker Mechanism Operating in the Low Corona as a Possible Energization Process

We draw a comparison between a solar energetic particle event associated with the release of a slow coronal mass ejection close to the sun, and the energetic particle population produced in high current density field-aligned current structures associated with auroral phenomena in planetary magnetospheres. We suggest that this process is common in CME development and lift-off in the corona, and may account for the electron populations that generate Type III radio bursts, as well as for the prompt energetic ion and electron populations typically observed in interplanetary space.

physics.space-ph↗

arXiv2018

Modelling of proton acceleration in application to a ground level enhancement

The source of high-energy protons (>500 MeV) responsible for the so-called ground level enhancements (GLEs) remains an open question in solar physics. One of the candidates is a shock wave driven by a coronal mass ejection, which is thought to accelerate particles via diffusive-shock acceleration. We perform physics-based simulations of proton acceleration using information on the shock and ambient plasma parameters derived from the observation of a real GLE event. We analyse the simulation results with the aim to find out which of the parameters are significant in controlling the acceleration efficiency and to get a better understanding of the conditions under which the shock can produce relativistic protons. We use results of the recently developed technique to determine the shock and ambient plasma parameters, applied to the 17 May 2012 GLE event, and carry out proton acceleration simulations with the Coronal Shock Acceleration model. We have performed proton acceleration simulations for nine individual magnetic field lines characterised by various plasma conditions. Analysis of the simulation results shows that the acceleration efficiency of the shock, i.e., its ability to accelerate particles to high energies, tends to be higher for those shock portions that are characterised by larger values of the scattering-centre compression ratio and/or the fast-mode Mach number. At the same time, the acceleration efficiency can be strengthened due to enhanced plasma density in the flux tube. Analysis of the delays between the flare onset and the production times of protons of 1 GV rigidity for different field lines in our simulations, and a subsequent comparison of those with the observed values indicate a possibility that quasi-perpendicular portions of the shock play the main role in producing relativistic protons.

astro-ph.SR↗

arXiv2018

CMEs in the Heliosphere: I. A Statistical Analysis of the Observational Properties of CMEs Detected in the Heliosphere from 2007 to 2017 by STEREO/HI-1

We present a statistical analysis of coronal mass ejections (CMEs) imaged by the Heliospheric Imager (HI) instruments aboard NASAs twin-spacecraft STEREO mission between April 2007 and August 2017 for STEREO-A and between April 2007 and September 2014 for STEREO-B. The analysis exploits a catalogue that was generated within the FP7 HELCATS project. Here, we focus on the observational characteristics of CMEs imaged in the heliosphere by the inner (HI-1) cameras. More specifically, in this paper we present distributions of the basic observational parameters - namely occurrence frequency, central position angle (PA) and PA span - derived from nearly 2000 detections of CMEs in the heliosphere by HI-1 on STEREO-A or STEREO-B from the minimum between Solar Cycles 23 and 24 to the maximum of Cycle 24; STEREO-A analysis includes a further 158 CME detections from the descending phase of Cycle 24, by which time communication with STEREO-B had been lost. We compare heliospheric CME characteristics with properties of CMEs observed at coronal altitudes, and with sunspot number. As expected, heliospheric CME rates correlate with sunspot number, and are not inconsistent with coronal rates once instrumental factors/differences in cataloguing philosophy are considered. As well as being more abundant, heliospheric CMEs, like their coronal counterparts, tend to be wider during solar maximum. Our results confirm previous coronagraph analyses suggesting that CME launch sites don't simply migrate to higher latitudes with increasing solar activity. At solar minimum, CMEs tend to be launched from equatorial latitudes while, at maximum, CMEs appear to be launched over a much wider latitude range; this has implications for understanding the CME/solar source association. Our analysis provides some supporting evidence for the systematic dragging of CMEs to lower latitude as they propagate outwards.

astro-ph.SR↗

arXiv2018

Shock location and CME 3D reconstruction of a solar type II radio burst with LOFAR

Type II radio bursts are evidence of shocks in the solar atmosphere and inner heliosphere that emit radio waves ranging from sub-meter to kilometer lengths. These shocks may be associated with CMEs and reach speeds higher than the local magnetosonic speed. Radio imaging of decameter wavelengths (20-90 MHz) is now possible with LOFAR, opening a new radio window in which to study coronal shocks that leave the inner solar corona and enter the interplanetary medium and to understand their association with CMEs. To this end, we study a coronal shock associated with a CME and type II radio burst to determine the locations at which the radio emission is generated, and we investigate the origin of the band-splitting phenomenon.

astro-ph.SR↗

arXiv2017

The magnetic connectivity of coronal shocks from behind-the-limb flares to the visible solar surface during $γ$-ray events

Context. The observation of >100 MeV γ-rays in the minutes to hours following solar flares suggests that high-energy particles interacting in the solar atmosphere can be stored and/or accelerated for long time periods. The occasions when γ-rays are detected even when the solar eruptions occurred beyond the solar limb as viewed from Earth provide favorable viewing conditions for studying the role of coronal shocks driven by coronal mass ejections (CMEs) in the acceleration of these particles. Aims: In this paper, we investigate the spatial and temporal evolution of the coronal shocks inferred from stereoscopic observations of behind-the-limb flares to determine if they could be the source of the particles producing the γ-rays. Methods: We analyzed the CMEs and early formation of coronal shocks associated with γ-ray events measured by the Fermi-Large Area Telescope (LAT) from three eruptions behind the solar limb as viewed from Earth on 2013 Oct. 11, 2014 Jan. 06 and Sep. 01. We used a 3D triangulation technique, based on remote-sensing observations to model the expansion of the CME shocks from above the solar surface to the upper corona. Coupling the expansion model to various models of the coronal magnetic field allowed us to derive the time-dependent distribution of shock Mach numbers and the magnetic connection of particles produced by the shock to the solar surface visible from Earth. Results: The reconstructed shock fronts for the three events became magnetically connected to the visible solar surface after the start of the flare and just before the onset of the >100 MeV γ-ray emission. The shock surface at these connections also exhibited supercritical Mach numbers required for significant particle energization. [...] (Abridged)

astro-ph.SR↗