Prediction of the in situ coronal mass ejection rate for solar cycle 25: Implications for Parker Solar Probe in situ observations
Christian Möstl, Andreas J. Weiss, Rachel L. Bailey, Martin A. Reiss, Tanja Amerstorfer, Jürgen Hinterreiter, Maike Bauer, Scott W. McIntosh, Noé Lugaz, David Stansby
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11 pages, 6 figures, accepted for publication in the Astrophysical Journal on 2020 September 17
The Parker Solar Probe (PSP) and Solar Orbiter missions are designed to make groundbreaking observations of the Sun and interplanetary space within this decade. We show that a particularly interesting in situ observation of an interplanetary coronal mass ejection (ICME) by PSP may arise during close solar flybys ($< 0.1$~AU). During these times, the same magnetic flux rope inside an ICME could be observed in situ by PSP twice, by impacting its frontal part as well as its leg. Investigating the odds of this situation, we forecast the ICME rate in solar cycle 25 based on 2 models for the sunspot number (SSN): (1) the forecast of an expert panel in 2019 (maximum SSN = 115), and (2) a prediction by McIntosh et al. (2020, maximum SSN = 232). We link the SSN to the observed ICME rates in solar cycles 23 and 24 with the Richardson and Cane list and our own ICME catalog, and calculate that between 1 and 7 ICMEs will be observed by PSP at heliocentric distances $< 0.1$ AU until 2025, including 1$σ$ uncertainties. We then model the potential flux rope signatures of such a double-crossing event with the semi-empirical 3DCORE flux rope model, showing a telltale elevation of the radial magnetic field component $B_R$, and a sign reversal in the component $B_N$ normal to the solar equator compared to field rotation in the first encounter. This holds considerable promise to determine the structure of CMEs close to their origin in the solar corona.
The Parker Solar Probe (PSP) has observed copious rapid magnetic field direction changes in the near-Sun solar wind. These features have been called "switchbacks," and their origin is a mystery. But their widespread nature suggests that they may be generated by a frequently occurring process in the Sun's atmosphere. We examine the possibility that the switchbacks originate from coronal jets. Recent work suggests that many coronal jets result when photospheric magnetic flux cancels, and forms a small-scale "minifilament" flux rope that erupts and reconnects with coronal field. We argue that the…
The Wide-field Imager for Parker Solar Probe (WISPR) captures unprecedented white-light images of the solar corona and inner heliosphere. Thanks to the uniqueness of Parker Solar Probe's (PSP) orbit, WISPR is able to image ``locally'' coronal structures at high spatial and time resolutions. The observed plane of sky, however, rapidly changes because of the PSP's high orbital speed. Therefore, the interpretation of the dynamics of the coronal structures recorded by WISPR is not straightforward. A first study, undertaken by \citet{Liewer2019}, shows how different coronal features (e.g., streamer…
The Parker or field line tangling model of coronal heating is investigated through long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry within the framework of reduced magnetohydrodynamics (RMHD). Slow photospheric motions induce a Poynting flux which saturates by driving an anisotropic turbulent cascade dominated by magnetic energy and characterized by current sheets elongated along the axial magnetic field. Increasing the value of the axial magnetic field different regimes of MHD turbulence develop with a bearing on coronal heating rates. In physical …
Many solar coronal jets result from erupting miniature-filament ("minifilament") magnetic flux ropes that reconnect with encountered surrounding far-reaching field. Many of those minifilament flux ropes are apparently built and triggered to erupt by magnetic flux cancelation. If that cancelation (or some other process) results in the flux rope's field having twist, then the reconnection with the far-reaching field transfers much of that twist to that reconnected far-reaching field. In cases where that surrounding field is open, the twist can propagate to far distances from the Sun as a magneti…
The Wide-field Imager for Solar PRobe (WISPR) obtained the first high-resolution images of coronal rays at heights below 15 R$_\odot$ when the Parker Solar Probe (PSP) was located inside 0.25 au during the first encounter. We exploit these remarkable images to reveal the structure of coronal rays at scales that are not easily discernible in images taken from near 1 au. To analyze and interpret WISPR observations, which evolve rapidly both radially and longitudinally, we construct a latitude versus time map using the full WISPR dataset from the first encounter. From the exploitation of this map…
NASA's Parker Solar Probe (Parker) spacecraft reached its first perihelion of 35.7 solar radii on November 5th, 2018. To aid in mission planning, and in anticipation of the unprecedented measurements to be returned, in late October, we developed a three-dimensional magnetohydrodynamic (MHD) solution for the solar corona and inner heliosphere, driven by the then available observations of the Sun's photospheric magnetic field. Our model incorporates a wave-turbulence-driven (WTD) model to heat the corona. Here, we present our predictions for the structure of the solar corona and the likely {\it …
Parker's coronal braiding and nanoflaring scenario predicts the development of tangential discontinuities and highly misaligned magnetic field lines, as a consequence of random buffeting of their footpoints due to the action of sub-photospheric convection. The increased stressing of magnetic field lines is thought to become unstable above some critical misalignment angle and to result into local magnetic reconnection events, which is generally referred to as Parker's `nanoflaring scenario'. In this study we show that the {\sl minimum (magnetic) energy principle} leads to a bifurcation of force…
We report observations of the total solar eclipse of 14 December 2020, during which a coronal mass ejection can be see n propagating. A comprehensive set of photographs covering a high dynamic range of exposure allow to characterize its dimensions. The displacement of the front can be seen occurring during the few minutes of totality.
Aims: We statistically investigate the plasma and magnetic field characteristics of the upstream regions of interplanetary coronal mass ejections (ICMEs) and their evolution as function of distance to the Sun in the inner heliosphere. We use a sample of 40 well-observed ICMEs from Helios 1/2 (0.3-1au) and 5 from Parker Solar Probe (0.32-0.75au). For each event we identify four main density structures, namely shock, sheath, leading edge (LE), and magnetic ejecta (ME) itself. Methods: We derive separately for each structure averaged plasma and magnetic field parameter values as well as duration …
The {\it Wide-field Imager for Solar Probe} (WISPR) on {\it Parker Solar Probe} (PSP), observing in white light, has a fixed angular field of view, extending from 13.5$^{\circ}$ to 108$^{\circ}$ from the Sun and approximately 50$^{\circ}$ in the transverse directions. Because of the highly elliptical orbit of PSP, the physical extent of the imaged coronal region varies directly as the distance from the Sun, requiring new techniques for analysis of the motions of observed density features. Here, we present a technique for determining the 3D trajectory of CMEs and other coronal ejecta moving rad…
The Wide-field Imager for Solar Probe (WISPR) onboard Parker Solar Probe (PSP), observing in white light, has a fixed angular field of view, extending from 13.5 degree to 108 degree from the Sun and approximately 50 degree in the transverse direction. In January 2021, on its seventh orbit, PSP crossed the heliospheric current sheet (HCS) near perihelion at a distance of 20 solar radii. At this time, WISPR observed a broad band of highly variable solar wind and multiple coronal rays. For six days around perihelion, PSP was moving with an angular velocity exceeding that of the Sun. During this p…
Suprathermal ions in the corona are thought to serve as seed particles for large gradual solar energetic particle (SEP) events associated with fast and wide coronal mass ejections (CMEs). A better understanding of the role of suprathermal particles as seed populations for SEP events can be made by using observations close to the Sun. We study a series of SEP events observed by the Integrated Science Investigation of the Sun (IS$\odot$IS) suite on board the Parker Solar Probe (PSP) from 2020 May 27 to June 2, during which PSP was at heliocentric distances between $\sim$0.4 and $\sim$0.2 au. The…
The Sun is the major source of heat and light in our solar system. The solar cycle is the 11-year cycle of solar activity that can be determined by the rise and fall in the numbers and surface area of sunspots. Solar activity is associated with several factors including radio flux, solar irradiance, magnetic field, solar flares, coronal mass ejections, and solar cycles. This study attempts to determine the Sun's activity specifically for the coronal mass ejection, its trend during solar cycle 23, and its apparent difference. A time series analysis was used to measure the CME data for larger ca…
The shape of the electron velocity distribution function plays an important role in the dynamics of the solar wind acceleration. Electrons are normally modelled with three components, the core, the halo, and the strahl. We investigate how well the fast strahl electrons in the inner heliosphere preserve the information about the coronal electron temperature at their origin. We analysed the data obtained by two missions, Helios spanning the distances between 65 and 215 R$_S$, and Parker Solar Probe (PSP) reaching down to 35 R$_S$ during its first two orbits around the Sun. The electron strahl wa…
Reconnection between pairs of solar magnetic flux elements, one open and the other a closed loop, is theorised to be a crucial process for both maintaining the structure of the corona and producing the solar wind. This 'interchange reconnection' is expected to be particularly active at the open-closed boundaries of coronal holes (CHs). Previous analysis of solar wind data at 1AU indicated that peaks in the flux of suprathermal electrons at slow-fast stream interfaces may arise from magnetic connection to the CH boundary, rather than dynamic effects such as compression. Further, offsets between…
We present a method for tracking and predicting the propagation and evolution of coronal mass ejections (CMEs) using the imagers on the STEREO and SOHO satellites. By empirically modeling the material between the inner core and leading edge of a CME as an expanding, outward propagating ellipsoid, we track its evolution in three-dimensional space. Though more complex empirical CME models have been developed, we examine the accuracy of this relatively simple geometric model, which incorporates relatively few physical assumptions, including i) a constant propagation angle and ii) an azimuthally s…
Stellar coronal mass ejections (CMEs) are a growing research field, especially during the past decade. The large number of so far detected exoplanets raises the open question for the CME activity of stars, as CMEs may strongly affect exoplanetary atmospheres. In addition, as CMEs contribute to stellar mass- and angular momentum loss and are therefore relevant for stellar evolution, there is need for a better characterization of this phenomenon. In this article we review the different methodologies used up to now to attempt the detection of stellar CMEs. We discuss the limitations of the differ…
Based on the method of finding coronal magnetic field value radial profiles B(R) described in (Gopalswamy and Yashiro, 2011), and applied for the directions close to the sky plane, we determined magnetic field value radial distributions along the directions close to the Sun-Earth axis. For this purpose, by using the method in (Xue, Wang, and Dou, 2005), from the SOHO/LASCO data, we found 3D characteristics for fast halo coronal mass ejections (HCMEs) and for the HCME-related shocks. Through these data, we managed to obtain the B(R) distributions as far as 43 solar radii from the Sun center, wh…
Solar coronal dimmings have been observed extensively in the past two decades and are believed to have close association with coronal mass ejections (CMEs). Recent study found that coronal dimming is the only signature that could differentiate powerful ares that have CMEs from those that do not. Therefore, dimming might be one of the best candidates to observe the stellar CMEs on distant Sun-like stars. In this study, we investigate the possibility of using coronal dimming as a proxy to diagnose stellar CMEs. By simulating a realistic solar CME event and corresponding coronal dimming using a g…
Limb Observations of Global Solar Coronal Extreme-ultraviolet Wavefronts: The Inclination, Kinematics, Coupling with the Expanding Coronal Mass Ejections, and Connection with the Coronal Mass Ejection Driven Shocks
During its first solar encounter, the Parker Solar Probe (PSP) acquired unprecedented up-close imaging of a small Coronal Mass Ejection (CME) propagating in the forming slow solar wind. The CME originated as a cavity imaged in extreme ultraviolet that moved very slowly ($<50$ km/s) to the 3-5 solar radii (R$_\odot$) where it then accelerated to supersonic speeds. We present a new model of an erupting Flux Rope (FR) that computes the forces acting on its expansion with a computation of its internal magnetic field in three dimensions. The latter is accomplished by solving the Grad-Shafranov equa…
We report the result of the first search for multipoint in situ and imaging observations of interplanetary coronal mass ejections (ICMEs) starting with the first Solar Orbiter (SolO) data in 2020 April - 2021 April. A data exploration analysis is performed including visualizations of the magnetic field and plasma observations made by the five spacecraft SolO, BepiColombo, Parker Solar Probe (PSP), Wind and STEREO-A, in connection with coronagraph and heliospheric imaging observations from STEREO-A/SECCHI and SOHO/LASCO. We identify ICME events that could be unambiguously followed with the STER…
Solar Coronal Mass Ejections (CMEs) are sometimes deflected during their propagation. This deflection may be the consequence of interaction between a CME and a coronal hole or the solar wind. We analyze 44 halo-CMEs whose deflection angle exceeds 90 degrees. The coronal magnetic field configuration is computed from daily synoptic maps of magnetic field from SOHO/MDI and SDO/HMI using a Potential Field Source Surface (PFSS) model. By comparing the ambient magnetic field configuration and the measured position angles (MPA) of the CMEs, we conclude that the deflection of 80% of the CMEs (35 of 44…
We present a novel three-dimensional (3D) model of coronal mass ejections (CMEs) that unifies all key evolutionary aspects of CMEs and encapsulates their 3D magnetic field configuration. This fully analytic model is capable of reproducing the global geometrical shape of a CME with all major deformations taken into account, i.e., deflection, rotation, expansion, "pancaking", front flattening and rotational skew. Encapsulation of 3D magnetic structure allows the model to reproduce in-situ measurements of magnetic field for trajectories of spacecraft-CME encounters of any degree of complexity. As…
We present an algorithm to detect the outer edges of Coronal Mass Ejection (CME) events as seen in differences of Heliospheric Imager STEREO SECCHI HI-1 images from either A or B spacecraft, as well as its implementation in Python.
Parker's model is one of the most discussed mechanisms for coronal heating and has generated much debate. We have recently obtained new scaling results in a two-dimensional (2D) version of this problem suggesting that the heating rate becomes independent of resistivity in a statistical steady state [Ng and Bhattacharjee, Astrophys. J., 675, 899 (2008)]. Our numerical work has now been extended to 3D by means of large-scale numerical simulations. Random photospheric footpoint motion is applied for a time much longer than the correlation time of the motion to obtain converged average coronal hea…
The Coronal Multichannel Polarimeter (CoMP) measures not only the polarization of coronal emission, but also the full radiance profiles of coronal emission lines. For the first time, CoMP observations provide high-cadence image sequences of the coronal line intensity, Doppler shift and line width simultaneously in a large field of view. By studying the Doppler shift and line width we may explore more of the physical processes of CME initiation and propagation. Here we identify a list of CMEs observed by CoMP and present the first results of these observations. Our preliminary analysis shows th…
Waiting time distributions of solar flares and {\sl coronal mass ejections (CMEs)} exhibit power law-like distribution functions with slopes in the range of $α_τ \approx 1.4-3.2$, as observed in annual data sets during 4 solar cycles (1974-2012). We find a close correlation between the waiting time power law slope $α_τ$ and the {\sl sunspot number (SN)}, i.e., $α_τ$ = 1.38 + 0.01 $\times$ SN. The waiting time distribution can be fitted with a Pareto-type function of the form $N(τ) = N_0$ $(τ_0 + τ)^{-α_τ}$, where the offset $τ_0$ depends on the instrumental sensitivity, the detection threshold…
We report on the first detection of nonthermal radio emission associated with a polar coronal mass ejection. We call the radio emission as diffuse interplanetary radio emission (DIRE), which occurs in the decameter-hectometric wavelengths. The radio emission originates from the shock flanks that interact with nearby streamers.
Motivated by recent observations of short-timescale variations in the infrared emission of circumstellar disks, we propose that coronal mass ejections can remove dust grains on timescales as short as a few days. Continuous monitoring of stellar activity, coupled to infrared observations, can place meaningful constraints on the proposed mechanism.
Suzaku detected an enhancement of soft X-ray background associated with solar eruptions on 2013 April 14-15. The solar eruptions were accompanied by an M6.5 solar flare and a coronal mass ejection with magnetic flux ropes. The enhanced soft X-ray background showed a slight variation in half a day and then a clear one in a few hours. The former spectrum was composed of oxygen emission lines, while the later one was characterized by a series of emission lines from highly ionized carbon to silicon. The soft X-ray enhancement originated from geocoronal solar wind charge exchange. However, there ap…
Solar coronal jets are small, transient, collimated ejections most easily observed in coronal holes (CHs). The upcoming Parker Solar Probe (PSP) mission provides the first opportunity to encounter CH jets in situ near the Sun and examine their internal structure and dynamics. Using projected mission orbital parameters, we have simulated PSP encounters with a fully three-dimensional magnetohydrodynamic (MHD) model of a CH jet. We find that three internal jet regions, featuring different wave modes and levels of compressibility, have distinct identifying signatures detectable by PSP. The leading…
The effects of a large coronal mass ejection (CME) on a solar coronal streamer located roughly 90 degrees from the main direction of the CME propagation observed on January 2, 2012 by the SOHO/LASCO coronagraph are analyzed. Radial coronal streamers undergo some bending when CMEs pass through the corona, even at large angular distances from the streamers. The phenomenon resembles a bending wave traveling along the streamer. Some researchers interpret these phenomena as the effects of traveling shocks generated by rapid CMEs, while others suggest they are waves excited inside the streamers by e…
We mode Solar coronal mass ejections (CMEs) as expanding force-fee magnetic structures and find the self-similar dynamics of configurations with spatially constant α, where {\bf J} =α{\bf B}, in spherical and cylindrical geometries, expanding spheromaks and expanding Lundquist fields correspondingly. The field structures remain force-free, under the conventional non-relativistic assumption that the dynamical effects of the inductive electric fields can be neglected. While keeping the internal magnetic field structure of the stationary solutions, expansion leads to complicated internal velociti…
Solar coronal mass ejections (CMEs) are the most significant drivers of adverse space weather at Earth, but the physics governing their propagation through the heliosphere is not well understood. While stereoscopic imaging of CMEs with the Solar Terrestrial Relations Observatory (STEREO) has provided some insight into their three-dimensional (3D) propagation, the mechanisms governing their evolution remain unclear due to difficulties in reconstructing their true 3D structure. Here we use a new elliptical tie-pointing technique to reconstruct a full CME front in 3D, enabling us to quantify its …
We present the first PSP-observed CME that hits a second spacecraft before the end of the PSP encounter, providing an excellent opportunity to study short-term CME evolution. The CME was launched from the Sun on 10 October 2019 and was measured in situ at PSP on 13 October 2019 and at STEREO-A on 14 October 2019. The small, but not insignificant, radial (~0.15 au) and longitudinal (~8 deg) separation between PSP and STEREO-A at this time allows for observations of both short-term radial evolution as well as investigation of the global CME structure in longitude. Although initially a slow CME, …
Interplanetary Coronal Mass Ejection (ICME) shocks are known to accelerate particles and contribute significantly to Solar Energetic Particle (SEP) events. We have performed Magnetohydrodynamic-Particle in Cell (MHD-PIC) simulations of ICME shocks to understand the acceleration mechanism. These shocks vary in Alfvénic Mach numbers as well as in magnetic field orientations (parallel \& quasi-perpendicular). We find that Diffusive Shock Acceleration (DSA) plays a significant role in accelerating particles in a parallel ICME shock. In contrast, Shock Drift Acceleration (SDA) plays a pivotal role …
We present a python-based tool to detect the occultation of background sources by foreground Solar coronal mass ejections. The tool takes as input standard celestial coordinates of the source and translates those to the Helioprojective plane, and is thus well suited for use with a wide variety of background astronomical sources. This tool provides an easy means to search through a large archival dataset for such crossings and relies on the well-tested Astropy and Sunpy modules.
We investigate how coronal mass ejections (CMEs) propagate through, and interact with, the inner heliosphere between the Sun and Earth, a key question in CME research and space weather forecasting. CME Sun-to-Earth kinematics are constrained by combining wide-angle heliospheric imaging observations, interplanetary radio type II bursts and in situ measurements from multiple vantage points. We select three events for this study, the 2012 January 19, 23, and March 7 CMEs. Different from previous event studies, this work attempts to create a general picture for CME Sun-to-Earth propagation and com…
This Topical Issue of Solar Physics, devoted to the study of flux-rope structure in coronal mass ejections (CMEs), is based on two Coordinated Data Analysis Workshops (CDAWs) held in 2010 (20 - 23 September in Dan Diego, California, USA) and 2011 (September 5-9 in Alcala, Spain). The primary purpose of the CDAWs was to address the question: Do all CMEs have flux rope structure? There are 18 papers om this topical issue, including this preface.
New study confirms conclusions made in [M. Eselevich, and V. Eselevich, 2008]; according to it, there is a disturbed region expended along the CME propagation direction in front of a coronal mass ejection whose velocity $u$ is lower than the critical $u_C$ relative to the surrounding coronal plasma. The time difference brightness (plasma density) in the disturbed region smoothly decreases to larger distances in front of CME. A shock wave forms at u higher than $u_C$ in the front part of the disturbed region manifested as a discontinuity in radial distributions of the difference brightness.
The Sun is an active star that can launch large eruptions of magnetised plasma into the heliosphere, called coronal mass ejections (CMEs). These ejections can drive shocks that accelerate particles to high energies, often resulting in radio emission at low frequencies (<200 MHz). To date, the relationship between the expansion of CMEs, shocks and particle acceleration is not well understood, partly due to the lack of radio imaging at low frequencies during the onset of shock-producing CMEs. Here, we report multi-instrument radio, white-light and ultraviolet imaging of the second largest flare …
Coronal "EIT waves" appear as EUV bright fronts propagating across a significant part of the solar disk. The intriguing phenomenon provoked continuing debates on their nature and their relation with coronal mass ejections (CMEs). In this paper, we first summarize all the observational features of "EIT waves", which should be accounted for by any successful model. The theoretical models constructed during the past 10 years are then reviewed. Finally, the implication of the "EIT wave" research to the understanding of CMEs is discussed. The necessity is pointed out to revisit the nature of CME fr…
The main objective of the study is to determine the probability distributions of the geomagnetic Dst index as a function of the coronal mass ejection (CME) and solar flare parameters for the purpose of establishing a probabilistic forecast tool for the geomagnetic storm intensity. Several CME and flare parameters as well as the effect of successive-CME occurrence in changing the probability for a certain range of Dst index values, were examined. The results confirm some of already known relationships between remotely-observed properties of solar eruptive events and geomagnetic storms, namely t…
A data-driven physics-based transport model of solar energetic particles accelerated by coronal mass ejection shocks propagating through the solar coronal and heliospheric magnetic fields
Coronal mass ejections (CMEs) are associated with the eruption of magnetic flux ropes (MFRs), which usually appear as hot channels in active regions and coronal cavities in quiet-Sun regions. CMEs often exhibit the classical three-part structure in the lower corona when imaged with white-light coronagraphs, including the bright front, dark cavity, and bright core. The bright core and dark cavity have been regarded as the erupted prominence and MFR, respectively, for several decades. However, recent studies clearly demonstrated that both the prominence and hot-channel MFR can be observed as the…
We analyse the evolution of a sigmoidal (S shaped) active region toward eruption, which includes a coronal mass ejection (CME) but leaves part of the filament in place. The X-ray sigmoid is found to trace out three different magnetic topologies in succession: a highly sheared arcade of coronal loops in its long-lived phase, a bald-patch separatrix surface (BPSS) in the hours before the CME, and the first flare loops in its major transient intensity enhancement. The coronal evolution is driven by photospheric changes which involve the convergence and cancellation of flux elements under the sigm…
On 2015 January 6-7, an interplanetary coronal mass ejection (ICME) was observed at L1. This event, which can be associated with a weak and slow coronal mass ejection, allows us to discuss on the differences between the boundaries of the magnetic cloud and the compositional boundaries. A fast stream from a solar coronal hole surrounding this ICME offers a unique opportunity to check the boundaries' process definition and to explain differences between them. Using Wind and ACE data, we perform a complementary analysis involving compositional, magnetic, and kinematic observations providing relev…
In this work, non-recurrent Forbush decreases (FDs) triggered by the passage of shock-driven interplanetary coronal mass ejections (ICMEs) have been analyzed. Fifty-nine ICMEs have been studied but only the 25% of them were associated to a FD. We find that shock-driving magnetic clouds (MCs) produce deeper FDs than shock-driving ejecta. This fact can be explained regarding to the observed growing trends between decreases in neutron monitor (NM) count rate and MC/ejecta speed and its associated rigidity. MCs are faster and have higher associated rigidities than ejecta. Also the deceleration of …
We discuss how simultaneous observations by multiple heliospheric imagers can provide some important information about the azimuthal properties of Coronal Mass Ejections (CMEs) in the heliosphere. We propose two simple models of CME geometry that can be used to derive information about the azimuthal deflection and the azimuthal expansion of CMEs from SECCHI/HI observations. We apply these two models to four CMEs well-observed by both STEREO spacecraft during the year 2008. We find that in three cases, the joint STEREO-A and B observations are consistent with CMEs moving radially outward. In so…
Mark 4 and LASCO C2, C3 coronagraph data analysis shows that, up to the distance $R\sim$ 5 R$_\odot$ from the center of the Sun, the thickness of a CME-generated shock front may be of order of the proton mean free path. This means that the energy dissipation mechanism in a shock front at these distances is collisional.
