Heliosphere Research Articles

Reacceleration of Galactic Cosmic Rays beyond the Knee at the Termination Shock of a Cosmic-Ray-driven Galactic Wind

The origin of cosmic rays (CRs) above the knee in the spectrum is an unsolved problem. We present a wind model in which interstellar gas flows along a nonrotating, expanding flux tube with a changing speed and cross-sectional area. CRs from Galactic sources, such as supernova remnants, which are coupled to the plasma via Alfvén waves, provide the main pressure source for driving this outflow. These CRs are then subject to diffusive shock reacceleration at the Galactic wind termination shock, which is located at a distance ∼200 kpc. Some of the highest-energy reaccelerated particles propagate upstream against the wind and can contribute to the petaelectronvolt to exaelectronvolt range of the spectrum. We analyze the conditions under which efficient reacceleration can occur and find that rigidities ∼10–40 PV can be obtained and that the termination shock may account for between 10% and 50% of the proton spectrum measured in IceCube/IceTop experiment. In our model, the termination shock is unable to fully explain the CR spectrum in the petaelectronvolt to exaelectronvolt range. The highest-energy particles that escape downstream from our termination shock, and similar shocks surrounding most galaxies, can be further accelerated by intergalactic shock fronts.

A Three-dimensional Model for the Evolution of Magnetohydrodynamic Turbulence in the Outer Heliosphere

We present a time-dependent, three-dimensional single-fluid model for the transport of magnetohydrodynamic (MHD) turbulence that is self-consistently evolving with a dynamic large-scale solar wind in the outer heliosphere. The emphasis is on the region beyond the termination shock, where the solar wind expands subsonically, as well as sub-Alfvénically and nonradially. In extension of earlier work, we refine the treatment of turbulence by considering, in addition to the Elsässer energies, a nonconstant energy difference (or residual energy) and by allowing each of these quantities its own characteristic correlation length scale. While the nonlinear effects in the equations for the Elsässer energies and their length scales are implemented using familiar von Kármán–Howarth style modeling of homogeneous MHD turbulence, the energy difference, which is not conserved in the absence of dissipation, and its length scale are modeled using distinct approaches. We also clarify the impact of the choice of measurement direction for correlation functions associated with two-dimensional fluctuations in transport models. Finally, we illustrate and study the solutions of the resulting six-equation model in detail.

Turbulence in Sources of Decimetric Flare Continua

Decimetric continua are commonly observed during long-lasting solar flares. Their frequency boundaries vary with time. We studied frequency boundary variations using the power spectrum analysis. Analyzing five decimetric continua, we found that their power spectra have a power-law form with the power-law index close to the Kolmogorov turbulence index −5/3. The same power index was also found in the power spectra of radio flux variations at frequencies in the range of the frequency boundary variations. Moreover, these frequency boundary variations were highly correlated with the radio flux ones. We interpret these results to be due to turbulent density variations in the reconnection plasma outflow to the termination shock formed above flare loops. In three cases of decimetric continua, we estimated the level of the plasma density turbulence to be 7.6 – 11.2% of the mean plasma density. We think that the analysis of variations of decimetric continua can be used in studies of the plasma turbulence in solar flares.

Extreme ion acceleration at extragalactic jet termination shocks

Context. Extragalactic plasma jets are some of the few astrophysical environments able to confine ultra-high-energy cosmic rays, but whether they are capable of accelerating these particles is unknown. Aims. In this work, we revisit particle acceleration at relativistic magnetized shocks beyond the local uniform field approximation by considering the global transverse structure of the jet. Methods. Using large two-dimensional particle-in-cell simulations of a relativistic electron-ion plasma jet, we show that the termination shock forming at the interface with the ambient medium accelerates particles up to the confinement limit. Results. The radial structure of the jet magnetic field leads to a relativistic velocity shear that excites a von Kármán vortex street in the downstream medium trailing behind an over-pressured bubble filled with cosmic rays. Particles are efficiently accelerated at each crossing of the shear flow boundary layers. Conclusions. These findings support the idea that extragalactic plasma jets may be capable of producing ultra-high-energy cosmic rays. This extreme particle acceleration mechanism may also apply to microquasar jets.

Space Plasma Physics: A Review

Owing to the ever-present solar wind, our vast solar system is full of plasmas. The turbulent solar wind, together with sporadic solar eruptions, introduces various space plasma processes and phenomena in the solar atmosphere all the way to Earth’s ionosphere and atmosphere and outward to interact with the interstellar media to form the heliopause and termination shock. Remarkable progress has been made in space plasma physics in the last 65 years, mainly due to sophisticated in situ measurements of plasmas, plasma waves, neutral particles, energetic particles, and dust via space-borne satellite instrumentation. Additionally, high-technology ground-based instrumentation has led to new and greater knowledge of solar and auroral features. As a result, a new branch of space physics, i.e., space weather, has emerged since many of the space physics processes have a direct or indirect influence on humankind. After briefly reviewing the major space physics discoveries before rockets and satellites (Section I), we aim to review all our updated understanding on coronal holes, solar flares, and coronal mass ejections, which are central to space weather events at Earth (Section II), solar wind (Section III), storms and substorms (Section IV), magnetotail and substorms, emphasizing the role of the magnetotail in substorm dynamics (Section V), radiation belts/energetic magnetospheric particles (Section VI), structures and space weather dynamics in the ionosphere (Section VII), plasma waves, instabilities, and wave-particle interactions (Section VIII), long-period geomagnetic pulsations (Section IX), auroras (Section X), geomagnetically induced currents (GICs, Section XI), planetary magnetospheres and solar/stellar wind interactions with comets, moons and asteroids (Section XII), interplanetary discontinuities, shocks and waves (Section XIII), interplanetary dust (Section XIV), space dusty plasmas (Section XV), and solar energetic particles and shocks, including the heliospheric termination shock (Section XVI). This article is aimed to provide a panoramic view of space physics and space weather.

TeV halos and the role of pulsar wind nebulae as sources of cosmic-ray positrons

The recent detection of the Geminga pulsar wind nebula (PWN) by HAWC in the multi-TeV band allows us to infer precious information about the transport of pairs in the immediate surroundings of the pulsar and on the spectrum of pairs contributed by a Geminga-like pulsar to the spectrum of pairs in the cosmic radiation. Moreover, this detection allows us to address the issue of how typical are the so-called TeV halos associated to pulsar wind nebulae. Our calculations confirm the need to have suppressed diffusion in a region of at least 20--50 pc around the pulsar, and are used here to infer precious constraints on the spectrum of pairs accelerated at the termination shock: more specifically, we discuss the conditions under which such a spectrum is consistent with that typically expected in a PWN and how it gets modified once it escapes the halo. Finally, we discuss the implications of the existence of a TeV halo around Geminga in terms of acceleration of protons in the pulsar environment, a topic of profound relevance for the whole field of particle acceleration and physics of pulsars.

High-energy cosmic rays and gamma-rays from star clusters: the case of Cygnus OB2

ABSTRACT We investigate the acceleration of cosmic rays at the termination shock that results from the interaction of the collective wind of star clusters with the surrounding interstellar medium. The solution of the transport equation of accelerated particles in the wind-excavated cavity, including energy losses due to CR interactions with neutral gas in the bubble, shows several interesting properties that are discussed in detail. The issue of the maximum energy of the accelerated particles is discussed with special care, because of its implications for the origin of Galactic cosmic rays. Gamma-ray emission is produced in the cavity due to inelastic pp scattering, while accelerated particles are advected downstream of the termination shock and diffuse at the same time. Both the spectrum and the morphology of such emission are discussed, with a comparison of our results with the observations of gamma-ray emission from the Cygnus OB2 region.

Faint but Not Forgotten. I. First Results from a Search for Astrospheres around AGB Stars in the Far-ultraviolet

Using the GALEX archive, we have discovered extended structures around ten asymptotic giant branch (AGB) stars (out of a total 92 searched) emitting in the far-ultraviolet (FUV) band. In all but one, we find the typical morphology expected for a spherical wind moving relative to, and interacting with, the interstellar medium (ISM) to produce an astrosphere. The exception is V Hya whose mass ejection is known to be highly aspherical, where we find evidence of its large parabolic outflows interacting with the ISM, and its collimated, extreme velocity outflows interacting with the circumstellar medium. For eight objects with relatively large proper motions, we find (as expected) that the termination-shock region lies in a hemisphere that contains the proper motion vector. Radial intensity cuts for each source have been used to locate the termination shock and the astropause’s outer edge. In a few objects, the cuts also reveal faint emission just outside the astropause that likely arises in shocked ISM material. We have used these data, together with published mass-loss rates and wind expansion velocities, to determine the total mass lost and duration for each source—we find that the duration of and total mass in the shocked wind are significantly larger than their corresponding values for the unshocked wind. The combination of FUV and far-IR data on AGB astrospheres provides a unique database for theoretical studies (numerical simulations) of wind–ISM interactions. We show that a Cyclical Spatial Heterodyne Spectrometer on a small space-based telescope can provide high-resolution spectra of astrospheres to confirm the emission mechanism.

Pickup Ion–Mediated Magnetic Reconnection in the Outer Heliosphere

Pickup ions (PUIs) play a crucial role in the heliosphere, contributing to the mediation of large-scale structures such as the distant solar wind, the heliospheric termination shock, and the heliopause. While magnetic reconnection is thought to be a common process in the heliosphere due to the presence of heliospheric current sheets, it is poorly understood how PUIs might affect the evolution of magnetic reconnection. Although it is reasonable to suppose that PUIs decrease the reconnection rate since the plasma beta becomes much larger than 1 when PUIs are included, we show for the first time that such a supposition is invalid and that PUI-induced turbulence, heat conduction, and viscosity can preferentially boost magnetic reconnection in heliospheric current sheets in the distant solar wind. This suggests that it is critical to include the effect of the turbulence, heat conduction, and viscosity caused by PUIs to understand the dynamics of magnetic reconnection in the outer heliosphere.

Cosmic gas highways in C-EAGLE simulations

Context. A substantial fraction of cosmic baryons is expected to hide in the form of diffuse warm-hot intergalactic medium (WHIM) at X-ray temperatures (T = 105 − 107 K). Due to the expected low density of WHIM, it has been very difficult to detect so far. A statistically significant sample of credible detections of the WHIM phase might help solve the problem of the missing cosmic baryons. While the majority of cosmic gas is approximately at rest inside the filaments of the Cosmic Web, the fraction of gas located close to galaxy clusters is falling towards them with substantial velocities. The infalling gas is influenced by the increasing density in the cluster vicinity and eventually undergoes a termination shock, which may boost its X-ray signal. Thus, the cluster outskirts are potential locations for improved detectability of the missing baryons. Aims. The primary goal of this work is to identify optimal locations of the enhanced X-ray emission and absorption, arising from the interaction of infalling filamentary gas with cluster material. Our further goal is to improve our understanding of the various physical processes affecting WHIM as it falls towards clusters of galaxies along the cosmic filaments. We aim to utilise this information for planning future X-ray observations of WHIM in cluster outskirts. Methods. We applied the DisPerSE filament finder to the galaxy distribution in the surroundings of a single Coma-like (M200 ∼ 1015.4 M⊙) simulated C-EAGLE cluster of galaxies. We characterised the distribution of the thermodynamic properties of the gas in such filaments and provided a physical interpretation for the results. This analysis serves as a proof of method to be applied to the full C-EAGLE sample in a future work. Results. We captured a large fraction (∼50%) of the hot (T > 105.5 K) gas falling towards the cluster in the detected filaments in the cluster outskirts. The gas in the filaments is in approximate free fall all the way down to the radial distance of ∼2 r200 from the cluster. At smaller radii, the filament gas begins to slow down due to the increasing pressure of the ambient gas; approximately half of the filament gas nevertheless penetrates into the cluster before being decelerated. The deceleration is accompanied by the conversion of gas bulk kinetic energy into heat. As a result, the density and temperature of the gas in the filaments increase from the general Cosmic Web level of ρ ∼ 10ρav (where ρav is the cosmic mean baryon density) and T = 105 − 106 K at r ∼ 4 r200 towards ρ ∼ 100ρav and T = 107 − 108 K at the virial boundary of the very massive cluster studied in this paper. Conclusions. The detection of the cosmic filaments of galaxies around clusters may provide a practical observational avenue for locating the densest and hottest phase of the missing baryons.

How catching the interstellar wind in the inner solar system led the way on a road to interdisciplinary research between heliophysics and astrophysics

Combined in situ observations of the interstellar wind through the solar system and of its pickup ions (PUIs), implanted after ionization in the solar wind, explain, in comparison with interstellar absorption lines of nearby stars, that the Sun is in an interaction region of the two nearest interstellar clouds. This new finding disrupts the long-held understanding that we are inside the local interstellar cloud (LIC). We discuss how space physics evolved toward such interdisciplinary studies between heliophysics and astrophysics. In 1984, the discovery of interstellar He+ PUIs exposed the very local interstellar medium to in situ diagnostics at 1AU. These PUIs provide the interstellar gas composition and form a stepping stone for the acceleration of ions, especially into anomalous cosmic rays. Using the Sun as a gravitational spectrograph, direct imaging of the neutral interstellar wind, first for He and then for H, O, and Ne, provides the interstellar gas velocity vector and temperature at the heliopause. Combining the interstellar gas flow vectors, those of secondary neutral He and O, and the interstellar magnetic field direction deduced from the interstellar H deflection and termination shock anisotropy seen by the Voyagers provides synergistically the heliosphere’s shape, its interaction with the interstellar medium, and constrains our radiation environment. This ISMF organizes the bright Ribbon seen in all-sky images of energetic neutral atoms with the potential to provide its precision determination. The elemental and isotopic composition from PUI and neutral gas observations constrains the galactic evolution and Big Bang cosmology, opening additional interdisciplinary opportunities.

Magnetohydrodynamic Turbulence Formation in Solar Flares: 3D Simulation and Synthetic Observations

Turbulent plasma motion is common in the universe and invoked in solar flares to drive effective acceleration leading to high-energy electrons. Unresolved mass motions are frequently detected in flares from extreme ultraviolet (EUV) observations, which are often regarded as turbulence. However, how this plasma turbulence forms during the flare is still largely a mystery. Here we successfully reproduce observed turbulence in our 3D magnetohydrodynamic simulation where the magnetic reconnection process is included. The turbulence forms as a result of an intricate nonlinear interaction between the reconnection outflows and the magnetic arcades below the reconnection site, in which the shear-flow-driven Kelvin–Helmholtz instability (KHI) plays a key role in generating turbulent vortices. The turbulence is produced above high-density flare loops and then propagates to chromospheric footpoints along the magnetic field as Alfvénic perturbations. High turbulent velocities above 200 km s−1 can be found around the termination shock, while the low atmosphere reaches turbulent velocities of 10 km s−1 at a layer where the number density is about 1011 cm−3. The turbulent region with maximum nonthermal velocity coincides with the region where the observed high-energy electrons are concentrated, demonstrating the potential role of turbulence in acceleration. Synthetic views in EUV and fitted Hinode-EUV Imaging Spectrometer spectra show excellent agreement with observational results. An energy analysis demonstrates that more than 10% of the reconnection-downflow kinetic energy can be converted to turbulent energy via KHI.

What is Hidden in the Planck Distribution Function and the Wien´s Peaks? III. Fission of Solar Photons into Thermons (“Dark Heat”)

There were derived many forms of the Planck distribution function (PDF) since its discovery by Planck in 1900 and formulae for the positions of Wien´s peaks in those distributions. There were published many attempts searching for the hidden carriers of heat because the existing known heat effects of photons cannot interpret all observed data. In this presented model we work with concept of fission of one Solar photon into two thermons – the missing carriers of heat. Properties of Solar photons and Solar thermons are compared for the surface of the Sun and in the vicinity of the Earth. Solar thermons obey the Stefan-Boltzmann law and their heat action can be experimentally analyzed in the whole volume of the Solar System. One of those effects can explain the microwave background radiation as the reflection of thermons on the surface of the Termination shock. The measure of the quantity of heat S for thermons is constant in agreement with the Carnot´s model. The specific heat of solids was newly interpreted as the joint action of three types of thermons with frequency ν/2, ν, and 2ν. The ratio of these three thermons can be experimentally determined from infrared spectra of those studied solids. This model could bring a new way to better describe the old, predicted concept of “dark heat” as appeared many times in the historical literature. We have summarized the known forms of the PDF and positions of Wien´s peaks in order to search some hidden properties in those mathematical structures. It will be shown that these very well-known formulae to all scholars might still keep some hidden surprising properties.

The strong effect of electron thermal conduction on the global structure of the heliosphere

ABSTRACTVoyager 1 and 2 crossed the heliopause at ∼122 au in 2012 and ∼119 au in 2018, respectively. It was quite a surprise because the thickness of the inner heliosheath obtained at that time by the existing time models of the global heliosphere was significantly larger (by 20–40 au). Until now, the problem of the heliosheath thickness has not been fully resolved. Earlier, in the frame of an oversimplified toy model of nearly isothermal solar wind plasma, it has been shown that the effect of electron thermal conduction may significantly reduce the thickness of the inner heliosheath. In this paper, we present the first results of our 3D kinetic-magnetohydrodynamic (MHD) model of the global heliosphere, where the effect of thermal electron conduction has been considered rigorously. The thermal conduction acts mainly along the magnetic field lines. Classical and saturated thermal fluxes are employed when appropriate. It is shown that the effects of thermal conduction are significant. The thickness of the inner heliospheric is reduced. It is a desired effect since it helps to reconcile the thickness obtained in the model with Voyager data. The other effects are the strong depletion of the heliosheath plasma temperature towards the heliopause and the increase of the plasma temperature in the supersonic solar wind upstream of the termination shock.

The Future is the Termination Shock: On the Antinomies and Psychopathologies of Geoengineering. Part Two

Abstract As capitalist society remains incapable of addressing climate breakdown, one measure is waiting in the wings: solar geoengineering. No other technology can cut global temperatures immediately. It would alleviate the symptoms of the crisis, not its causes. But might it be combined with radical emissions cuts? This essay, the final instalment of two, subjects geoengineering to a materialist psychoanalysis and argues that it represents a fantasy of repression, setting itself up for a dreadful return of the repressed.

Probing the Length of the Heliospheric Tail with Energetic Neutral Atoms (ENAs) from 0.52 to 80 keV

The shape of the heliosphere is currently under active debate. Energetic neutral atoms (ENAs) offer the best method for investigating the global structure of the heliosphere. To date, the Interstellar Boundary Explorer (IBEX) and the Ion and Neutral Camera (INCA) that was on board Cassini provide the only global ENA observations of the heliosphere. While extensive modeling has been done at IBEX-Hi energies (0.52–6 keV), no global ENA modeling has been conducted for INCA energies (5.2–55 keV). Here, we use an ENA model of the heliosphere based on hybrid results that capture the heating and acceleration of pickup ions (PUIs) at the termination shock to compare modeled global ENA results with IBEX-Hi and INCA observations using both a long- and short-tail model of the heliosphere. We find that the modeled ENA results for the two heliotail configurations produce similar results from the IBEX-Hi through the INCA energies. We conclude from our modeled ENAs, which only include PUI acceleration at the termination shock, that ENA observations in currently available energy ranges are insufficient for probing the shape and length of the heliotail. However, as a prediction for the future IMAP-Ultra mission (3–300 keV) we present modeled ENA maps at 80 keV, where the cooling length (∼600 au) is greater than the distance where the long- and short-heliotail models differ (∼400 au), and find that IMAP-Ultra should be able to identify the shape of the heliotail, predicting differences in the north lobe to downwind flux ratio between the models at 48%.

Phenomenological modelling of the Crab Nebula’s broadband energy spectrum and its apparent extension

Context. The Crab Nebula emits exceptionally bright non-thermal radiation across the entire wavelength range from the radio to the most energetic photons. So far, the underlying physical model of a relativistic wind from the pulsar terminating in a hydrodynamic standing shock has remained fairly unchanged since the early 1970s when it was first introduced. One of the predictions of this model is an increase in the toroidal magnetic field downstream from the shock where the flow velocity drops quickly with increasing distance until it reaches its asymptotic value, matching the expansion velocity of the nebula. Aims. The magnetic field strength in the nebula is poorly known. Using the recent measurements of the spatial extension and improved spectroscopy of the gamma-ray nebula, it has become –for the first time – feasible to determine in a robust way both the strength as well as the radial dependence of the magnetic field in the downstream flow. Methods. In this work, we introduce a detailed radiative model which was used to calculate the emission from non-thermal electrons (synchrotron and inverse Compton) as well as from thermal dust present in the Crab Nebula in a self-consistent way to compare it quantitatively with observational data. Special care was given to the radial dependence of the electron and seed field density. Results. The radiative model was used to estimate the parameters related to the electron populations responsible for radio and optical/X-ray synchrotron emission. In this context, the mass of cold and warm dust was determined. A combined fit based upon a χ2 minimisation successfully reproduced the complete data set used. For the best-fitting model, the energy density of the magnetic field dominates over the particle energy density up to a distance of ≈1.3 rs (rs: distance of the termination shock from the pulsar). The very high energy (VHE: E > 100 GeV) and ultra-high energy (UHE: E > 100 TeV) gamma-ray spectra set the strongest constraints on the radial dependence of the magnetic field, favouring a model where B(r) = (264 ± 9) μG(r/rs)−0.51 ± 0.03. For a collection of VHE measurements during epochs of higher hard X-ray emission, a significantly different solution B(r) = (167 ± 5) μG(r/rs)−0.29(+0.03, −0.06) is found. Conclusions. The high energy (HE: E > 100 MeV) and VHE gamma-ray observations of the Crab Nebula lift the degeneracy of the synchrotron emission between particle and magnetic field energy density. The reconstructed magnetic field and its radial dependence indicates a ratio of Poynting to kinetic energy flux σ ≈ 0.1 at the termination shock, which is ≈30 times larger than estimated up to now. Consequently, the confinement of the nebula would require additional mechanisms to slow the flow down through, for example, excitation of small-scale turbulence with possible dissipation of the magnetic field.

Understanding the TeV γ-ray emission surrounding the young massive star cluster Westerlund 1

Context. Young massive star clusters (YMCs) have increasingly become the focus of discussions on the origin of galactic cosmic rays (CRs). The proposition that CRs are accelerated inside superbubbles (SBs) blown by the strong winds of these clusters avoids issues faced by the standard paradigm of acceleration at supernova remnant shocks. Aims. We provide an interpretation of the latest TeV γ-ray observations of the region around the YMC Westerlund 1 taken with the High Energy Stereoscopic System (H.E.S.S.) in terms of diffusive shock acceleration at the cluster wind termination shock, taking the spectrum and morphology of the emission into account. As Westerlund 1 is a prototypical example of a YMC, this study is relevant to the general question about the role of YMCs for the Galactic CR population. Methods. We generated model γ-ray spectra, characterised particle propagation inside the SB based on the advection, diffusion, and cooling timescales, and constrained key parameters of the system. We considered hadronic emission from proton-proton interaction and subsequent pion decay and leptonic emission from inverse Compton scattering on all relevant photon fields, including the cosmic microwave background, diffuse and dust-scattered starlight, and the photon field of Westerlund 1 itself. The effect of the magnetic field on cooling and propagation is discussed. Klein-Nishina effects are found to be important in determining the spectral evolution of the electron population. Results. A leptonic origin of the bulk of the observed γ-rays is preferable. The model is energetically plausible, consistent with the presence of a strong shock, and allows for the observed energy-independent morphology. The hadronic model faces two main issues: confinement of particles to the emission region, and an unrealistic energy requirement.

On the Self-Similarity in an Annular Isolator under Rotating Feedback Pressure Perturbations

In this paper, the transient flow simulation in an annular isolator under rotating feedback pressure perturbations simplified from the rotating denotation wave (RDW) is performed. The instantaneous flow characteristics and the self-similarity of the isolator flow-field are investigated in detail. It is found that a helical moving shock wave (MSW) and a quasi-toroidal terminal shock wave (TSW) are induced in the isolator. Hence, the flow-fields on the meridian planes could be classified into three zones, i.e., the undisturbed zone, the terminal shock wave/moving shock wave/boundary layer interaction (TSW/MSW/BLI) zone and the moving shock wave/boundary layer interaction (MSW/BLI) zone. The TSW/MSW/BLI zone is characterized by the coupling of the TSW/BLI and the MSW/BLI due to their small axial distance, which intensifies the adverse pressure gradient on the meridian planes, thus rolling up large separation bubbles developing along the MSW driven by the circular pressure gradient. In the MSW/BLI zone, the shock induces the boundary layer to separate, forming a helical vortex located at the foot of the MSW. During the upstream propagation process, the pattern of the MSWs transforms from a moving normal shock wave to a moving oblique shock wave with decreased strength. Moreover, after the collision with the MSWs, P, Temp and S of the flow elevate with the prompt decrease of va, while vθ increases to a higher level. Despite the deflection effect of the MSWs on the streamlines, the flow direction of the air still maintains an almost axial position at the exit, except in the adjacent region of the MSW. Likewise, three types of zones can be determined in the flow pattern at the exit: the rotating detonation wave/boundary layer interaction (RDW/BLI) zone, the expansion zone, and the vortices discharge zone. Comparing the transient flow patterns at different moments in one cycle and between adjacent cycles, an interesting discovery is that the self-similarity property is observed in the flow-field of the annular isolator under rotating feedback pressure perturbations. The global flow structure of the isolator at different moments shows good agreement despite its rotation with the RDW, and the surface pressure profiles of the corresponding meridian planes all match perfectly. Such a characteristic indicates that the rotation angular velocity of the TSW and the MSW are equal and hold invariant, and the isolator flow could be regarded as a quasi-steady flow. On this basis, the theoretical model of the inclination angles of the MSW by the coordinate transformation and velocity decomposition is developed and validated. The relative errors of the inclination angles between the predicted and measured results are below 3%, which offers a rapid method to predict the shape of the MSW, along with a perspective to better understand the physical meaning of the shape of the MSW.

An Anomalous Cosmic-Ray Mediated Termination Shock: Implications for Energetic Neutral Atoms

The Voyager 2 crossing of the termination shock indicated that most of the upstream energy from the thermal solar wind ions was transferred to pickup ions (PUIs) and other energetic particles downstream of the shock. We use hybrid simulations at the termination shock for the Voyager 2, flank, and tail directions to evaluate the distributions of different ion species downstream of the shock over the energy range of 0.52–55 keV. Here, we extend the work of Gkioulidou et al., which showed an energy-dependent discrepancy between modeled and energetic neutral atom (ENA) observations, and fit distributions to a hybrid model to show that a population of PUIs accelerated via diffusive shock acceleration (DSA) to become low-energy anomalous cosmic rays (ACRs) can bridge the gap between modeled and observed ENA fluxes. Our results with the inclusion of DSA via hybrid fitting give entirely new and novel evidence that DSA at the termination shock is likely to be an important physical process. These ACRs carry a significant fraction of the energy density at the termination shock (22%, 13%, and 19% in the Voyager 2, flank, and tail directions, respectively). Using these ACRs in global ENA modeling of the heliosphere from 0.52 to 55 keV, we find that scaling factors as large as 1.8–2.5 are no longer required to match ENA observations at energies of ∼1–4 keV. Large discrepancies between modeled and observed ENAs only remain over energies of 4–20 keV, indicating that there may be a further acceleration mechanism in the heliosheath at these energies.