Ion cyclotron waves at Io: implications for the temporal variation of Io's atmosphere

When the flowing torus plasma encounters the upper atmosphere of Jupiter's moon, Io, newly created ions are rapidly accelerated by the motional electric field. Many of these ions are reneutralized and form a spray of fast neutrals that travel far away from Io before being reionized by photoionization and impact. These ions, now far from Io, are unstable to the generation of ion cyclotron waves. These waves in turn act as a mass spectrometer allowing Galileo magnetic measurements to be used to probe the composition of the atmosphere of Io and how it varies in time and in space. We now have six Galileo passes by Io on which we have measurements with sufficient cadence to examine the ion cyclotron waves. One of these passes, on Galileo's 32nd orbit has not been discussed previously. These passes provide sufficient observations to begin to distinguish the sources of variability. We find that while the atmosphere of Io varies temporally throughout the mission, it also has a spatial variation in composition at any instant of time.     

Io's volcanic control of Jupiter's extended neutral clouds

Dramatic changes in the brightness and shape of Jupiter's extended sodium nebula are found to be correlated with the infrared emission brightness of Io. Previous imaging and modeling studies have shown that varying appearances of the nebula correspond to changes in the rate and the type of loss mechanism for atmospheric escape from Io. Similarly, previous IR observational studies have assumed that enhancements in infrared emissions from Io correspond to increased levels of volcanic (lava flow) activity. In linking these processes observationally and statistically, we conclude that silicate volcanism on Io controls both the rate and the means by which sodium escapes from Io's atmosphere. During active periods, molecules containing sodium become an important transient in Io's upper atmosphere, and subsequent photochemistry and molecular-ion driven dynamics enhance the high speed sodium population, leading to the brightest nebulas observed. This is not the case during volcanically quiet times when omni-present atmospheric sputtering ejects sodium to form a modest, base-level nebula. Sodium's role as a “trace gas” of the more abundant species of sulfur (S) and oxygen (O) is less certain during volcanic episodes. While we suggest that volcanism must also affect the escape rates of S and O, and consequently their extended neutral clouds, the different roles played by lava and plume sources for non-sodium species are far too uncertain to make definitive comparisons at this time.     

Observation of Mercury's sodium exosphere during the transit on November 9, 2006

A rare, but normal, astronomical event occurred on November 9th 2006 (JST) as Mercury passed in front of the Sun from the perspective of the Earth. The abundance of the sodium vapor above the planet limb was observed by detecting an excess absorption in the solar sodium line D₁ during this event. The observation was performed with a 10-m spectrograph of Czerny-Turnar system at Domeless Solar Tower Telescope at the Hida Observatory in Japan. The excess absorption was red-shifted by 10 pm relative to the solar line, and was measured at the dawnside (eastside) and duskside (westside) of Mercury. Between the dawn and dusksides, an asymmetry of total sodium abundance was clearly identified. At the dawnside, the total sodium column density was 6.1×10¹⁰ Na atoms/cm², while it was 4.1×10¹⁰ Na atoms/cm² at the duskside. The investigation of dawn-dusk asymmetry of the sodium exosphere of Mercury is a clue to understand the release mechanism of sodium from the surface rock. Our result suggests that a thermal desorption is a main source process for sodium vapor in the vicinity of Mercury.     

The variation of Io's auroral footprint brightness with the location of Io in the plasma torus

Ultraviolet and near-infrared observations of auroral emissions from the footprint of Io's magnetic Flux Tube (IFT) mapping to Jupiter's ionosphere have been interpreted via a combination of the unipolar inductor model [Goldreich, P., Lynden-Bell, D., 1969. Astrophys. J. 156, 59-78] and the multiply-reflected Alfvén wave model [Belcher, J.W., 1987. Science 238, 170-176]. While both models successfully explain the general nature of the auroral footprint and corotational wake, and both predict the presence of multiple footprints, the details of the interaction near Io are complicated [Saur, J., Neubauer, F.M., Connerney, J.E.P., Zarka, P., Kivelson, M.G., 2004. In: Bagenal, F., Dowling, T.E., McKinnon, W.B. (Eds.), Jupiter: The Planet, Satellites and Magnetosphere. Cambridge University Press, Cambridge, UK, pp. 537-560; Kivelson, M.G., Bagenal, F., Kurth, W.S., Neubauer, F.M., Paranicas, C., Saur, J., 2004. In: Bagenal, F., Dowling, T.E., McKinnon, W.B. (Eds.), Jupiter: The Planet, Satellites and Magnetosphere. Cambridge University Press, Cambridge, UK, pp. 513-536]. The auroral footprint brightness is believed to be a good remote indicator of the strength of the interaction near Io, indicating the energy and current strength linking Io with Jupiter's ionosphere. The brightness may also depend in part on local auroral acceleration processes near Jupiter. The relative importance of different physical processes in this interaction can be tested as Jupiter's rotation and Io's orbital motion shift Jupiter's magnetic centrifugal equator past Io, leading to longitudinal variations in the plasma density near Io and functionally different variations in the local field strength near Jupiter where the auroral emissions are produced. Initial HST WFPC2 observations found a high degree of variability in the footprint brightness with time, and some evidence for systematic variations with longitude [Clarke, J.T., Ben Jaffel, L., Gérard, J.-C., 1998. J. Geophys. Res. 103, 20217-20236], however the data were not of sufficient quality to determine functional relationships. In this paper we report the results from a second, more thorough study, using a series of higher resolution and sensitivity HST STIS observations and a model for the center to limb dependence of the optically thin auroral emission brightness based on measurements of the auroral curtain emission distribution with altitude. A search for correlations between numerous parameters has revealed a strong dependence between Io's position in the plasma torus and the resulting footprint brightness that persists over several years of observations. The local magnetic field strength near Jupiter (i.e. the size of the loss cone) and the expected north/south asymmetry in auroral brightness related to the path of currents generated near Io through the plasma torus en route to Jupiter appear to be less important than the total plasma density near Io. This is consistent with the near-Io interaction being dominated by collisions of corotating plasma and mass pickup, a long-standing view which has been subject to considerable debate. The brightness of the auroral footprint emissions, however, does not appear to be proportional to the incident plasma density or energy, and the interpretation of this result will require detailed modeling of the interaction near Io.     

Post-solidification cooling and the age of Io's lava flows

The modeling of thermal emission from active lava flows must account for the cooling of the lava after solidification. Models of lava cooling applied to data collected by the Galileo spacecraft have, until now, not taken this into consideration. This is a flaw as lava flows on Io are thought to be relatively thin with a range in thickness from ∼1 to 13 m. Once a flow is completely solidified (a rapid process on a geological time scale), the surface cools faster than the surface of a partially molten flow. Cooling via the base of the lava flow is also important and accelerates the solidification of the flow compared to the rate for the ‘semi-infinite’ approximation (which is only valid for very deep lava bodies). We introduce a new model which incorporates the solidification and basal cooling features. This model gives a superior reproduction of the cooling of the 1997 Pillan lava flows on Io observed by the Galileo spacecraft. We also use the new model to determine what observations are necessary to constrain lava emplacement style at Loki Patera. Flows exhibit different cooling profiles from that expected from a lava lake. We model cooling with a finite-element code and make quantitative predictions for the behavior of lava flows and other lava bodies that can be tested against observations both on Io and Earth. For example, a 10-m-thick ultramafic flow, like those emplaced at Pillan Patera in 1997, solidifies in ∼450 days (at which point the surface temperature has cooled to ∼280 K) and takes another 390 days to cool to 249 K. Observations over a sufficient period of time reveal divergent cooling trends for different lava bodies [examples: lava flows and lava lakes have different cooling trends after the flow has solidified (flows cool faster)]. Thin flows solidify and cool faster than flows of greater thickness. The model can therefore be used as a diagnostic tool for constraining possible emplacement mechanisms and compositions of bodies of lava in remote-sensing data.     

Lava lakes on Io: observations of Io's volcanic activity from Galileo NIMS during the 2001 fly-bys

Galileo's Near-Infrared Mapping Spectrometer (NIMS) obtained its final observations of Io during the spacecraft's fly-bys in August (I31) and October 2001 (I32). We present a summary of the observations and results from these last two fly-bys, focusing on the distribution of thermal emission from Io's many volcanic regions that give insights into the eruption styles of individual hot spots. We include a compilation of hot spot data obtained from Galileo, Voyager, and ground-based observations. At least 152 active volcanic centers are now known on Io, 104 of which were discovered or confirmed by Galileo observations, including 23 from the I31 and I32 Io fly-by observations presented here. We modify the classification scheme of Keszthelyi et al. (2001, J. Geophys. Res. 106 (E12) 33 025-33 052) of Io eruption styles to include three primary types: promethean (lava flow fields emplaced as compound pahoehoe flows with small plumes <200 km high originating from flow fronts), pillanian (violent eruptions generally accompanied by large outbursts, >200 km high plumes and rapidly-emplaced flow fields), and a new style we call “lokian” that includes all eruptions confined within paterae with or without associated plume eruptions). Thermal maps of active paterae from NIMS data reveal hot edges that are characteristic of lava lakes. Comparisons with terrestrial analogs show that Io's lava lakes have thermal properties consistent with relatively inactive lava lakes. The majority of activity on Io, based on locations and longevity of hot spots, appears to be of this third type. This finding has implications for how Io is being resurfaced as our results imply that eruptions of lava are predominantly confined within paterae, thus making it unlikely that resurfacing is done primarily by extensive lava flows. Our conclusion is consistent with the findings of Geissler et al. (2004, Icarus, this issue) that plume eruptions and deposits, rather than the eruption of copious amounts of effusive lavas, are responsible for Io's high resurfacing rates. The origin and longevity of islands within ionian lava lakes remains enigmatic.     

Temporal behavior of the SO 1.707 μm ro-vibronic emission band in Io's atmosphere

We report observations of the ro-vibronic a¹Δ→X³Σ⁻ transition of SO at 1.707 μm on Io. These data were taken while Io was eclipsed by Jupiter, on four nights between July 2000 and March 2003. We analyze these results in conjunction with a previously published night to investigate the temporal behavior of these emissions. The observations were all conducted using the near-infrared spectrometer NIRSPEC on the W.M. Keck II telescope. The integrated emitted intensity for this band varies from 0.8×¹⁰²⁷ to 2.4×¹⁰²⁷ photons/s, with a possible link to variations in Loki's infrared brightness. The band-shapes imply rotational temperatures of 550-1000 K for the emitting gas, lending further evidence to a volcanic origin for sulfur monoxide. An attempt to detect the B¹Σ→X³Σ⁻ transition of SO at 0.97 μm was unsuccessful; simultaneous detection with the 1.707 μm band would permit determination of the SO column abundance.     

Mapping of Io's thermal radiation by the Galileo photopolarimeter-radiometer (PPR) instrument

Between 1999 and 2002, the Galileo spacecraft made 6 close flybys of Io during which many observations of Io's thermal radiation were made with the photopolarimeter-radiometer (PPR). While the NIMS instrument could measure thermal emission from hot spots with T>200 K, PPR was the only Galileo instrument capable of mapping the lower temperatures of older, cooling lava flows, and the passive background. We tabulate all data taken by PPR of Io during these flybys and describe some scientific highlights revealed by the data. The data include almost complete coverage of Io at better than 250 km resolution, with extensive regional coverage at higher resolutions. We found a modest poleward drop in nighttime background temperatures and evidence of thermal inertia variations across the surface. Comparison of high spatial resolution temperature measurements with observed daytime SO₂ gas pressures on Io provides evidence for local cold trapping of SO₂ frost on scales smaller than the 60 km resolution of the PPR data. We also calculated the power output from several hot spots and estimated total global heat flow to be about 2.0-2.6 W m⁻². The low-latitude diurnal temperature variations for the regions between obvious hot spots are well matched by a laterally-inhomogeneous thermal model with less than 1 W m⁻² endogenic heat flow.     

Impact of electron chemistry on the structure and composition of Io's atmosphere

Two-dimensional model calculations (altitude and solar zenith angle) are performed to investigate the impact of electron chemistry on the composition and structure of Io's atmosphere. The calculations are based upon the model of Wong and Smyth (2000, Icarus 146, 60-74) for Io's SO₂ sublimation atmosphere with the addition of new electron chemistry, where the interactions of the electrons and neutrals are treated in a simple fashion. The model calculations are presented for Io's atmosphere at western elongation (dusk ansa) for both a low-density case (subsolar temperature of 113 K) and a high-density case (subsolar temperature of 120 K). The impact of electron-neutral chemistry on the composition and structure of Io's atmosphere is confined primarily to an interaction layer. The penetration depth of the interaction layer is limited to high altitudes in the thicker dayside atmosphere but reaches the surface in the thinner dayside and/or nightside atmosphere at larger solar zenith angles. Within most of the thicker dayside atmosphere, the column density of SO₂ is not significantly altered by electrons, but in the interaction layer all number densities are significantly altered: SO₂ is reduced, O, SO, S, and O₂ are greatly enhanced, and O, SO, and S become comparable to SO₂ at high altitudes. For the thinner nightside atmosphere, the species number densities are dramatically altered: SO₂ is drastically reduced to the least abundant species of the SO₂ family, SO and O₂ are significantly reduced at all altitudes, and O and S are dramatically enhanced and become the dominant species at all altitudes except near the surface. The interaction layer also defines the location of the emission layer for neutrals excited by electron impact and hence determines the fraction of the total neutral column density that is visible in remote observation. Electron chemistry may also impact the ratio of the equatorial to polar SO₂ column density deduced from Lyman-α images and the north-south alternating and System III longitude-dependent asymmetry observed in polar O and S emissions.     

First observation of energetic neutral atoms in the Venus environment

The ASPERA-4 instrument on board the Venus Express spacecraft offers for the first time the possibility to directly measure the emission of energetic neutral atoms (ENAs) in the vicinity of Venus. When the spacecraft is inside the Venus shadow a distinct signal of hydrogen ENAs usually is detected. It is observed as a narrow tailward stream, coming from the dayside exosphere around the Sun direction. The intensity of the signal reaches several , which is consistent with present theories of the plasma and neutral particle distributions around Venus.     

Comparative study of ion cyclotron waves at Mars, Venus and Earth

Ion cyclotron waves are generated in the solar wind when it picks up freshly ionized planetary exospheric ions. These waves grow from the free energy of the highly anisotropic distribution of fresh pickup ions, and are observed in the spacecraft frame with left-handed polarization and a wave frequency near the ion’s gyrofrequency. At Mars and Venus and in the Earth’s polar cusp, the solar wind directly interacts with the planetary exospheres. Ion cyclotron waves with many similar properties are observed in these diverse plasma environments. The ion cyclotron waves at Mars indicate its hydrogen exosphere to be extensive and asymmetric in the direction of the interplanetary electric field. The production of fast neutrals plays an important role in forming an extended exosphere in the shape and size observed. At Venus, the region of exospheric proton cyclotron wave production may be restricted to the magnetosheath. The waves observed in the solar wind at Venus appear to be largely produced by the solar-wind-Venus interaction, with some waves at higher frequencies formed near the Sun and carried outward by the solar wind to Venus. These waves have some similarity to the expected properties of exospherically produced proton pickup waves but are characterized by magnetic connection to the bow shock or by a lack of correlation with local solar wind properties respectively. Any confusion of solar derived waves with exospherically derived ion pickup waves is not an issue at Mars because the solar-produced waves are generally at much higher frequencies than the local pickup waves and the solar waves should be mostly absorbed when convected to Mars distance as the proton cyclotron frequency in the plasma frame approaches the frequency of the solar-produced waves. In the Earth’s polar cusp, the wave properties of ion cyclotron waves are quite variable. Spatial gradients in the magnetic field may cause this variation as the background field changes between the regions in which the fast neutrals are produced and where they are re-ionized and picked up. While these waves were discovered early in the magnetospheric exploration, their generation was not understood until after we had observed similar waves in the exospheres of Mars and Venus.     

Expected heliospheric attributes of Jovian pickup ions from the extended neutral gas disk

The MIMI CHEMS Instrument on the Cassini Orbiter detected Jovian pickup ions almost an AU upstream of Jupiter during the 2001 flyby. The clue to their planetary origin is the presence of singly ionized sulfur ions in quantities exceeding those expected from the interstellar gas entering the heliosphere (Nature 415 (2002) 994). Earlier modeling of the extended Jovian neutral gas disk suggested how the combination of the orbiting, localized Jovian source and interplanetary ionization processes should combine to produce a distinctive reservoir for heliospheric pickup ion production, different from its interstellar gas counterpart. Here the expected characteristics of pickup ions from the Jovian source are considered using a simplified model. The results provide an idea of the signatures in physical and phase space that reflect both the initial velocities and directionalities of the parent neutral population. Long-term measurements can easily test for these attributes given sufficient spatial and ion energy coverage.     

Impacts as sources of the exosphere on Mercury

Chemical processes associated with meteoroid bombardment of Mercury are considered. Meteoroid impacts lead to production of metal atoms as well as metal oxides and hydroxides in the planetary exosphere. By using quenching theory, the abundances of the main Na-, K-, Ca-, Fe-, Al-, Mg-, Si-, and Ti-containing species delivered to the exosphere during meteoroid impacts were estimated. Based on a correlation between the solar photo rates and the molecular constants of atmospheric diatomic molecules, photolysis lifetimes of metal oxides and SiO are estimated. Meteoroid impacts lead to the formation of hot metal atoms (0.2-0.4 eV) produced directly during impacts and of very hot metal atoms (1-2 eV) produced by the subsequent photolysis of oxides and hydroxides in the exosphere of Mercury. The concentrations of impact-produced atoms of the main elements in the exosphere are estimated relative to the observed concentrations of Ca, assumed to be produced mostly by ion sputtering. Condensation of dust grains can significantly reduce the concentrations of impact-produced atoms in the exosphere. Na, K, and Fe atoms are delivered to the exosphere directly by impacts while Ca, Al, Mg, Si, and Ti atoms are produced by the photolysis of their oxides and hydroxides. The chemistry of volatile elements such as H, S, C, and N during meteoroid bombardment is also considered. Our conclusions about the temperature and the concentrations of impact-produced atoms in the exosphere of Mercury may be checked by the Messenger spacecraft in the near future and by BepiColombo spacecraft some years later.     

On the escape of particles from cosmic ray modified shocks

Stationary solutions to the problem of particle acceleration at shock waves in the non-linear regime, when the dynamical reaction of the accelerated particles on the shock cannot be neglected, are known to show a prominent energy flux escaping from the shock towards upstream infinity. On physical grounds, the escape of particles from the upstream region of a shock has to be expected in all those situations in which the maximum momentum of accelerated particles,   p _max  , decreases with time, as is the case for the Sedov–Taylor phase of expansion of a shell supernova remnant, when both the shock velocity and the cosmic ray induced magnetization decrease. In this situation, at each time t , particles with momenta larger than   p _max( t )  leave the system from upstream, carrying away a large fraction of the energy if the shock is strongly modified by the presence of cosmic rays. This phenomenon is of crucial importance for explaining the cosmic ray spectrum detected at the Earth. In this paper, we discuss how this escape flux appears in the different approaches to non-linear diffusive shock acceleration, and especially in the quasi-stationary semi-analytical kinetic ones. We apply our calculations to the Sedov–Taylor phase of a typical supernova remnant, including in a self-consistent way particle acceleration, magnetic field amplification and the dynamical reaction on the shock structure of both particles and fields. Within this framework, we calculate the temporal evolution of the maximum energy reached by the accelerated particles and of the escape flux towards upstream infinity. The latter quantity is directly related to the cosmic ray spectrum detected at the Earth.     

X-ray probes of magnetospheric interactions with Jupiter's auroral zones, the Galilean satellites, and the Io plasma torus

Remote observations with the Chandra X-ray Observatory and the XMM-Newton Observatory have shown that the jovian system is a source of X-rays with a rich and complicated structure. The planet's polar auroral zones and its disk are both powerful sources of X-ray emission. Chandra observations revealed X-ray emission from the Io plasma torus and from the Galilean moons Io, Europa, and possibly Ganymede. The emission from the moons is due to bombardment of their surfaces by highly energetic magnetospheric protons, and oxygen and sulfur ions. These ions excite atoms in their surfaces leading to fluorescent X-ray emission lines. These lines are produced against an intense background continuum, including bremsstrahlung radiation from surface interactions of primary magnetospheric and secondary electrons. Although the X-ray emission from the Galilean moons is faint when observed from Earth orbit, an imaging X-ray spectrometer in orbit around one or more of these moons, operating from 200 eV to 8 keV with 150 eV energy resolution, would provide a detailed mapping of the elemental composition in their surfaces. Surface resolution of 40 m for small features could be achieved in a 100-km orbit around one moon while also remotely imaging surfaces of other moons and Jupiter's upper atmosphere at maximum regional resolutions of hundreds of kilometers. Due to its relatively more benign magnetospheric radiation environment, its intrinsic interest as the largest moon in the Solar System, and its mini-magnetosphere, Ganymede would be the ideal orbital location for long-term observational studies of the jovian system. Here we describe the physical processes leading to X-ray emission from the surfaces of Jupiter's moons and the properties required for the technique of imaging X-ray spectroscopy to map the elemental composition of their surfaces, as well as studies of the X-ray emission from the planet's aurora and disk and from the Io plasma torus.     

The variability of volcanic activity at Zamama, Culann, and Tupan Patera on Io as seen by the Galileo Near Infrared Mapping Spectrometer

Zamama, Culann, and Tupan Patera are three large, persistent volcanic centers on the jovian moon Io. As part of an ongoing project to quantify contributions from individual volcanic centers to Io’s thermal budget, we have quantified the radiant flux from all suitable observations made by the Galileo Near Infrared Mapping Spectrometer (NIMS) of these volcanoes, in some cases filling omissions in previous analyses. At Zamama, after a long period of cooling, we see a peak in thermal emission that corresponds with new plume activity. Subsequently, toward the end of the Galileo epoch, thermal emission from Zamama drops off in a manner consistent with a greatly reduced eruption rate and the cooling of emplaced flows. Culann exhibits possible episodic activity. We present the full Tupan Patera NIMS dataset and derive new estimates of thermal output and temporal behavior. Eruption rates at these three volcanoes are on the order of 30 m³ s⁻¹, consistent with a previous analysis of NIMS observations of Prometheus, and nearly an order of magnitude greater than Kilauea volcano, Hawai’i, Earth’s most active volcano. We propose that future missions to the jovian system could better constrain activity at these volcanoes and others where similar styles of activity are taking place by obtaining data on a time scale of, ideally, at least one observation per day. Observations at similar or even shorter timescales are desirable during initial waxing phases of eruption episodes. These eruptions are identifiable from their characteristic spectral signatures and temporal behavior.     

Light scattering by complex particles in the Moon's exosphere: Toward a taxonomy of models for the realistic simulation of the scattering behavior of lunar dust

It is suspected that the lunar exosphere has a dusty component dispersed above the surface by various physical mechanisms. Most of the evidence for this phenomenon comes from observations of “lunar horizon glow” (LHG), which is thought to be produced by the scattering of sunlight by this exospheric dust. The characterization of exospheric dust populations at the Moon is key to furthering our understanding of fundamental surface processes, as well as a necessary requirement for the planning of future robotic and human exploration.We present a model to simulate the scattering of sunlight by complex lunar dust grains (i.e. grains that are non-spherical and can be inhomogeneous in composition) to be used in the interpretation of remote sensing data from current and future lunar missions. We numerically model lunar dust grains with several different morphologies and compositions and compute their individual scattering signatures using the Discrete Dipole Approximation (DDA). These scattering properties are then used in a radiative transfer code to simulate the light scattering due to a dust size distribution, as would likely be observed in the lunar exosphere at high altitudes 10's of km. We demonstrate the usefulness and relevance of our model by examining mode: irregular grains, aggregate of spherical monomers and spherical grains with nano-phase iron inclusions. We subsequently simulate the scattering by two grain size distributions (0.1 and radius), and show the results normalized per-grain. A similar methodology can also be applied to the analysis of the LHG observations, which are believed to be produced by scattering from larger dust grains within about a meter of the surface.As expected, significant differences in scattering properties are shown between the analyses employing the widely used Mie theory and our more realistic grain geometries. These differences include large variations in intensity as well as a positive polarization of scattered sunlight caused by non-spherical grains. Positive polarization occurs even when the grain size is small compared to the wavelength of incident sunlight, thus confirming that the interpretation of LHG based on Mie theory could lead to large errors in estimating the distribution and abundances of exospheric dust.     

Diffusive propagation of fast particles in the presence of a moving shock wave

Based on an analytical model, we determined the temporal dynamics of the spectral shape and spatial distribution of the particles that were impulsively (in time) injected with a specified spectrum in the vicinity of a moving plane shock front. We obtained a condition to determine the influence of the shock front on the particle propagation, where the spatial diffusion coefficient of the particles plays a major role. Diffusive shock acceleration is shown to strongly affect low-energy particles (the intensity maximum coincides spatially with the shock front; hard and soft spectral regions are formed in the spectrum) and weakly affect high-energy particles (the time at which the intensity reaches its maximum is well ahead of the shock arrival time; the spectral shape does not change). In events accompanied by a significant increase in the turbulence level, the influence of the shock front on high-energy particles can change from weak to strong. This change shows up in the spatial distribution and spectral shape of the particles. The dynamics of the particle intensity, calculated with the diffusion coefficients that were determined in accordance with the quasi-linear theory for measured turbulence levels, qualitatively corresponds to the observed solar energetic-particle intensity.     

A nonlinear theory of stellar wind with allowance for the influence of relativistic particles

We solve the nonlinear problem of the dynamics of a steady-state, spherically symmetric stellar wind by taking into account particle acceleration to relativistic energies near the shock front. The particles are assumed to be accelerated through the Fermi mechanism, interacting with stellar-wind turbulence and crossing many times the shock front that separates the supersonic and subsonic stellar-wind regions. We take into account the influence of the accelerated particles on hydrodynamic plasma-flow parameters. Our method allows all hydrodynamic parameters of the shock front and plasma in the supersonic region to be determined in a self-consistent way and the accelerated-particle energy spectrum to be calculated. Our numerical and analytic calculations show that the plasma compression ratio at the shock front increases compared to the case where there are no relativistic particles and that the velocity profile in the supersonic region acquires a characteristic kink. The shape of the energy spectrum for the accelerated particles and their pressure near the front are essentially determined by the presumed dependence of the diffusion coefficient on particle energy, which, in turn, depends on the scale distribution of turbulent pulsations and other stellar-wind inhomogeneities.