The solar modulation of electrons in the heliosphere

The propagation and modulation of electrons in the heliosphere play an important part in improving our understanding and assessment of the modulation processes. A full three-dimensional numerical model is used to study the modulation of galactic electrons, from Earth into the inner heliosheath, over an energy range from 10 MeV to 30 GeV. The modeling is compared with observations of 6–14 MeV electrons from Voyager 1 and observations at Earth from the PAMELA mission. Computed spectra are shown at different spatial positions. Based on comparison with Voyager 1 observations, a new local interstellar electron spectrum is calculated. We find that it consists of two power-laws: In terms of kinetic energy E, the results give E ^?1.5 below ～500 MeV and E ^?3.15 at higher energies. Radial intensity profiles are computed also for 12 MeV electrons, including a Jovian source, and compared to the 6–14 MeV observations from Voyager 1. Since the Jovian and galactic electrons can be separated in the model, we calculate the intensity of galactic electrons below 100 MeV at Earth. The highest possible differential flux of galactic electrons at Earth with E=12 MeV is found to have a value of 2.5×10^?1 electrons m^?2?s^?1?sr^?1?MeV^?1 which is significantly lower (a factor of 3) than the Jovian electron flux at Earth. The model can also reproduce the extraordinary increase of electrons by a factor of 60 at 12 MeV in the inner heliosheath. A lower limit for the local interstellar spectrum at 12 MeV is estimated to have a value of (90±10) electrons m^?2?s^?1?sr^?1?MeV^?1.     

The time-dependent transport of cosmic rays in the heliosphere

The modulation of cosmic rays (CRs) in the heliosphere is a dynamic and therefore a highly time-dependent process. Numerical models with only a time-dependent neutral sheet prove to be successful when moderate to low solar activity occurs but fail to describe large and discrete steps in modulated CRs when solar activity is high. To explain this feature of heliospheric modulation, the concept of global merged interaction regions (GMIRs) is required. The combination of gradient, curvature and neutral sheet drifts with these GMIRs has so far been the most successful approach in explaining the 11-year and 22-year cycles in the long-term modulation of CRs.     

The expected pulsations of the heliosphere relevant to cosmic ray variations

The possible natural large-scale pulsations of the solar wind cavity are examined. The period of the pulsationsT2R/a (R is the size of the cavity,a is the sound velocity in the interstellar space near the solar system) may vary from a year to tens of years. The relevant new type of cosmic ray variations is predicted.     

The global modulation of Galactic and Jovian electrons in the heliosphere

A full three-dimensional, numerical model is used to study the modulation of Jovian and Galactic electrons from 1 MeV to 50 GeV, and from the Earth into the heliosheath. For this purpose the very local interstellar spectrum and the Jovian electron source spectrum are revisited. It is possible to compute the former with confidence at kinetic energies \(E < 50~\mbox{MeV}\) since Voyager 1 crossed the heliopause in 2012 at \(\sim 122~\mbox{AU}\), measuring Galactic electrons at these energies. Modeling results are compared with Voyager 1 observations in the outer heliosphere, including the heliosheath, as well as observations at or near the Earth from the ISSE3 mission, and in particular the solar minimum spectrum from the PAMELA space mission for 2009, also including data from Ulysses for 1991 and 1992, and observations above 1 MeV from SOHO/EPHIN. Making use of the observations at or near the Earth and the two newly derived input functions for the Jovian and Galactic electrons respectively, the energy range over which the Jovian electrons dominate the Galactic electrons is determined so that the intensity of Galactic electrons at Earth below 100 MeV is calculated. The differential intensity for the Galactic electrons at Earth for \(E = 1~\mbox{MeV}\) is \(\sim 4\) electrons \(\mbox{m}^{-2}\,\mbox{s}^{-1}\,\mbox{sr}^{-1}\,\mbox{MeV}^{-1}\), whereas for Jovian electrons it is \(\sim 350\) electrons \(\mbox{m}^{-2}\,\mbox{s}^{-1}\,\mbox{sr}^{-1}\,\mbox{MeV}^{-1}\). At \(E = 30~\mbox{MeV}\) the two intensities are the same; above this energy the Jovian electron intensity quickly subsides so that the Galactic intensity completely dominates. At 6 MeV, in the equatorial plane the Jovian electrons dominate but beyond \(\sim 15~\mbox{AU}\) the Galactic intensity begins to exceed the Jovian intensity significantly.     

Low-resolution spectra of the Io plasma torus 2 days after the Ulysses encounter

Low-resolution spectra of the Io plasma torus have been obtained on 10 and 11 February 1992 (2 days after the Ulysses encounter) using the 2 m telescope of the Bulgarian National Observatory. The spectra show the forbidden line emissions of S⁺ (λλ 6716, 6731 Å) and S²⁺ (λ 6312 Å). Measured intensities are compared with a Voyager-type model. The intensity distribution of [SII] is found to deviate from the model predictions which indicates a change in the torus at the Ulysses encounter when compared with the Voyager epoch. A corotating structure was observed, both in [SII] and [SIII], at λ_III = 170°, showing that the torus was not azimuthally symmetric. The λ 6716/λ 6731 and λ 6731/ λ 6312 line ratios indicate a higher electron density at the time of the Ulysses observations. Additionally, the shift of the torus caused by the dawn-dusk electric field could be observed. Peak intensities in [SII] were found at 5.66 ± 0.02 R_J on the West ansa and 5.91 ± 0.04 R_J on the East.     

The angular distribution of cosmic rays at the boundary of the heliosphere

Measurements of the sidereal daily variation of the muon intensity at a depth of 60 m.w.e. have been carried out in London using telescopes inclined at 70° to the zenith for the period 1972 to the present. The direction of maximum sensitivity for these telescopes lies in the Earth's equatorial plane and the asymptotic directions of look at the boundary of the heliosphere have been determined by integrating the equation of motion of the primary particles in a model interplanetary magnetic field. In this way the measured sidereal variation can be related to the cosmic ray intensity distribution in interstellar space. It is shown that the observational data are consistent with an axially symmetric intensity distribution of the form ΔI = 0.09 (1 + cosα) % where ΔI is the direction from the mean intensity and α is measured from the direction of maximum intensity which lies at 1^Π = 250° b^Π = ?60°. The most likely interpretation of this result is that the axis of this distribution corresponds to the local direction of the interstellar magnetic field and that the cosmic rays have a bulk streaming motion of 65±15 km s^?1 along the field direction.     

Cosmic rays in the heliosphere: Observations

This contribution to the 100th commemoration of the discovery of cosmic rays (6–8 August, 2012 in Bad Saarow, Germany) is about observations of those cosmic rays that are sensitive to the structure and the dynamics of the heliosphere. This places them in the energy range of 10⁷–10¹⁰ eV. For higher energies the heliosphere becomes transparent; below this energy range the particles become strictly locked into the solar wind. Rather than give a strict chronological development, the paper is divided into distinct topics. It starts with the Pioneer/Voyager missions to the outer edges of the heliosphere, because the most recent observations indicate that a distinct boundary of the heliosphere might have been reached at the time of the meeting. Thereafter, the Ulysses mission is described as a unique one because it is still the only spacecraft that has explored the heliosphere at very high latitudes. Next, anomalous cosmic rays, discovered in 1972–1974, constitute a separate component that is ideally suited to study the acceleration and transport of energetic particles in the heliosphere. At this point the history and development of ground-based observations is discussed, with its unique contribution to supply a stable, long-term record. The last topic is about solar energetic particles with energies up to ∼10¹⁰ eV.     

North-south asymmetry of the heliosphere from cosmic-ray observations

The evidence that the heliosphere retains a pronounced north-south asymmetry during a long period (five solar cycles) is discussed. A modification of the standard model for the interplanetary magnetic field that provides the observed asymmetry is considered.     

Ulysses observations of cosmic gamma-ray bursts

We review the current status of the Ulysses mission and summarize the results to date of the GRB experiment. This instrument detects bursts at the rate of about one every 3.5 days, and the localization data are being disseminated rapidly via the BACO-DINE and NMSU networks. The mission should operate through 2001, and future missions to Mars starting in 1996 will complete the 3rd Interplanetary Network.     

IMF-sense-dependent cosmic ray anisotropy produced from diffusion-convection in heliosphere

An IMF-sense-dependent first order (or unidirectional) anisotropy of cosmic rays, which is produced perpendicularly to the ecliptic from the radial density gradient in solar system, has been confirmed by Swinson. In the present paper, we point out the existence of IMF-sense-dependent higher order anisotropies, based on the simulation of cosmic ray diffusion-convection in the heliomagnetosphere. In order to confirm their existence, we demonstrate some examples of the observed cosmic ray daily variation which is supposed to be due to these anisotropies.     

Propagation of galactic cosmic rays in the outer heliosphere

The propagation of galactic cosmic rays in heliospheric magnetic fields is studied. An approximate solution to the cosmic ray transport equation has been derived on the basis of a method that takes into account the small value of anisotropy of particle angular distribution. The spatial and energy distributions of the cosmic ray intensity and anisotropy have been investigated, and estimates of cosmic ray energy flux have been carried out.     

The effect of solar wind latitudinal dependence on the cosmic-ray propagation in the heliosphere

We have investigated how the latitude dependence of the solar wind velocity (SWV) influenced the cosmic-ray (CR) modulation and distribution in the heliosphere. The dependence proposed by Fry and Akasofu (1987) is used:v _SW=v _O+v ₁(1-cos ⁿ _m , where the SWV,v _SW is a function of the heliomagnetic latitude _m andv ₀ andv ₁ are constants. An estimation of the diffusion and drift terms in the transport equation is made, which shows that towards the poles the effects of the drift transfer decrease, while the diffusion terms in the equation increase due to the change of the interplanetary magnetic field (IMF) geometry. The numerical solutions of the two-dimensional (2-D) transport equation show that when the SWV changes with latitude: (1) The CR intensities away from the neutral sheet are larger for both IMF polarity periods in comparison with the case when the SWV does not change with the latitude. (2) The latitude gradients are negative during negative magnetic polarity periods. (3) The Voyager 1 and Voyager 2 long-time observations showing greater galactic CR intensities nearer the Sun at greater distances, could be explained by the proposed model.     

Magnetic field configuration of the heliosphere in interstellar space

A model of the heliospheric magnetic field configuration is constructed by including a uniform interstellar magnetic field to the model proposed by Akasofu et al. (1980).     

The regimes of the east-west and the radial anisotropies of cosmic rays in the heliosphere

The observations obtained over the last 23 y suggest that there are two distinct physical states of the heliosphere. One state covers the period 1957–1970 when the diurnal anisotropy consists of the azimuthal component only. One may define this period as the regime of the East-West (co-rotation) anisotropy. The period 1971–1979 is characterized by the appearance of a radial anisotropy, which attains a maximum amplitude in 1976, when the solar activity is minimum. There appears to exist an inverse correlation between the amplitude of the radial anisotropy and solar activity. The amplitude of the EastWest anisotropy varies with time during this latter period and may also be rigidity-dependent. In 1976 the amplitude of the East-West anisotropy is zero for the underground muon data obtained at Embudo and has a lower value for the neutron monitor data obtained at Deep River. On the other hand, the amplitude of the radial anisotropy depends weakly upon the primary rigidity. The period 1971–1979 thus defines the regime of the radial anisotropy. The physical state of the heliosphere is very stable during the regime of the East-West anisotropy and extremely dynamic during the regime of the radial anisotropy. The heliosphere appears to switch from one physical state to another following the onset of the solar polar field reversal.     

Combined fitting of Ulysses/COMPTEL GRB spectra

This paper describes a comparison of observations of the HH 30 jet/counterjet system and theoretical models of jets propagating in a strongly stratified medium. We find that the observed westward bending of the HH 30 jet and counterjet can be explained as the result of a plane-parallel pressure stratification of the surrounding environment. This model predicts specific properties for the kinematics of the outflow, that could be straight-forwardly checked with future spectroscopic and proper motion studies of HH 30.     

The magnetohydrodynamic turbulent cascade in the ecliptic solar wind: Study of Ulysses data

The occurrence of a nonlinear turbulent energy cascade in solar wind plasma has been recently established through the observation of an exact law from spacecraft measurements. The main results obtained in the fast, polar wind measured by Ulysses spacecraft are reviewed here. In particular, the turbulent cascade is seen as the mean to provide the energy necessary for the local heating in the non-adiabatic expansion of the solar wind. The importance of the density fluctuations in enhancing the turbulent energy transport is also evidenced. The ecliptic wind data measured by Ulysses are studied here in the same framework. This has been done by separating fast and slow streams, in order to avoid mixing of different physical conditions. The results further support the need for separate analysis of the two types of wind.     

Evolution of fast and slow shock interactions in the inner heliosphere

We use a one-dimensional, time-dependent adaptive grid MHD code to study the interaction between fast and slow shocks in the solar wind. Our results show that: (1) a forward slow shock (FSS) can be destroyed by a forward fast shock (FFS) that overtakes it from behind; (2) two propagating FSSs can merge into a stronger FSS; (3) a strong FSS can survive by following a strong forward fast shock; and (4) the strength of a FSS is decreased by following an FFS. These simulation results reproduce an important feature of the Helios observations (Richter, 1987) where transient fast shocks were more frequently followed within a few hours by slow shock ype discontinuities rather than by fast reverse shocks.     

Interstellar pickup protons and solar wind heating in the outer heliosphere

The ionization of hydrogen atoms that penetrate into the heliosphere from the interstellar medium gives rise to a peculiar population of energetic protons (interstellar pickup protons) in the solar wind. The short-wavelength Alfvènic turbulence in the outer heliosphere is entirely attributable to the source associated with the instability of the initial anisotropic pickup proton velocity distribution. The bulk of the generated turbulent energy is subsequently absorbed by the pickup protons themselves through the cyclotron-resonance particle-wave interaction, and only an insignificant fraction of this energy can be transferred to the solar wind protons and heat them up.     

Evolution of fast and slow shock interactions in the inner heliosphere

We use a one-dimensional, time-dependent adaptive grid MHD code to study the interaction between fast and slow shocks in the solar wind. Our results show that: (1) a forward slow shock (FSS) can be destroyed by a forward fast shock (FFS) that overtakes it from behind; (2) two propagating FSSs can merge into a stronger FSS; (3) a strong FSS can survive by following a strong forward fast shock; and (4) the strength of a FSS is decreased by following an FFS. These simulation results reproduce an important feature of the Helios observations (Richter, 1987) where transient fast shocks were more frequently followed within a few hours by slow shock ype discontinuities rather than by fast reverse shocks.