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Register a new userThe Rigidity Dependence of the Diffusion Coefficient in the Heliosheath and an Explanation of the Extreme Solar Modulation Effects for Cosmic Ray Electrons from 3-60 MeV Observed at Voyager 1
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We believe that the extreme solar modulation of 3-60 MeV Galactic electrons measured by Voyager in the heliosheath and the interpretation of this new data in terms of the rigidity dependence of the diffusion coefficient at low rigidities presented in this paper represents a major step in understanding diffusion theory as it applies to energetic particles. This description uses electron spectra measured at 5 different epochs and distances within the heliosheath. The diffusion dependence needed to explain the remarkable solar modulation effects observed for both electrons and higher rigidity protons as one progresses from the heliopause inward by ~25 AU to the termination shock really has two distinct rigidity regimes. Above a rigidity ~Pc the diffusion coefficient has a dependence ~beta P, the modulation is ~P and its magnitude increases linearly with radius in AU according to the integral of dr/K. This integral defines a potential, beta, called the modulation potential, thus explaining the proton variations. At rigidities <Pc, the diffusion coefficient is ~beta and independent of rigidity. The modulation is also independent of rigidity but its magnitude depends on the modulation potential, thus explaining the electron modulation. One needs both electron and proton observations, together, to recognize the physical description of the solar modulation process. For the first time we have been able, using proton data at high rigidities and electron data at low rigidities, to put together a picture of the high and low rigidity diffusion coefficients and how they affect energetic particles in an astrophysical scale environment.
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Voyager 1 has entered regions of different propagation conditions for energetic cosmic rays in the outer heliosheath beginning at a distance of about 111 AU from the Sun. This conclusion is based on the fact that the low energy 6-14 MeV galactic electron intensity suddenly increased by ~20% over a time period leg 10 days and the electron radial intensity gradient abruptly decreased from ~19%/AU to ~8%/AU at 2009.7 at a radial distance of 111.2 AU. A sudden radial gradient change was also observed at this time for >200 MeV protons. The gradients were constant during the time period before and after the electron increase. At about 2011.2 at a distance of 116.6 AU a second abrupt intensity increase was observed, this time for both electrons and protons. The increase for electrons was ~25% and occurred over a time period ~15 days or less. For >200 MeV protons the increase at this time was ~5% (unusually large) and occurred over a longer time period ~50 days. Between about 2011.2 and 2011.6, radial intensity gradients ~18%/AU and 3%/AU were observed for electrons and protons, respectively. These gradients were very similar to those observed for these particles before the 1st sudden increase at 2009.7. These large positive gradients observed after 2011.2 indicate that V1, although it has entered a different propagation region, is still within the overall heliospheric modulating region at least up to a time ~2011.6 (118.0 AU). In this paper we will discuss these events in more detail and consider possibilities for their explanation that have recently been suggested.
The recovery of cosmic ray Carbon nuclei of energy ~20-125 MeV/nuc in solar cycle #23 from 2004 to 2010 has been followed at three locations, near the Earth using ACE data and at V2 between 74-92 AU and also at V1 beyond the heliospheric termination shock at between 91-113 AU. To describe the observed intensity changes and to predict the absolute intensities measured at all three locations we have used a simple spherically symmetric (no drift) two-zone heliospheric transport model with specific values for the diffusion coefficient in both the inner and outer zones. The diffusion coefficient in the outer zone is determined to be ~5-10 times smaller than that in the inner zone out to 90 AU. For both V1 and V2 the calculated C nuclei intensities agree within an average of pm 10% with the observed intensities. Because of this agreement between V1 and V2 observations and predictions there is no need to invoke an asymmetrical squashed heliosphere or other effects to explain the V2 intensities relative to V1 as is the case for He nuclei. The combination of the diffusion parameters used in this model and the interstellar spectrum give an unusually low overall solar modulation parameter phi = 250 MV to describe the Carbon intensities observed at the Earth in 2009. At all times both the observed and calculated spectra are very closely ~ E1.0 as would be expected in the adiabatic energy loss regime of solar modulation.
We suggest an analogy between energetic particle and magnetic field observations made by the Voyager 1 spacecraft in the distant heliosheath at 122 AU in August 2012, and those made in the distant geomagnetic tail by the ISEE 3 spacecraft in 1982-1983, despite large differences in the time and distance scales. The analogy suggests that in August, 2012, Voyager 1 may not have moved from the anomalous cosmic ray (ACR)-dominated heliosheath into the interstellar medium but into a region equivalent to the lobes of the geomagnetic tail, composed of heliospheric field lines which have reconnected with the interstellar medium beyond the spacecraft and so are open to the entry of cosmic rays, while heliospheric particles (e.g., ACRs) are free to escape, and which maintain a ~Parker spiral configuration. The heliopause, analogous to the magnetopause forming the outer boundary of the lobes, may then lie beyond this so-called heliocliff. Even if this analogy is incorrect, the remarkable similarities between the energetic particle and magnetic field observations in these very different regions are worth noting.
Studies on Voyager 1 using the CRS instrument have shown the presence of sub-MeV electrons in the interstellar medium beyond the heliopause. We believe that these electrons are the very low energy tail of the distribution of galactic GeV cosmic ray electrons produced in the galaxy. If so this observation places constraints on the origin and possible source distribution of these electrons in the galaxy. The intensities of these electrons as well as MeV protons and other higher energy electrons and nuclei have been followed outward from the Earth to beyond the heliopause during the 40 years of the Voyager mission. Among the other new features found in this study of the radial dependence of the electron intensity in the heliosphere are: 1. The heliosheath is a source of sub-MeV electrons as well as the already known anomalous cosmic rays of MeV and above, none of which appear to escape from the heliosphere because of an almost impenetrable heliopause at these lower energies; 2. Solar modulation effects are observed for these MeV electrons throughout the heliosphere. These modulation effects are particularly strong for electrons in the heliosheath and comprise over 90 percent of the observed intensity change of these electrons of 10-60 MeV between the Earth and the heliopause. Even for nuclei of 1 GV in rigidity, over 30 percent of the total intensity difference between the Earth and the LIM occurs in the heliosheath; 3. The 2 MeV protons studied here for the first time beyond the heliopause are also part of the low energy tail of the spectrum of galactic cosmic ray protons, similar to the tail noted above for sub MeV galactic cosmic ray electrons.
The recovery of cosmic ray He nuclei of energy ~150-250 MeV/nuc in solar cycle #23 from 2004 to 2010 has been followed at the Earth using IMP and ACE data and at V2 between 74-92 AU and also at V1 beyond the heliospheric termination shock (91-113 AU). The correlation coefficient between the intensities at the Earth and at V1 during this time period is remarkable (0.921), after allowing for a ~0.9 year delay due to the solar wind propagation time from the Earth to the outer heliosphere. To describe the intensity changes and to predict the absolute intensities measured at all three locations we have used a simple spherically symmetric (no drift) two-zone heliospheric transport model with specific values for the diffusion coefficient in both the inner and outer zones. The diffusion coefficient in the outer zone, assumed to be the heliosheath from about 90 to 120 (130) AU, is determined to be ~5 times smaller than that in the inner zone out to 90 AU. This means the Heliosheath acts much like a diffusing barrier in this model. The absolute magnitude of the intensities and the intensity changes at V1 and the Earth are described to within a few percent by a diffusion coefficient that varies with time by a factor ~4 in the inner zone and only a factor of ~1.5 in the outer zone over the time period from 2004-2010. For V2 the observed intensities follow a curve that is as much as 25% higher than the calculated intensities at the V2 radius and at times the observed V2 intensities are equal to those at V1. At least one-half of the difference between the calculated and observed intensities between V1 and V2 can be explained if the heliosphere is squashed by ~10% in distance (non-spherical) so that the HTS location is closer to the Sun in the direction of V2 compared to V1.
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