On their way through the heliosphere, galactic cosmic rays (GCRs) are modulated by various effects before they can be detected at Earth. This process can be described by the Parker equation, which ...calculates the phase space distribution of GCRs depending on the main modulation processes: convection, drifts, diffusion, and adiabatic energy changes. A first‐order approximation of this equation is the force field approach, reducing it to a one‐parameter dependency, the solar modulation potential ϕ. Utilizing this approach, it is possible to reconstruct ϕ from ground‐based and spacecraft measurements. However, it has been shown previously that ϕ depends not only on the local interstellar spectrum (LIS) but also on the energy range of interest. We have investigated this energy dependence further, using published proton intensity spectra obtained by PAMELA and heavier nuclei measurements from IMP‐8 and ACE/CRIS. Our results show severe limitations at lower energies including a strong dependence on the solar magnetic epoch. Based on these findings, we will outline a new tool to describe GCR proton spectra in the energy range from a few hundred MeV to tens of GeV over the last solar cycles. In order to show the importance of our modification, we calculate the global production rates of the cosmogenic radionuclide 10Be which is a proxy for the solar activity ranging back thousands of years.
Key Points
We demonstrate significant rigidity dependence of force field approach
We introduce two‐parameter modification as simple and sufficient work‐around
We provide rigidity‐dependent solar modulation potential for 1973‐2016
The Ulysses spacecraft had been the first to orbit the Sun over its poles and to explore the heliosphere at these high heliolatitudes. It has now completed three fast latitude scans, two at solar ...minimum and one at solar maximum. Since its launch in October 1990, this mission has led to several surprising discoveries concerning energetic particles, cosmic rays, Jovian electrons, the solar wind, the heliospheric magnetic field and the global features of the heliosphere. This review addresses the propagation and modulation of cosmic rays and other charged particles from an observational point of view with emphasis on what has been learned from exploring the inner heliosphere to high heliolatitudes.
Context. During the transition from solar cycle 23 to 24 from 2006 to 2009, the Sun was in an unusual solar minimum with very low activity over a long period. These exceptional conditions included a ...very low interplanetary magnetic field (IMF) strength and a high tilt angle, which both play an important role in the modulation of galactic cosmic rays (GCR) in the heliosphere. Thus, the radial and latitudinal gradients of GCRs are very much expected to depend not only on the solar magnetic epoch, but also on the overall modulation level. Aims. We determine the non-local radial and the latitudinal gradients of protons in the rigidity range from ~0.45 to 2 GV. Methods. This was accomplished by using data from the satellite-borne experiment Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) at Earth and the Kiel Electron Telescope (KET) onboard Ulysses on its highly inclined Keplerian orbit around the Sun with the aphelion at Jupiter’s orbit. Results. In comparison to the previous A> 0 solar magnetic epoch, we find that the absolute value of the latitudinal gradient is lower at higher and higher at lower rigidities. This energy dependence is therefore a crucial test for models that describe the cosmic ray transport in the inner heliosphere.
Context. Among others, shocks are known to be accelerators of energetic charged particles. However, many questions regarding the acceleration efficiency and the required conditions are not fully ...understood. In particular, the acceleration of electrons by shocks is often questioned. Aims. In this study we determine the efficiency of interplanetary shocks for <100 keV electrons, and for ions at ~0.1 and ~2 MeV energies, as measured by the Solar Electron and Proton Telescope (SEPT) instruments aboard the twin Solar Terrestrial Relations Observatory (STEREO) spacecraft. Methods. We employ an online STEREO in situ shock catalog that lists all shocks observed between 2007 and mid 2014 (observed by STEREO A) and until end of 2013 (observed by STEREO B). In total 475 shocks are listed. To determine the particle acceleration efficiency of these shocks, we analyze the associated intensity increases (shock spikes) during the shock crossings. For the near-relativistic electrons, we take into account the issue of possible ion contamination in the SEPT instrument. Results. The highest acceleration efficiency is found for low energy ions (0.1 MeV), which show a shock-associated increase at 27% of all shocks. The 2 MeV ions show an associated increase only during 5% of the shock crossings. In the case of the electrons, the shocks are nearly ineffective. Only five shock-associated electron increases were found, which correspond to only 1% of all shock crossings.
With Voyager1 crossing the outer boundary of our solar system at the end of 2012, for the first time in the instrumental era an unmodulated local interstellar spectrum (LIS) at galactic particle ...energies below ~500 MeV has been measured. On the basis of these as well as Payload for Antimatter Matter Exploration and Light‐nuclei Astrophysics (PAMELA) and Alpha Magnetic Spectrometer (AMS02) measurements, most recently, three new LIS models have been proposed in the literature. In this study we compare the newest LIS models to previously most often used ones. Thereby, we investigate and discuss the influence of these LIS models on the terrestrial production rates of the cosmogenic radionuclides 10Be and 14C, which are produced due to the interaction of galactic and solar cosmic rays with atmospheric constituents. After being transported within the atmosphere they are preserved in natural archives such as, e.g., ice sheets or tree rings, forming a unique tool to study the solar modulation of thousands of years back in time. To parameterize the heliospheric modulation we apply the force‐field approximation for the individual LIS models from which LIS‐dependent solar modulation parameter (ϕ) values are derived. Furthermore, we present updated sets of linear regression functions containing the opportunity to convert the LIS‐dependent ϕ values between the investigated LIS models. The results are then applied to a long‐term reconstruction of the solar modulation parameter.
Key Points
Comparison of the new LIS models with previously used models
Investigation of the LIS‐dependent differences in the 10Be and 14C production rates
Updated reconstruction of the solar activity over the past 1000 years
Late on 2011 November 3, STEREO-A, STEREO-B, MESSENGER, and near-Earth spacecraft observed an energetic particle flux enhancement. Based on the analysis of in situ plasma and particle observations, ...their correlation with remote sensing observations, and an interplanetary transport model, we conclude that the particle increases observed at multiple locations had a common single-source active region and the energetic particles filled a very broad region around the Sun. The active region was located at the solar backside (as seen from Earth) and was the source of a large flare, a fast and wide coronal mass ejection, and an EIT wave, accompanied by type II and type III radio emission. In contrast to previous solar energetic particle events showing broad longitudinal spread, this event showed clear particle anisotropies at three widely separated observation points at 1 AU, suggesting direct particle injection close to the magnetic footpoint of each spacecraft, lasting for several hours. We discuss these observations and the possible scenarios explaining the extremely broad particle spread for this event.
We investigate multi-spacecraft observations of the 17 January 2010 solar energetic particle event. Energetic electrons and protons have been observed over a remarkable large longitudinal range at ...the two STEREO spacecraft and SOHO, suggesting a longitudinal spread of nearly 360 degrees at 1 AU. The flaring active region, which was on the backside of the Sun as seen from Earth, was separated by more than 100 degrees in longitude from the magnetic footpoints of each of the three spacecraft. The event is characterized by strongly delayed energetic particle onsets with respect to the flare and only small or no anisotropies in the intensity measurements at all three locations. The presence of a coronal shock is evidenced by the observation of a type II radio burst from the Earth and STEREO-B. In order to describe the observations in terms of particle transport in the interplanetary medium, including perpendicular diffusion, a 1D model describing the propagation along a magnetic field line (model 1) (Dröge,
Astrophys. J
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, 1027 – 1039,
2003
) and the 3D propagation model (model 2) by Dröge
et al
. (
Astrophys. J
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, 912 – 919,
2010
) including perpendicular diffusion in the interplanetary medium have been applied. While both models are capable of reproducing the observations, model 1 requires injection functions at the Sun of several hours. Model 2, which includes lateral transport in the solar wind, reveals high values for the ratio of perpendicular to parallel diffusion. Because we do not find evidence for unusual long injection functions at the Sun, we favor a scenario with strong perpendicular transport in the interplanetary medium as an explanation for the observations.
We analyze 65–105 keV electrons in the 7 February 2010 solar electron event observed simultaneously by STEREO‐A, STEREO‐B, and ACE. A method to reconstruct the full‐electron pitch angle distributions ...from the four Solar Electron and Proton Telescope sensors on STEREO‐A/B and the Solar Electron and Proton Telescope instrument on ACE in the energy range of approximately 60–300 keV for periods of incomplete angular coverage is presented. A transport modeling based on numerical solutions of a three‐dimensional particle propagation model which includes pitch angle scattering and focused transport is applied to the intensity and anisotropy profiles measured on all three spacecraft. Based on an analysis of intensity gradients observed between the three spacecraft, we find that the lateral transport of the electrons occurs partially close to the Sun, due to effects of nonradial divergence of magnetic field lines or particle diffusion, and partially in the interplanetary medium. For the mean free paths characterizing the electron diffusion parallel and perpendicular to the interplanetary magnetic field, we derive values of λ∥∼ 0.1 AU and λ⟂∼ 0.01 AU. In comparison with results from other particle events which we had previously analyzed in a similar manner we discuss whether the diffusion mean free paths parallel and perpendicular to the average magnetic field might be related with each other, and whether the particle transport perpendicular to the average magnetic field is more likely due to particles following meandering magnetic field lines, or due to particles being scattered off individual field lines.
Key Points
We analyze solar electrons observed simultaneously on the STEREO‐A/B and ACEA numerical simulation of the three‐dimensional electron transport is presentedParallel and perpendicular diffusion coefficients are derived
Context. In February 2011, the two STEREO spacecrafts reached a separation of 180 degrees in longitude, offering a complete view of the Sun for the first time ever. When the full Sun surface is ...visible, source active regions of solar energetic particle (SEP) events can be identified unambiguously. STEREO, in combination with near-Earth observatories such as ACE or SOHO, provides three well separated viewpoints, which build an unprecedented platform from which to investigate the longitudinal variations of SEP events. Aims. We show an ensemble of SEP events that were observed between 2009 and mid-2013 by at least two spacecrafts and show a remarkably wide particle spread in longitude (wide-spread events). The main selection criterion for these events was a longitudinal separation of at least 80 degrees between active region and spacecraft magnetic footpoint for the widest separated spacecraft. We investigate the events statistically in terms of peak intensities, onset delays, and rise times, and determine the spread of the longitudinal events, which is the range filled by SEPs during the events. Energetic electron anisotropies are investigated to distinguish the source and transport mechanisms that lead to the observed wide particle spreads. Methods. According to the anisotropy distributions, we divided the events into three classes depending on different source and transport scenarios. One potential mechanism for wide-spread events is efficient perpendicular transport in the interplanetary medium that competes with another scenario, which is a wide particle spread that occurs close to the Sun. In the latter case, the observations at 1 AU during the early phase of the events are expected to show significant anisotropies because of the wide injection range at the Sun and particle-focusing during the outward propagation, while in the first case only low anisotropies are anticipated. Results. We find events for both of these scenarios in our sample that match the expected observations and even different events that do not agree with the scenarios. We conclude that probably both an extended source region at the Sun and perpendicular transport in the interplanetary medium are involved for most of these wide-spread events.
Studies of the propagation of charged energetic particles in the Earth's magnetic field go back to Carl Størmer. In the end, his investigations finally lead to the definition of the so-called cutoff ...rigidity RC; that is, the minimum momentum per charge a particle must have in order to reach a certain geographical location. Employing Monte Carlo simulations with the PLANETOCOSMICS code we investigate the correlation between the geomagnetic field structure and the cutoff rigidity. We show that the geometry of the magnetic field has a considerable influence on the resulting cutoff rigidity distribution. Furthermore, we will present a simple geometry-based parameter, δB, which is able to reflect the location-dependent cutoff rigidity. We show that this correlation is also visible in the temporal evolution of the Earth's magnetic field, at least over the last 100 yr. Using latitude scans with neutron monitors, changes of the relative counting rates at different positions are calculated, showing small variations for, e.g., Kiel and Moscow, while large ones occur at Mexico City as well as on the British Virgin Islands.
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