New reconstruction of event-integrated spectra (spectral fluences) for major solar energetic particle events

Fluences of solar energetic particles (SEPs) are not easy to evaluate, especially for high-energy events (i.e. ground-level enhancements, GLEs). Earlier estimates of event-integrated SEP fluences for GLEs were based on partly outdated assumptions and data, and they required revisions. Here, we present the results of a full revision of the spectral fluences for most major SEP events (GLEs) for the period from 1956 -- 2017 using updated low-energy flux estimates along with greatly revisited high-energy flux data and applying the newly invented reconstruction method including an improved neutron-monitor yield function. Low- and high-energy parts of the SEP fluence were estimated using a revised space-borne/ionospheric data and ground-based neutron monitors, respectively. The measured data were fitted by the modified Band function spectral shape. The best-fit parameters and their uncertainties were assessed using a direct Monte Carlo method. As a result, a full reconstruction of the event-integrated spectral fluences was performed in the energy range above 30 MeV, parametrised, and tabulated for easy use along with estimates of the 68% confidence intervals. This forms a solid basis for more precise studies of the physics of solar eruptive events and the transport of energetic particles in the interplanetary medium, as well as the related applications.Comment: 19 pages, 3 figures, to be published in Astronomy and Astrophysic

New reconstruction of event-integrated spectra (spectral fluences) for major solar energetic particle events

Aims. Fluences of solar energetic particles (SEPs) are not easy to evaluate, especially for high-energy events (i.e. ground-level enhancements, GLEs). Earlier estimates of event-integrated SEP fluences for GLEs were based on partly outdated assumptions and data, and they required revisions. Here, we present the results of a full revision of the spectral fluences for most major SEP events (GLEs) for the period from 1956 to 2017 using updated low-energy flux estimates along with greatly revisited high-energy flux data and applying the newly invented reconstruction method including an improved neutron-monitor yield function.Methods. Low- and high-energy parts of the SEP fluence were estimated using a revised space-borne/ionospheric data and ground-based neutron monitors, respectively. The measured data were fitted by the modified Band function spectral shape. The best-fit parameters and their uncertainties were assessed using a direct Monte Carlo method.Results. A full reconstruction of the event-integrated spectral fluences was performed in the energy range above 30 MeV, parametrised and tabulated for easy use along with estimates of the 68% confidence intervals.Conclusions. This forms a solid basis for more precise studies of the physics of solar eruptive events and the transport of energetic particles in the interplanetary medium, as well as the related applications.</p

Consistency of the average flux of solar energetic particles over timescales of years to megayears

Aims. Solar energetic particles (SEPs) have been measured directly in space over the past decades. Rare extreme SEP events are studied based on terrestrial cosmogenic proxy data for the past ten millennia. Lunar rocks record the average SEP fluxes on the megayear timescale. The question of whether the SEP fluxes averaged over different timescales are mutually consistent is still open. Here we analyze these different datasets for mutual consistency.Methods. Using the data from directly measured SEPs over the past decades and reconstructions of extreme SEP events in the past, we built a distribution function of the occurrence of annual SEP fluences for SEPs with energies above 30, 60, 100, and 200 MeV. The distribution function was fit with the Weibull and other types of distributions, and the long-term average SEP flux was computed and compared with the megayear SEP flux estimated from lunar data.Results. In contrast to the current paradigm, the direct space-era data are not representative of the long-term averaged SEP flux because they are only 20-55% of it, while the major fraction was formed by rare extreme SEP events in the past. The combined statistics of direct and proxy data are fully consistent with megayear lunar data, implying that our knowledge of the whole range of the SEP fluxes, from frequent weak to rare extreme events, is now consistent.</p

High-Resolution Spectral and Anisotropy Characteristics of Solar Protons During the GLE N(circle)73 on 28 October 2021 Derived with Neutron-Monitor Data Analysis

The first ground-level enhancement of the current Solar Cycle 25 occurred on 28 October 2021. It was observed by several space-borne and ground-based instruments, specifically neutron monitors. A moderate count-rate increase over the background was observed by high-altitude polar stations on the South Pole and Dome C stations at the Antarctic plateau. Most of the neutron monitors registered only marginal count-rate increases. Using detrended records and employing a method verified by direct space-borne measurements, we derive the rigidity spectra and angular distributions of the incoming solar protons in the vicinity of Earth. For the analysis, we employed a newly computed and parameterized neutron-monitor yield function. The rigidity spectra and anisotropy of solar protons were obtained in their time evolution throughout the event. A comparison with the Solar and Heliospheric Observatory/Energetic and Relativistic Nuclei and Electron (SOHO/ENRE) experiment data is also performed. We briefly discuss the results derived from our analysis

Extreme Solar Events: Setting up a Paradigm

The Sun is magnetically active and often produces eruptive events on different energetic and temporal scales. Until recently, the upper limit of such events was unknown and believed to be roughly represented by direct instrumental observations. However, two types of extreme events were discovered recently: extreme solar energetic particle events on the multi-millennial time scale and super-flares on sun-like stars. Both discoveries imply that the Sun might rarely produce events, called extreme solar events (ESE), whose energy could be orders of magnitude greater than anything we have observed during recent decades. During the years following these discoveries, great progress has been achieved in collecting observational evidence, uncovering new events, making statistical analyses, and developing theoretical modelling. The ESE paradigm lives and is being developed. On the other hand, many outstanding questions still remain open and new ones emerge. Here we present an overview of the current state of the art and the forming paradigm of ESE from different points of view: solar physics, stellar–solar projections, cosmogenic-isotope data, modelling, historical data, as well as terrestrial, technological and societal effects of ESEs. Special focus is paid to open questions and further developments. This review is based on the joint work of the International Space Science Institute (ISSI) team #510 (2020–2022)

Study of cosmic-ray variability using ground-based and space-borne data

Abstract Cosmic rays (CRs) are charged particles with energies above 1 MeV, accelerated in sources outside of the Earth’s magnetosphere. The variability of their fluxes, caused by solar modulation and solar eruptive events, is an important field of astroparticle physics, and represents the main focus of this study. The main instruments to study the cosmic-ray variability are neutron monitors (NMs), located at different locations around the globe, and space-borne experiments. A NM is an integral detector so that its response is integrally related to CR fluxes via NM response function. Space-borne experiments have particle detectors that allow to directly register different CR particles. In this work both data from NMs and space-borne experiments are combined to study the variability of CRs. In particular, the reconstruction of the solar modulation potential ϕ applying the simplified force-field (FF) model of the solar modulation of cosmic rays was performed using in-situ cosmic-ray fluxes measured by both the PAMELA and AMS-02 experiments together with NM data for the period from 2006 to 2017. Validation of the FF model for periods of different solar activity levels was further performed, and it was found that such an approximation performs better during solar minima, but disagrees with the observations of up to ≈ 10% during solar maximum. This makes the FF model approach not well suited for detailed studies of the solar modulation processes. At the same time, this precision is adequate to quantify the condition of the heliospheric modulation and to study its long-term variability. To study solar energetic particle (SEP) fluxes using NM data, a new method of “effective rigidity” was proposed, allowing to reconstruct high-energy SEP integral fluences recorded during ground level enhancement (GLE) events. A significant advantage of this novel method is that it is a non parametric one and thus the spectral shape of the SEP fluence can be deduced directly from the reconstructed data. Reconstructions of the SEP fluences for two recent GLEs, #69 and #71, using this newly developed method, yield a very good agreement with the laborious method of the full fluence reconstruction using NM data, and with PAMELA measurements (for GLE #71), but disagree with earlier simplified estimations based on NM data. The NM data analysis was performed using the NM yield function by Mishev et al. [2013], which was validated using the AMS-02 data for protons and helium for a time period between 2011 to 2017 and showed the best performance among other modern yield functions. Improved knowledge of the CR variability is crucially important for e.g. CR-induced atmospheric effects, including the production of cosmogenic isotopes

Fluences of solar energetic particles for last three GLE events:comparison of different reconstruction methods

Abstract Fluxes of solar energetic particles (SEPs), produced and accelerated in and in the vicinity of the Sun, are an important part of cosmic ray induced terrestrial effects such as ionizing radiation on the Earth’s orbit, which affects the exposure to radiation in space as well as the atmospheric ionization. Calculation of these effects requires the knowledge of the integral fluences of SEPs. High-energy solar particles are subject of special interest since they can significantly contribute to the total radiation dose and/or ionization. The main instrument to study the high-energy SEP events is a network of ground-based neutron monitors (NMs), used over the years to register a specific class of SEP, which is called ground-level enhancement (GLE) events. Up today, we possess records from 72 GLE events. Reconstruction of SEP integral and differential fluxes for GLE events using NM data is not an easy task, requires a careful and precise calculation of particle transport in the magnetosphere, atmosphere, and detector itself. In this work, we compare two methods of fluence reconstruction, “fast” and “full”, for the last three registered GLE events and additionally verify one of them using PAMELA experimental data

Pion decay model of the Tibet-ASγ PeV gamma-ray signal

Abstract The Tibet-ASγ Collaboration has recently reported a measurement of diffuse γ-ray flux from the outer Galactic disk in the energy range reaching PeV. We complement this measurement with the Fermi/LAT measurement of the diffuse flux from the same sky region and study the pion decay model of the combined Fermi/LAT + Tibet-ASγ spectrum. We find that within such a model the average cosmic-ray spectrum in the outer Galactic disk has the same characteristic features as the local cosmic-ray spectrum. In particular, it experiences a hardening at several hundred GV rigidity and a knee feature in the PV rigidity range. The slope of the average cosmic-ray spectrum above the break is close to the locally observed slope of the helium spectrum γ ≃ 2.5, but is harder than the slope of the local proton spectrum in the same rigidity range. Although the combination of Fermi/LAT and Tibet-ASγ data points to the presence of the knee in the average cosmic-ray spectrum, the quality of the data is not yet sufficient for the study of knee shape and cosmic-ray composition

Effective energy of cosmogenic isotope (¹⁰Be, ¹⁴C and ³⁶Cl) production by solar energetic particles and galactic cosmic rays

Abstract Cosmogenic isotopes ¹⁴C, ¹⁰Be and ³⁶Cl measured in datable natural archives provide the only known quantitative proxy for cosmic-ray (CR) and solar-activity variability before the era of direct measurements. Studies of relations between the measured isotope concentrations and CR variability require complicated modeling including the isotope production and transport in the terrestrial system. Here we propose a rough “effective energy” method to make quick estimates of the CR variability directly from the cosmogenic data using an approximate linear scaling between the measured isotope concentrations and the energy-integrated flux of CR above the effective energy. The method is based on the thoroughly computed effective yield function presented here. A simple way to account for the variable geomagnetic field is also provided. The method was developed for both solar energetic particles (SEPs) and galactic cosmic ray (GCR) variability and is shown to provide a robust result within 20% and 1% accuracy, respectively, without an assumption of the specific spectral shape. Applications of the effective-energy method to the known extreme SEP events and the secular GCR variability are discussed. The new method provides a simple and quick tool to assess the CR variability in the past. On the other hand, it does not supersede the full detailed modeling required for precise results

Effective rigidity of a polar neutron monitor for recording ground-level enhancements

Abstract The “effective” rigidity of a neutron monitor for a ground-level enhancement (GLE) event is defined so that the event-integrated fluence of solar energetic protons with rigidity above it is directly proportional to the integral intensity of the GLE as recorded by a polar neutron monitor, within a wide range of solar energetic-proton spectra. This provides a direct way to assess the integral fluence of a GLE event based solely on neutron-monitor data. The effective rigidity/energy was found to be 1.13 – 1.42 GV (550 – 800 MeV). A small model-dependent, systematic uncertainty in the value of the effective rigidity is caused by uncertainties in the low-energy range of the neutron-monitor yield function, which requires more detailed computations of the latter