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

A solar cycle of cosmic ray fluxes for 2006–2014:comparison between PAMELA and neutron monitors

Abstract A comparison of cosmic proton spectra directly measured by the Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) experiment during 2006–2014 with data of polar neutron monitors for the same time interval is presented. It is shown that the measured spectra are well described by the force-field model for the modulation potential range 350–750 MV. The obtained modulation potential agrees with that calculated from the data of the world neutron monitor network for low solar activity between 2006 and 2012 but diverges during the maximum of solar cycle. The empirical relation between the modulation potential and the (inverted) neutron monitor count rate appears somewhat steeper than the modeled one, as confirmed also by data from fragmentary balloon-borne measurements. A reason for the discrepancy is unclear and calls for additional study using independent data sets

Neutron monitor altitude-dependent yield function and its application to an analysis of neutron-monitor data

Abstract An updated yield function (YF) of a standard NM64 neutron monitor (NM) is computed for different atmospheric depths from sea level to 500 g/cm² (∼5.7 km altitude) and is presented as a full parametrization. The NM YF was computed using the PLANETOCOSMICS simulation tool based on the GEANT4 package, applying the NRLMSISE-00 atmospheric model. The yield function was validated using the cosmic-ray spectra directly measured in space by the AMS-02 experiment during the period May 2011 through May 2017 and confronted with count rates of all NM64-type NMs being in operation during this period. Using this approach, the stability of all selected NMs was analyzed for the period 2011–2017, most of NMs appear very stable and suitable for studies of long-term solar modulation of cosmic rays. However, some NMs suffer from instabilities like trends, apparent jumps, or strong seasonal waves in the count rates

New method of assessment of the integral fluence of solar energetic (> 1 GV rigidity) particles from neutron monitor data

Abstract A new method to reconstruct the high-rigidity part (≥ 1 GV) of the spectral fluence of solar energetic particles (SEP) for GLE events, based on the world-wide neutron monitor (NM) network data, is presented. The method is based on the effective rigidity Reff and scaling factor Keff. In contrast to many other methods based on derivation of the best-fit parameters of a prescribed spectral shape, it provides a true non-parametric (viz. free of a priori assumptions on the exact spectrum) estimate of fluence. We reconstructed the SEP fluences for two recent GLE events, #69 (20 Jan. 2005) and #71 (17 May 2012), using four NM yield functions: (CD00 — Clem and Dorman in Space Sci. Rev.93, 335, 2000), (CM12 — Caballero-Lopez and Moraal in J. Geophys. Res.117, A12103, 2012), (Mi13 — Mishev, Usoskin, and Kovaltsov in J. Geophys. Res.118, 2783, 2013), and (Ma16 — Mangeard et al. in J. Geophys. Res.121, 7435, 2016b). The results were compared with full reconstructions and direct measurements by the PAMELA instrument. While reconstructions based on Mi13 and CM12 yield functions are consistent with the measurements, those based on CD00 and Ma16 ones underestimate the fluence by a factor of 2 – 3. It is also shown that the often used power-law approximation of the high-energy tail of SEP spectrum does not properly describe the GLE spectrum in the NM-energy range. Therefore, the earlier estimates of GLE integral fluences need to be revised

Application of verified neutron monitor yield function for GLE analysis

Abstract Systematic study of solar energetic particles provides an important basis to understand their acceleration and propagation in the interplanetary space. After solar eruptive processes, such as solar flares and/or coronal mass ejections, solar ions are accelerated to high energy. In the majority of cases, the maximum energy of the accelerated solar ions is several tens of MeV/nucleon, but in some cases, it exceeds 100 MeV/nucleon or even reaches the GeV/nucleon range. In this case, the energy is high enough, so that solar ions generate an atmospheric cascade in the Earth’s atmosphere, whose secondary particles reach the ground, being eventually registered by ground-based detectors, specifically neutron monitors. This particular class of events is known as ground-level enhancements (GLEs). Several methods for analysis of GLEs, using neutron monitor data were developed over the years. Here, we present a method for assessment of the spectral and angular characteristics of the GLEs using data from the world-wide NM network, namely by modeling the global neutron monitor network response with a new verified yield function. The method is based on consecutive steps, specifically detailed computation of asymptotic cones and rigidity cut-off of each station used in the analysis and optimization of the global neutron monitor response over experimental and modeled count rate increases. The method is compared with other methods, including in-situ measurements. A very good agreement between our method and space-borne measurements with PAMELA space probe, specifically the derived fluence of solar protons during GLE 71 was achieved, therefore verification of the method is performed

Updated neutron‐monitor yield function:bridging between in situ and ground‐based cosmic ray measurements

Abstract An updated yield function for a standard NM64 neutron monitor (NM) is computed and extended to different atmospheric depths from sea level to 500 g/cm² (∼5.7 km altitude) and is presented as lookup tables and a full parametrization. The yield function was validated using the cosmic ray spectra directly measured in space by the AMS‐02 experiment during the period May 2011 through May 2017 and confronted with count rates of all NM64‐type NMs being in operation during this period. Using this approach, stability of all the selected NMs was analyzed for the period 2011–2017. Most of NMs appear very stable and suitable for studies of long‐term solar modulation of cosmic rays. However, some NMs suffer from instabilities like trends, apparent jumps, or strong seasonal waves in the count rates