Cosmic Ray Spectrum Research Articles

Attaining the PeV frontier of the cosmic ray spectrum in space with HERD

The High Energy cosmic-Radiation Detection facility (HERD) is a calorimetric experiment planned to be launched in 2027. It will be operational for at least 10 years on board the China Space Station. With HERD we will measure the energy flux of cosmic protons and heavier nuclei from 30 GeV up to, for the first time in space, a few PeV. We will search for signatures of annihilation and decay products of dark matter in the energy spectrum of cosmic electrons and gamma rays from 10 GeV to 100 TeV. A wide field of view monitoring of the gamma-ray full-sky from 100 MeV will also be performed. The five HERD subdetectors, the calorimeter (CALO), the scintillating fiber tracker (FIT), the plastic scintillator detector (PSD), the silicon charge detector (SCD) and the transition radiation detector (TRD), are currently under development. The design, prospects and expected performance of HERD, as well as its contribution to the multimessenger astronomy will be presented in this contribution.

The energy spectrum of ultra-high energy cosmic rays measured at the Pierre Auger Observatory and the Telescope Array

In the study of cosmic rays, the measurement of the energy spectrum of the primaries is one of the main issues and provides fundamental information on the most energetic phenomena in the Universe. At ultrahigh energies, beyond 1018 eV, the cosmic rays are studied by the two largest observatories built so far, the Pierre Auger Observatory and the Telescope Array. Both observatories are based on a hybrid design and reported a measurement of the energy spectrum using the high duty cycle of the surface detector and the calorimetric estimation of the energy scale provided by the fluorescence detector. The differences among the reported spectra are scrutinized by a working group made by members of the Pierre Auger and Telescope Array Collaborations. The two measurements have been found well in agreement below 1019 eV while, at higher energies, they show an energy-dependent difference that is beyond the systematic uncertainties associated to the energy scale. In this contribution we review the status and perspectives of the working group activities including new studies aiming at addressing the impact on the flux measurement at the highest energies of potential biases in the estimation of the shower size.

Measurement of Cosmic-ray Energy Spectrum with the TALE Detector in Hybrid Mode

The TA Low-energy Extension (TALE) experiment extends the energy range observed by the TA experiment to below 1016 eV. We aim to study the transition from galactic to extragalactic cosmic rays. The TALE detector is a hybrid apparatus composed of fluorescence telescopes and surface detectors. The surface detectors are arranged to be suitable for hybrid energy spectrum measurements in the low-energy region. We measured the energy spectrum with the 392 hours observation data of the TALE hybrid detector. This energy spectrum measurement will play an important role in understanding the transition from cosmic rays of galactic origin to those of extragalactic origin.

The energy spectrum of cosmic rays above 6 PeV as measured at the Pierre Auger Observatory

Since 2004, the Pierre Auger Collaboration has measured, with unprecedented precision, one of the most important features of ultra-high-energy cosmic rays, the energy spectrum. Located in the Southern hemisphere, the Observatory comprises an array of 1660 water-Cherenkov detectors covering 3000 km² overlooked by 27 fluorescence telescopes. Five sets of measurements have been used to reconstruct the spectrum from 6 PeV to beyond 100 EeV. The highest-energy events, recorded by surface detectors on a 1500 m triangular grid, are reconstructed differently depending on their inclination (vertical events below 60° and inclined ones above 60°). A cross-check of these measurements is made using ‘hybrid events’, in which there are simultaneous detections at both the fluorescence detectors and at least one surface detector. Events with energies below 3 EeV have been studied using a nested array with a spacing of 750 m and using the Cherenkov light recorded with three high-elevation telescopes. In this contribution, updated methods for the reconstruction of all events are discussed, together with their associated uncertainties. A combination of all data sets is reported to construct a spectrum above 6 PeV to the highest energies. A detailed discussion of the spectral features will be presented.

Single source scenario describing the very end of the cosmic ray energy spectrum

The energy spectrum of cosmic rays is steeply falling with a suppression of the flux at the highest energies caused by energy losses during propagation or by reaching the maximum energy of cosmic accelerators. The energy spectrum at the highest energies is currently measured with high precision by two experiments, Telescope Array in the Northern hemisphere and the Pierre Auger Observatory in the Southern hemisphere. In this work, we study the possibility of explaining the shape of the energy spectrum above 1019.5 eV measured by the Pierre Auger Observatory with a single source. Using CRPropa 3 numerical simulations of cosmic ray propagation in the Universe we show possible features of such a single source that would be able to create a shape of the energy spectrum compatible with the measurement including limitations on the source distance, spectral index and mass composition.

Reconstruction of the muon production longitudinal profiles in extensive air showers

Muons produced in extensive air showers have large decay lengths and small radiative energy losses, enabling a large fraction of them to reach surface and underground detector arrays while keeping relevant information about the hadronic interactions that occurred high in the atmosphere. We can relate a muon’s arrival time and position at the detector to its production depth in the atmosphere. The total delay of muons with respect to the shower plane is primarily due to their geometric path and energy, we call these contributions the geometric and kinematic delays, respectively. We are working on the improvement of the current kinematic delay parameterizations using Deep Neural Networks for muons arriving at surface and underground detector arrays. We aim to reconstruct the longitudinal profile of muons for future arrays of buried scintillator detectors at energies from around the second knee to the ankle of the cosmic ray spectrum, where there is an overlap with the nominal energies at the LHC. Given the low acceptance of scintillator detectors to inclined air showers and the richness of the forward physics near the shower core, we aim at applying a radial cut of 200 m instead of the usual 1000 m used in previous works.

Latest results from the DAMPE space mission

The space-based DAMPE (DArk Matter Particle Explorer) particle detector has been taking data for more than 7 years since its successful launch in December 2015. Its main scientific goals include the indirect search for dark matter signatures in the cosmic lepton and gamma-ray spectra, the study of galactic cosmic rays up to energies of hundreds of TeV and studies on highenergy gamma ray astronomy. The measurement of galactic cosmic ray spectra are reported here, those being fundamental tools to investigate the mechanisms of acceleration at their sources and propagation through the interstellar medium. Results on proton and helium, which revealed new spectral features, are described. Ongoing analyses on the cosmic ray light, medium and heavy mass nuclei are outlined, together with studies of the so-called secondary cosmic rays. Latest results on gamma-ray astronomy and dark matter search will be also summarized.

The transition from Galactic to extragalactic cosmic rays: The high–energy end of the Galactic spectrum

Understanding the transition from Galactic to extragalactic cosmic rays (CRs) is essential to make sense of the Local cosmic ray spectrum. Several models have been proposed to account for this transition in the 0.1 - 10 × 1018 eV range. For instance: ankle models, where the change from a steep Galactic component to a hard extragalactic spectrum occurs in the 4 − 10 × 1018 eV region, dip models, where the interactions of CR protons with the CMB producing electron-positron pairs shape the ankle, or mixed composition models, in which extragalactic CRs are composed of nuclei of various types. In all these scenarios, the low-energy part of the transition involves the high-energy part of the Galactic component. Therefore, any information on the Galactic component, such as maximum energy, chemical composition, and spectrum after propagation, is crucial to understanding the Galactic-extragalactic transition. We briefly review the high-energy part of the CR spectrum expected from the best potential sources of Galactic CRs.

Interpreting the cosmic ray spectrum and composition measurements across the ankle and up to the highest energies with the data of the Pierre Auger Observatory

In this work we present a combined fit of the energy spectrum and mass composition data above 6×1017 eV as measured by the Pierre Auger Collaboration and we show that our data can be reproduced by the superposition of two (or more) components, either Galactic or extragalactic. We use a simple astrophysical model with two extragalactic components, one dominant at high energy and the other at low energy, whose superposition generates the so-called “ankle” feature. We find that the component dominating the low (high) energy region is required to be emitted from the sources with a very soft (hard) spectrum. In our best fit scenario the sources contributing above the ankle emit a mixed and increasingly heavier mass composition, whereas a mix of protons and intermediate-mass nuclei is observed below the ankle, which reach the Earth almost una↵ected by the propagation in the intergalactic space. The possible presence of a Galactic population providing the intermediate-mass contribution at low energy is also explored. In order to evaluate our capability to constrain astrophysical models, we finally discuss the impact on the fit results of the main experimental systematic uncertainties and of the assumptions on the quantities a↵ecting propagation, both in the atmosphere and in the intergalactic medium.

Constraining ultra-high-energy cosmic ray composition through cross-correlations

The chemical composition of the highest end of the ultra-high-energy cosmic ray spectrum is very hard to measure experimentally, and to this day it remains mostly unknown. Since the trajectories of ultra-high-energy cosmic rays are deflected in the magnetic field of the Galaxy by an angle that depends on their atomic number Z, it could be possible to indirectly measure Z by quantifying the amount of such magnetic deflections. In this paper we show that, using the angular harmonic cross-correlation between ultra-high-energy cosmic rays and galaxies, we could effectively distinguish different atomic numbers with current data. As an example, we show how, if Z = 1, the cross-correlation can exclude a 39% fraction of Fe56 nuclei at 2σ for rays above 100 EeV.

GLE73 Event (October 28, 2021) in Solar Cosmic Rays

Results are presented from analyzing the GLE73 event in terms of solar cosmic rays. The GLE73 event raised the count by 2–6% at polar stations of the World Neutron Monitor Network. A direct solution to the inverse problem is found, along with and the energy spectra of solar cosmic rays at the boundary of the magnetosphere are obtained and the pitch angle distribution of the flux.

Quantitative study of the hardening in the Alpha Magnetic Spectrometer nuclei spectra at a few hundred GV

The most significant feature in the cosmic-ray (CR) nuclei spectra is the spectral hardening at a few hundred GV. It is important to know whether the hardening of different nuclei species is the same or not for constructing CR sources and propagation models. In this work, we collect the recently released AMS-02 CR nuclei spectra of primary species (proton, helium, carbon, oxygen, neon, magnesium, silicon, and iron), secondary species (lithium, beryllium, boron, and fluorine), and hybrid species (nitrogen, sodium, and aluminum) and study the break positions and the spectral index differences (less and greater than the break rigidity) of the spectral hardening quantitatively. The results show us that the CR nuclei spectral hardening at a few hundred GV has hybrid origins. In detail, the dominating factors of the spectral hardening for primary and secondary CR nuclei species are different: the former comes from the superposition of different kinds of CR sources, while the latter comes from the propagation process. Both of these factors influence all kinds of CR nuclei spectra, just with different weights.

Constraining the Position of the Knee in the Galactic Cosmic-Ray Spectrum with Ultra-high-energy Diffuse γ-Rays

The diffuse γ-ray emission was measured up to 957 TeV by the Tibet-ASγ experiment recently. Assuming that it is produced by the hadronic interaction between cosmic-ray nuclei and the interstellar medium, it requires that the cosmic-ray nuclei should be accelerated well beyond PeV energies. Measurements of the cosmic-ray spectra for different species show diverse results at present. The Tibet experiments showed that the spectrum of proton plus helium has an early knee below PeV. If this is correct, the diffuse γ-ray emission would suggest an additional component of Galactic cosmic rays above PeV energies. This second component may originate from a source population of so-called PeVatrons revealed by recent ultra-high-energy γ-ray observations and could contribute to the cosmic-ray fluxes up to the energy of the second knee. On the other hand, the KASCADE measurement showed that the knee of protons is higher than PeV. In this case, the diffuse γ-rays observed by Tibet-ASγ can be well accounted for by only one cosmic-ray component. These two scenarios (i.e., the Tibet and KASCADE knees) could be distinguished by the spectral structures of diffuse γ-rays and cosmic-ray nuclei. Future measurements of spectra of individual nuclei by HERD and LHAASO experiments and diffuse γ-rays by LHAASO can jointly constrain these two scenarios.

Standard self-confinement and extrinsic turbulence models for cosmic ray transport are fundamentally incompatible with observations

ABSTRACT Models for cosmic ray (CR) dynamics fundamentally depend on the rate of CR scattering from magnetic fluctuations. In the ISM, for CRs with energies ∼MeV-TeV, these fluctuations are usually attributed either to ‘extrinsic turbulence’ (ET) – a cascade from larger scales – or ‘self-confinement’ (SC) – self-generated fluctuations from CR streaming. Using simple analytic arguments and detailed ‘live’ numerical CR transport calculations in galaxy simulations, we show that both of these, in standard form, cannot explain even basic qualitative features of observed CR spectra. For ET, any spectrum that obeys critical balance or features realistic anisotropy, or any spectrum that accounts for finite damping below the dissipation scale, predicts qualitatively incorrect spectral shapes and scalings of B/C and other species. Even if somehow one ignored both anisotropy and damping, observationally required scattering rates disagree with ET predictions by orders of magnitude. For SC, the dependence of driving on CR energy density means that it is nearly impossible to recover observed CR spectral shapes and scalings, and again there is an orders-of-magnitude normalization problem. But more severely, SC solutions with super-Alfvénic streaming are unstable. In live simulations, they revert to either arbitrarily rapid CR escape with zero secondary production, or to bottleneck solutions with far-too-strong CR confinement and secondary production. Resolving these fundamental issues without discarding basic plasma processes requires invoking different drivers for scattering fluctuations. These must act on a broad range of scales with a power spectrum obeying several specific (but plausible) constraints.

Constraining the charge-sign and rigidity-dependence of solar modulation

Our ability to identify the sources of cosmic rays and understand how these particles propagate through the interstellar medium is hindered by the combined effects of the solar wind and its embedded magnetic field, collectively known as solar modulation. In this paper, we build upon our previous work to model and constrain the effects of solar modulation on the cosmic-ray spectrum, using data from AMS-02 and BESS Polar II collected between 2007 and 2012, during which the heliospheric magnetic field was in a state of negative polarity. Our model uses measurements of the heliospheric magnetic field and the tilt angle of the heliospheric current sheet to accurately predict the effects of solar modulation as a function of time, charge, and rigidity. By incorporating data from a period of negative polarity, we have been able to robustly observe and constrain the charge-dependent effects of solar modulation.

The Impact of Crystal Light Yield Non-Proportionality on a Typical Calorimetric Space Experiment: Beam Test Measurements and Monte Carlo Simulations

Calorimetric space experiments were employed for the direct measurements of cosmic-ray spectra above the TeV region. According to several theoretical models and recent measurements, relevant features in both electron and nucleus fluxes are expected. Unfortunately, sizable disagreements among the current results of different space calorimeters exist. In order to improve the accuracy of future experiments, it is fundamental to understand the reasons of these discrepancies, especially since they are not compatible with the quoted experimental errors. A few articles of different collaborations suggest that a systematic error of a few percentage points related to the energy-scale calibration could explain these differences. In this work, we analyze the impact of the nonproportionality of the light yield of scintillating crystals on the energy scale of typical calorimeters. Space calorimeters are usually calibrated by employing minimal ionizing particles (MIPs), e.g., nonshowering proton or helium nuclei, which feature different ionization density distributions with respect to particles included in showers. By using the experimental data obtained by the CaloCube collaboration and a minimalist model of the light yield as a function of the ionization density, several scintillating crystals (BGO, CsI(Tl), LYSO, YAP, YAG and BaF2) are characterized. Then, the response of a few crystals is implemented inside the Monte Carlo simulation of a space calorimeter to check the energy deposited by electromagnetic and hadronic showers. The results of this work show that the energy scale obtained by MIP calibration could be affected by sizable systematic errors if the nonproportionality of scintillation light is not properly taken into account.

Constraining the charge-, time-, and rigidity-dependence of cosmic-ray solar modulation with AMS-02 observations during Solar Cycle 24

Our basic theoretical understanding of the sources of cosmic rays and their propagation through the interstellar medium is hindered by the Sun, that through the solar wind affects the observed cosmic-ray spectra. This effect is known as solar modulation. Recently released cosmic-ray observations from the Alpha Magnetic Spectrometer (AMS-02) and publicly available measurements of the solar wind properties from the Advanced Composition Explorer and the Wilcox observatory allow us to test the analytical modeling of the time-, charge- and rigidity-dependence of solar modulation. We rely on associating measurements on the local heliospheric magnetic field and the heliospheric current sheet's tilt angle, to model the time-dependence and amplitude of cosmic-ray solar modulation. We find evidence for the solar modulation's charge- and rigidity-dependence during the era of solar cycle 24. Our analytic prescription to model solar modulation can explain well the large-scale time-evolution of positively charged cosmic-ray fluxes in the range of rigidities from 1 to 10 GV. We also find that cosmic-ray electron fluxes measured during the first years of cycle 24 are less trivial to explain, due to the complex and rapidly evolving structure of the Heliosphere's magnetic field that they experienced as they propagated inwards.

Highly collimated microquasar jets as efficient cosmic-ray sources

Context. Supernova remnants (SNRs) are currently believed to be the main sites of origin for Galactic cosmic rays. This scenario, however, fails to explain some of the features observed in the cosmic-ray spectrum. Microquasars have been proposed as additional candidates, as their non-thermal emission indicates the existence of efficient particle acceleration mechanisms in their jets. Only a few initial attempts have been made so far to quantify the contribution of microquasars to the Galactic cosmic-ray population. A promising scenario envisages the production of relativistic neutrons in the jets that decay outside the system, injecting relativistic protons to the surroundings. The first investigations of this scenario suggest that microquasars might stand as a fair alternative to cosmic-ray sources. Aims. We aim to assess the role played by the degree of collimation of the jet on the cosmic-ray energetics in the neutron-carrier scenario, as well as the location and size of the emission region and the interactions of protons with photon fields. Our goal is to explain the Galactic component of the observed proton cosmic-ray spectrum at energies higher than ∼10 GeV and to relate the aforementioned jet properties with the power and spectral index of the produced cosmic rays. Methods. Here, we improve upon previous analytical models of relativistic particle transport in microquasar jets by including prescriptions for the jet geometry and convection within it. We introduced the neutron component through catastrophic terms that couple the proton and neutron transport equations, then we computed the escape and decay of these neutrons. Finally, we followed the propagation of the decay products and obtained the proton cosmic-ray spectrum once the particles reached the interstellar medium. Results. We find that collimated jets, with compact acceleration regions close to the jet base, are very efficient sources that could deliver a fraction of up to ∼0.01 of their relativistic proton luminosity into cosmic rays. Collimation is the most significant feature regarding efficiency: a well-collimated jet might be four orders of magnitude more efficient than a poorly collimated one. These sources produce a steep spectral index of ∼2.3 at energies up to ∼10 TeV. Conclusions. Single microquasars may rival SNRs with respect to the power injected to the interstellar medium through cosmic rays. The main advantage of the former is the production of a steeper spectrum than the latter that is closer to what has been observed. The predictions of our model may be used to infer the total contribution of the population of Galactic microquasars to the cosmic ray population and, therefore, to quantitatively assess their significance as cosmic-ray sources.

Observation of Spectral Structures in the Flux of Cosmic-Ray Protons from 50GeV to 60TeV with the Calorimetric Electron Telescope on the International Space Station.

A precise measurement of the cosmic-ray proton spectrum with the Calorimetric Electron Telescope (CALET) is presented in the energy interval from 50GeV to 60TeV, and the observation of a softening of the spectrum above 10TeV is reported. The analysis is based on the data collected during ∼6.2 years of smooth operations aboard the International Space Station and covers a broader energy range with respect to the previous proton flux measurement by CALET, with an increase of the available statistics by a factor of ∼2.2. Above a few hundred GeV we confirm our previous observation of a progressive spectral hardening with a higher significance (more than 20 sigma). In the multi-TeV region we observe a second spectral feature with a softening around 10TeV and a spectral index change from -2.6 to -2.9 consistently, within the errors, with the shape of the spectrum reported by DAMPE. We apply a simultaneous fit of the proton differential spectrum which well reproduces the gradual change of the spectral index encompassing the lower energy power-law regime and the two spectral features observed at higher energies.

Development of the photo-diode subsystem for the HERD calorimeter double-readout

The measurement of cosmic-ray individual spectra provides unique information regarding the origin and propagation of astro-particles. Due to the limited acceptance of current space experiments, protons and nuclei around the “knee” region (∼ 1 PeV) can only be observed by ground based experiments. Thanks to an innovative design, the High Energy cosmic-Radiation Detection (HERD) facility will allow direct observation up to this energy region: the instrument is mainly based on a 3D segmented, isotropic and homogeneous calorimeter which properly measures the energy of particles coming from each direction and it will be made of about 7500 LYSO cubic crystals. The read-out of the scintillation light is done with two independent systems: the first one based on wave-length shifting fibers coupled to Intensified scientific CMOS cameras, the second one is made of two photo-diodes with different active areas connected to a custom front-end electronics. This photo-diode system is designed to achieve a huge dynamic range, larger than 107, while having a small power consumption, few mW per channel. Thanks to a good signal-to-noise ratio, the capability of a proper calibration, by using signals of both non-interacting and showering particles, is also guaranteed. In this paper, the current design and the performance obtained by several tests of the photo-diode read-out system are discussed.