UHECR Spectrum Research Articles

Where Did the Amaterasu Particle Come From?

The Telescope Array Collaboration recently reported the detection of a cosmic-ray particle, “Amaterasu,” with an extremely high energy of 2.4 × 1020 eV. Here we investigate its probable charge and the locus of its production. Interpreted as a primary iron nucleus or slightly stripped fragment, the event fits well within the existing paradigm for UHECR composition and spectrum. Using the most up-to-date modeling of the Galactic magnetic field strength and structure, and taking into account uncertainties, we identify the likely volume from which it originated. We estimate a localization uncertainty on the source direction of 6.6% of 4π or 2726 deg2. The uncertainty of magnetic deflections and the experimental energy uncertainties contribute about equally to the localization uncertainty. The maximum source distance is 8–50 Mpc, with the range reflecting the uncertainty on the energy assignment. We provide sky maps showing the localization region of the event and superimpose the location of galaxies of different types. There are no candidate sources among powerful radio galaxies. An origin in active galactic nuclei or star-forming galaxies is unlikely but cannot be completely ruled out without a more precise energy determination. The most straightforward option is that Amaterasu was created in a transient event in an otherwise undistinguished galaxy.

Revisiting ultrahigh-energy constraints on decaying superheavy dark matter

We revisit constraints on decaying very heavy dark matter (VHDM) using the latest ultrahigh-energy cosmic-ray (UHECR; $E\gtrsim 10^{18}$ eV) data and ultrahigh-energy (UHE) $\gamma$-ray flux upper limits, measured by the Pierre Auger Observatory. We present updated limits on the VHDM lifetime ($\tau_\chi$) for masses up to $\sim10^{15}$~GeV, considering decay into quarks, leptons, and massive bosons. In particular, we consider not only the UHECR spectrum but their composition data that favors heavier nuclei. Such a combined analysis improves the limits at $\lesssim 10^{12}$ GeV because VHDM decay does not produce UHECR nuclei. We also show that the constraints from the UHE $\gamma$-ray upper limits are $\sim10$ more stringent than that obtained from cosmic rays, for all of the Standard Model final states we consider. The latter improves our limits to VHDM lifetime by a factor of two for dark matter mass $\gtrsim10^{12}$ GeV.

Espresso and Stochastic Acceleration of Ultra-high-energy Cosmic Rays in Relativistic Jets

Abstract In the espresso scenario, ultra-high-energy (UHE) cosmic rays (CRs) are produced via a one-shot reacceleration of galactic-like CRs in the relativistic jets of active galactic nuclei, independently of the scattering rate dictated by magnetic fluctuations. In Mbarek & Caprioli (2019) we traced test-particle CRs in high-resolution magnetohyrodynamic (MHD) jet simulations and found that the associated spectral slope, chemical composition, and anisotropy are consistent with UHECR phenomenology. In this work, we extend such an analysis by including subgrid pitch-angle scattering to model small-scale magnetic turbulence that cannot be resolved by MHD simulations. We find that a large scattering rate unlocks stochastic acceleration and fosters the energization of lower-energy CRs, which eventually leads to harder UHECR spectra. Yet, the particles that achieve the highest energies (up to the Hillas limit) are invariably produced by espresso acceleration and their spectrum is independent of the assumed subgrid scattering rate.

Ultrahigh energy cosmic rays and neutrinos from light nuclei composition

The baryonic mass composition of ultrahigh energy ($\gtrsim 10^{18}$ eV) cosmic rays (UHECRs) at injection accompanied by their interactions on universal photon backgrounds during propagation directly governs the UHECR flux on the Earth. Secondary neutrinos and photons produced in these interactions serve as crucial astrophysical messengers of UHECR sources. A modeling of the latest data obtained by the Pierre Auger Observatory (PAO) suggests a mixed element composition of UHECRs with the sub-ankle spectrum being explained by a different class of sources than the super-ankle region ($> 10^{18.7}$ eV). In this work, we obtain two kinds of fit to the UHECR spectrum -- one with a single population of sources comprising of $^1$H and $^2$He, over an energy range commencing at $\approx 10^{18}$ eV -- another for a mixed composition of representative nuclei $^1$H, $^4$He, $^{14}$N and $^{28}$Si at injection, for which a fit is obtained from above $\approx 10^{18.7}$ eV. In both cases, we consider the source emissivity evolution to be a simple power-law in redshift. We test the credibility of H+He composition by varying the source properties over a wide range of values and compare the results to that obtained for H+He+N+Si composition, using the Monte Carlo simulation tool CRPropa 3. The secondary electrons and photons are propagated using the cosmic ray transport code DINT. We place limits on the source spectral index, source evolution index and cutoff rigidity of the source population in each case by fitting the UHECR spectrum. Cosmogenic neutrino fluxes can further constrain the abundance fraction and maximum source redshift in case of light nuclei injection model.

UHECR acceleration at GRB internal shocks

We study the acceleration of CR protons and nuclei at GRB internal shocks. Physical quantities and their time evolution are estimated using the internal shock modeling implemented by Daigne & Mochkovitch 1998. We consider different hypotheses about the way the energy dissipated at internal shocks is shared between accelerated CR, e- and B field. We model CR acceleration at mildly relativistic shocks, including all the significant energy loss processes. We calculate CR and neutrino release from single GRBs, assuming that nuclei heavier than protons are present in the relativistic wind. Protons can only reach maximum energies of ~ 10^19.5 eV, while intermediate and heavy nuclei are able to reach values of ~ 10^20 eV and above. The spectra of nuclei escaping from the acceleration site are found to be very hard while the combined spectrum of protons and neutrons is much softer. We calculate the diffuse UHECR flux expected on Earth using the GRB luminosity function from Wanderman & Piran 2010. Only the models assuming that the prompt emission represent a very small fraction of the energy dissipated at internal shocks, and that most of this dissipated energy is communicated to accelerated CR, are able to reproduce the magnitude of the UHECR flux observed. For these models, the observed shape of the UHECR spectrum can be well reproduced and the evolution of the composition is compatible with the trend suggested by Auger. We discuss implications of the softer proton component for the GCR to EGCR transition in the light of the recent composition analyses (KASCADE-Grande experiment). The associated secondary particle diffuse fluxes do not upset any current observational limit. Diffuse neutrino flux from GRB sources should however be detected with the lifetime of neutrino observatories.

Multi-messenger aspects: Composition, propagation, & acceleration

Using recent Pierre Auger Observatory results on the UHECR spectrum and composition, the requirements placed on the sources of these particles are discussed. In this sense, the author interprets the term “multi-messenger” throughout as to refer to the additional information provided by the composition. The spatial distribution of these sources is investigated along with the energy distribution of UHECR they output. These investigations reveal the need for local UHECR sources which output a hard spectrum of intermediate/heavy UHECR. These results demand that local (<80 Mpc) UHECR sources exist, placing exciting and difficult requirements on the local extragalactic candidate sources. Angular correlation studies in collaboration with composition information also demonstrated to offer great potential for isolating the UHECR source distance for which an angular clustering of events is found. Specifically, for the case a correlation of the 13 events correlated with the direction of Cen A, it is shown that the composition information, and specifically, the lack of a lower energy proton correlation, can potentially constrain the source distance to be less than 15 Mpc. The fragility of nuclei with accelerators are also used to place constraints are on the source environment. These constraints motivate 0.1–1000 mG strength magnetic fields exist within the source and that quasi-relativistic scatterers are also present. A specific example of a diffuse large scale “nuclei friendly” accelerator, which meets the outline constraints is put forward.

Anisotropy expectations for ultra-high-energy cosmic rays with future high-statistics experiments

UHECRs have attracted a lot of attention due to their challengingly high energies and their potential value to constrain physical processes and astrophysical parameters in the most energetic sources of the universe. Current detectors have failed to detect significant anisotropies which had been expected to allow source identification. Some indications about the UHECR composition, which may become heavier at the highest energies, has even put into question the possibility that such a goal could be achieved soon. We investigate the potential value of a new-generation detector, with 10 times larger exposure, to overcome the current situation and make significant progress in the detection of anisotropies and thus in the study of UHECRs. We take as an example the expected performances of the JEM-EUSO, assuming a uniform full-sky coverage with a total exposure of 300,000 km2 sr yr. We simulate realistic UHECR sky maps for a wide range of possible astrophysical scenarios allowed by the current constraints, taking into account the energy losses and photo-dissociation of the UHECRs, as well as their deflections by magnetic fields. These sky maps, built for the expected statistics of JEM-EUSO as well as for the current Auger statistics, as a reference, are analyzed from the point of view of their intrinsic anisotropies, using the two-point correlation function. A statistical study of the resulting anisotropies is performed for each astrophysical scenario, varying the UHECR source composition and spectrum as well as the source density. We find that significant anisotropies are expected to be detected by a next-generation UHECR detector, for essentially all the astrophysical scenarios studied, and give precise, quantitative meaning to this statement. Our results show that a gain of one order of magnitude in exposure would make a significant difference compared to the existing detectors.

NEUTRINO AND UHECR SPECTRA FROM MRK 421

We present the neutrino and UHECR spectra obtained from a detailed fitting of the spectral energy distribution (SED) of Mrk 421 (March 2001) using two variations of the leptohadronic model. In particular, while the low-energy component (optical to X-rays) of the SED is fitted by synchrotron emission of primary electrons in both models, the high-energy one (GeV-TeV gamma-rays) is synchrotron emission attributed either to ultra-high energy protons (LHs model) or to secondary electrons produced by the decay of charged pions (LHπ model). In the LHπ case we find that the produced neutrino spectra are sharply peaked at Eν ~ 30 PeV with a peak flux slightly below the IC-40 sensitivity limit for Mrk 421. In the LHs model, on the other hand, the neutrino spectra fall well outside the PeV energy range, but the calculated E ~ 30 EeV — UHECR flux at earth is close to that observed by HiresI, Telescope Array and Pierre Augere experiments.

The measurement of UHECR spectrum with the HiRes experiment in stereo mode

In this paper, the energy spectrum of UHECR with energy above 10 18.2 eV has been measured with HiRes detector in stereo mode. The cosmic ray events reconstruction has been presented briefly. A new direction reconstruction method has been introduced. The resolution of arrival direction is about 0.44 degree and the energy resolution is about 10%. The detector aperture is studied in detail, and an aerosol free aperture is given. At last, the result on the UHECR spectrum is presented and its uncertainty is discussed.

Signatures of the extragalactic cosmic-ray source composition from spectrum and shower depth measurements

We discuss the differences induced by the assumed composition of extragalactic sources on the predicted UHECR spectrum and the energy evolution of $ $, i.e. the mean value of the atmospheric depth at the cosmic-ray air shower maximum. We show that different assumptions for the source power evolution do not modify our earlier finding that in the case of a mixed composition the ankle can be interpreted as the end of the transition from galactic to extragalactic cosmic rays. We show the characteristic features in the shape of $ $(E) that are associated with this transition for each cosmic-ray composition model. These characteristic features are present whatever the hadronic model used for the calculation. In the mixed composition cases, a signature of the interactions of nuclei with the photon backgrounds is also expected above $10^{19}$ eV. The comparisons with Stereo HiRes and Fly's Eye data favour an extragalactic mixed composition and the corresponding interpretation of the ankle. Confrontation of model predictions with future data at the highest energies will allow a better determination of the transition features and of the cosmic-ray source composition, independently of hadronic models. We also emphasize that in the pure proton case, a combined analysis of the spectrum and composition below the ankle could lead to constraints on the source power evolution with redshift.

A dip in the UHECR spectrum and the transition from galactic to extragalactic cosmic rays

The dip is a feature in the diffuse spectrum of ultra-high energy (UHE) protons in the energy range 1 × 10 18–4 × 10 19 eV, which is caused by electron–positron pair production on the cosmic microwave background (CMB) radiation. For a power-law generation spectrum E −2.7, the calculated position and shape of the dip is confirmed with high accuracy by the spectra observed by the Akeno-AGASA, HiRes, Yakutsk and Fly’s Eye detectors. When the particle energies, measured in these detectors, are calibrated by the dip, their fluxes agree with a remarkable accuracy. The predicted shape of the dip is quite robust: it is modified very weakly when the discreteness and inhomogeneities in the source distribution are taken into account, and for different regimes of propagation (from rectilinear to diffusive). The cosmological evolution of the sources, with parameters inspired by observations of Active Galactic Nuclei (AGN), also results in the same shape of the dip. The dip is modified strongly when the fraction of nuclei heavier than protons is high at injection, which imposes some restrictions on the mechanisms of acceleration operating in UHECR sources. The existence of the dip, confirmed by observations, implies that the transition from galactic to extragalactic cosmic rays occurs at E ≲ 1 × 10 18 eV. We show that at energies lower than a characteristic value E cr ≈ 1 × 10 18 eV, determined by the equality between the rate of energy losses due to pair production and adiabatic losses, the spectrum of extragalactic cosmic rays flattens in all cases of interest, and it provides a natural transition to a steeper galactic cosmic ray spectrum. This transition occurs at some energy below E cr, corresponding to the position of the so-called second knee. We discuss extensively the constraints on this model imposed by current knowledge of acceleration processes and sources of UHECR and compare it with the traditional model of transition at the ankle.

GZK photons as UHECR above 1019 eV

‘‘GZK photons’’ are produced by extragalactic nucleons through the resonant photoproduction of pions. We present the expected range of the GZK photon fraction of UHECR, assuming a particular UHECR spectrum and primary nucleons, and compare it with the minimal photon fraction predicted by Top-Down models.

Dip in UHECR spectrum as signature of proton interaction with CMB

Ultrahigh energy (UHE) extragalactic protons propagating through cosmic microwave radiation (CMB) acquire the spectrum features in the form of the dip, bump (pile-up protons) and the Greisen–Zatsepin–Kuzmin (GZK) cutoff. We have performed the analysis of these features in terms of the modification factor. This analysis is weakly model-dependent, especially in case of the dip. The energy shape of the dip is confirmed by the Akeno-AGASA data with χ2=19.06 for d.o.f.=17 with two free parameters used for comparison. The agreement with HiRes data is also very good. This is the strong evidence that UHE cosmic rays observed at energies 1×1018–4×1019 eV are extragalactic protons propagating through CMB. The dip is also present in case of diffusive propagation in magnetic field.

Injection spectrum of ultrahigh energy cosmic rays in the top-down scenario

We analyze the uncertainties involved in obtaining the injection spectra of UHECR particles in the top-down scenario of their origin. We show that the DGLAP $Q^2$ evolution of fragmentation functions (FF) to $Q=M_X$ (mass of the X particle) from their initial values at low $Q$ is subject to considerable uncertainties. We therefore argue that, for $x\lsim 0.1$ (the $x$ region of interest for most large $M_X$ values of interest, $x\equiv 2E/M_X$ being the scaled energy variable), the FF obtained from DGLAP evolution is no more reliable than that provided, for example, by a simple Gaussian form (in the variable $\ln(1/x)$) obtained under the Modified Leading Log Approximation (MLLA). Additionally, we find that for $x\gsim0.1$, the evolution in $Q^2$ of the singlet FF, which determines the injection spectrum, is ``minimal'' -- the singlet FF changes by barely a factor of 2 after evolving it over $\sim$ 14 orders of magnitude in $Q\sim M_X$. We, therefore, argue that as long as the measurement of the UHECR spectrum above $\sim10^{20}\ev$ is going to remain uncertain by a factor of 2 or larger, it is good enough for most practical purposes to directly use any one of the available initial parametrisations of the FFs in the $x$ region $x\gsim0.1$ based on low energy data even without evolving them to the requisite $Q^2$ value.

Monocular UHECR spectra as measured by HiRes

We have measured the spectrum of UHE cosmic rays in monocular mode using separately both detectors the High Resolution Fly's Eye experiment. We describe the two detectors and the basic methods of analysis, and we present our measured spectra. We compare these spectra with that produced by an astrophysical source model with galactic and uniformly distributed extra-galactic sources. We also compare our spectra to the spectra produced by the AGASA experiment.

Ultra high energy cosmic rays: clustering, GUT scale and neutrino masses

The clustering of ultra high energy (above 5 · 10 19 eV) cosmic rays (UHECR) suggests that they might be emitted by compact sources. We present a statistical analysis on the source density based on the multiplicities. The propagation of UHECR protons is studied in detail. The UHECR spectrum is consistent with the decay of GUT scale particles and/or with the Z-burst. The predicted GUT mass is m x = 10 b GeV, where b = 14.6 −1.7 +1.6. Our neutrino mass prediction depends on the origin of the power part of the spectrum: m ν = 2.75 −0.97 +1.28 eV for halo and 0.26 −0.14 +0.20 eV for extragalactic (EG) origin.

Constraints on the ultrahigh-energy photon flux using inclined showers from the Haverah Park array

We describe a method to analyze inclined air showers produced by ultrahigh-energy cosmic rays using an analytical description of the muon densities. We report the results obtained using data from inclined events $(60\ifmmode^\circ\else\textdegree\fi{}&lt;\ensuremath{\theta}&lt;80\ifmmode^\circ\else\textdegree\fi{})$ recorded by the Haverah Park shower detector for energies above ${10}^{19} \mathrm{eV}.$ Using mass independent knowledge of the UHECR spectrum obtained from vertical air shower measurements and comparing the expected horizontal shower rate to the reported measurements we show that above ${10}^{19} \mathrm{eV}$ less than $48%$ of the primary cosmic rays can be photons at the $95%$ confidence level and above $4\ifmmode\times\else\texttimes\fi{}{10}^{19} \mathrm{eV}$ less than $50%$ of the cosmic rays can be photonic at the same confidence level. These limits place important constraints on some models of the origin of ultrahigh-energy cosmic rays.