Extra-galactic Cosmic Rays

The extragalactic region starts somewhere below the ankle of cosmic rays. Where exactly it starts and which are the sources it is still a puzzle, as well as if the spectrum ends as foreseen by GZK.

The Ankle and the End of the Spectrum

Two review articles on UHECR were written by Kotero et Olinto 2011 and Letessier-Selvon & Stanev, 2011. There is not yet a confirmed model to explain acceleration of CRs from the knee up to $10^{19}\rm{eV}$, where there is a flattening in the spectrum dubbed the ankle. The ankle is often interpreted as the transition between galactic and extragalactic sources. The flux above this energy is typically one particle per kilometer square per year per stereoradian. These low fluxes are only accessiblefrom large ground-based installations. CRs above the ankle are usually referred as Ultra High-Energy Cosmic Rays (UHECRs). A proton of these energies ($\sim 10^{18}{\rm eV}$) has a gyroradious of $\rm kpc$in a typical magnetic field. Therefore, based on the containment arguments only we can assume that UHECRs are of extra-Galactic origin. The composition of UHECRs is not trivial, as it is deeply convoluted with the physics of CRs air-showers, and in this region accelerator data cannot provide useful benchmarks for hadronic models.

At energies of $\sim 10^{19}{\rm eV}$, protons from CRs can interact with the $2.7\;^\circ \rm{K}$photons of the Cosmic Microwave Background (CMB) via the $\Delta$resonances, as for example:

$$p + \gamma_{CMB} \rightarrow \Delta^+ \rightarrow p(n) + \pi^0(\pi^+)$$

This reaction eventually should produce a cut-off in the observable CRs spectrum. This is known in the literature as the GZK-effect by an american sceintist K.I. Greisen and 2 Russian colleagues Zatsepin, and Kuzmin, who predicted it in the same year, though in different continents (K. Greisen paper, G.T. Zatsepin and V.A. Kuszmin paper). It was just the year after the discovery by Penzias and Wilson in 1965 of the cosmic MW background radiation (CMB). They understood that the CMB limits determines the high energy end of UHECRs and as well limits their horizon when used for astrophysical observations. You find the derivation of the threshold for the above reaction and also the calculation of the UHECRs 'horizon' in the section linked below.

Special Relativity and High-Energy Astrophysical Phenomena

Due to the GZK effect, protons of energies of $5\times 10^{19} {\rm eV}$cannot travel distances longer than a few tens of ${\rm Mpc}$. It is, however, unclear if the observed end of the CRs spectrum is indeed due to the GZK cutoff or a limit in the maximum energy attainable by the CRs sources, a phenomenological model usually referred as to the exhaustion of the sources which is based on the simple Hillas' argument. Part of the difficulty stems from the fact that composition studies at this energies are very difficult, and different composition support different arguments. A pure proton composition of UHECR favors the GZK interpretation, while a heavy composition (iron, etc.) hints at the exhaustion of the sources.

PAO recently updated the spectrum shown in the plot above of the UHECR in this paper.

The PAO spectrum from the paper linked above.

It reported on the energy spectrum measurement above $2.5 \times 10^{18}$ eV based on 215'030 events: at about $1.3 \times 10^{19}$ eV, the spectral index changes from 2.51 ± 0.03 (stat.) ± 0.05 (sys.) to 3.05 ± 0.05 (stat.) ± 0.10 (sys.), evolving to 5.1 ± 0.3 (stat.) ± 0.1 (sys.) beyond $5 \times 10^{19}$ eV. The energy resolution (which is very relevant since the spectra are also multiplied by powers of the energy to better show the features) improves from RMS ≈ 20% at $2×10^{18}$ eV to ≈ 7% at $2×10^{19}$ eV and is constant thereafter. The to it bias is zero above $2.5×10^{18}$ eV and increases smoothly going to lower energies and larger zenith angles: at $10^{18}$ eV it is ≈ 10% at the zenith and ≈30% at zenith = $60^\circ$ . These features of the spectrum, together with measurements on their composition in this paper, can be reproduced in models with energy-dependent mass composition.

In summary, the CR spectrum exhibits the following features:

1. A softening around $E ≃ 1.5 \times 10^{17}$ eV, commonly called the second knee.

2. A marked flattening of the spectrum commonly called the “ankle” observed by both Auger and Telescope Array at $E≃5.0 \times 10^{18}$eV

3. Between the second knee and the “ankle” the all particle spectrum is well described by a simple power law (Auger measures the spectral index $\gamma_1 = 3.27 \pm 0.05$in the entire energy range and TA measures $\gamma_1 = 3.28 \pm 0.02.$

4. A strong suppression of the flux is observed at $E = 5 \times 10^{19} \rm eV.$

5. The Auger collaboration has fitted the spectral shape between the ankle and the high energy suppression as a broken power law with a spectral break at $(13 \pm 1 \pm 2)×10^{18}$ eV, and exponents $\gamma_2$ ≃ 2.51 ± 0.03 ± 0.05 and $\gamma_3$ ≃ 3.05 ± 0.04 ± 0.10 in the lower and higher energy range. Above $5 \times 10^{19} \rm eV$ the spectral index increases sharply to 5.1 ± 0.3 (stat.) ± 0.1 (sys.) The spectrum measured by Telescope Array in the same range in consistent with an unbroken power law of slope 2.68 ± 0.02 (see the paper here from which the plot below is taken).

Comparison of the spectrum measured by PAO and TA

The composition of UHECRs:

The composition of cosmic rays is traditionally measured through the depth of the maximum of the longitudinal shower development$X_{max}$ and its statistical fluctiations RMS. The average shower maximum. The average of the maximum shower depth, $<X_{max}>$, scales approximately as ln(E/A), where E is the energy and A is the atomic mass of the primary cosmic ray which generated the shower (see, e.g., Letessier-Selvon & Stanev 2011 and references therein). On average the shower maximum for protons occurs deeper in the atmosphere than that for the same energy iron nucleus, $<X_{max,p}> > <X_{max,Fe}>$.

In addition, proton showers fluctuate more about $<X_{max}>$ providing another measure of composition, for example, the root mean square fluctuations about the mean value $<X_{max}>$. Another useful measure of composition is the particle content of the shower such as the number of muons: proton showers have fewer muons than showers caused by heavier nuclei with the same energy. In practice, observed shower maxima and particle numbers are compared with Monte Carlo airshower simulations which involve an extrapolation to higher energies of hadronic interactions known at energies of laboratory accelerators (> 10 TeV in the centre of mass).

The measured composition by PAO from the longitudinal shower development

In this paper, PAO also used a new variable, introduced in by P. Younka & M. Risse, 2012: the statistical correlation factor r between the depth of the shower maximum $X_{max}$and the muon shower size $N_{\mu}$, when these observables are measured simultaneously for a set of air showers. These variables are described when we addressed the Cosmic Ray Showers.

PAO observed that the UHECR composition in the ankle region at log(E/eV) = 18.5 − 19.0 differs significantly from expectations for pure primary cosmic-ray compositions. A light composition made up of proton and helium only is equally inconsistent with observations. The data are explained well by a mixed composition including nuclei with mass A > 4. This disfavours proton-dominated scenarios, such as the proton dip model, with almost pure compositions. A proton dominated flux below the ankle region is a necessary condition for this model to be verified. In the dip model, the ankle is the imprint of $e^+ e^-$ pair production in extragalactic propagation, which requires a proton-dominated composition for $E \ge 10^{18} \rm eV$. The injection spectra are softer than for mixed models for a wide range of evolution models, though models with proton primaries can also fit the measured UHECR spectrum with harder injection with a high-energy transition from galactic to extragalactic cosmic rays assumed at the ankle (Wibig & Wolfendale 2004). In this model the composition of UHECRs is predicted to be heavy or even iron dominated due to galactic sources, such as neutron stars and local γ-ray bursts. In the case of extragalactic sources, a flux suppression is expected at the highest energies for both protons and nuclei due to the GZK effect. In scenarios with galactic or cosmologically local sources, this drop in the flux would correspond to the maximum energy at which particles are injected;

See this review paper describing models and the plot below.

Spectrum of UHECRs multiplied by E^3(data from by HiRes I (Abbasi et al. 2009) and Auger (Abraham et al. 2010b)). Overlaid are spectra obtained for different models of the Galactic to extragalactic transition and different injected chemical compositions and spectral indices.

The energy density of UHECRs:

The energy density in cosmic rays above $5×10^{18}$ eV is (5.66 ± 0.03 (stat.) ± 1.40 (sys.)) $\times 10^{53}$ erg Mpc $^{−3}$ . This number is relevant because it can be used to understand which population of sources can produce such an observed energy. This amounts to $\sim 6 \times 10^{44} \rm \, erg \, Mpc^{-3} yr^{-1}$ above $5×10^{18}$ eV at a redshift of zero. Classes of extragalactic sources that match such rates in the gamma-ray band include active galactic nuclei and starburst galaxies. The flux pattern from these objects also provides an indication of anisotropy in UHECR arrival directions.