Long standing open problems

The origin of spectral structures in the cosmic ray all-particle flux, where the spectrum hardened or softened away from a single power law, have been studied for decades, nev-ertheless no solid conclusions have been drawn. These longstanding mysteries challenge the standard cosmic ray paradigm and potentially hint the existence of new physics.

1.2.4.1 Knee

At ∼ 4 PeV, the cosmic ray all-particle spectrum is softened from E^−2.7 to E⁻³, and it’s called the knee of the spectrum. The origin of the knee is broadly agreed to be the transition of the cosmic ray composition from proton domination to heavier nuclei domination. As heavier nuclei are much less abundant than proton, the cosmic ray all-particle spectrum is expected to be softer at the region dominated by heavier nuclei. The different domination of proton and heavier nuclei could be based on the fact that the most reasonable cosmic ray accelerator, the shock wave from supernova remnants, accelerates

particle according to their rigidity, in other words the maximum achievable rigidity of different nuclei is the same. Hence a common limit on the rigidity for proton and heavier nuclei translates to different limits on energy due to different mass, i.e. different energy domination of light and heavier nuclei.

Such a rigidity-dependent limitations could have two origins. First, as explained above the limitations of highest possible rigidity might due to that cosmic ray sources in the galaxy are inefficient to accelerate particle to energy above these limitations [39, 40]. Such limitations could also be explained through propagation effects that the galaxy is not able to confine particles with such high rigidity due to limitations of the size of the galaxy and the strength of the galactic magnetic field [41]. These two assumptions, from source and from propagation, both predict a rigidity dependent knee position hence they cannot be distinguished by the determination of cosmic ray composition at the knee energy.

Knee positions of individual cosmic ray species shed lights on the origin of the knee.

At energy range around the knee, the cosmic ray direct detection is not feasible with the current generation of space missions due to the limited statistic from limited acceptance or/and exposure time. So far, indirect detections on the ground are performed, which has large particle identification uncertainty, introducing difficulties to determine the exact knee energies of individual cosmic ray species. The knee energy for proton has been measured indirectly and found to be 500 TeV by Tibet Asγ [42], and to be up to 4 PeV by KASCADE and KASCADE-Grande [43] which is the same energy as the knee of the all-particle spectrum. The variation on the measured knee energy introduces different issues:

1. At the situation of low knee energy (few hundred TeV), which is easily achieved by current acceleration models, the cutoff of the galactic cosmic ray spectrum would fall well below 0.1 EeV [33]. To match with the observed cosmic ray spectrum cutoff at ∼10²⁰ eV = 100 EeV, an additional high energy galactic cosmic ray component or the present of extragalactic CRs at relatively low energy is required;

2. Instead, a knee energy at ∼4 PeV naturally fill up the gap between the knee up to the cutoff without the requirement of the additional galactic high-energy component.

However, another problem arises: whether the galactic cosmic ray sources have the

ability of accelerating particles up to PeV, i.e. the existence of galactic PeVatron (see Section 1.3.3).

1.2.4.2 the second knee and the ankle - transition from galactic to extra-galactic?

At ∼ 500 PeV, there is the second knee of the cosmic ray all-particle spectrum, where the spectrum is softened again by ∼0.2. This is a relatively new discovery by Akeno experiment in 1992 [44]. Another transition exists at ∼3×10¹⁸ eV, known as the ankle, where the spectrum is hardened. These structures are very likely related to the transition of the galactic component to the extragalactic component of cosmic rays.

It’s quite reasonable to consider the ankle as the transition [45] since it offers a natural explanation of the sharp raise of the spectrum. Considering the knee of cosmic rays is rigidity dependent and it has the highest possible knee energy for proton at 4 PeV, the corresponding knee rigidity will be 4 PV for all particle species. Hence the knee of Iron, the most abundant heavy nuclei in cosmic ray, will be at 4×26∼100 PeV = 10¹⁷eV. The second knee can then be recognized as the knee of the Iron spectrum, the bulk of cosmic rays at such energy. The second knee is still an order of magnitude lower than the ankle energy, so another cosmic ray component, galactic or even extragalactic, is required to fill up the gap between the second knee and the ankle. If the third component is unrelated to the low energy galactic one from standard supernovae remnants below the second knee, the ”fine-tuning problem” arises since the observed smooth transition indicates a close normalization between these two cosmic ray components.

If instead the transition energy is assigned to the second knee, the ankle will be a structure on the extragalactic cosmic ray spectrum through either propagation effects or from the sources of extragalactic cosmic rays.

The determination of the transition energy between the second knee and the ankle bases on the difference between the galactic and extragalactic cosmic rays in such energy range, namely the composition and the anisotropy:

• Due to the rigidity dependent knee position, the galactic cosmic ray spectrum should be Iron dominated close to the its end. Similar behavior is expected for extragalactic

component however with a shift to higher energies. Hence at the transition energy, the extragalactic components should be lighter than the galactic one.

• The galactic components should be ”well mixed” through diffusion in the ISM while a larger anisotropy is expected for extragalactic components since they travel inside the galaxy almost on straight line with ultra-high energy.

The composition measurement [46] observed that the Iron dies out before 7×10¹⁷ eV.

Combining with the anisotropy measurement [47], cosmic rays above 3×10¹⁷ eV must be of extragalactic origin. Hence the second knee should be considered as the sign of the transition from galactic component to extragalactic component for cosmic rays. On the other hand, the origin of the ankle as a structure of the extragalactic cosmic rays remains unclear. The ankle might be explained as the pipe-up protons [48] that have lost energy at the GZK cutoff, which will be explained in Section 1.2.4.3. However, the indication of a mixture composition between the light and heaver nuclei [49] disfavored such a propagation origin of the ankle, which requires a proton domination for cosmic rays at ultra-high energy.

1.2.4.3 Cutoff of the spectrum

Fig. 1-2 clearly shows a cutoff at ∼10²⁰ eV for the all-particle cosmic ray spectrum.

The famous Greisen–Zatsepin–Kuzmin (GZK) cutoff introduces a steepening on the proton spectrum at∼5×10¹⁹eV [50,51]. Ultra-high energy protons are assumed to lose energy rapidly by the interaction with the cosmic microwave background (CMB) photon through photo-pion production:

p+γ →p+π⁰, p+γ →n+π⁺. (1.51) If the high energy cosmic rays are still dominated by protons, the GZK cutoff naturally produced the spectrum cutoff on all-particle spectrum.

However, ground base measurements indicated that the ultra-high energy cosmic ray (UHECR) has mixed mass composition rather than purely light or purely heavy compo-nent [49]. Such a mix composition disfavors the explanation of the cutoff by propagation effects such as GZK cutoff, which requires proton dominated composition. Note that

the mass composition measurement has large uncertainty due to the description of cross sections at such energy and further studies are still needed.

1.3 Anomaly in the galactic cosmic rays in the