Cosmic rays

The term CRs is nowadays used to define the energetic particles arriving from outside of our atmosphere. As mentioned before, they are composed mainly by protons and He nuclei, while only 1% is formed by electrons, positrons, neutrons and heavier nuclei. Gamma rays are also considered part of the CRs. They can be measured directly with balloon experiments or satellites.

Normally these techniques explore CRs up to 10¹⁴eV. Higher energies can be studied by indirect observations in ground based experiments. These detectors observe the secondary particles pro-duced in the Extended Air Showers (EASs), i.e. cascades of particles originate by the interaction of primary CRs with the nuclei of the Earth’s atmosphere. These EASs, first detected by Pierre Auger in 1938, can extend hundred meters on the ground. The study of CRs led to important discoveries, such as the existence of the positron (e⁺) or pions. However, many question lack for an answer yet, as e.g.which are the sources responsible for the CRs production?.

Figure 1.1:CR spectrum obtained with data from different experiments. Credit: Hanlon (2010).

1.1.1 Spectrum

The CR spectrum extends from 10⁸ to 10²¹ eV, approximately (see Figure 1.1). Particles with energy below∼ 1 GeV have solar origin, as the solar magnetic field in the wind blocks particles at those energies arriving from outside from the solar system. The rest of the spectrum is well-defined by a broken power law,dN/dE ∝ E^−Γ, with 3 different photon indicesΓ. The first part, from∼ 100 MeV up to∼ 5 PeV, presents a photon index of Γ ∼ 2.7. Its upper limit is known asknee, which is charge dependent: particles with higher charge will extend thekneeto higher energies. The second region covers the range from thekneeup to∼ 3 EeV, the so-calledankle, in which the spectrum follows a power law withΓ ∼ 3. Finally, beyond∼ 3 EeV, the spectrum hardens again (withΓ∼ 2.6) up to∼ 30 EeV. The different slopes are thought to be related with the origin of the CRs. Particles with energies covering the first range up to thekneeare believed to be accelerated inside our Galaxy, whilst particles above theankleseem to have extragalactic origin. Between thekneeand theanklethe origin is not that clear. Several proposals were made to explain the steepening of the spectrum at theknee: changes on the acceleration mechanism, as e.g. two-step acceleration in the Supernova Remnants (SNRs), first at the front shock and re-aceleration in the inner pulsar-driven remnant (Bell 1991; see Section ??); leakage of CRs out of the Galaxy by diffuse propagation (Ptuskin et al. 1993) or even a cutoffof light elements (Antoni et al. 2005).

The CR spectrum is affected at the edge by the so-called Greisen-Zatsepin-Kuzmin (GZK) cutoff(Figure 1.2). This cutoffis produced by the interaction of the CRs with energies & 10²⁰ eV with the Cosmic Microwave Background (CMB), which gives rise to hadrons as a product of

∆resonance:

p+γC MB→ ∆⁺ → p+π⁰ (1.1)

p+γC MB →∆⁺→ n+π⁰ (1.2)

This interaction also limits the maximum distance that the CRs with energies greater than 10²⁰eV can travel to∼50 Mpc.

1.1.2 Cosmic ray acceleration

CRs, as charged particles, can be accelerated within magnetic and electric fields. Nevertheless, it is thought that the bulk of CRs are accelerated through diffuse shock acceleration mechanisms.

These processes can be split into two main mechanisms, proposed by Enrico Fermi (Fermi 1949) whose names arise from:first orderandsecond orderFermi acceleration. They are differentiated attending to the features of the moving plasma.

First orderFermi acceleration: The acceleration takes places in a plasma that presents shock waves (blobs of material moving at supersonic velocities) and magnetic field in-homogeneities. The particles get accelerated every time they cross the shock wave. The energy gained in each reflection is proportional to the relative velocity between the shock and the particle, h∆E/Ei ∝ vrel/c, and therefore the larger the difference, the larger the energy gain. The number of times that a particle cross the shock is directly proportional to

Figure 1.2: CR flux measurements by Auger and Telescope Array (TA) Collaboration, where a cutoffat energies∼10²¹eV is evidenced. Taken from Kampert & Tinyakov (2014).

the magnetic field strength. Thus, the crossing frequency is higher as larger the magnetic field strength is. This efficient mechanism is thought to be the responsible of the particle acceleration up to TeV and PeV ranges.

Second orderFermi acceleration: This acceleration happens within moving magnetized clouds. The energy gained by the particles in each interaction with the magnetized material is proportional to the square of the speed of the moving cloud, h∆E/Ei ∝ (vcloud/c)². However, this acceleration is not very efficiency: typical values ofvcloud/c∼ 10⁻⁵lead to a gain ofh∆E/Ei ∼10⁻¹⁰ per interaction.

If particles escape from the acceleration region, they will not be able to gain more energy.

Thus, the maximum energy that the accelerated CRs can reach is limited by the radius of the circular motion they describe under the presence of an uniform magnetic field, the so-called Larmor radius or gyroradius. This gyroradius cannot exceed the size of the acceleration region, otherwise the particle would not be confined on this region anymore. This geometrical constraint is known asHillas criterion. The maximum energy,Emax, can be expressed as follows:

Emax= 10¹⁸eVq R kpc

! B µG

!

(1.3) whereqis the charge of the particle,Rand Bare the radius and magnetic field of the accel-eration region, respectively.

Figure 1.3, the so-called Hillas plot, shows the relation between the magnetic field strength and the radius of the acceleration region. The diagonal lines confine the allowed region for acceleration of different particles with certain energy.

The possible astrophysical sources responsible for the production of CRs, both galactic and extragalactic, are explained in Section 1.2.3. As mentioned before, in order to study the CRs origin, we need to make use of neutral particles observations, as gamma rays.

Figure 1.3: Hillas plot that depict the possible CR sources as a function of their magnetic field strength and size. The lines indicate the allowed acceleration region for different particles at a maximum energy (solid red line for protons with Emax = 1 ZeV= 10²¹ eV, dashed red line for protons withEmax = 100 EeV= 10²⁰eV, and solid green line for Fe nuclei withE_max =100 EeV= 10²⁰eV). Objects below each line cannot accelerate those particles up to the indicated energies Hillas (1984).