Metodología

Once candidate sources have been explained in previous Section, a new question appears. Is it possible to make cosmic ray astronomy?. In order to answer, the propagation of cosmic rays from their source to Earth must be studied, which involve to consider how magnetic fields could affect their trajectory and which interactions may suffer. This Section is devoted to these questions.

Magnetic fields

UHECR astronomy would be possible if the original particle direction during its travel from the source to the Earth were conserved. Unfortunately, charged cosmic rays are deflected by the galactic and extragalactic magnetic fields. The problem could be solved if all the quantities needed to determine the primary deflection were known, such as the

Figure 2.4: (a) Deflections of UHECRs in the local supercluster (from [38]). (b) Projected view of 20 trajectories of proton primaries emanating from a point source for several energies. Each proton is tracked until it reaches a physical distance from the source of 40 Mpc (from [39]).

strength and orientation of the magnetic field, the charge of the cosmic particle and the distance between the source and the Earth.

The magnetic field of the Galaxy can be described as the superposition of two com- ponents, one regular and one chaotic. The regular component has an intensity of some few µG and lies on the galactic plane. The chaotic component has an intensity of the same order of magnitude but it is produced from magnetic clouds generated from the motion of ionized gas. If only the regular component is considered, the characteristic de- flection of a particle of energy E in the magnetic field B is given by the Larmor radius as

RL(kpc) ' E(EeV )_ZB(µG). Given a nucleus of charge Z, as the energy increases, the gyroradius

of the nucleus becomes comparable or larger than the transversal dimension of the con- finement region and, consequently, the nucleus can escape from the Galaxy. Therefore, at energies above 1017 _{eV protons could escape while Iron nuclei are confined inside the}

Galaxy at least up to energies around 1019 _eV.

At high energies, as well as the galactic cosmic rays are able to escape from the Galaxy, extragalactic particles are able to penetrate in the galactic confinement region. That is possible if extragalactic particles are able to reach our Galaxy. In fact, in the energy

range between 5 · 1017 _{and the 3 · 10}18 _{eV (the energies corresponding to the second knee}

and the ankle of the spectrum respectively, as will be explained later), all kind of nuclei, starting from protons up to Iron nuclei, are able to arrive from the local universe.

On the other hand, the extragalactic magnetic fields are almost unknown but an upper limit of around 1 nG is usually accepted.

An estimation of the deflection angle in a constant magnetic field which perpendicular component to the particle momentum is B⊥ over a distance d is given by [40]:

θ(E, d) = 0.52o_Z µ E 1020_eV ¶₋₁µ B⊥ 10−9_G ¶ µ d 1Mpc ¶ (2.2) In case of a proton of ∼ 1020 _{eV, the deviation is less than 1}o _{in two scenarios: in the}

Galaxy where magnetic field is typically of ∼ µG on a distance ∼ kpc, or outside the Galaxy where the extragalactic magnetic field is the order of ∼ nG over a distance of the order of Mpc. The predicted cosmic ray deflections in the local supercluster are shown in Fig. 2.4(a), where values between 0 and 1◦ _{are found. As it can be seen in Eq. 2.2,}

higher the energy of the cosmic ray is, lower is the deflection (see Figure 2.4(b)), so that the door is opened to make cosmic ray astronomy at the highest energies. More detailed calculations could be found in [31, 41, 42].

Interactions of CRs during propagation and the GZK effect

Unfortunately, propagation through galactic and extragalactic magnetic fields is not the only problem. Cosmic rays may interact with background radiation fields like the cosmic microwave background (CMB), the infrared background (IB) and radio background (RB), losing energy. Other energy losses are due to the Hubble expansion of the Universe and due to the interaction with dust, but they are not significant at the energies of our interest. The most important interaction at the highest energies is the GZK effect proposed by Greisen, Zatsepin, and Kuz’min [43, 44] just a bit later than the CMB discovery by Penzias and Wilson in 1965 [45]. They independently pointed out that this radiation would make the Universe opaque to cosmic rays of sufficiently high energy. Protons with an energy

Figure 2.5: Reduction of primary proton energy due to GZK effect. At 1022 _{eV particle}

would be reduced in energy to 1020 _{eV after traveling ∼ 100 Mpc (from [46]).}

exceeding E ∼ 5 · 1019_{eV (called GZK threshold) have a large probability to interact with}

the CMB photons, losing energy by pion photo-production:

p + γCM B → p + Π0

→ n + Π+ _(2.3)

These interactions occur via the ∆+ _{resonance whose cross section at that energy is very}

high (∼ 10−28_cm−2_{). Assuming typical value for the CMB photon density (400cm}−3_),

the mean free path1 _{for a proton can be estimated as ∼ 8 Mpc. The energy loss per}

interaction for the proton is ∼ 20%, giving an attenuation length2 _{of the order of some}

tenths of Mpc, beyond which the proton energy falls below the GZK threshold. Fig. 2.5 shows how the energy of a proton degrades due to successive interactions with the CMB. On the other hand, the neutron decay length (n → p + e−_{+ ν}

e) is about 1 Mpc at 1020

eV, so that it decays before interacting.

If cosmic rays are protons, another energy loss process will be important between 1018

eV and the GZK threshold. It is the photo-pair production when protons interact with

1_{The average distance covered by a particle between subsequent interactions}

photons of the CMB producing a electron-positron pair (p + γCM B → p + e++ e−). The

energy loss in each interaction is small. It may, however, contribute to the shape of the spectrum at these energies if the primaries are protons from distant sources. At lower energies the attenuation length tends to become constant and equal to the energy loss due to the expansion of the universe (∼ 4 Gpc).

If cosmic rays are nuclei of mass A, they will undergo due to photo-disintegration and pair production, both with CMB and IR backgrounds:

A + γCM B,IR → (A − 1) + N

→ (A − 2) + 2N

→ A + e+_{+ e}− _(2.4)

Since the energy is shared between nucleons, the threshold energy for these processes increases compared to that of protons. The inelasticity is lower by a factor ∼ 1/A, while the cross section increases with Z2 _{. This means that the loss length, in case of heavy}

nuclei, will be smaller (∼ 1 Mpc) with respect to protons, but it occurs at a higher energies.

Finally, if cosmic rays are photons, the dominant interaction is pair production with the cosmic background photons (γ + γCM B,RB → e++ e−). Pair creation with the CMB is

important above 4·1014_{eV while attenuation from pair creation with the radio background}

dominates the energy loss above 2 · 1019 _{eV. On the other hand, at energies higher than}

1022 _{eV, the attenuation length grows to values of order of 100 Mpc, making possible the}

hypothesis of photons as primary of extremely-high energy cosmic rays. In fact, these photons could produce secondary photons at energies higher than the GZK-threshold. If this were the case, a secondary photon spectrum ∝ E−2_{should be observed, independently}

on the source spectrum.

Is charged particle astronomy possible?

The interaction processes explained below are summarized in Fig. 2.6 and they have significant implications on the cosmic ray spectrum and on the possibility of making

Figure 2.6: Several interactions with the CMB. The curves labeled p+γCM B → e++e−+p

and F e+γCM B → e++e−+F e are the distances for which the proton and the iron nucleus

lose 1/e of their energy due to pair production. p + γCM B → N + π is the mean free path

for photo-pion production. F e + γCM B → nucleus + n or 2n is the mean free path for

spallation. γ + γCM B → e++ e− is the mean free path for pair creation for photons with

the CMB. n → p + e + ν is the mean decay length for a neutron. Figure from [47].

cosmic ray astronomy. First, due to the GZK effect, the observed spectrum should not extend, except at greatly reduced flux, beyond about several times 1019 _{eV. This expected}

suppression in the energy flux is known as the GZK suppression. Nevertheless, it does not mean that no event could be detected above this energy. In fact, some of them have been detected and are known as Super-GZK events. Second, Super-GZK events must have a nearby origin, cosmologically speaking, closer than one hundred of Mpc, usually called the GZK-sphere or the GZK-horizon. Otherwise, their energy would have been reduced below the GZK threshold due to this effect.

Besides their interaction with cosmic photon backgrounds, charged particles are also affected by the presence of magnetic fields in the media they traverse. The intensity and

topology of this fields is mostly unknown in the intergalactic medium but, if nG intensities are assumed, as a naive interpretation of Faraday rotation measurements would suggest, then protons at the highest energies could have gyroradii in excess of 100 Mpc. Therefore, charged cosmic rays originated at sources located at less that a few tens of Mpc, should keep enough directional information at Earth to produce observable anisotropy and make their astrophysical counterparts visible. The later opens the possibility of a charged particle astronomy in a similar sense as traditional photon-astronomy. At energies below few 1019 _{eV, the deflection due to the intergalactic and galactic magnetic fields combined}

is probably too large and only lower momenta of anisotropy can be expected even with very high statistics available. It is very likely that the same considerations apply, even at the highest energies, for nuclei heavier than protons. In any case, even for protons, only sources inside the GZK-sphere (. 100 Mpc) could be explored due to the combined effects of intervening radiation backgrounds and magnetic fields.

It must be noted that some proposed exotic neutral particles, if they do exist, and neutrinos, if detected in enough quantities, may help probe a deeper portion of universe while keeping directional information.