Juego y fantasía: reflexiones preliminares

Note that gamma rays with energies from & 100 MeV up to multi-TeV discussed here have much higher energies than gamma rays produced in radioactive decays (∼MeV). For a dis- cussion on extraterrestrial radioactive gamma ray emission see, e.g., Diehl & Timmes (1998). The discussed here HE and VHE gamma rays can only be produced by the interactions of relativistic particles. From now on gamma ray is used for HE and VHE gammas, if not mentioned explicitly else.

This section describes the most important production mechanisms for gamma rays (see also Longair (2010)). The production mechanisms of gamma rays are usually divided into two groups: leptonic processes and hadronic processes. The naming refers to the nature of the in- teracting relativistic particle, i.e. leptonic processes for electrons (and positrons) and hadronic processes for protons. Two competing processes exist for leptonic gamma ray production:

ˆ Inverse Compton scattering (IC)is the interaction between a (relativistic) electron

and ambient photons. Hereby most of the electron’s energy is transferred to the photon, thus reaching VHE. The IC process can be divided in the Thompson regime (α1) and the Klein-Nishina regime (α1) depending on the ratio between the photon energy in the rest frame of the electron and the rest mass of the electronα=E_γ0/mec2.

– In the Thompson regime the cross section is independent of the energy and given by the Thompson cross σT section. The maximum energy of the photon after

the scattering in the laboratory frame is: Eγ,max,T ≈ 4γ2Eγ,0 where γ is the

Lorentz factor of the electron and Eγ,0 the initial energy of the photon in the

laboratory frame. Assuming a electron population in the form of a power law

E−Γe _{the resulting photon spectrum will be also a power law but with a harder}

slope Γγ = (Γe+ 1)/2.

– In the Klein-Nishima regime the energy transfer to the photon is∝ γme i.e., the

photon obtains all the energy from the electron in one interaction. The cross section can be approximated as σkn ≈ πre21α

(

ln 2α+ 1₂). Here re is the classical

electron radius. The cross section decreases roughly with 1/γresulting in a photon spectrum with a softer slope of Γγ= (Γe+ 1).

The overall photon spectrum produced by IC scattering of relativistic electrons on am- bient photon fields has a typical structure of an asymmetric peak: at high energies the suppression of the cross section in the Klein-Nishina regime leads to a significant steep- ening of the spectrum. The efficiency of the gamma ray production by the IC depends linearly on the density of the photon field and thus a higher density of background pho- tons leads to a higher gamma ray luminosity. In addition to locally varying photon fields (e.g. star light, or reprocessed starlight) the cosmic microwave background (CMB) acts as a persistent target for IC scattering of relativistic electrons throughout the universe.

ˆ Bremsstrahlungis the interaction of electrons with ambient matter. Here, electrons

are decelerated in the electric field of nuclei emitting energy in form of a photon. On average one or two photons are emitted per radiation length. The average energy of an

2.3 Gamma rays

emitted photon is ∼ 1/3 of the energy of the electron. An electron population in the form of a power law will produce a gamma-ray spectrum of the same power law form. The magnitude of the cross section depends on the chemical composition (σBrems ∝Z2)

and the degree of ionization of the medium.

In the hadronic channel gamma rays are almost exclusively produced in inelastic proton- proton collisions. Therefore, the intensity of the expected hadronic gamma ray emission depends strongly on the product of CR density and ambient matter density. Such collisions produce mesons and in particular pions. Example interactions are:

p + p→π0 + p + p (2.15)

p + p→π0 + π+ + π−+ p + p (2.16)

p + p→π± + n +X . (2.17)

Charged pions will decay into muons (finally to electrons and positrons) and neutrinos. For typical slopes around −2 and e/p-ratios of ∼ 1/50 the secondary electrons (positrons) pro- duced in pp-collisions play no role as an additional source for gamma ray production for SNRs. The main decay channel (>99%) of the neutral pion is:

π0 →2γ (2.18)

In average about one tenth of the energy of the primary CR proton is transfered into each gamma. The cross section for π0 production is almost independent of energy. Thus, the slope of the produced gamma-ray spectrum is identical to the spectral slope of the protons. A unique footprint of the hadronic channel is the production of highly relativistic neutrinos which come from the decay of charged pions.

Comparing the efficiency of the gamma ray production in leptonic and hadronic channels one finds that, almost independent of the environment, leptonic gamma ray emission is produced more efficiently. The typical cooling time τ = _dE/dtE for relativistic particles affected by the different processes are:

ˆ IC scattering (assuming for simplicity scattering on CMB only):

τIC ≈

2.3×1012

γ years (2.19)

ˆ Bremsstrahlung3:

τBrems ≈106/nyears, (2.20)

wheren is the ambient particle number per cm3_.

ˆ Pion production (inelastic pp-collisions)

τpp≈107/nyears (2.21)

3_{A primordial hydrogen and helium contribution as a fully ionized target material was assumed. Furthermore}

the weak energy dependence on the cross section was neglected. The lifetime for ultra relativistic electrons (γ&108_{) might thus be slightly over estimated. It is important that Bremsstrahlung of electrons is usually}

Chapter 2 Cosmic rays and gamma rays

An important competing process of energy loss for electrons is synchrotron radiation in am- bient magnetic fields. This mechanism does not result in the production of VHE gamma rays (at least for the typical environments of the sources discussed here) but rather in radio and x-ray emission and can even reach to HE (i.e., Crab Nebula). The cooling time of a relativistic electron affected by synchrotron radiation depends quadratically on the magnetic field strength and linearly on the energy of the electron:

τSync= 2.4×1013 γ ( B µG )2 years (2.22)

Assuming 1 TeV particles in a typical average interstellar medium (n = 1/cm3, B = 3µG) one can estimate the relative importance of the individual processes. The cooling times in years for electrons are: τIC ≈1.2×105,τBrems ≈1×106, and τSync ≈1×106. For protons

the cooling time due to inelastic pp interactions is τpp ≈107 years, one order of magnitude

higher. Here, the most dominant emission in the gamma-regime arises from IC scattering. However, synchrotron losses are important when considering the total flux.

10 5 _{0.1 1000} 107 ₁₀11 ₁₀15 E [eV] 10 20 10 18 10 16

Sync.

IC + Brems. + Pion decay

Brems.

IC

Pion decay

Figure 2.5: Example of the broad band spectral energy distribution in arbitrary units caused by a power law distribution of relativistic electrons and protons (electron proton ratio = 1). The slope of both distributions is -2, and an exponential cut-off has been assumed at 1014 eV. The parameters of the interstellar material chosen are:

n= 1,B = 3µG, and only CMB photons have been considered as target photons for IC scattering. The kinematic cut-off in the emission produced via pion decay is indicated by the dashed line. It can be seen that electrons radiate more efficiently than protons and that IC dominates in low density media. Courtesy of Sara Rebecca Gozzini, private communication.

2.3 Gamma rays

Figure 2.5 shows the multi wavelength spectra of non-thermal radiation produced by a power law distribution of relativistic electrons and protons (e/p=1, slope=-2).

The high gamma-ray emissivity of electrons is one of the main challenges for the identification of hadronic sources. Depending on the environment (i.e., density, photon field, and magnetic field) the gamma ray emission can be dominated by different processes or be a combination thereof. Only in regions with high density and strong magnetic fields the hadronic process may become the dominant gamma-ray production mechanism.

At this point the following aspects should be stressed: only a hadronically dominated gamma- ray emission allows straightforward conclusions on the proton- and thus on the CR spectrum. However, leptonically dominated gamma-ray emission does not exclude the presence of a significant component of relativistic protons. Moreover, as the spectrum of the underlying particle distribution is not a priori known, VHE gamma-ray without further multiwavelength data are not able to distinguish between a hadronic or a leptonic scenario.