10. Messengers from the High-Energy Universe

10.1.2.1 Leptonic Gamma Ray Production Models

Photons cannot be directly accelerated; however, mechanisms exist such that photons of rather large energies are radiated. We examine in this subsection radiation processes just involving leptons (they are called “leptonic” photoproduction mechanisms). In particular, we shall sketch the simplest self-sustaining acceleration mechanism, the synchrotron self-Compton restricted to a single acceleration region.

Synchrotron Radiation. High-energy photon emission in a magnetic field is in the beginning generally due to synchrotron radiation. The dynamics of charged particles is strongly influenced through the Lorentz force by the magnetic fields present in astrophysical environments. Accelerated relativistic particles radiate synchrotron photons; the power loss for a charged particle of mass M and charge Ze can be expressed as

(10.17)

It is immediately evident from Eq. 10.17 that synchrotron energy loss is by far more important for electrons than for protons.

Compton scattering and “inverse Compton” process. The Compton scattering of a photon by an electron is a relativistic effect, by which the frequency of a photon changes due to a scattering. In the scattering of a photon by an electron at rest, the wavelength shift of the photon can be expressed as

where is the angle of the photon after the collision with respect to its line of flight. As evident from the equation and from the physics of the problem, the energy of the scattered photon cannot be larger than the energy of the incident photon. However, when low-energy photons collide with high-energy electrons instead than with electrons at rest, their energy can increase: such process is called inverse Compton (IC) scattering. This mechanism is very effective for boosting (for this reason it is called “inverse”) the photon energy, and is important in regions of high soft-photon energy density and energetic electron density.

Synchrotron Self-Compton. The simplest purely leptonic mechanism we can draw for photon “acceleration”—a mechanism we have seen at work in astrophysical objects—is the so-called self-synchrotron Compton (SSC) mechanism. In the SSC, ultrarelativistic electrons accelerated in a magnetic field—such as the field present in the accretion region of AGN, or in the surrounding of SNR—generate synchrotron photons. The typical values of the fields involved are such that the synchrotron photons have an energy spectrum peaked in the infrared/X-ray range. Such photons in turn interact via Compton scattering with their own parent electron population (Fig. 10.7); since electrons are ultrarelativistic (with a Lorentz factor   10), the energy of the rescattered photon can be boosted by a large factor.

For a power law population of relativistic electrons with a differential spectral index q and a blackbody population of soft photons at a temperature T, mean photon energies and energy distributions can be calculated for electron energies in the Thomson regime and in the relativistic Klein–Nishina regime:

(10.18)

(10.19)

(10.20)

(10.21)

where denotes the scattered photon’s energy, denotes the energy of the parent electron, and denotes the energy of the seed photon. Note that an observer sees a power-law synchrotron spectrum only if no absorption of photons happens. Sources in which all produced photons are not absorbed are called optically thin. In an optically thick source, significant self-absorption can happen, modifying the shape of the synchrotron spectrum and typically sharpening the cutoff.

A useful approximate relation linking the electron’s energy and the Comptonized photon’s energy is given by:

The Compton component can peak at GeV–TeV energies; the two characteristic synchrotron and Compton peaks are clearly visible on top of a general dependence. Figure 10.8 shows the resulting energy spectrum. This behavior has been verified with high accuracy on the Crab Nebula and on several other emitters, for example on active galactic nuclei. If in a given region the photons from synchrotron radiation can be described by a power law with spectral index p, in the first approximation the tails at the highest energies from both the synchrotron and the Compton mechanisms will have a spectral index p. Note, however, that since he Klein–Nishina cross section is smaller than the Thomson cross section, the Compton scattering becomes less efficient for producing gamma rays at energies larger than TeV.

A key characteristics of the SSC model is a definite correlation between the yields from synchrotron radiation and from IC during a flare (it would be difficult to accommodate in the theory an “orphan flare,” i.e., a flare in the IC region not accompanied by a flare in the synchrotron region). Although most of the flaring activities occur almost simultaneously with TeV gamma ray and X-ray fluxes, observations of 1ES 1959650 and other AGN have exhibited VHE gamma ray flares without their counterparts in X-rays. The SSC model has been very successful in explaining the SED of AGN, but flares observed in VHE gamma rays with absence of high activity in X-rays are difficult to reconcile with the standard SSC.

10.1.2.2 Hadronic Models and the Production of Gamma Rays and Neutrinos

Alternative and complementary models of VHE emission involve cascades initiated by primary protons/nuclei that had been accelerated in the system. The beam of accelerated hadrons collides with a target of nucleons (for example, a molecular cloud) or with a sea of photons, coming from the synchrotron radiation or the bremsstrahlung of electrons accelerated or starlight (hadronic photoproduction).

In either case, the energy of the primary protons is expected by the physics of hadronic cascades to be one-two orders of magnitude larger than the energy of gamma rays, since the dominant mechanism for photon production is the decay of the secondary mesons into  pairs at the end of the hadronic cascade. The study of rays can thus provide insights on the acceleration of charged cosmic rays. Photons coming from decay have in general energies larger than photons from synchrotron radiation.

A characteristics of hadroproduction of gamma rays is a peak at MeV in the spectral energy distribution, which can be related to a component from decay; this feature, which is almost independent of the energy distribution of mesons and consequently of the parent protons, is called the “pion bump”, and can be explained as follows. In the rest frame of the neutral pion, both photons have energy  MeV and momentum opposite to each other. Once boosted for the energy E of the emitting , the probability to emit a photon of energy is constant over the range of kinematically allowed energies (the interval between and , see Exercise 2). The spectrum of gamma rays for an arbitrary distribution of neutral pions is thus a superposition of rectangles for which only one point at is always present. This should result in a spectral maximum independent of the energy distribution of parent pions.

The existence of a hadronic component has been demonstrated from the experimental data on galactic SNRs and from the region of the GC (see later), and could explain the production of cosmic ray hadrons at energies up to almost the knee. The detection of orphan AGN flares and, more recently, of a simultaneous gamma ray-neutrino flare from an AGN, indicated evidence for hadronic production of gamma rays in such sources powered by supermassive black holes.

Let us shortly examine the relation between the high-energy part of the spectra of secondary photons and the spectra of primary cosmic rays (we shall assume protons) generating them. We shall in parallel examine the case of the spectra of secondary neutrinos, which are copiously produced in the decays of , also present in the final states, and whose rate is closely related to the rate– neutrinos could become, if large enough detectors are built, another powerful tool for the experimental investigation. We shall follow here an analytical approach; it should be noted however that Monte Carlo approaches in specialized software programs called SIBYLL, QGSJet, EPOS and DPMJet provide much more precise results, and are normally used in scientific publications.

Proton-nucleon collisions. In beam dump processes of protons against molecular clouds, at c.m. energies much larger than the pion mass, the cross section is about 30–40 mb. The final state is dominated by particles emitted with small transverse momentum (soft or low- processes). Almost the same number of , and are produced, due to isospin symmetry. The s decay immediately into two gamma rays; the charged pions decay into , with the decaying into (charge conjugates are implicitly included). Thus, there are three neutrinos for each charged pion and three neutrinos for every gamma ray; each neutrino has approximately 1/4 of the energy in the laboratory, while each photon has on average half the energy of the .

We assume the cross section for proton-proton interactions to be constant,  cm. If generic hadrons of mass number A constitute the beam instead of protons, one can approximate . The average pion multiplicity (shared democratically among each pion species , and ) is approximately proportional to the square root of the c.m. energy as modeled by Fermi and Landau (Chap. 6); we can approximate, for incident protons,

(10.22)

where is the threshold energy for pion production, less than 1 GeV - we can neglect it at large proton energies. Consequently, the average pion energy at the source is related to the proton energy, in the direction of flight of the proton, by

where is the Lorentz boost of the proton.

The generic pion distribution from the hadronic collision, assuming equipartition of energy among pions, can be written as

(10.23)

where is the density of hadrons in the target, l is the depth ( is the column density), is the proton rate. If the differential proton distribution per energy and time interval at the source is

(10.24)

making in the integral (10.23) the substitution the pion spectrum at the source is

(10.25)

The photon spectrum is finally

(10.26)

This simple analytic result comes from an approximation of the interaction, but the result is not far from that of a complete calculation. Equation (10.26) provides us with an estimate of the total photon flux at the source. The spectral behavior of the protons can be estimated from diffusive shock acceleration and a spectral index can be assumed.

The treatment of the neutrino case proceeds along the same line; one has

(10.27)

Photoproduction interactions have a cross section of a fraction of mb, smaller than the proton-proton interaction by two orders of magnitude. They are thus important in environments where the target photon density is much higher than the matter density – this is the case of many astrophysical systems, like the neighborhood of SMBHs in AGN.

One can imagine that photoproduction of neutrinos and photons happens mainly via the resonance: . The cross sections for the processes and at the resonance are in the approximate ratio of 2:1, due to isospin balance (Chap. 5). The process happens beyond the threshold energy for producing a :

(10.28)

where is the energy of the target photon. The cross section for this reaction peaks at photon energies of about in the proton rest frame. In the observer’s frame the energy of the target photon is such that 0.35, with in EeV and in eV. For UV photons, with a mean energy of 40 eV, this translates into a characteristic proton energy of some 10 PeV.

The photon and neutrino energies are lower than the proton energy by two factors which take into account (i) the average momentum fraction carried by the secondary pions relative to the parent proton² () and (ii) the average fraction of the pion energy carried by the photon in the decay chain (1/2) and by the neutrinos in the decay chain (roughly 3/4 of the pion energy because equal amounts of energy are carried by each lepton). Thus:

(10.29)

The photon and neutrino spectra are related. All the energy of the ends up in photons and 3/4 of the energy goes to neutrinos, which corresponds to a ratio of neutrino to gamma luminosities (/)

(10.30)

This ratio is somewhat reduced taking into account that some of the energy of the accelerated protons is lost to direct pair production ().

If a source is occulted by the presence of thick clouds or material along the line of sight to the Earth, however, gamma rays are absorbed while neutrinos survive.

An approximate expression for the relation between the neutrino and the gamma-ray fluxes produced from hadronic cascades holds if the proton energy spectrum can be described by a power law, or by an exponential:

(10.31)

The production rate of gamma rays is not necessarily the emission rate observed: photons can be absorbed, and the photon field reduces the pionic gamma rays via pair production.

10.1.2.3 Nuclear Processes and Gamma Rays in the MeV Range

Protons at energies below the pion production threshold (about 300 MeV) can be at the origin of gamma rays through nuclear excitation of the ambient medium. De-excitation of the target nuclei leads to gamma ray lines in the energy region between several hundred keV to several MeV. The most distinct features in the overall nuclear gamma-ray spectrum appear around 4.4 MeV (from C), 6.1 MeV (from O), 0.85 MeV (from Fe), etc.

Gamma ray line emission is expected also from radioactive isotopes synthesised in stellar interiors or during supernova explosions. Since nucleosynthesis can be effective only in very dense environments, to survive and be observed gamma-ray lines should be produced by abundant isotopes with long lifetimes. The best candidates are lines from Al and Fe for the production of diffuse galactic emission, and from Be, Ti and Ni produced during transient phenomena.

10.1.3.1 Origin from WIMPs

Dark matter candidates (WIMPs in particular, as discussed in Chap. 8) are possible sources of, e.g., photons, electrons and positrons, and neutrinos via a top-down mechanism.

As discussed in Chap. 8, the normalized relic density of dark matter (DM) particles can be expressed as

The value for the interaction rate corresponds to a cross section of the order of 10 pb, typical for weak interactions at a scale GeV. This is the so-called “WIMP miracle”: a weakly interacting massive particle would be a good DM candidate. WIMP masses can be expected in the range between 10 GeV and a few TeV.

Given the expected amount of WIMP dark matter in the current Universe and the annihilation cross section, it is likely that DM is subject to self-annihilations. To be able to self-annihilate, the DM particle must either coincide with its antiparticle, or be present in both the particle and antiparticle states. In the annihilation (or decay) of the dark matter particles all allowed standard model particles and antiparticles could be produced, and gamma rays and/or charged particles are present in the final states (in the last case, with no preference between matter and antimatter, contrary to the standard sources of cosmic rays).

Where dark matter densities are large, the probability that WIMPs encounter each other and annihilate is enhanced, being proportional to . The problem is that we know the dark matter density in the halos of galaxies, while the extrapolation to big density cores (like, for example, galactic centers are expected to be) relies on models – this fact holds also for the Milky Way. If one can trust the extrapolations of DM density, one can predict the expected annihilation signal when assuming a certain interaction rate or put limits on this quantity in the absence of a signal (see Sect. 10.4.2.4).

10.2.1.1 Neutron Stars; Pulsars

When a star collapses into a neutron star, its size shrinks to some 10–20 km, with a density of about kg/m. Since angular momentum is conserved, the rotation can become very fast, with periods of the order of a few ms up to 1 s. Neutron stars in young SNRs are typically pulsars (short for pulsating stars), i.e., they emit a pulsed beam of electromagnetic radiation. Since the magnetic axis is in general not aligned to the rotation axis, two peaks corresponding to each of the magnetic poles can be seen for each period (Fig. 10.10).

The rotating period for young pulsars can be estimated using basic physics arguments. A star like our Sun has a radius km and a rotation period of days, so that the angular velocity is rad/s. After the collapse, the neutron star has a radius 10 km. From angular momentum conservation, one can write:

The gravitational collapse amplifies the stellar magnetic field. As a result, the magnetic field near the NS surface is extremely high. To obtain an estimate of its magnitude, let us use the conservation of the magnetic flux during the contraction. Assuming the magnetic field to be approximately constant over the surface,

For a typical value of kG, the magnetic fields on the surface of the neutron star is about G. This estimate has been experimentally confirmed by measuring energy levels of free electrons in the pulsar strong magnetic fields. In a class of neutron stars called magnetars the field can reach G.

Typical pulsars emitting high-energy radiation have cutoffs of the order of a few GeV. More than hundred HE pulsars emitting at energies above 100 MeV have been discovered by the Fermi-LAT until 2013. They are very close to the solar system (Fig. 10.11, left), most of the ones for which the distance has been measured being less that a few kpc away. A typical spectral energy distribution is shown in Fig. 10.11, right. The pulsar in Crab Nebula is not typical, being one of the two (together with the Vela pulsar) firmly detected up to now in VHE (Fig. 10.12)—Crab and Vela were also the first HE pulsars discovered in the late 1970s.

10.2.1.2 Binary Systems

Neutron stars and BHs and other compact objects are frequently observed orbiting around a companion compact object or a non-degenerate star (like in the binary LS I61 303). In binary systems mass can be transferred to the (more) compact object, accreting it. Shocks between the wind of the massive companion and the compact object can contribute to the production of non-thermal emission in X-rays or even in gamma rays. Due to the motion of ionized matter, very strong electromagnetic fields are produced in the vicinity of the compact object, and charged particles can be accelerated to high energies, generating radiation.

10.2.1.3 Supernova Remnants and Particle Acceleration

Supernova remnants (SNRs) are characterized by expanding ejected material interacting with ambient gas through shock fronts, with the generation of turbulent magnetic fields, of the order of G to 1 mG. Typical velocities for the expulsion of the material out of the core of the explosion are of the order of 3000–10 000 km/s for a young ( yr) SNR. The shock slows down over time as it sweeps up the ambient medium, but it can expand over tens of thousands of years and over tens of parsecs before its speed falls below the local sound speed.³

Based on their emission and morphology (which are actually related), SNRs are generally classified under three categories: shell-type, pulsar wind nebulae (PWN), and composite (a combination of the former, i.e., a shell-type SNR containing a PWN). The best known case of a PWN is the Crab Nebula, powered by the central young (1000 year) pulsar B053121. Crab Nebula emits radiation across a large part of the electromagnetic spectrum, as seen in Fig. 10.13 – and qualitatively one can see in this figure the SSC mechanism at work with a transition at GeV between the synchrotron and the IC emissions. One can separate the contribution of the pulsar itself to the photon radiation from the contribution of the PWN (Fig. 10.12).

Note that sometimes in the literature shell-type supernova remnants are just called SNRs and distinguished from PWN, but this is not the convention used in this book.

The evolution of a SNR can be described by a free expansion phase, an adiabatic phase, a radiative phase and a dissipation phase (Fig. 10.14).

When the supernova remnant slows to the speed of the random velocities in the surrounding medium, after roughly 30 000 years, it merges into the general turbulent flow, contributing its remaining kinetic energy to the turbulence, and spreading around heavy atoms which can be recycled in the ISM.

A young supernova remnant has the ideal conditions for the Fermi 1st order acceleration. The maximum energy that a charged particle could achieve is given by the rate of energy gain, multiplied by the time spent in the shock. In the Fermi first-order model,

(10.35)

(Sect. 10.1.1); is of the order of the Larmor radius (see Sect.  10.2) .

(10.36)

Finally

(10.37)

Inserting in Eq. 10.37 G as a typical value of the magnetic field B, and assuming , where is the radius of the supernova remnant, we obtain:

(10.38)

The shock acceleration of interstellar particles in SNR explains the spectrum of cosmic ray protons up to few hundreds of TeV, close to the region where the knee begins (see Fig. 10.1).

An important consequence of (10.38) is that the maximum energy is proportional to the charge Z of the ion, and it is thus higher for multiply ionized nuclei with respect to a single-charged proton. In this model, the knee is explained as a structure due to the different maximum energy reached by nuclei with different charge Z (Fig. 10.15). Note that the proportion to Z is an underestimate of the actual proportion, since in addition to the acceleration efficiency growing with Z the escape probability from the galaxy decreases with Z.

10.2.3.1 Blazars

Blazars accelerate particles to the highest observed energies, and are therefore of high interest.

Observationally, blazarsare divided into two main subclasses depending on their spectral properties.

Blazar population studies at radio to X-ray frequencies indicate a redshift distribution for BL Lacs peaking at 0.3, with only few sources beyond 0.8, while the FSRQ population is characterized by a rather broad maximum at 0.6–1.5.

10.2.3.2 Non-AGN Extragalactic Gamma Ray Sources

At TeV energies, the extragalactic ray sky is completely dominated by blazars. At present, more than 50 objects have been discovered and are listed in the online TeV Catalog. Only 3 radio galaxies have been detected at TeV energies (Centaurus A, M87 and NGC 1275).

The two most massive closeby starburst (i.e., with an extremely large rate of star formation) galaxies NGC 253 and M82 are the only extragalactic sources detected at TeV energies for which the accretion disk-jet structure is not evidenced.

At GeV energies, a significant number (about 1/3 ot the total sample) of unidentified extragalactic objects has been detected by the Fermi-LAT (emitters that could not be associated to any known object), and few non-AGN objects have been discovered. Among non-AGN objects, there are several local group galaxies (LMC, SMC, M31) as well as galaxies in the star formation phase (NGC 4945, NGC 1068, NGC 253, and M82).

CRs might be accelerated by SNRs or other structures related to star formation activity.

10.2.3.3 The Gamma Ray Yield from Extragalactic Objects

The observed VHE spectra at high energies are usually described by a power law . The spectral indices need to be fitted from a distribution deconvoluted from absorption in the Universe, since the transparency of the Universe depends on energy; they typically range in the interval from 2 to 4, with some indications for spectral hardening with increasing activity. Emission beyond 10 TeV has been established, for close galaxies like Mrk 501 and Mrk 421. Some sources are usually detected during high states (flares) only, with low states falling below current sensitivities.

Observed VHE flux levels for extragalactic objects range typically from 1 % of the Crab Nebula steady flux (for the average/steady states) up to 10 times as much when the AGN are in high activity phases. Since TeV instruments are now able to detect sources at the level of 1 % of the Crab, the variability down to few minute scale of the near and bright TeV-emitting blazars (Mrk 421 and Mrk 501) can be studied in detail. Another consequence of the sensitivity of Cherenkov telescopes is that more than one extragalactic object could be visible in the same field of view.

The study and classification of AGN and their acceleration mechanisms require observations from different instruments. The spectral energy distributions (SEDs) of blazars can span almost 20 orders of magnitude in energy, making simultaneous multiwavelength observations a particularly important diagnostic tool to disentangle the underlying nonthermal processes. Often, SEDs of various objects are obtained using nonsimultaneous data—which limits the accuracy of our models.

In all cases, the overall shape of the SEDs exhibits the typical broad double-hump distribution, as shown in Fig. 10.17 for three AGN at different distances. The SEDs of all AGN considered show that there are considerable differences in the position of the peaks of the two components and in their relative intensities. According to current models, the low-energy hump is interpreted as due to synchrotron emission from highly relativistic electrons, and the high-energy bump is related to inverse Compton emission of various underlying radiation fields, or decays, depending on the production mechanism in action (Sect. 10.1.2). Large variability is present, especially at optical/UV and X-ray frequencies.

Variability is also a way to distinguish between hadronic and leptonic acceleration modes. In a pure leptonic mode, one expects that in a flare the increase of the synchrotron hump is fully correlated to the increase of the IC hump; in a hadronic mode, vice versa, one can have a “orphan flare” of the peak corresponding to decay.

Studies on different blazar populations indicate a continuous spectral trend from FSRQ to LBL to IBL to HBL, called the “blazar sequence.” The sequence is characterized by a decreasing source luminosity, increasing synchrotron peak frequency, and a decreasing ratio of high- to low-energy component (Fig. 10.17).

10.2.5.1 Gamma Rays and the Origin of Cosmic Rays from SNRs

Among the categories of possible cosmic ray accelerators, several have been studied in an effort to infer the relation between gamma rays and charged particles. In the Milky Way in particular, SNRs are, since the hypothesis formulated by Baade and Zwicky in 1934, thought to be possible cosmic ray accelerators; according to the Hillas plot, this acceleration can go up to energies up to the order the PeV. The particle acceleration in SNRs is likely to be accompanied by production of gamma rays due to interactions of accelerated protons and nuclei with the ambient medium.

The conjecture has a twofold justification. From one side, SNRs are natural places in which strong shocks develop and such shocks can accelerate particles. On the other side, supernovae can easily account for the required energetics. In addition, there are likely molecular clouds and photon fields which allow the reprocessing of accelerated protons–thus one can expect sizable gamma-ray and neutrino emission. Nowadays, as a general remark, we can state that there is no doubt that SNR accelerate (part of the) galactic CR, the open questions being: which kind of SNR; in which phase of their evolution SNR really do accelerate particles; and if the maximum energy of these accelerated particles can go beyond 1 PeV, and thus get insights on the nature, the energy and the composition of the knee.

A very important step forward in this field of research was achieved in the recent years with an impressive amount of experimental data at TeV energies, by Cherenkov telescopes (H.E.S.S., MAGIC, VERITAS), and at GeV energies, by the Fermi-LAT and AGILE satellites.

In SNRs with molecular clouds, in particular, a possible mechanism involves a source of cosmic rays illuminating clouds at different distances, and generating hadronic showers by pp collisions. This allows to spot the generation of cosmic rays by the study of photons coming from decays in the hadronic showers.

Recent experimental results support the “beam dump” hypothesis of accelerated protons on molecular clouds or photon fields from the imaging of the emitter. An example is the SNR IC443. In Fig. 10.20, a region of acceleration at GeV energies is seen by the Fermi-LAT. It is significantly displaced from the centroid of emission detected at higher energies by the MAGIC gamma ray telescope–which, in turn, is positionally consistent with a molecular cloud. The spectral energy distribution of photons also supports a two-component emissions, with a rate of acceleration of primary electrons approximately equal to the rate of production of protons. Such a 2-region displaced emission morphology has been also detected in several other SNRs (W44 and W82 for example).

A characteristics of hadroproduction of gamma rays is the presence of a “pion bump” at MeV in the spectral energy distribution, which can be related to decay; this feature has been observed in several SNRs, see for example Fig. 10.21. Unfortunately, present gamma-ray detectors are not very sensitive in the region of few tens of MeV, and the reconstruction of the pion bump is not very accurate.

Besides indications from the studies of the morphology and from the shape of the SED, the simple detection of photons of energies of the order of 100 TeV and above could be a direct indication of production via decay, since the emission via leptonic mechanisms should be strongly suppressed at those energies where the inverse Compton scattering cross section enters the Klein–Nishina regime. A cosmic-ray accelerator near the PeV has likely been found in the vicinity of the GC.

10.2.5.2 Where Are the Galactic PeVatrons?

We saw that cosmic rays up to the knee are accelerated in the galaxy; this implies that our galaxy contains petaelectronvolt accelerators, often called PeVatrons.

Cosmic ray acceleration has been proven in particular in some stellar endproducts, as we have just seen; however, these sources display an exponential-like cutoff, or an index break, significantly below 100 TeV. This implies that none of these can be identified as a PeVatron. Now the question is: where are the PeVatrons?

Recent measurements of the galactic center region by H.E.S.S. have shown that gamma-ray emission is compatible with a steady source accelerating CRs up to PeV energies within the central 10 pc of the galaxy. The supermassive black hole Sagittarius A* could be linked to this possible PeVatron.

From an annulus centered at Sagittarius (Sgr) A* (see Fig. 10.22, left) the energy spectrum of the diffuse -ray emission (Fig. 10.22, right) has been extracted. The best fit to the data is found for a spectrum following a power law extending with a photon index 2.3 to energies up to tens of TeV, without any indication of a cutoff. Since extremely-high energy -rays might result from the decay of neutral pions produced by pp interactions, the derivation of such hard power-law spectrum implies that the spectrum of the parent protons should extend to energies close to 1 PeV. The best fit of a -ray spectrum from neutral pion decays is found for a proton spectrum following a pure power-law with index 2.4. In the future, with larger and more sensitive neutrino detectors, pp interactions of 1 PeV protons could also be studied by the observation of emitted neutrinos.

Although its current rate of particle acceleration is not sufficient to provide a substantial contribution to galactic CR, Sagittarius A* could have plausibly been more active over the last  years, and therefore should be considered as a sizable source of PeV galactic cosmic rays. However, the hypothesis is speculative; moreover, the identification of the source remains unclear, since the GC region is very confused, and several other VHE gamma-ray sources exist.

Crab Nebula is a PWN currently showing no clear cutoff, and the gamma-ray emission reaches some 100 TeV and beyond, as shown by HEGRA, MAGIC and H.E.S.S.. Although there is no direct indication that it is a hadron accelerator from the morphology or from the SED, the fact itself that photon energies are so high disfavors a purely leptonic origin of gamma rays, due to Klein–Nishina suppression: Crab could likely be a PeVatron as well.

10.2.5.3 Testing if Cosmic Rays Originate from AGN

As the energetics of SNRs might explain the production of galactic CR, the energetics of AGN might explain the production of CR up to the highest energies. In the Hillas relation, the magnetic field and the typical sizes are such that acceleration is possible (Table 10.1).

Where molecular clouds are not a likely target, as, for example, in the vicinity of supermassive black holes, proton–photon interactions can start the hadronic shower.

Although the spatial resolution of gamma ray telescopes is not yet good enough to study the morphology of extragalactic emitters, a recent study of a flare from the nearby galaxy M87 (at a distance of about 50 Mly, i.e., a redshift of 0.0004) by the main gamma telescopes plus the VLBA radio array has shown, based on the VLBA imaging power, that this AGN accelerates particles to very high energies in the immediate vicinity (less than 60 Schwarzschild radii) of its central black hole. This galaxy is very active: its black hole, of a mass of approximately 7 billion solar masses, accretes by 2 or 3 solar masses per year. A jet of energetic plasma originates at the core and extends outward at least 5000 ly.

Also Centaurus A, the near AGN for which some weak hint of correlation with the Auger UHE data exists, has been shown to be a VHE gamma emitter.

The acceleration of hadrons above 1 EeV has been proven very recently to correlate with the position of AGN, and in particular one blazar has been identified as a hadron accelerator at some tens of PeV. These two evidences will be discussed in detail later, in Sect. 10.4.1.7 and in Sect. 10.4.3.2 respectively.

10.2.6.1 Testing if Ultra-High-Energy Cosmic Rays Originate from GRBs

IceCube has been searching for neutrinos arriving from the direction and at the time of a gamma-ray burst. After more than one thousand follow-up observations, none was found, resulting in a limit on the neutrino flux from GRBs of less than one per cent. This focuses to an alternative explanation for the sources of extragalactic cosmic rays: active galactic nuclei.

10.3.3.1 Propagation of Galactic Cosmic Rays and Interaction with the Interstellar Medium

Cosmic rays produced in distant sources have a long way to cross before reaching Earth. Those produced in our galaxy (Fig. 10.25) suffer diffusion in magnetic fields of the order of a , convection by galactic winds, spallation ⁵ in the interstellar medium, radioactive decays, as well as energy losses or gains (reacceleration). At some point they may arrive to Earth or just escape the galaxy. Low-energy cosmic rays stay within the galaxy for quite long times. Typical values of confinement times of years are obtained measuring the ratios of the abundances of stable and unstable isotopes of the same element (for instance Be/Be, see below).

All these processes must be accounted in coupled transport equations involving the number density of each cosmic ray species of atomic number and mass number as a function of position, energy and time. These differential equations, can, for instance, be written as:

(10.44)

In the above equation:

• The term on the right side accounts for the sources (injection spectrum).

• The second term accounts for diffusion and convection:

  • describes diffusion: when at a given place N is high compared to the surroundings (a local maximum of concentration), particles will diffuse out and their concentration will decrease. The net diffusion is proportional to the Laplacian of the number density through a parameter D called diffusion coefficient or diffusivity, whose dimensions are a length squared divided by time;

  • describes convection (or advection), which is the change in density because of a flow with velocity .

• The third term accounts for the changes in the energy spectrum due to energy losses or reacceleration – we assume that energy is lost, or gained, at a rate .

• The fourth term accounts for the losses due to spallation, radioactive decays, and probability of escaping the galaxy. n is the number density of the interstellar medium (ISM) .

• The fifth term accounts for the gains due to the spallation or decays of heavier elements.

These equations may thus include all the physics process and all spatial and energy dependence but the number of parameters is large and the constraints from experimental data (see below) are not enough to avoid strong correlations between them. The solutions can be obtained in a semi-analytical way or numerically using sophisticated codes (e.g., GALPROP), where three-dimensional distributions of sources and the interactions with the ISM can be included.

Simpler models, like for example “leaky box” models, are used to cope with the main features of the data. In the simplest version the leaky box model consists in a volume (box) where there are sources uniformly distributed and charged cosmic rays freely propagate with some probability of escaping from the walls (see Fig. 10.26). Diffusion and convection effects are incorporated in the escape probability (lifetime). The stationary equation of the leaky box can be written as:

(10.45)

Here once again the first term on the right side accounts for the sources and the second and the third, respectively, for the losses (due to spallation, radioactive decays, and escape probability) and the gains (spallation or decays of heavier elements). In a first approximation, the dependence of the escape time on the energy and the charge of the nucleus can be computed from the diffusion equations, the result being . For the values of size and magnetic field typical of the Milky Way, .

All these models are adjusted to the experimental data and in particular to the energy dependence of the ratios of secondary elements (produced by spallation of heavier elements during their propagation) over primary elements (produced directly at the sources) as well as the ratios between unstable and stable isotopes of the same element (see Fig. 10.27). Basically all nuclei heavier than He (at primordial nucleosynthesis only H and He nuclei were present, with a ratio 3:1) are produced by nuclear fusion inside stars, generating energy to support them. Nuclear fusion proceeds up to the formation of nuclei with ; stellar nucleosynthesis, while producing carbon, nitrogen and oxygen, does not increase the abundance of light nuclei (lithium, beryllium, and boron). Heavier elements up to iron are only synthesized in massive stars with . Once Fe becomes the primary element in the core of a star, further compression does not ignite nuclear fusion anymore; the star is unable to thermodynamically support its outer envelope and initiates its gravitational collapse and its eventual explosion; nuclei formed during stellar nucleosynthesis are released in the galaxy and can be recycled for the formation of new stars. The secondary abundances are tracers of spallation processes of primary CRs with the ISM. The unstable secondary nuclei that live long enough to be useful probes of CRs propagation are Be ( Myr), Al ( Myr), Cl ( Myr), and Mn ( Myr). The most used probe is Be which has a lifetime similar to the escape time of 10 years from the galaxy and which is produced abundantly in the fragmentation of C, N, and O.

We can further simplify the last equation depending if we are dealing with primary or secondary CR: for primaries we can neglect spallation feed-down (i.e., they are not produced by heavier CR), while for secondaries we can neglect production by sources (). For example, let us assume now a primary cosmic nucleus P at speed and energy E, assumed stable (most nuclei are stable, one exception being Be which is unstable through beta decay). The equation can be written as:

where is the density of targets and is the mean free path in g/cm.

While is the same for all nuclei with same rigidity at the same energy, depends on the mass of the nucleus. The equation suggests that at low energies the spectra for different primary nuclei can be very different (e.g. for Fe interaction losses dominate over escape losses), but ratios should be approximately constant at high energies if particles come from the same source.

For high-energy protons with interaction lengths much larger than the escape length, the equation can be even further simplified to

and if (first order Fermi acceleration mechanism) we expect .

Secondary/primary ratios (Fig. 10.27, right) show a strong energy dependence at high energies as a result of the increase of the escape probability, while primary/primary ratios (Fig. 10.27, left) basically do not depend on energy. By measuring primary/primary and secondary/primary ratios as a function of energy we can infer the propagation and diffusion properties of cosmic rays.

One should note that in the propagation of electrons and positrons the energy losses are much higher (dominated by synchrotron radiation and inverse Compton scattering) and the escape probability much higher. Thus leaky box models do not apply to electrons and positrons. Primary TeV electrons lose half their total energy within a distance smaller than few hundreds parsec from the source.

10.3.3.2 The SNR Paradigm

The energy density of CRs, extrapolated outside the reach of the solar wind (i.e., above 1–2 GeV), is

The luminosity of galactic CR sources must provide this energy density, taking into account a residence time  yr of CR in the galactic disk (note that the product of the residence time to the ISM density in the galaxy is constrained by the B/C ratio). With  cm (for kpc and pc) as volume of the galactic disc, the required luminosity is  erg/s. In a core-collapse SN, the average energy output is  erg. Taking into account a rate of a supernova every 30 years, a SNR efficiency in particle acceleration could explain all galactic cosmic rays.

10.3.3.3 Extragalactic Cosmic Rays: The GZK Cutoff and the Photodisintegration of Nuclei

Extragalactic cosmic rays might cross large distances (tens or hundreds of Mpc) in the Universe. Indeed the Universe is full of CMB photons ( photons/cm—see Chap. 8) with a temperature of  K ( eV). Greisen and Zatsepin, and Kuzmin, realized independently early in 1966 that for high-energy protons the inelastic interaction

is likely leading to a strong decrease of the proton interaction length. The proton threshold energy for the process is called the “GZK cutoff”; its value is given by relativistic kinematics:

(10.46)

The pion photoproduction cross section, , reaches values as large as b just above the threshold (with a plateau for higher energies slightly above b). The mean free path of the protons above the threshold is thus:

(10.47)

In each GZK interaction the proton looses on average around 20 % of its initial energy.

A detailed computation of the effect of such cutoff on the energy spectrum of ultrahigh-energy cosmic ray at Earth would involve not only the convolution of the full CMB energy spectrum with the pion photoproduction cross section but also the knowledge of the sources, their location and energy spectrum as well as the exact model of expansion of the Universe (CMB photons are redshifted). An illustration of the energy losses of protons as a function of their propagation distance is shown in Fig. 10.28 without considering the expansion of the Universe. Typically, protons with energies above the GZK threshold energy after 50–100 Mpc loose the memory of their initial energy and end up with energies below the threshold.

The decay of the neutral and charged pions produced in these GZK interactions will originate, respectively, high-energy photons and neutrinos which would be a distinctive signature of such processes.

At a much lower energy ( eV) the conversion of a scattered CMB photon into an electron–positron pair may start to occur, what was associated by Hillas and Berezinsky to the existence of the ankle (this is the so-called “dip model”, Sect. 10.4.1).

Heavier nuclei interacting with the CMB and Infrared Background (IRB) photons may disintegrate into lighter nuclei and typically one or two nucleons. The photodisintegration cross section is high (up to mb) and is dominated by the Giant Dipole resonance with a threshold which is a function of the nuclei binding energy per nucleon (for Fe the threshold of the photon energy in the nuclei rest frame is MeV). Stable nuclei thus survive longer. The interaction length of Fe, the most stable nucleus, is, at the GZK energy, similar to the proton GZK interaction length. Lighter nuclei have smaller interaction lengths and thus the probability of interaction during their way to Earth is higher.

10.4.1.1 Energy Spectrum

The energy spectrum of charged cosmic rays reaching the atmosphere spans over many decades in flux and energy, as we have seen in the beginning of this Chapter (Fig. 10.1).

At low energies, GeV, the fluxes are high (thousands of particles per square meter per second) while there is a strong cutoff at about 10 eV–at the highest energies ever observed, GeV, there is less than one particle per square kilometer per century. The cosmic rays at the end of the known spectrum have energies well above the highest beam energies attained in any human-made accelerator and their interactions on the top of the Earth atmosphere have center-of-mass energies of a few hundred TeV (the design LHC beam energy is GeV); at these energies, however, the flux of cosmic rays is highly suppressed. This fact affects the choice of experiments to detect cosmic rays: one can study the energies up to the knee with satellites, while above the knee one must rely on ground-based detectors. Above a few GeV the intensity of the cosmic rays flux follows basically a power law,

with the differential spectral index being typically between 2.7 and 3.3. Below a few GeV, the flux is modulated by the solar activity and in particular by the magnetic field from the Sun–notice that these effects are variable in time.

The small changes in the spectral index can be clearly visualized multiplying the flux by some power of the energy. Figure 10.32 shows a suggestive anthropomorphic representation of the cosmic ray energy spectrum obtained multiplying the flux by . Two clear features corresponding to changes in the spectral index are observed. The first, called the knee, occurs around  eV, and it is sometimes associated to the transition from galactic to extragalactic cosmic rays; it corresponds to a steepening from a spectral index of about 2.7 to a spectral index of about 3.1. The second clear feature, denominated the “ankle,” occurs around  eV and its nature is still controversial. Another feature, called the second knee, marks a steepening to from about 3.1 to about 3.3, at an energy of about 400 PeV.

The number of primary nucleons per GeV from about 10 GeV to beyond 100 TeV is approximately

(10.56)

where E is the energy per nucleon in GeV.

A strong suppression at the highest energies, eV, is nowadays clearly established (Fig. 10.32); it may result, as explained in Sect. 10.3.3.3, from the so-called GZK mechanism due to the interaction of highly energetic protons with the Cosmic Microwave Background (CMB). However, a scenario in which an important part of the effect is a change of composition (from protons to heavier nuclei, which undergo nuclear photodisintegration⁶) and the exhaustion of the sources is not excluded as it will be discussed in Sect. 10.4.1.6.

10.4.1.2 Composition

The composition and energy spectrum of cosmic rays is not a well-defined problem: it depends on where experiments are performed. One could try a schematic separation between “primary” cosmic rays—as produced by astrophysical sources—and “secondaries”—those produced in interactions of the primaries with interstellar gas or with nuclei in the Earth’s atmosphere. Lithium, beryllium and boron, for example, are very rare products in stellar nucleosynthesis, and thus are secondary particles, as well as antiprotons and positrons—if some antimatter is primary is a question of primary interest.

The interaction with the Earth’s atmosphere is particularly important since it changes drastically the composition of cosmic rays. In the cases in which the flux of cosmic rays has to be measured at ground (for example, high-energy cosmic rays, at energies above hundreds GeV, where the low flux makes the use of satellites ineffective) one needs nontrivial unfolding operations to understand the primary composition. What one observes is a cascade shower generated by a particle interacting with the atmosphere, and the unfolding of the fundamental properties (nature and energy of the showering particle) requires the knowledge of the physics of the interaction at energies never studied at accelerators: experimental data are thus less clear.

Accessing the composition of cosmic rays can be done, in the region below a few TeV, at the top or above the Earth atmosphere by detectors placed in balloons or satellites able, for example, of combining the momentum measurement with the information from Cherenkov detectors, or transition radiation detectors.

The absolute and relative fluxes of the main hadronic components of cosmic rays measured directly is shown in Fig. 10.33, and compared to the relative abundances existing in the solar system. To understand this figure, one should take into account the fact that nuclei with even number of nucleons are more stable, having higher binding energy because of pairing effects.

Besides a clear deficit of hydrogen and helium in the cosmic rays compared to the composition of the solar system, the main features from this comparison are the agreement on the “peaks” (more tightly bounded even-Z nuclei) and higher abundances for cosmic rays on the “valleys.” These features can be explained within a scenario where primary cosmic rays are produced in stellar end-products, being the “valley” elements mainly secondaries produced in the interaction of the primaries cosmic rays with the interstellar medium (“spallation”).

Direct composition measurements are not possible above a few hundred GeV. For extensive air shower (EAS, see Chap. 4) detectors, effective at higher energies, being able to distinguish between a shower generated by a proton or by a heavier particle is a more difficult task. Variables which may allow the disentangling between protons and heavier nuclei, as it will be discussed in Sect. 10.4.1.6, are: in ground sampling detectors, the muonic contents of the air shower; at high energies in shower detectors, the depth of the maximum of the shower (the so-called ). A summary plot including these higher energy is shown in Fig. 10.34.

There is experimental evidence that the chemical composition of cosmic rays changes after the knee region with an increasing fraction of heavy nuclei at higher energy, at least up to about 10 eV (see Sect. 10.4.1.6).

10.4.1.3 Electrons and Positrons

High-energy electrons and positrons have short propagation distances (less than a few hundred parsec, as seen before) as they lose energy through synchrotron and inverse Compton processes while propagating through the galaxy. Their spectra, which extend up to several TeV, are therefore expected to be dominated by local electron accelerators or by the decay/interactions of heavier particles nearby. Positrons in particular could be the signature of the decay of dark matter particles.

The experimental data on the flux of electrons plus positrons suggested in a recent past the possible evidence a bump-like structure (ATIC balloon experiment results) at energies between 250 and 700 GeV. These early results were not confirmed by later and more accurate instruments like the Fermi satellite Large Area Tracker (Fermi-LAT), AMS-02 and DAMPE, as it is shown in Fig. 10.35. However, either in the individual flux of positrons or in its fraction with respect to the total flux of electrons plus positrons (Fig. 10.36 ), an excess in the high-energy positron fraction with respect to what expected from known sources (basically the interactions of cosmic rays with the interstellar medium), first observed by PAMELA and thus called the PAMELA effect, was clearly confirmed by AMS-02.

This is indeed quite intriguing: in a matter-dominated Universe, one would expect this ratio to decrease with energy, unless specific sources of positrons are present nearby. If these sources are heavy particles decaying into final states involving positrons, one could expect the ratio to increase, and then steeply drop after reaching half of the mass of the decaying particle. If an astrophysical source of high-energy positrons is present, a smooth spectrum is expected, while in the case of the origin from DM, a steep fall comes from kinematics. The present data is compatible both with the presence of nearby astrophysical sources, though not fully known, and with a hypothetical dark-matter particle with a mass of around 1 TeV, but there is not a definite answer yet. The most recent data on the abundance of high-energy pulsars nearby might justify an astrophysical explanation of this excess but not the results in antiproton observed also by AMS-02 as discussed in the next section.

10.4.1.4 Antiprotons

Data are shown in Fig. 10.37. The antiprotonto proton ratio stays constant from 20 to 400 GeV. This behavior cannot be explained by secondary production of antiprotons from ordinary cosmic ray collisions. In contrast with the excess of positrons, the excess of antiprotons cannot be easily explained from pulsar origin. More study is needed, and this is certainly one of the next frontiers.

10.4.1.5 Cosmic Rays at the Earth’s Surface: Muons

Most charged particles on the top of the atmosphere are protons; however, the interaction with the atoms of the atmosphere itself has the effect that the nature of particles reaching ground does not respect the composition of cosmic rays. Secondary muons, photons, electrons/positrons and neutrinos are produced by the interaction of charged cosmic rays in air, in addition to less stable particles. Note that the neutron/proton ratio changes dramatically in such a way that neutrons, which are 10 % of the total at the atmosphere’s surface, become roughly 1/3 at the Earth’s surface.

Astrophysical muons can hardly reach the Earth’s atmosphere due to their lifetime ( s); this lifetime is however large enough, that secondary muons produced in the atmosphere can reach the Earth’s surface, offering a wonderful example of time dilation: the space crossed on average by such particles is , and already for (i.e., an energy of about 5 GeV) they can travel 20, 30 km, which roughly corresponds to the atmospheric depth. Muons lose some 2 GeV by ionization when crossing the atmosphere.

Charged particles at sea level are mostly muons (see Fig. 10.38), with a mean energy of about 4 GeV.

The flux of muons from above 1 GeV at sea level is about 60 mssr. A detector looking at the horizon sees roughly one muon per square centimeter per minute. The zenith angular distribution for muons of 3 GeV is , being steeper at lower energies and flatter at higher energies: low energy muons at large angles decay before reaching the surface. The ratio between and is due to the fact that there are more than in the proton-initiated showers; there are about 30 % more than at momenta above 1 GeV/c.

A fortiori, among known particles only muons and neutrinos reach significant depths underground. The muon flux reaches 10 m s sr under 1 km of water equivalent (corresponding to about 400 m of average rock) and becomes about 10 m s sr at 10 km of water equivalent.

10.4.1.6 Ultrahigh-Energy Cosmic Rays

Ultra-High-Energy Cosmic Rays (UHECR) are messengers from the extreme Universe and a unique opportunity to study particle physics at energies well above those reachable at the LHC. However, their limited flux and their indirect detection have not yet allowed to answer to the basic, and always present, questions: Where are they coming from? What is their nature? How do they interact?

The energy spectrum of the UHECR is nowadays well measured up to 10eV (see Fig. 10.39). The strong GZK-like suppression at the highest energies may be interpreted assuming different CR composition and source scenarios. Indeed, both pure proton and mixed composition scenarios are able to describe the observed features. In the case of a pure proton scenario, the ankle would be described by the opening, at that energy, of the pair production channel in the interaction of the incoming protons with the CMB photons (this is called the “dip model”), while the suppression at the highest energies would be described in terms of the predicted GZK effect. In the case of mixed composition scenarios such features may be described by playing with different source distributions and injection spectra, assuming that the maximum energy that each nucleus may attain, scales with its atomic number Z. An example of composition fit is given in Fig. 10.39, where the Pierre Auger Observatory data are fitted to a mixed composition scenario. The solution of such puzzle may only be found with the experimental determination of the cosmic ray composition from detailed studies on the observed characteristics of the extensive air showers.

The depth of the maximum number of particles in the shower, , schematically represented in Fig. 10.40), is sensitive to the cross-section of the primary cosmic ray interaction in the air. Thus it can be used either to measure the cross-section, if the composition is known, or, since the cross section for a nucleus grows with its atomic number, to determine the composition, if the nuclei-air interaction cross-sections at these energies are assumed to be described correctly by the model extrapolations of the cross-sections measured at lower energies from the accelerators. Indeed, may be defined as the sum of the depth of the first interaction and a shower development length (see Fig. 10.40):

The experimental distribution is then the convolution of the X distribution with the distribution (which has a shape similar to the distribution) and a detector resolution function (see Fig. 10.41). The distribution of , in the case of a single component composition, should be just a negative exponential, exp where is the interaction length which is proportional to the inverse of the cosmic ray–air interaction cross section. Thus, the tail of the observed distribution reflects the exponential distribution of the lighter cosmic ray component (smaller cross-section, deeper penetration).

The measured distribution by the Pierre Auger collaboration in the energy bin 10–10eV for the 20 % of the most deeply penetrating showers is shown in Fig. 10.42. It follows the foreseen shape with a clear exponential tail. The selection of the most deeply penetrating showers strongly enhances the proton contents in the data sample since the proton penetrate deeply in the atmosphere than any other nuclei.

The conversion of the exponential index of the distribution tail to a value of proton-air cross section is performed using detailed Monte Carlo simulations. The conversion to proton–proton total and inelastic cross section is then done using the Glauber model which takes into account the multi-scattering probability inside the nuclei (Sect. 6.​4.​7). The Auger result is shown in Fig. 10.43 together with accelerator data–namely with the recent LHC results, as well as with the expected extrapolations of several phenomenological models. The experimental results confirm the evolution of the proton–proton cross section as a function of the energy observed so far, and give a strong indication that the fraction of protons in the cosmic ray “beam” is important at least up to 10 eV.

The study of the first two momenta of the distribution ( and the RMS) is nowadays the main tool to constrain hadronic interactions models and hopefully access the cosmic ray composition. The mean and the RMS of the distributions measured by the Pierre Auger collaboration as a function of the energy are shown in Fig. 10.44 and compared to the prediction for pure p, He, N and Fe. A fit to extract the fractions of each of these components as a function of the energy was then performed assuming several different hadronic interaction models. The results indicate evidence of a change of the cosmic ray composition from light elements (with a large fraction of protons) at lower energies to heavier elements (He or N depending on the hadronic model) but a negligible abundance of Fe at least until 10 eV. However, none of the current simulation models fits perfectly the data.

Only qualitative and quantitative improvements in the understanding of the shower development, for example, accessing direct experimental information on the muon contents and improving the modelling of hadronic interactions in Monte Carlo simulations, may clarify this striking open question. The scenario in which the strong GZK-like suppression at the highest energies is due to the exhaustion of the sources and that the higher number of muons in the shower are due to bad modelling of the hadronic interactions is nowadays the most widely accepted. “New physics” scenarios providing, for instance, a sudden increase of the proton-proton cross section (related to the access of a new scale of interaction below the parton scale) are however not excluded.

10.4.1.7 Correlation of Charged Cosmic Rays with Sources

When integrating over all energies, say, above a few GeV, the arrival direction of charged cosmic rays is basically isotropic—a fact which can find explanation in the effect of the Galactic magnetic field smearing the directions–the Compton-Getting effect, a dipole anisotropy of about 0.6% resulting from the proper motion of Earth in the rest frame of cosmic ray sources, has to be subtracted. However, Milagro, IceCube, HAWC, ARGO-YBJ and the Tibet air shower array have observed additional small large-scale anisotropies (at the level of 10), and small small-scale anisotropies (at the level of about 1010) in an energy range from a few tens of GeV to a few hundreds of TeV (see Fig. 10.45). Its origin is still under debate; the disentangling of its probable multiple causes is not easy. There is no simple correlation of anisotropies with known astrophysical objects.

At extremely high energies, instead, statistically significant anisotropies have been found – and their interpretation is straightforward.

To accelerate particles up to the ultra-high-energy region above the EeV, 10 eV, one needs conditions that are present in astrophysical objects such as the surroundings of SMBHs in AGN, or transient high-energy events such as the ones generating gamma ray bursts. Galactic objects are not likely to be acceleration sites for particles of such energy, and coherently we do not observe a concentration of UHECRs in the galactic plane; in addition, the galactic magnetic field cannot confine UHECRs above eV within our Galaxy.

Under the commonly accepted assumptions of a finite horizon (due to a GZK-like interaction) and of extragalactic magnetic fields in the range (1 nG–1 fG), the number of sources is relatively small and thus some degree of anisotropy could be found studying the arrival directions of the cosmic rays at the highest energies. Such searches have been performed extensively in the last years either by looking for correlations with catalogs of known astrophysical objects or by applying sophisticated self-correlation algorithms at all angular scales. Indication for intermediate-scale anisotropy, namely correlated to Active Galactic Nuclei and Star-forming or Starburst Galaxies catalogs, have been reported by the Pierre Auger Observatory. At large scales,

• In about 30 000 cosmic rays with energies above 8 EeV recorded over a period of 12 years, corresponding to a total exposure of 76 800 km sr year, the Pierre Auger Observatory has evidenced at more than a dipole anisotropy of about 6.5% towards (see Fig. 10.46).

  If ultrahigh-energy cosmic rays originate from an inhomogeneous distribution of sources and then diffuse through intergalactic magnetic fields, one can expect dipole amplitudes growing with energy, reaching 5–20% at 10 EeV. If the sources were distributed like galaxies, the distribution of which has a significant dipolar component, a dipolar cosmic-ray anisotropy would be expected in a direction similar to that of the dipole associated with the galaxies. For the infrared-detected galaxies in the 2MRS catalog,⁷ the flux-weighted dipole points in galactic coordinates in the direction , about 55 away from the dipole direction found by Auger. However, as shown in Fig. 10.46, the effect of galactic magnetic fields is to get the two directions closer; in addition, the correlation between the visible flux and the cosmic ray flux is just qualitative.

  The conclusion is that the anisotropy seen by Auger strongly supports, and probably demonstrates, the hypothesis of an extragalactic origin for large part of the highest-energy cosmic rays; the origin is in particular related to AGN.

• In 2007 the Pierre Auger collaboration claimed with a significance larger than a hot spot near the Centaurus A AGN, at a distance of about 5 Mpc. Cen A is also a VHE gamma-ray emitter. However, the data collected after 2007 have not increased the significance of the detection.

• the Telescope Array Project observes at energies above 57 EeV a hot spot, with best circle radius: 25, near the region of the Ursa Major constellation.

10.4.2.1 Hunting Different Sources and Source Types

The study of the galactic sources continues and their morphology and the SED of the emitted photons are telling us more and more, also in the context of multiwavelength analyses; in the future, the planned Cherenkov Telescope Array (CTA) will give the possibility to explore the highest energies, and to contribute, together with high-energy CR detectors and possibly with neutrino detectors, to the final solution of the CR problem.

One of the main results from the next-generation detectors will probably be the discovery of new classes of CR sources. The key probably comes from dedicating effort to surveys, which constitute an unbiased, systematic exploratory approach. Surveys of different extents and depths are amongst the scientific goals of all major planned facilities.

The key for such surveys are today gamma detectors (and in the future neutrino detectors as well).

More than half of the known VHE gamma-ray sources are located in the Galactic plane. Galactic plane surveys are well suited to Cherenkov telescopes given the limited area to cover, as well as their low-energy thresholds and relatively good angular resolution (better than 0.1 to be compared to for EAS detectors). CTA, investing 250 h (3 months) of observation, can achieve a 3 mCrab sensitivity (being the flux limit on a single pointing roughly proportional to , where is the observation time) on the galactic plane. More than 300 sources are expected at a sensitivity based on an extrapolation of the current “” diagram⁸ for VHE galactic sources (Fig. 10.48).

All-sky VHE surveys are well suited to EAS arrays that observe the whole sky with high duty cycles and large field of view. MILAGRO and the Tibet air shower arrays have carried out a survey for sources in the Northern hemisphere down to an average sensitivity of 600 mCrab above 1 TeV; HAWC has a sensitivity of 50 mCrab in a year, at median energy around 1 TeV. EAS detectors like HAWC can then “guide” the CTA. A combination of CTA and the EAS can reach sensitivities better than 30 mCrab in large parts of the extragalactic sky. The survey could be correlated with maps obtained by UHE cosmic ray and high-energy neutrino experiments.

Roughly, 5500 HE emitters above 100 MeV have been identified up to now, mostly by the Fermi-LAT, and some 200 of them are VHE emitters as well (Fig. 10.3).

About half of the gamma ray emitters are objects in our galaxy; at TeV energies most of them can be associated to different kinds of supernova remnants (SNR), while at MeV to GeV energies they are mostly pulsars; the remaining half are extragalactic, and the space resolution of present detectors (slightly better than 0.1) is not good enough to associate them with particular points in the host galaxies; we believe, however, that they are produced in the vicinity of supermassive black holes in the centers of the galaxies (see Sect. 10.2 and 10.4.1.7).

The strongest steady emitters are galactic objects; this can be explained by the fact that, being closer, they suffer a smaller attenuation. The observed strongest steady emitter at VHE is the Crab Nebula. The energy distribution of the photons from Crab Nebula is typical for gamma sources (see the explanation of the “double-hump” structure in Sect. 10.1.2.1), and it is shown in Fig. 10.13.

10.4.2.2 Transient Phenomena and Gamma Ray Bursts; Quasiperiodical Emissions

Among cosmic rays, gamma rays are important not only because they point to the sources, but also because the sensitivity of present instruments is such that transient events (in jargon, “transients”) can be recorded. Sources of HE and VHE gamma rays (some of which might likely be also sources of charged cosmic rays, neutrinos and other radiation) were indeed discovered to exhibit transient phenomena, with timescales from few seconds to few days.

The sky exhibits in particular transient events from steady emitters (“flares”) and burst of gamma rays from previously dark regions (“gamma ray bursts”). The phenomenology of such events is described in the rest of this section.

Short timescale variability has been observed in the gamma emission at high energies for several astrophysical objects, both galactic and extragalactic, in particular binary systems, and AGN. For binary systems the variability is quasiperiodical and can be related to the orbital motion, while for AGN it must be related to some cataclysmic events; this is the phenomenon of flares. Flares observed from Crab Nebula have, as today, no universally accepted interpretation.

Flares. Flares are characteristic mostly of extragalactic emitters (AGN). Among galactic emitters, the Crab Nebula, which was for longtime used as a “standard candle” in gamma astrophysics, has been recently discovered to be subject to dramatic flares on timescales of 10 h. The transient emission briefly dominates the flux from this object with a diameter of 10 light-years—which is the diameter of the shell including the pulsar remnant of the imploded star, and corresponds to roughly 0.1 as seen from Earth.

Very short timescale emission from blazars have also been observed in the TeV band, the most prominent being at present the flare from the AGN PKS 2155-304 shown in Fig. 10.49: a flux increase by a factor larger than ten with respect to the quiescent state, with variability on timescales close to 1 min. Note that the Schwarzschild radius of the black hole powering PKS2155 is about 10 light seconds (corresponding to 10 solar masses), which has implications on the mechanisms of emission of gamma rays (see later).

Indeed the gamma ray sky looks like a movie rather than a picture, the most astonishing phenomenon being the explosion of gamma ray bursts.

Gamma Ray Bursts. Gamma Ray Bursts (GRBs) are extremely intense and fast shots of gamma radiation. They last from fractions of a second to a few seconds and sometimes up to a thousand seconds, often followed by “afterglows” orders of magnitude less energetic than the primary emission after minutes, hours, or even days. GRBs are detected once per day on average, typically in X-rays and soft gamma rays. They are named GRByymmdd after the date on which they were detected: the first two numbers after “GRB” correspond to the last two digits of the year, the second two numbers to the month, and the last two numbers to the day. A progressive letter (“A,” “B,” ...) might be added—it is mandatory if more than one GRB was discovered in the same day, and it became customary after 2010.

Their position appears random in the sky (Fig. 10.50), which suggests that they are of extragalactic origin. A few of them per year have energy fluxes and energies large enough that the Fermi-LAT can detect them (photons of the order of few tens of GeV have been detected in a few of them). Also in this case the sources appear to be isotropic.

The energy spectrum is nonthermal and varies from event to event, peaking at around a few hundred keV and extending up to several GeV. It can be roughly fitted by phenomenological function (a smoothly broken power law) called “Band spectrum” (from the name of David Band who proposed it). The change of spectral slope from a typical slope of −1 to a typical slope of −2 occurs at a break energy which, for the majority of observed bursts, is in the range between 0.1 and 1 MeV. Sometimes HE photons are emitted in the afterglows.

During fractions of seconds, their energy emission in the gamma ray band exceeds in some cases the energy flux of the rest of the Universe in the same band. The time integrated fluxes range from about to about erg/cm. If the emission were isotropic, the energy output would on average amount to a solar rest-mass energy, about erg; however, if the mechanism is similar to the one in AGN the emission should be beamed,⁹ with a typical jet opening angle of a few degrees. Thus the actual average energy yield in rays should be erg. This value can be larger than the energy content of a typical supernova explosion, of which only 1 % emerges as visible photons (over a time span of thousands of years).

The distribution of their duration is bimodal (Fig. 10.18), and allows a first phenomenological classification between “short” GRBs (lasting typically 0.3 s; duration is usually defined as the time T90 during which 90 % of the photons are detected) and “long” GRBs (lasting more than 2 s, and typically 40 s). Short GRBs are on average harder than long GRBs.

GRBs are generally very far away, typically at and beyond (Fig. 10.51). The farthest event ever detected is a 10-s long GRB at , called GRB090423, observed by the Swift satellite (the burst alert monitor of Swift being sensitive to energies up to 0.35 MeV).

Short GRBs have been associated to the merging of pairs of compact objects. For long GRBs in several cases the emission has been associated with a formation of a supernova, presumably of very high mass (a “hypernova”). Possible mechanisms for GRBs will be discussed in Sect. 10.2.4.

Binary Systems. Binary stars (i.e., pairs of stars bound by gravitational interaction) are frequent in the Universe: most solar-size and larger stars reside in binaries. Binary systems in which one object is compact (a pulsar, a neutron star, or a black hole) have been observed to be periodical emitters of gamma radiation.

Finally, binary systems in which one object is compact (a pulsar, a neutron star, or a black hole) have been observed to be periodical emitters of gamma radiation.

A particular class of binary systems are microquasars, binary systems comprising a black hole, which exhibit relativistic jets (they are morphologically similar to the AGN). In quasars, the accreting object is a supermassive (millions to several billions of solar masses) BH; in microquasars, the mass of the compact object is only a few solar masses.

10.4.2.3 Diffuse Regions of Photon Emission; the Bubbles

As the space resolution of the Fermi-LAT and of the Cherenkov telescopes are of the order of 0.1, we can image diffuse structure only in the Milky Way: the other galaxies will mostly appear like a point. Morphology studies at VHE are basically limited to structures within our Galaxy.

Morphology of SNR is in particular one of the keys to understand physics in the vicinity of matter at high density—and one of the tools to understand the mechanism of acceleration of cosmic rays. Sometimes SNRs and the surrounding regions are too large to be imaged by Cherenkov telescopes, which typically have fields of view of 3–4. A large field of view is also essential to understand the nature of primary accelerators in pulsar wind nebulae (PWN), as discussed in Sect. 10.2.1.3: it would be important to estimate the energy spectrum as a function of the angular distance to the center of the pulsar to separate the hadronic acceleration from the leptonic acceleration. The highest energy electrons lose energy quickly as they propagate away from the source; this is not true for protons.

Intermediate emission structures, a few degrees in radius, have been observed by MILAGRO and ARGO, which can be attributed to diffusion of protons within the interstellar medium.

A surprising discovery by Fermi-LAT was the existence of a giant structure emitting photons in our galaxy, with size comparable to the size of the galaxy itself: the so-called Fermi bubbles. These two structures, about 50 000-light-years across (Fig. 10.52), have quite sharp boundaries and emit rather uniformly in space with an energy spectrum peaking at a few GeV but yielding sizable amount of energy still up to 20 GeV.

Although the parts of the bubbles closest to the Galactic plane shine in microwaves as well as gamma rays, about two-thirds of the way out the microwave emission fades and only X- and gamma rays are detectable.

Possible explanations of such a large structure are related to the past activity of the black hole in the center of the Milky Way. A large-scale structure of the magnetic field in the bubble region might indicate an origin from the center of the galaxy, where magnetic fields are of the order of 100 G, and might also explain the mechanism of emission as synchrotron radiation from trapped electrons. However, this explanation is highly speculative, and as of today the reason for the emission is unknown.

10.4.2.4 Results on WIMPs

WIMPs are mostly searched in final states of their pair annihilation or decay involving antimatter and gamma rays. We shall refer in the following, unless explicitly specified, to a scenario in which secondary particles are produced in the annihilation of pairs of WIMPs.

Dark matter particles annihilating or decaying in the halo of the Milky Way could produce an excess of antimatter, and thus, an observable flux of cosmic positrons and/or antiprotons. This could explain the so-called PAMELA anomaly, i.e., the excess of positron with respect to models just accounting for secondary production (Fig. 10.36). Most DM annihilation or decay models can naturally reproduce the observed rise of the positron fraction with energy, up to the mass of the DM candidate (or half the mass, depending if the self-annihilation or the decay hypothesis is chosen). This flux is expected not to be directional. The measured antiproton flux also shows unexpected features with respect to the hypothesis of pure secondary production.

It is plausible that both the positron excess and the excess observed in the electron/positron yield with respect to current models (see Sect. 10.4.1) can be explained by the presence of nearby sources, in particular pulsars, which have indeed been copiously found by the Fermi-LAT (Sect. 10.2.1.1). AMS-02 is steadily increasing the energy range over which positrons and electrons are measured, as well as the statistics. If the positron excess is originated from a few nearby pulsars, it would probably give an anisotropy in the arrival direction of cosmic rays at the highest energies—there is a tradeoff here between distance and energy, since synchrotron losses are important; in addition, the energy spectrum should drop smoothly at the highest energies. A sharp cutoff in the positron fraction would instead be the signature of a DM origin of the positron excess; the present data do not demonstrate such a scenario, but they cannot exclude it, either: the attenuation of the positron/electron ratio observed by AMS-02 at several hundred GeV is consistent with the production from a particle at the TeV scale.

For what concerns photons, the expected flux from dark matter annihilation can be expressed as

(10.57)

The astrophysical factor, proportional to the square of the density, is also called the “boost factor”. DM-induced gamma rays could present sharp spectral signatures, like for instance or annihilation lines, with energies strictly related to the WIMP mass. However, since the WIMP is electrically neutral, these processes are loop suppressed and therefore should be rare. WIMP-induced gamma rays are thus expected to be dominated by a relatively featureless continuum of by-products of cascades and decays (mostly from ) following the annihilation in pairs of quarks or leptons. The number of resulting gamma rays depends quadratically on the DM density along the line of sight of the observer. This motivates search on targets, where one expects DM density enhancements. Among these targets are the galactic center, galaxy clusters, and nearby dwarf spheroidal galaxies. Of course, an additional proof is given by proximity, to reduce the attenuation.

Unfortunately, as said before, dark matter densities are not known in the innermost regions of galaxies, where most of the signal should come from: data allow only the computation in the halos, and models helping in the extrapolation to the centers frequently disagree (Sect. 8.​1.​4). Observations of galaxy rotation curves favor constant density cores in the halos; unresolved “cusp” substructures can have a very large impact, but their existence is speculative—however, since they exist for baryonic matter, they are also likely to exist for DM. This uncertainty is typically expressed by the so-called “boost factor,” defined as the ratio of the true, unknown, line-of-sight integral to the one obtained when assuming a smooth component without substructure.

A summary of the present results from searches in the photon channel is plotted in Fig. 10.53 together with extrapolation to the first three years of data collection by the next generation detector CTA, and with a collection of 10 years of data by Fermi (to be reached in 2019). Note that the Fermi discovery potential continues to extend linearly with time, being its background negligible.

Neutrinos. Equation (10.57) holds for neutrinos as well, but the branching fractions into neutrinos are expected to be smaller, due to the fact that the radiative production of neutrinos is negligible. In addition, experimental detection is more difficult. However, the backgrounds are smaller with respect to the photon case.

Balancing the pros and the cons, gamma rays are the best investigation tool in case the emission comes from a region transparent to photons. However, neutrinos are the best tool in case DM is concentrated in the center of massive objects, the Sun for example, which are opaque to gamma rays. Once gravitationally captured by such massive objects, DM particles lose energy in the interaction with nuclei and then settle into the core, where their densities and annihilation rates can be greatly enhanced; only neutrinos (and axions) can escape these dense objects. The centers of massive objects are among the places to look for a possible neutrino excess from DM annihilation using neutrino telescopes.

No signal has been detected up to now (as in the case of axions from the Sun). A reliable prediction of the sensitivity is difficult, depending on many uncertain parameters like the annihilation cross section, the decay modes and the capture rate. The first two uncertainties are common to the photon channels.

10.4.2.5 Lorentz Symmetry Violation

Variable gamma-ray sources in the VHE region, and in particular AGN, can provide information about possible violations of the Lorentz invariance in the form of a dispersion relation for light expected, for example, in some quantum gravity (QG) models.

Lorentz invariance violation (LIV) at the n-th order in energy can be heuristically incorporated in a perturbation to the relativistic Hamiltonian:

(10.58)

which implies that the speed of light () could have an energy dependence. From the expression , the modified dispersion relation of photons can be expressed by the leading term of the Taylor series as an energy-dependent light speed

(10.59)

where n = 1 or n = 2 corresponds to linear or quadratic energy dependence, and is the sign of the LIV correction. If , high-energy photons travel in vacuum slower (faster) than low-energy photons.

The scale at which the physics of space–time is expected to break down, requiring modifications or the creation of a new paradigm to avoid singularity problems, is referred to as the “QG energy scale”, and is expected to be of the order of the Planck scale—an energy GeV—or maybe lower, if new particles are discovered at an intermediate scale.

Because of the spectral dispersion, two GRB photons emitted simultaneously by the source would arrive on Earth with a time delay () if they have different energies. With the magnification of the cosmological distances of the GRBs and the high energies of these photons, the time delay () caused by the effect of Lorentz invariance violation could be measurable. Taking account of the cosmological expansion and using Eq. 10.59, we write the formula of the time delay as:

(10.60)

Here, is the arrival time of the high-energy photon, and is the arrival time of the low-energy photon, with and being the photon energies measured at Earth.

For small z, and at first order,

where s is Hubble’s time.

AGN flares (Sect. 10.4.2.2) can be used as experimental tools: they are fast and photons arriving to us travel for long distances.

Mkn 501 (z 0.034) had a spectacular flare between May and July 2005; it could be analyzed by the MAGIC telescope. The MAGIC data showed a negative correlation between the arrival time of photons and their energy (Fig. 10.54), yielding, if one assumes that the delay is due to linear QG effects, to an evaluation of . H.E.S.S. observations of the flare in PKS 2155 (Fig. 10.49), however, evidenced no effect, allowing to set a lower limit .

Lately, several GRBs observed by the Fermi satellite have been used to set more stringent limits. A problem, when setting limits, is that one does not know if photon emission at the source is ordered in energy; thus one has to make hypotheses—for example, that QG effects can only increase the intrinsic dispersion.

The Fermi satellite derived strong upper limits at 95 % C.L. from the total degree of dispersion, in the data of four GRBs:

In most QG scenarios violations to the universality of the speed of light happen at order larger than 1: with . In this case the VHE detectors are even more sensitive with respect to other instruments like Fermi; for the data from PKS 2155 give .

10.4.2.6 Possible Anomalous Photon Propagation Effects

Some experimental indications exist, that the Universe might be more transparent to gamma rays than computed in Sect. 10.3.4.

As discussed before, the existence of a soft photon background in the Universe leads to a suppression of the observed flux of gamma rays from astrophysical sources through the pair-production process. Several models have been proposed in the literature to estimate the spectral energy density (SED) of the soft background (EBL); since they are based on suitable experimental evidence (e.g., deep galaxy counts), all models yield consistent results, so that the SED of the EBL is fixed to a very good extent. Basically, the latter reproduces the SED of star-forming galaxies, which is characterized by a visible/ultraviolet hump due to direct emission from stars and by an infrared hump due to the emission from the star-heated warm dust that typically hosts the sites of star formation.

Among the possible explanations, a photon mixing with axion-like particles (ALPs), predicted by several extensions of the standard model (Sect. 8.​5.​1), can fix the EBL crisis, and obtain compatibility on the horizon calculation. Since ALPs are characterized by a coupling to two photons, in the presence of an external magnetic field B photon-ALP oscillations can show up. Photons are supposed to be emitted by a blazar in the usual way; some of them can turn into ALPs, either in the emission region, or during their travel. Later, some of the produced ALPs can convert back into photons (for example, in the Milky Way, which has a relatively large magnetic field) and ultimately be detected. In empty space this would obviously produce a flux dimming; remarkably enough, due to the EBL such a double conversion can make the observed flux considerably larger than in the standard situation: in fact, ALPs do not undergo EBL absorption (Fig. 10.56).

We concentrate now on the photon transition to ALP in the intergalactic medium. The probability of photon-ALP mixing depends on the value and on the structure of the cosmic magnetic fields, largely unknown (see Sect. 10.3.1).

Both the strength and the correlation length of the cosmic magnetic fields do influence the calculation of the conversion probability. In the limit of low conversion probability, if s is the size of the typical region, the average probability of conversion in a region is

(10.61)

where is the transverse component of the magnetic field.

For a magnetic field of 0.1–1 nG, and a cellular size structure  Mpc, any ALP mass below 10 eV, with a coupling such that GeV GeV (well within the region experimentally allowed for mass and coupling) can explain the experimental results (Fig. 10.55).

Another possible explanation for the hard spectra of distant blazars, needing a more fine tuning, is that line-of-sight interactions of cosmic rays with CMB radiation and EBL generate secondary gamma rays relatively close to the observer.

LIV and Photon Propagation

A powerful tool to investigate Planck scale departures from Lorentz symmetry could be provided by a possible change in the energy threshold of the pair production process of gamma rays from cosmological sources. This would affect the optical depth, and thus, photon propagation.

In a collision between a soft photon of energy and a high-energy photon of energy E, an electron–positron pair could be produced only if E is greater than the threshold energy , which depends on and .

Note that also the violation of the Lorentz invariance changes the optical depth. Using a dispersion relation as in Eq. 10.58, one obtains, for and unmodified law of energy–momentum conservation, that for a given soft-photon energy , the process is allowed only if E is greater than a certain threshold energy which depends on and . At first order:

(10.62)

The limit corresponds to the special-relativistic result = /. For and sufficiently small values of (and correspondingly large values of ) the Planck scale correction cannot be ignored.

This provides an opportunity for tests based on dynamics. As an example, a 10 TeV photon and a 0.03 eV photon can produce an electron–positron pair according to ordinary special-relativistic kinematics, but they cannot produce a pair according to the dispersion relation in Eq. 10.58, with and . The non-observation of EeV gamma rays has already excluded a good part of the parameter range of terms suppressed to first and second order in the Planck scale.

The situation for positive is somewhat different, because a positive decreases the energy requirement for electron–positron pair production.

A Win–Win Situation: Determination of Cosmological Parameters

If no indications of new physics (LIV, anomalous propagation) will be found after all, since the optical depth depends also on the cosmological parameters (Eq. 10.55), its determination constrains the values of the cosmological parameters if the EBL is known, and if only standard processes are at work.

A determination of and independent of the luminosity–distance relation currently used by the Supernovae 1 A observations can be obtained from the spectra of distant AGN.

10.4.3.1 Neutrinos from SN1987A

On February 23, 1987, a supernova was observed in the Large Magellanic Cloud (LMC), a galaxy satellite of the Milky Way (about 10 solar masses, i.e., 1 % of the Milky Way) at a distance of about 50 kpc from the Earth. As it was the first supernova observed in 1987, it was called SN1987A; it was also the first supernova since 1604 visible with the naked eye. The event was associated with the collapse of the star Sanduleak-69202, a main sequence star of mass about 20 solar masses.

Three hours before the optical detection, a bunch of neutrinos was observed on Earth. SN1987A was the first (and the only up to now) unambiguous detection of neutrinos that can be localized from a source other from the Sun: three water Cherenkov detectors, Kamiokande, the Irvine–Michigan–Brookhaven (IMB) experiment, and the Baksan detector observed 12, 8, and 5 neutrino interaction events, respectively, over a 13 s interval (Fig. 10.57). Within the limited statistics achieved by these first-generation detectors, the number of events and the burst duration were consistent with standard estimates of the energy release and cooling time of a supernova. The energy of neutrinos can be inferred from the energy of the recoil electrons to be in the tens of MeV range, consistent with the origin from a collapse.

The optical counterpart reached an apparent magnitudeof about 3. No very high-energy gamma emission was detected (in 1987 gamma detectors were not operating), but gamma rays at the intermediate energies characteristic of gamma transitions could be recorded.

SN1987A allowed also investigations on particle physics properties of neutrinos. The neutrino arrival time distribution sets an upper limit of 10 eV on the neutrino mass; the fact that they did not spread allows setting an upper limit on the magnetic moment where is the Bohr magneton. A determination of the neutrino velocity can also be derived, being consistent with the speed of light within two parts in .

10.4.3.2 Very-High-Energy Neutrinos

The IceCube experiment at the South Pole reported for the first time in 2013 the detection of astrophysical neutrinos; after a few years the evidence is much stronger and tens of astrophysical neutrinos are collected every year. IceCube detects the Cherenkov radiation in the Antarctic ice generated by charged particles, mostly muons, produced by neutrino interactions.

Both methods for selecting cosmic neutrinos harvest together about 1 event/month, twice that if one can tolerate a background. Standard model physics allows one to infer the energy spectrum of the parent neutrinos – for the highest energy event the most likely energy of the parent neutrino is almost 10 PeV. Data indicate an excess of neutrino events with respect to atmospheric neutrinos above 30 TeV. The cosmic flux above 100 TeV is well described by a power law

(10.63)

To give an example, the ratio between the neutrino flux and the charged cosmic ray flux at 100 TeV is

The energy and zenith angle dependence observed for completely contained events, shown in Fig. 10.58, is consistent with expectations for a flux of neutrinos produced by cosmic accelerators – a purely atmospheric component is excluded at more than .

Considerations based on the expected fluxes allow predicting that in a few years we shall reach the statistics required to identify their origin by matching arrival directions with astronomical maps.

Figure 10.59 shows in galactic coordinates the arrival directions of cosmic neutrinos for four years of events with interaction vertices inside the detector. The observed neutrino flux is consistent with an isotropic distribution of arrival directions and equal contributions of all neutrino flavours.

A variety of analyses suggest that the cosmic neutrino flux dominates the atmospheric background above an energy that may be as low as 30 TeV, with an energy spectrum that cannot be described as a single power, as was the case for the muon neutrino flux through the Earth for energies exceeding 220 TeV. This is reinforced by the fact that fitting the excess flux in different ranges of energy yields different values for the power-law exponent.

Gamma rays at energies above some 100 TeV are likely to interact with background photons before reaching Earth. The resulting electromagnetic shower subdivides the initial photon energy, resulting in multiple photons in the GeV–TeV energy range by the time the shower reaches Earth. After accounting for the cascading of the PeV photons in cosmic radiation backgrounds between source and observation, a gamma-ray flux similar to the IceCube neutrino flux matches the extragalactic high-energy gamma-ray flux observed by the Fermi satellite as shown in Fig. 10.47, right.

10.4.3.3 The First Multimessenger Neutrino-Gamma Detection: EHE170922

On September 22, 2017, IceCube detected an extremely-high-energy neutrino event, consisting in a muon coming from the bottom of the detector through the Earth with an estimated energy between 100 TeV and 150 TeV, likely produced by a neutrino of energy of TeV. Promptly alerted, the Fermi LAT and MAGIC detected at more than a flare from the blazar TXS 0506 +056, at a redshift , within the region of sky consistent with the 50% probability region of the IceCube neutrino (about one degree in size). The MAGIC detection allowed to determine that the electromagnetic emission had a cutoff at a few hundred GeV.

The simultaneous emission of gamma rays and neutrinos from the same source proves that the “hadronic mechanism” has been seen at work. The estimated energy of a proton producing such a high energy neutrino in a “beam dump” is

(10.64)

an energy above the knee and well appropriate for a blazar; blazar models prefer the target to be a photon gas.

This event opened the era of multimessenger astronomy with neutrinos. The present detection rate of astrophysical neutrinos is (1 event/month), and it is thus likely that such events will not be common in the future. It sets however a benchmark for the size of future IceCube-like detectors: a size ten times larger will almost certainly allow detecting clusters of neutrinos from astrophysical hadronic accelerators, as well as larger numbers of neutrinos from a flare like the one detected.

It is important to note that the cutoff energy in the gamma rays detected is much lower than the neutrino energy. This is a consequence of the fact that the energy of the gamma rays is degraded due to the interaction with photons and matter when traveling in the jet and during their cosmic voyage, and agrees qualitatively with the effect shown in Fig. 10.58, right.

10.4.4.1 GW170817, the First Multimessenger Discovery of a Binary Neutron Star Merger

The first observation of a single astrophysical source through both gravitational and electromagnetic waves happened on August 17, 2017. LIGO/Virgo detected a gravitational wave signal possibly associated with the merger of two neutron stars (GW170817), and  s later the Fermi Gamma-Ray Burst Monitor and the INTEGRAL SPI/ACS detector observed independently in the same sky region (Fig. 10.64) a short, 2 s long, GRB (GRB 170817A) whose time-averaged spectrum is well fit by a power law function with an exponential high-energy cutoff at keV. The masses of the initial neutron stars were estimated to be in the range [1.36, 2.26] solar masses and [0.86, 1.36] solar masses respectively, while the final mass was estimated to be . These observations were followed by an extensive multimessenger campaign covering all the electromagnetic spectrum as well as the neutrino channel: a bright optical transient (SSS17a) was discovered in the NGC 4993 galaxy located at 40 Mpc of the Earth by the Swope Telescope in South America and shortly after by five more teams. The follow-up was then done by ground and space observatories all around the world: X-ray and radio counterparts were discovered respectively 9  days and 16  days after the merger, while no neutrino candidates were seen.

The neutron star merger event is thought to result in a “kilonova” , characterized by a short GRB followed by a longer optical afterglow. A total of 16 000 times the mass of the Earth in heavy elements is believed to have formed; for some of them spectroscopical signatures have been observed.

Unlike all previous GW detections, corresponding to BH mergings and not expected to produce a detectable electromagnetic signal, the aftermath of this merger was seen by 70 observatories across the electromagnetic spectrum, marking a significant breakthrough for multi-messenger astronomy and opening a new era. Several events of this kind can be expected in the future.

10.5.2.1 The Region till a Few MeV

Unfortunately, it is experimentally difficult to study. It requires an efficient instrument working in the Compton regime with an excellent background subtraction, and possibly with sensitivity to the measurement of polarization. Since COMPTEL, which operated two decades ago, no space instrument obtained extra-solar gamma-ray data in the few MeV range; now we are able to build an instrument one-two orders of magnitudes more sensitive than COMPTEL based on silicon detector technology, state-of-the-art analog readout, and efficient data acquisition.

Several proposals of satellites have been made, and convergence is likely for an experiment to be launched around 2028.

10.5.2.2 The GeV Region

It is difficult to think for this century of an instrument for GeV photons improving substantially the performance of the Fermi LAT: the cost of space missions is such that the size of Fermi cannot be reasonably overcome with present technologies. New satellites in construction (like the Chinese-Italian mission HERD) will improve some of the aspects of Fermi, e.g., calorimetry. For sure a satellite in the GeV region with sensitivity comparable with Fermi will be needed in space (Fermi could in principle operate till 2028).

10.5.2.3 The Sub-TeV and TeV Regions

CTA appears to have no rivals for the gamma astrophysics in the sub-TeV and TeV (from a few GeV to a few TeV) energy regions. These are crucial regions for fundamental physics, and for astronomy.

PeVatrons and the nature of the emitters in the galaxy will be studied in detail. WIMPs will be tested with the “right” sensitivity up to 1 TeV.

CTA will be probably upgraded including state-of-the art photon detection devices of higher efficiencies with respect to the present ones; it can in principle operate till 2050.