Since the discovery of Cosmic Rays (CRs) by Victor Hess in 1912, the origin of this radiation has remained a mystery. Despite extensive efforts we still do not have a coherent theory which can explain a great variety of the features of CRs.
What do we know about Cosmic Rays?
Actually, we know a lot. In particular, we know that CRs consist mainly of primary protons, nuclei and electrons, i.e. particles directly accelerated to relativistic energies by powerful objects, which plausibly are different from ordinary stars. At the same time, a major fraction of some species of CRs, in particular the nuclei of the (Li,Be,B) group, as well as the anti-particles (positrons and antiprotons) have a secondary origin. They are produced by primary CRs interacting with the ambient interstellar gas, and partly with the thermal plasma (and, perhaps, also with low-frequency photon fields) inside the accelerators. Anti-particles can be produced also in some exotic processes like evaporation of primordial black holes or annihilation of dark matter. However the current data do not show convincing evidence of a significant fraction of "exotic" positrons and antiprotons in CRs. The secondary particles carry important information about the history of CRs during their passage through the galactic magnetic fields. In particular they tell us about the average time spent by CRs in the disk before they escape the Galaxy, tesc ~ 107 yr. We know quite well the flux and the energy spectrum of CRs, and we know that the energy spectrum of CRs extends to extremely high energies, E ~ 1020 eV and even beyond (see Fig. 4.1). The energy spectrum of electrons is measured up to
The proton-to-electron ratio at GeV energies is about 100; at 1 TeV the content of electrons does not exceed 10-3 (see Fig. 4.2).
The CR spectrum has two distinct features – the so-called knee and ankle around 1015 eV and 1018 eV, respectively (see Fig. 4.1). It is believed that all particles below the knee are of galactic origin, and that the Extremely High Energy Cosmic Rays (EHECRs) above the ankle are produced/accelerated outside of the Galactic Disk – in the Halo of our Galaxy, or in powerful extragalactic objects like AGN, Radiogalaxies and Clusters of Galaxies.
The acceleration, accumulation and effective mixture of nonthermal particles, through their diffusion and convection in galactic magnetic fields, produce the so-called "sea" of Galactic Cosmic Rays (GCRs). The average density of GCRs throughout the Galactic Disk is determined by operation of all galactic sources over a relatively long time period, comparable with the escape time of CRs of about
Assuming that the level of the "sea" of GCRs is not far from the directly measured fluxes of CRs, we can estimate the average energy density of CRs in the Galactic Disk, 
More than 90 percent of this density is contributed by particles with energy
Within the homogeneous disk model,we then can derive the luminosity (acceleration power) of the Galaxy in
is the volume of the disk where CRs are effectively confined. Although this estimate cannot guarantee an accuracy of better than a factor of a few, it is quite independent of model parameters. For the fixed mass of the diffuse gas
is reduced to
is the mean amount of matter ("grammage") traversed by CRs. This parameter is determined by the content of secondary nuclei in CRs, and for the bulk of the observed CRs is about several g/cm2. Thus, the CR production rate in the Galaxy can be estimated solely on the basis of CR measurements, namely from the total flux and the secondary-to-primary ratio of CRs, being rather independent of details characterising their confinement region (density, volume, etc.). In particular, both the disk and halo confinement models give approximately the same CR production rates (see e.g. Berezinsky et al., 1990).
We know, from the energy-dependence of the secondary-to primary ratio of CRs, that the acceleration spectra of individual CR sources are significantly harder than the spectrum of the locally measured CRs, and therefore (supposedly) the spectrum of the "sea" of GCRs. The average source (acceleration) spectrum of CRs is believed to be described by a differential power-law index r close to 2.1 (see e.g. Swordy, 2001), although a steeper source spectrum with r up to 2.4 cannot be excluded, if CRs are additionally re-accelerated in the interstellar medium (e.g. Seo and Ptuskin, 1994).
And finally, we know that the pressure of CRs is comparable with the pressure of galactic magnetic fields, as well as with the turbulent and thermal pressure of the interstellar gas. This implies that GCRs play an important role in the dynamical balance of our Galaxy, and perhaps have also a non-negligible impact on interstellar chemistry through the heating and ionization of the interstellar medium (see e.g. Wolfendale, 1993).
What we do not know about Cosmic Rays?
The irony of the discipline called Astrophysics of Cosmic Rays is that, in spite of the considerable experimental material and extensive theoretical efforts, we still do not have a definite opinion about the origin of these relativistic particles.
We do not know what part of the observed CR spectrum is in fact of Galactic origin – below the knee around 1015 eV or does it extend to the ankle at 1018 eV?
Fig. 4.1 Summary of measurements of the broad-band spectrum of high energy cosmic rays.
There is more confidence in the assumption that particles from the Extremely High Energy (EHE) domain above 1018 eV are produced outside the Galaxy (see e.g. Cronin, 1999; Nagano and Watson, 2000). These particles cannot be produced in the Galactic Disk, otherwise significant anisotropies would then be expected, in contrast to observations. However, the association of these particles with the Halo of our Galaxy cannot be ruled out, in particular within the so-called "top-down" scenarios, in which the observed particles are not result of classical acceleration (the "bottom-up" scenario), but may originate from decays of relic topological defects (Berezinsky et al., 1998) or super-massive particles (Berezinsky et al., 1997a; Birkel and Sarkar et al., 1998) clustered in the Galactic Halo.
Fig. 4.2 Two-component approach to the observed CR electron flux.The thin solid line represents the Local ("L") component of electrons that originates from a single, t = 105 yr old burst-like source at r = 100 pc and t = 105 yr. The dashed line represents the Galactic ("G") component assuming a homogeneous distribution of CR sources in the Galactic Disk. The 3dot-dashed line corresponds to secondary electrons and positrons produced by galactic cosmic rays. The calculations are normalised to the observed flux at 10 GeV. The required energy release in electrons with power-law index r = 2.2 is We = 1.1 X 1048 erg. The spectrum of protons from the same local source assuming Wp = 3 • 1050 erg is also shown (dot-dashed line). The range of measured CR proton fluxes is indicated by the hatched region.
We do not know what powers the CR accelerators, and how they work. We do not know how many and which type of sources are responsible for the observed CR fluxes. Moreover, we are not fully confident that the bulk of directly observed CRs are contributed by sources distributed in the entire Galactic Disk. Paradoxically, we cannot exclude the scenario in which these particles may have a local origin, being contributed by a few sources or even a single nearby object. This statement is true at least for very high energy CR electrons. Because of severe radiative losses, the source(s) of the observed TeV electrons cannot be located well beyond a few 100 pc (Nishimuara et al., 1980), and therefore the sheer fact of extension of the observed electron spectrum to TeV energies is an unambiguous indicator of existence of a nearby cosmic Tevatron(s).This means that the assumption of a continuous distribution of sources of CR electrons would have to be valid down to scales of ~ 100 pc. Otherwise, the correct approach to the interpretation of the observed CR electron flux requires a separate treatment for two different components: (1) the contribution from one or a few nearby local sources (L-component), and (2) the contribution from sources at large distances, typically beyond 1 kpc, which may still be treated in the framework of the traditional assumption of a uniform and continuous (in space and time) source distribution in the Galactic Disk (G-component). Fig. 4.2 shows that the two-component approach describes reasonably well the observed flux of CR electrons from GeV to TeV energies.
Formally, a single local source can explain the entire CR population up to the knee around 1015 eV. Such a possibility is demonstrated in Fig. 4.2. Although the assumed total energy budget Wp = 3 • 1050 erg seems somewhat high, it can be reduced by a significant factor assuming a somewhat smaller distance to the source. The contribution from several local sources is another possible option. Also, better agreement with the experimental data, especially at low energies, can be readily achieved assuming a specific energy dependence for the diffusion coefficient. Should we take such an attractive (or rather provocative) possibility too seriously? In recent years Erlykin and Wolfendale (1997, 2000) have claimed empirical evidence for a complex structure in the CR spectrum in the region of the knee attributing it to the effect of explosion of a single, recent, nearby supernova. Although this claim has not received a supportive response from other experts in the field of air-shower physics (see e.g. Schatz, 2002), the idea of a single CR source is a hypothesis in its own right and should not be necessarily related to the existence or lack of a specific structure in the knee.
The "local single CR source" hypothesis implies a dramatic revision of the current belief that the bulk of cosmic rays we detect are part of the "sea" of GCRs. Therefore it needs thorough inspection both on theoretical and experimental grounds. At the same time, the fact that we cannot firmly rule out such a possibility reflects the poor status of the field. A pessimist may even argue that CR measurements alone are a priori not sufficient to solve the problem. However, the Cosmic Ray Community does not share such a pessimistic view.
Common beliefs and "nasty" problems
It is widely believed that Supernova Remnants (SNRs) are the major source population in our Galaxy responsible for the observed CRs. The main phe-nomenological argument, recognised at very beginning of astrophysical interest in the problem (see e.g. Ginzburg and Syrovatski, 1964), is based on the fact that the power to maintain the galactic population of CRs is estimated to be a few percent of the total mechanical energy released by SNe explosions in our Galaxy. It is notable that as early as 1933 W.Baade and F.Zwickey realized the possible association of cosmic rays with super-novae, based on the comparable energies characterising these two phenomena. This is, of course, an important, but not decisive, argument, given that other potential source populations like pulsars, young stars with powerful mechanical winds, microquasars, gamma-ray bursts etc. can also meet, at least formally, this energy requirement. In this regard, note, for example, that the mechanical power of the jets of the galactic microquasar SS 433 is comparable with the total production rate of CRs in the Galaxy.
The second, equally important argument in favour of SNRs comes from theory. Actually, the only model of particle acceleration developed at a level which allows quantitative calculations is diffusive shock acceleration applied to the strong shocks in SNRs (see e.g. Drury, 1983; Blandford and Eichler, 1987; Berezhko and Krymsky, 1988; Jones and Ellison, 1991). Over last 20 years the basic properties of this model have been comprehensively checked by many theorists using different mathematical approaches. Recently, there have been important developments in the field based on the non-linear treatment of the problem (for review see Malkov and Drury, 2001; Drury et al., 2001). In particular, it has been clearly understood that nonlinear reaction effects on the shock structure are unavoidable, if the process is to operate with high efficiency. On the other hand, the efficiency of acceleration of particles, i.e. the fraction of the mechanical energy of the shock transfered to non-thermal particles, should be very high, 10 per cent or more, in order to explain the observed CR flux. Therefore, nonlinear shock acceleration seems to be a key element in the SNR paradigm of GCRs. This allows conclusive observational predictions given the inflexibility (in a good sense) of the nonlinear shock acceleration theory. The distinct feature of this model is the very hard, power-law type (although not precisely power-law) energy distribution with differential spectral index r close to 2.
The high efficiency coupled with hard acceleration spectra extending well beyond 10 TeV, should lead to detectable Y-ray fluxes of hadronic origin. Thus, the best way to check the hypothesis is to search for n0-decay Y-ray signals, especially at TeV energies, from 103-104 yr old shell type SNRs (Drury et al., 1994; Naito and Takahara, 1994). TeV Y-rays have indeed been reported from three famous SNRs – SN 1006, RX J1713.7-3946 and Cas A.These are, however, objects where ultrarel-ativistic electrons are at least equally plausible as parent particles. On the other hand, other SNRs, like Y Cygni and IC 433, where Y-rays of hadronic origin are expected to dominate , have not shown TeV emission. Currently, this fact is interpreted by many as a failure of SNRs in general, and diffusive shock acceleration in particular, to produce the bulk of GCRs. However, given the limited sensitivity of current detectors, as well as large uncertainties in key model parameters, these conclusions in many cases are poorly justified and, in fact, misleading. Driven by an ultimate desire for dramatic revisions of the current concepts, the claims about the difficulties associated with Y-ray observations are premature and, to a large extent, exaggerated. At the same time, GLAST and the new generation of IACT arrays like H.E.S.S., VERITAS and CANGAROO-III, will be able to probe the SNR visibility in n0-decay Y-rays at a level which must provide, even under the most pessimistic model assumptions, a decisive test for the SNR origin of galactic cosmic rays.
Another test of diffusive shock acceleration may come from studies of the secondary component of CRs produced by primary particles interacting with the interstellar medium (ISM). The CR data for the B/C ratio detected up to ~ 100 GeV/amu, derived assuming a simple propagation model, favour a quite strong energy dependence of the escape time of CRs from the Galactic Disk,
Applied to protons, this requires a source spectral index of
which agrees with the index anticipated by nonlinear shock acceleration. Note that the source spectral index derived in this way is distinctly harder than the values of r ~ 2.3 — 2.4 favoured by re-acceleration models of CR propagation (Drury et al., 2001). Thus, any independent evidence of significant re-acceleration of CRs in the interstellar medium would work against the nonlinear shock acceleration.
On theoretical grounds, the diffusive shock acceleration model faces several challenges or "nasty problems" (Drury et al., 2001) like the "injection problem" and the "maximum energy problem", recently critically reviewed by Kirk and Dendy (2001), Drury (2001) and Malkov and Drury (2001). Diffusive shock acceleration requires particles with energy at least several times larger than the thermal energy of the plasma, and it is not yet clear how to get particles from the thermal pool accelerated to supra-thermal energies. Recent theoretical progress in this direction (e.g. Malkov and Volk, 1995; Dieckmann et al., 2000) provides optimism that eventually the injection problem will be resolved, most likely through extensive numerical simulations (Kirk and Dendy, 2001).
The problem of the maximum achievable energy problem is an old one and has a vital implication for the SNR paradigm of GCRs. In diffusive shock acceleration theory, the maximum energy of particles is achieved during the so-called free-expansion phase which, however, does not last long enough to allow acceleration of particles up to the highly desired point, the knee around 1015 eV. Therefore, violation of the so-called "upper limit" of Lagage and Cesarsky (1983), which, for the standard SNR parameters, the shock speed, duration of the free-expansion phase, and the ambient magnetic field, cannot significantly exceed 1014 eV, remains as one of the highest priorities of current theoretical studies.
A promising way has recently been suggested by Lucek and Bell (2000). They showed that cosmic ray streaming drives large-amplitude Alfvenic waves which may amplify the magnetic field non-linearly to many times the pre-shock value. Thus, the cosmic rays themselves provide the field necessary for their effective acceleration! The increased magnetic field reduces the acceleration time, and correspondingly increases the maximum particle energies to 1015 eV and even beyond. Needless to say that this effect, if confirmed by independent theoretical investigations, would be the solution of the 20-year old "maximum energy" problem. Ideally speaking, the most elegant version of the SNR paradigm of galactic cosmic rays should allow shock acceleration of particles up to the "ankle" around 1018 eV. The smooth transition of the spectrum from the "sub-knee" to the "above the knee" region of the spectrum, which over 3 decades up to 1018 eV continues as steep power-law with r ~ 3, not only indicates a possible galactic origin for this part of the spectrum, but also favours the same acceleration mechanism (and sources) responsible for the CR spectrum from 1 GeV to 1018 eV. Although the model of Lucek and Bell (2000) allows acceleration of protons up to 1017 eV, in their second paper Bell and Lucek (2001) argued that expansion into a pre-existing stellar wind may increase the maximum cosmic ray energy by an additional factor of 10. Acceleration of particles well beyond the knee is possible also by shocks in so-called Superbubbles – a "multiple supernova remnant" powered by SN explosions and winds of luminous stars in OB associations (e.g. Parizot, 2000; Bykov, 2001). Particle acceleration by multiple shocks (Bykov and Toptygin, 2001) in such systems has features similar to the standard picture in isolated SNRs, but because of larger dimensions particles may achieve energies up to 1018 eV.
Finally, this brief overview of the status of origin of galactic cosmic rays would be biased if we concluded without remarking that in the future we may need to invoke, despite all the pleasing features and advantages of the SNR paradigm of GCRs, other source populations, pulsars, X-ray binaries with relativistic jets, or something else, and develop new acceleration theories to explain the phenomenon called Galactic Cosmic Rays.
Searching for sites of production of GCRs
As discussed above, after several decades of intensive experimental and theoretical studies, our knowledge about the accelerators of galactic cosmic rays continues to be quite limited and inconclusive. The main obstacle to revealing the production sites and acceleration mechanisms of GCRs is the effective diffusion of charged particles in interstellar magnetic fields, which results in the confusion of individual contributors to the "sea" of GCRs, and significantly modifies the original (source) spectra of accelerated particles. Therefore, it is believed that the resolution of these long-standing questions will be provided by gamma-ray astronomy, i.e. through indirect but (almost) model-independent measurements of secondary Y-rays . The basic idea of this approach is straightforward and concerns both the acceleration and propagation aspects of the problem. While the localised sources of Y-rays pinpoint the sites of particle acceleration, the angular and spectral distributions of the diffuse Y-ray emission of the Galactic Disk contain information about the character of propagation of both the electronic and nu-cleonic components of CRs in the galactic magnetic fields. The realization of this seminal prediction recognised by pioneers of the field in the 1950s and 1960s is still considered as one of the major goals of Y-ray astronomy. The non-thermal synchrotron radiation contains additional and complementary information at radio and possibly also at X-ray wavelengths, but it concerns only the electronic component of CRs in two extreme energy bands, typically below 1 GeV and above 100 TeV, respectively. TeV neutrinos carry adequate information about the nucleonic component of CRs as well, but the sensitivities of the current high energy neutrino projects do not adequately match, even under extreme model assumptions, the neutrino fluxes expected from interactions of GCRs.
The study of the diffuse Y-radiation by the SAS-II and COS B satellite experiments, and especially by the EGRET instrument aboard the Compton GRO, have already made a significant contribution to the current knowledge of spatial distribution of relatively low energy, 1 to 100 GeV, CRs in the Galactic Disk. Furthermore, many famous galactic objects representing different classes of potential accelerators of GCRs like pulsars (e.g. Crab, Vela, and Geminga), shell-type supernova remnants (e.g. IC 433 and Y Cygni), giant molecular clouds (GMCs) and associated star formation regions (e.g. Orion and p Ophiuchus complexes), are identified by EGRET as sources of 100 MeV radiation (Hartman et al., 1999). At the same time, most of the EGRET sources, especially the objects at low- and mid-galactic latitudes, still do not have clear counterparts at other wavelengths.The next generation space-based Y-ray detector, GLAST, with its superior flux sensitivity and good angular resolution should be able to reveal the nature of these Y-ray hot spots. For bright sources with flat Y-ray spectra, GLAST can provide spectral coverage up to energies of ^100 GeV. This ensures the great role of GLAST for future studies of GCRs of intermediate energies, typically between 1 GeV and 1 TeV.
Even so, the energy coverage of GLAST will not tell us much about the sources responsible for the formation of the most energetic part of the spectrum of GCRs which extends to the knee around
This is the domain of ground-based Y-ray detectors. The range of flux sensitivities that could be achieved by future Y-ray detectors is shown in Fig. 1.2. It is seen that GLAST and the forthcoming IACT arrays can probe Y-ray point sources in a very broad energy region from 0.1 GeV to 10 TeV, at the level of energy fluxes between
Thus, all point galactic sources with luminosities down to
can be detected by GLAST and/or IACT arrays. Note that for both GLAST and stereoscopic IACT systems with angular resolution of about 0.1° — 0.2°, the "point" source implies an angular size less than a few arcminutes. Thus, the detection of extended sources with angular size of about 1° would require an order of magnitude higher y-ray luminosities. The GeV luminosities of the EGRET sources detected at low galactic latitudes exceed
Therefore, most of
the EGRET sources should be seen in TeV Y-rays, provided that the Y-ray spectra extend unbroken to the TeV region with differential photon index 
for point sources and
for extended "1°" sources.
Since the spectra of particle acceleration (e.g. by SNR shocks) generally are expected to be significantly harder than the locally observed spectrum of CRs, the failure to detect TeV Y-rays from EGRET sources can be interpreted as a result of "early" cutoffs in the source spectra below 1 TeV. If so, the EGRET sources cannot (at first glance) be considered as important contributors, at least at high energies, to the "sea" of GCRs. However, the lack of TeV Y-rays from GeV sources can be result of propagation effects, namely energy-dependent escape of accelerated particles from the source. Generally the confinement time of particles in the source decreases with energy (the leakage of particles becomes easier at high energies), therefore the quasi-stationary spectrum of particles established in the source could be significantly steeper than the acceleration spectrum. Correspondingly, even for a hard, e.g. E-2 type, particle acceleration spectrum, the secondary Y-rays produced by interactions of relativistic particles inside the sources, could have quite a steep spectrum – just opposite to the common belief in which the hardest Y-ray spectra are expected from CR accelerators themselves.
This effect is illustrated in Fig. 4.3. It is assumed that high energy protons are injected into a dense region of size R = 3 pc, gas density n = 100 cm-3, and magnetic field .
These parameters are typical for the so-called giant molecular clouds – possible sites of particle acceleration and gamma-ray production. The acceleration spectrum of protons is assumed to be a power-law with an index a = 2.1, and exponential cutoff at 1015 eV. The time history of acceleration is assumed as
with
This assumption implies that the acceleration rate was essentially constant over the first 103 years, but has later decreased with time as t-2. Finally, the confinement time of particles was approximated in the form
yr,where k =1 corresponds to the slowest possible escape in the Bohm diffusion regime. One can see that for the chosen parameters of the ambient medium and acceleration rate, the proton escape results in a significant suppression of TeV Y-rays, especially at observation epochs t > 104 yr, even if the particle escape proceeds in the regime close to the Bohm diffusion.
Thus, the study of a cosmic accelerator by detecting Y-rays from the central source cannot be complete because it contains information only about relatively low-energy particles effectively confined in the source. In many cases the detection of Y-rays from regions surrounding the accelerator could add much to our knowledge about the highest energy particles which quickly escape from the source and thus do not contribute to the Y-ray production inside the source.
Fig. 4.3 Expected Y-ray spectra at different observation epochs — t = 103, 104 and 105 years after the start of operation of the proton accelerator, for three different assumptions concerning the escape time of particles from the Y-ray production region: k =1, 30, 1000.
For "typical" CR accelerators, e.g. SNR with a total energy release in protons of less than
the extension of these regions cannot significantly exceed several tens of parsecs, because at such large distances from the source, the density of relativistic particles becomes negligible compared to the level of the "sea"of GCRs (see below). Also, the detection of extended sources is quite difficult due to the backgrounds caused by diffuse galactic Y-rays (for GLAST) and local CRs (for ground-based detectors).
The existence of a powerful particle accelerator by itself is not yet sufficient for effective Y-ray production. Clearly, an additional component – a dense gas target – is required. Giant Molecular Clouds (GMCs) are perfect objects to play that role in our Galaxy. They are physically connected with star formation regions which are believed to be the most probable sites for the production of galactic cosmic rays. Fig. 1.5 illustrates the Y-ray production by molecular clouds located in the vicinity of a particle accelerator where the energy density of CRs can significantly exceed the level of the "sea" of GCRs of about 1 eV/cm3.
The low-energy ambient photon fields play a similar role for tracing VHE (multi-TeV) electrons through their inverse Compton radiation. With some exceptions (e.g. Crab Nebula, Cas A) the 2.7 K CMBR significantly dominates over other photon fields for the production of IC Y-ray emission. Therefore, the detection and identification of the inverse Compton radiation component associated with the 2.7 K CMBR should allow us to find the sources of ultra-relativistic electrons, and study the propagation features of these electrons in the regions not far from their birth sites.
Because of its universal character and the precisely measured energy spectrum and density, the 2.7 K CMBR may serve as an ideal target also for the search and study of extremely high energy,
protons in the vicinity of their extragalactic accelerators like AGN, radiogalaxies, clusters of galaxies, etc., through the radiation components initiated by the secondary products of interactions of protons with the 2.7 K CMBR.
