Electron bremsstrahlung
Below 1 GeV, bremsstrahlung Y-rays are produced by the same electrons responsible for the galactic synchrotron radio emission. Therefore the differential flux J(E) of this radiation in the region from 30 MeV to ~ 1 GeV should have a characteristic power-law slope with an index coinciding with the spectral index of the radio electrons
The results of numerical calculations are shown in Fig. 4.18 by open dots assuming a standard composition of the interstellar gas.
The comparison of the bremsstrahlung gamma- and radio synchrotron fluxes produced by the same
electrons gives:
where Fi0mhz is the radio flux from the galactic plane. Since the latter cannot be less (and, presumably, is even several times higher) than the
detected from the direction of galactic poles (Webber et al. 1980), the contribution of bremsstrahlung to the overall flux of
Y-rays should be significant, unless we assume either an unrealistically high magnetic field
and/or unrealistically
low gas column density
.
It is interesting to compare the bremsstrahlung flux in the energy region E ~ 30 MeV with the ‘NIR’ component of the IC flux in the region E ~ 10 MeV. Both radiation components are due the same electrons, although contributed by two different, low-energy and high-energy, parts of the power-law distribution of radio electrons, respectively:
In the region
the bremsstrahlung flux is contributed by electrons with
(i.e. outside the domain of the radio emitting electrons) where the ionization losses cause significant flattening of the electron spectra. This results in a drop of
by a factor of 1.5 compared to
For
the overall IC flux at 10 MeV is comparably contributed by both NIR and 2.7 K CMBR target photons. Taking all these effects into account, we may conclude that around E ~ 10 MeV bremsstrahlung should dominate the overall diffuse emission of the galactic plane. This is confirmed by the accurate numerical calculations presented in Fig. 4.18.
Annihilation of CR positrons in flight
A non-negligible fraction of the diffuse Y-radiation below 10 MeV could be due to annihilation of relativistic positrons in flight.The differential spectrum of Y-rays produced in the annihilation of a fast positron on electrons of the ambient thermal gas with density ne is described by Eq.(3.6). For a power-law distribution of positrons, the spectrum of annihilation radiation at energies E ^ mec2 has an almost power-law behaviour given by Eq.(3.8). The annihilation to bremsstrahlung flux ratio Jann/Jbrem does not depend on the ambient gas density and, for given content of positrons,
depends only on the energy distribution of electrons.
The flux of annihilation radiation calculated for the electron spectrum from Fig. 4.17 assuming = 0.5, is shown in Fig. 4.18. It is seen that the contribution of the annihilation radiation at 1 MeV exceeds the contributions of other radiation processes. Thus, depending on the (unknown) content of low-energy (< 10 MeV) positrons in CRs, this process may result in a significant enhancement of the diffuse radiation at MeV energies. In this regard it is interesting to note that at Ee < 1 GeV the fraction of positrons in the local (directly measured) component of CR electrons gradually increases, reaching > 0.3 at Ee ~ 100 MeV (Fanslow et al., 1969).
Generally, the assumption that the annihilation of supra-thermal positrons in flight may significantly contribute to the diffuse low-energy Y-radiation of the inner Galaxy would imply also a high flux of 0.511 MeV annihilation line radiation. The OSSE measurements (Purcell et al., 1993) indicate that the positron annihilation in the ISM proceeds predominantly (— 97%, Kinzer et al., 1996) through the positronium state, the annihilation radiation of which consists of two components – the narrow 0.511 annihilation line and the Y-ray continuum below 0.5 MeV. At energies E ~ (0.2 — 0.5) MeV the diffuse Y-ray emission of the inner Galaxy is contributed mainly by the fluxes of these two components of the annihilation radiation (not shown in Fig. 4.18). The total flux of these photons is at the level
(see Kinzer et al. 1996), which is equivalent to
for the 3.8° x 11.4° field of view of the OSSE instrument.
Approximately 20 per cent of relativistic positrons annihilate in flight in the same medium where they cool due to Coulomb and bremsstrahlung energy losses.The integrated flux of the annihilation radiation by relativistic electrons shown in Fig. 4.18 (dotted curve), is
Therefore one could expect that the photon flux of annihilation radiation of thermalized positrons should be as high as
quite comparable with the OSEE observations. And, vice versa, if the observed diffuse annihilation line at 0.511 MeV is due to positrons injected in the ISM with relatively high, 
energies (e.g. by pulsars), we should expect collateral continuous MeV radiation from positrons (before their thermalization) at a level comparable with the fluxes shown in Fig. 4.18. If the positrons are produced with low energies,
they arise from ^-decay of radioactive nuclei, the continuous MeV radiation obviously cannot have an annihilation origin.
The overall fluxes of diffuse Y-rays of electronic origin without and with the annihilation radiation are shown in Fig. 4.18 by heavy solid and dashed curves, respectively. It is seen that the Y-radiation produced by CR electrons is significantly below the measured fluxes in the entire energy range from 100 MeV to 30 GeV. Although, due to the lack of independent information on the spectrum of high energy electrons, the predicted Y-ray fluxes contain significant uncertainties, the gap by a factor of 5 to 7 around 1 GeV is not easy to fill by any reasonable set of model parameters. Moreover, the flat shape of the overall flux produced by CR electrons cannot explain the "GeV bump" without violation of the fluxes observed at lower energies. More naturally, this bump can be related to interactions of CR protons and nuclei with the interstellar gas.
Gamma rays of nucleonic origin
The inelastic collisions of CR protons and nuclei with the interstellar gas result in Y-ray emission through production and subsequent decay of secondary
For a power-law energy distribution of protons, the differential production spectrum of this radiation J(E) has a distinct maximum at 100 MeV, which in the
presentation is shifted to 
thus shaping the so-called "GeV bump" in the spectral energy distribution (SED), provided that the spectrum of protons is steeper than E-2.
In Fig. 4.19a the SED of
Y-rays calculated for power-law CR spectra are shown, assuming for the product of the CR energy density and the hydrogen column density
The fluxes produced by protons are multiplied by the factor
which takes into account the overall contribution from nuclei both in CRs and the ISM.
The dashed curve in Fig. 4.19a is the diffuse Y-ray flux calculated for the local CR proton flux which is described by a power-law energy distribution (e.g. Simpson, 1983) with spectral index r = 2.75:
Above 1 GeV, the calculated Y-ray spectrum fails to explain the diffuse flux observed Y-ray flux by a factor of 1.5-2. This deficit cannot be overcome by increasing wp or NH, otherwise the flux at sub-GeV energies would be over-predicted by the same factor. The assumption of a hard power law index for CRs in the Galactic Disk, rp = 2.3 (dot-dashed line), explains the data at ~ 1 GeV, but over-predicts the flux at higher energies. And finally, a moderately steep spectrum of protons with
(solid line) satisfactorily explains the spectral shape of the observed excess around several GeV, except for the point at 2 GeV which appears « 20% higher.
There is another, perhaps more attractive, possibility providing a somewhat better fit for the GeV Y-ray spectrum, namely assuming the following energy distribution of protons in the inner Galaxy:
Fig. 4.19 Spectra of
Y-rays. The CR proton energy distributions are given:
(a) (left) by a single power-law with 3 different indices Tp: 2.75 (curve 1), 2.5 (curve 2), and 2.3 (curve 3); and (b) (right figure) in the form of Eq.(4.31) with
and three different values for E*: 3 GeV (curve 1), 20 GeV (curve 2), and 100 GeV (curve 3). The fluxes are calculated assuming
(a), and
The data points are the fluxes detected by EGRET from the inner Galaxy.
This equation implies a power-law spectrum of protons with
below some E*, but gradual steepens to
at higher energies,
E*. Actually, a proton energy distribution of this kind can be naturally formed in the ISM. Indeed, the energy distribution of the protons, which do not suffer significant energy losses, can be approximated by
For a power-law acceleration spectrum with r0, this is easily reduced to the form of Eq.(4.31) if the diffusive escape time of CRs becomes comparable with the convective escape time at
(see Eq. 4.22). The results of numerical calculations presented in Fig. 4.19b show that the GeV bump in the observed Y-ray spectrum can be nicely explained by a hard spectrum of accelerated protons with
additionally
assuming an energy-dependent (£ = 0.65) diffusive escape of particles from the Galactic Disk which leads to the steepening of the CR spectrum above E* = 20 GeV.
Overall gamma ray fluxes
The radiation mechanisms discussed above significantly contribute to one or more energy intervals of the broad-band diffuse Y-ray emission of the Galactic Disk. Therefore, any attempt to interpret the observed diffuse Y-radiation, even in a specifically limited spectral band, cannot be treated separately, but rather should be conducted within a multi-wavelength approach to the problem.
Fig. 4.20 demonstrates that the Y-ray data from ~ 1 MeV to 30 GeV can be adequately explained with a set of quite reasonable parameters characterising both the cosmic rays and the interstellar medium. For the calculations a mean line-of-sight depth for the inner Galactic Disk of = 15 kpc and a column density of
are assumed. This corresponds to a mean gas density along the line of sight at low galactic latitudes of about
The energy densities of CR protons and electrons in the inner Galaxy are normalised to
and
respectively. Interestingly, the latter is larger by a factor of 1.5 than the energy density of local CR electrons, while the required energy density of protons is « 20 % less than the observed one. It should be noticed, however, that these estimates are inversely proportional to the hydrogen column density NH, the uncertainty of which exceeds the above deviations, and therefore does not allow the derivation of the the average density of CRs in the Galactic Disk to an accuracy of better than « 50%. At the same time, the required spectral shape of protons in the inner Galaxy at low energies deviates noticeably from the local proton spectrum given by Eq.(4.30).
In Fig. 4.20, injection spectra of electrons and protons are assumed with power-law index r = 2.1. For the adopted escape times of
the diffusive escape time becomes equal to the time of convective escape at E = 5.8 GeV. Note that the decrease of E*, as compared with the ‘best fit’ value E* = 20 GeV in Fig. 4.19b, is necessitated by the significant contribution of the IC component to the overall flux (especially at high energies). This demonstrates the importance of the multi-wavelength approach to the modelling of the diffuse Y-radiation even for specific, relatively narrow, energy bands.
Fig. 4.20 The fluxes of diffuse radiation produced by electronic and nucleonic components of cosmic rays in the inner Galaxy. The calculations are performed for hard power-law injection spectra of electrons and protons with
and for the following parameters characterising the CR propagation:
Other model parameters are:
The contributions from
(thin solid line), bremsstrahlung (dashed), the total inverse Compton (dot dashed), and positron annihilation in flight for
(dotted line) are shown. The heavy dashed and solid lines represent the overall fluxes with and without the contribution from the positron annihilation radiation, respectively.
Below 100 MeV the observed Y-ray fluxes are due mainly to the IC and bremsstrahlung components. At energies below several MeV the annihilation radiation of relativistic electrons contributes significantly to the overall flux, and may even exceed the individual fluxes of both bremsstrahlung and IC Y-rays, provided that at energies below 100 MeV the positron content in the electronic component of the galactic cosmic rays is significant. The heavy dashed curve in Fig. 4.20 shows the overall ("IC+bremsstrahlung+annihilation") flux. For comparison, the COMPTEL data points (Hunter et al., 1997b) corrected for contamination caused by annihilation of thermalised positrons (Purcell et al., 1993), are shown by stars. One can see that the annihilation of positrons "in flight", on top of the IC and bremsstrahlung fluxes, fits the COMPTEL measurements rather well.
Among the principal radiation mechanisms of diffuse Y-rays in the region
the prompt Y-ray line emission produced by sub-relativistic cosmic rays (SRCRs) via nuclear de-excitation should also be mentioned. The emissivity of the total (unresolved) Y-ray line emission in the energy range between several hundred keV and several MeV, normalised to the energy density of SRCRs
and calculated for the standard cosmic compositions of CRs and the interstellar gas, is about 2 x 10-25 ph/s H-atom (Ramaty et al., 1979). This implies that for
the energy flux of this component of gamma radiation cannot exceed
Thus, this radiation mechanism cannot be responsible for more than several per cent of the observed Y-ray flux at MeV energies, unless the energy density of SRCRs in the ISM exceeds by 1.5-2 orders of magnitude the "nominal" energy density of CRs in the relativistic regime of about 1 eV/cm3. Although quite speculative, such high densities of SRCRs cannot be ruled out. Moreover, recently Boldt (1999) and Dogiel et al. (2002) argued that the hard X-ray emission from the galactic ridge, which likely has non-thermal origin, is produced by bremsstrahlung of sub-relativistic protons or electrons. The bremsstrahlung of sub-relativistic particles, both of protons or electrons, in the cold medium is a rather inefficient mechanism of radiation. Namely, because of ionization losses only < 10-5 part of the kinetic energy is released in the form of non-thermal X-rays (Skibo et al., 1996; Dogiel et al., 2002).
Assuming that bremsstrahlung X-rays are produced directly in the regions of particle acceleration with plasma temperatures of about several hundred eV, one may somewhat reduce the requirement to the energy output of quasi-thermal electrons, which however still remains uncomfortably high, at the level of 1041 erg/s (Dogiel et al., 2002).
The production of X-rays through proton bremsstrahlung is tightly connected with the prompt 7-ray line emission due to the excitation of the nuclei (primarily Fe, C, O, etc.) of the of ambient gas by the same subrel-ativistic protons. This allows robust upper limits on the contribution of proton bremsstrahlung to X-rays from the fluxes of diffuse Y-rays observed at MeV energies. The studies by Pohl (1998) and Valinia et al. (2000), based on the comparison of the observed keV and MeV fluxes, lead to the conclusion that indeed the proton bremsstrahlung alone could not be responsible for the bulk of the diffuse galactic X-ray emission. And finally, the hard X-ray fluxes extending to 200 keV cannot be explained by proton bremsstrahlung, because the energy of protons producing 200 keV X-rays, E > (mp/me)EX — 400 MeV would over-produce n0-decay Y-rays.
Synchrotron radiation of ultra-relativistic electrons is an alternative mechanism to explain the diffuse X-ray emission of the Galactic Disk. An obvious advantage of this mechanism, compared with the bremsstrahlung of sub-relativistic particles, is its almost 100% efficiency of transformation of the particle kinetic energy into X-rays. On the other hand, this mechanism requires, for any reasonable ambient magnetic field, more than 100 TeV electrons in the ISM. Since the rates of acceleration by SNR shocks are not sufficient to compensate for the severe synchrotron losses, these electrons can hardly be produced in SNRs. Pulsar-driven nebulae (plerions) seem more probable sites for the acceleration of such energetic electrons through the wind termination shocks. Interestingly, since the same electrons also produce, through IC scattering on the 2.7 K CMBR, ultra-high energy Y-rays, the magnetic field in the regions of production of hard synchrotron X-rays should be quite large, B > 20 ^G,otherwise the IC fluxes would exceed the flux upper limits at energies E > 100 to 1000 TeV reported by the by CASA-MIA (Borione et al., 1998) and KASCADE (G. Schatz, private communication) collaborations (see Fig. 4.21).
The life-time of Ee 100 TeV electrons does not exceed several hundred years, therefore they cannot propagate more than a few tens of parsecs from their acceleration sites. This means that the diffuse X-ray background, as well as the accompanying IC radiation should have a "cell – structure", i.e. they consist of superpositions of contributions from a large number of unresolved extended sources along the line of sight.
The broad-band diffuse radiation flux shown in Fig. 4.21 is calculated in the framework of a model which assumes that besides the main population of CRs (presumably accelerated by the SNR shocks), there is also a second electron population beyond 100 TeV (accelerated presumably by the pulsar wind termination shocks). The acceleration power in the second electron component, which is needed to explain the hard X-ray background, is about 6 x 1036 erg/s per kpc3, or x 1039 erg/s in the entire inner Galactic Disk. If these electrons are associated with pulsar winds, for « 104 sources this would imply a rather modest mean acceleration power per "old pulsar" of about 3 x 1035 erg/s, i.e. three orders of magnitude less than the power of the relativistic electron-positron wind of the Crab pulsar. The kick velocities of pulsars can be of order from a few 100 to ~ 1000 km/s, thus the 106 yr old pulsars would be able to propagate to distances < (0.3 — 1) kpc, contributing therefore to the emission at galactic latitudes of up to several degrees. If so, we may expect an interesting effect of a gradual spectral hardening of radiation arriving from higher galactic latitudes. The detection of this flat IC component, which at high latitudes may dominate, at least at TeV energies, over the significantly suppressed n0-decay radiation, should be possible by GLAST and forthcoming IACT arrays.
Probing the diffuse 7-ray background on small scales
The diffuse galactic gamma-ray background consists of the truly diffuse emission that is produced in the interaction of CRs with the interstellar gas and photon fields, and of contributions from unresolved discrete sources. Actually, if the "sea" of GCRs is described by the steep, E-2’75 type spectrum of local CRs (curve 1 Fig. 4.19a), a new component of radiation would be required to explain the so-called "GeV excess" detected by EGRET1. Pohl et al. (1997) have noticed that pulsars can account for up to 20 per cent of the diffuse emission above 1 GeV in selected regions of the ISM, albeit that they cannot be responsible for all the GeV excess.
Fig. 4.21 The broad-band diffuse background radiation from the Galactic plane in terms of the two-component model of relativistic electrons. The heavy solid line corresponds to the flux produced by the electrons of the first (main) CR population, with the same model parameters as in Fig. 4.20, but for S = 0.7 and k+ = 0.3. The heavy dashed line shows the overall flux including the contribution from the second population of electrons accelerated to energies Eo = 250 TeV. The local mean magnetic field of the region where the second electron population is confined is assumed B = 25 ^G. The fluxes of galactic diffuse radiation at Y-rays detected by COMPTEL and EGRET, and at X-rays detected by RXTE (Valinia and Marshall, 1998) and OSSE (Kinzer et al., 1997), as well as the upper flux limits at very high energies reported by the Whipple (Le Bohec et al., 2000), HEGRA and CASA-MIA (Borione et al., 1998) collaborations, are also shown.
Berezhko and Volk (2000) argued that a significant fraction of the diffuse radiation from inner Galaxy can be contributed by unresolved SNRs, assuming that approximately 10 SNRs of an age younger than 105 yr can on average lie within 1° of the galactic center. This model predicts a hard Y-ray spectrum up to 1 TeV energies with an absolute flux around 1 TeV of about 10-8 erg/cm2s sr, i.e. a factor of 2 higher than the fluxes of the truly diffuse radiation shown in Fig. 4.20 and 4.21. This flux from the direction of the galactic center can be readily detected by the H.E.S.S. IACT array. Important support for this model would be the resolution of individual contributors and their identification with known SNRs. Since this radiation is supposed to be a superposition of contributions from < 10 SNRs within a 1 ° field of view, the fluxes of individual contributors are expected at the level of 10-12 erg/cm2s at 1 TeV and a factor of 3 higher at several GeV.
In principle, these sources can be resolved both at GeV and TeV energies by GLAST and H.E.S.S., respectively.
A large contribution to the diffuse background at low galactic latitudes may come from "active" molecular clouds. The propagation of CRs in the Galactic Disk implies an effective mixture of contributions from individual sources/accelerators of CRs on a ~ 107 yr timescale. Therefore one cannot expect a strong gradient of CR density on large, kpc scales. However, strong variations are possible on smaller scales, in particular in the l < 100 pc regions around the CR accelerators, where the CR density may significantly exceed the average density of the "sea" of GCRs. If these regions also host massive gas clouds, we may expect enhanced Y-ray emission within l/d ~ 0.5°(d/10 kpc)-1. Speculating now that a significant fraction of the diffuse Y-ray background is produced selectively, being a result of radiation from regions containing both particle accelerators and massive gas clouds, one may explain in a quite natural way the hard spectra of radiation observed by EGRET above 1 GeV. Indeed, if Y-rays are produced at interactions of clouds with relatively fresh (recently accelerated) particles with spectra that have not yet suffered strong modulation (steepening) due to propagation effects, the resulting Y-ray spectra should be significantly harder than the typical Y-ray spectrum produced by the "sea" of GCRs in regions of the ISM far from the cosmic accelerators. Such an assumption agrees with the correlation observed between Y-ray intensity and the hydrogen column density (Hunter et al., 1997) which in the galactic plane is predominantly due to molecular clouds.
If a significant fraction of the diffuse Y-ray background is indeed contributed by regions of enhanced CR density surrounding the particle accelerators, then we should expect non-negligible fluctuations, both in the spectral shape and in the absolute flux on scales less than 1°. In Fig. 4.22a the diffuse Y-ray fluxes detected by EGRET within a 10-3 sr solid angle, corresponding to regions on sky with angular radius « 1°, are shown. The largest flux, marked as "GD(C)", corresponds to the radiation that arrives from direction of the Galactic Center, namely to the average flux detected from the region with galactic coordinates l ^0° and 2° < b < 6° (Hunter et al., 1997). It is approximated as
The curve marked as "GD(A)" in Fig. 4.22a corresponds to the flux from the Anti-center region, namely l ^180° and 6° < b < 10° (Hunter et al., 1997). It is approximated as
Note that the EGRET measurements of the diffuse galactic radiation do not extend beyond 30 GeV, but in Fig. 4.22a we extrapolate the fluxes up to 300 GeV. Interestingly, the highest energy Y-rays detected by EGRET around 300 GeV belong to the isotropic (extragalactic) diffuse background radiation (Sreekumar et al., 1998). This component, marked in Fig. 4.22 as "EGB", is described by a hard power-law spectrum,
For comparison, in Fig. 4.22a
Y-ray fluxes of individual supernova remnants and "passive" molecular clouds are also shown. For the differential flux of a "typical" Y-ray emitting SNR, the following approximation is used (see Sec. 5.1)
where
is the total energy of accelerated CRs contained in the remnant,
is the gas density in the remnant, and
is the distance to the source.
The differential flux of Y-rays from a "passive" GMC (see Sec. 4.2) at energies above 1 GeV is approximated as
where
is the total mass of the cloud.
And finally, in Fig. 4.22a we present the spectrum of CR ray electrons observed in the solar vicinity. Although the intensity of these particles exceeds by two orders of magnitude or more the flux of diffuse Y-rays, the active anti-coincidence shields of the satellite based detectors effectively protect the Y-ray telescopes from charged particles. At the same time the showers produced by CR electrons constitute the main background for imaging Cherenkov telescope arrays operating in the sub-100 GeV regime.
The minimum size of angular cells chosen for the the study of the spatial variation of the spectrum of diffuse Y-rays is determined by the angular resolution of detectors and the accumulated photon statistics. Because of the small detection area and limited angular resolution, the spatially resolved spectral analysis of EGRET has been performed using 10° x 4° bins with < 40 per cent statistical errors and a highest interval of 1-30 GeV (Hunter, 2001). GLAST, with significantly improved angular resolution and larger detection area, should be able to derive Y-ray spectra for smaller bins and upper energies of 100 GeV. Fig. 4.23 shows the number of Y-rays above given energy E per degree2 expected for 1 year of scanning mode operation by GLAST (Hunter, 2001). It is seen that GLAST has the potential to derive spectra up to 80 GeV and 15 GeV for 4 deg2 bins from the directions of the galactic center and anti-center, respectively, if one requires at least 10 detected photons. At the same time, GLAST should be able to image the Y-ray emission towards the galactic center above 1 GeV on much smaller scales, < 1 deg2 (down to 0.3° x 0.3° limited by angular resolution at 1 GeV), albeit without adequate spectral information.
The extension of spectral studies of the diffuse background beyond 10 GeV with < 1/3° resolution is of great interest, because these measurements would allow us to trace propagation of CRs on scales less than 100 pc even for very distant (d > 10 kpc) regions of the Galactic Disk.
Fig. 4.22 (a) Fluxes of diffuse galactic Y-ray emission within a 10-3 sr solid angle detected by EGRET towards the galactic center, GD(C), and anti-center, GD(A). For comparison, the flux of the (isotropic) extragalactic background radiation (EGB) detected by EGRET up to 300 GeV is also shown. The curves marked "SNR" and "GMC" represent the fluxes of a "standard" SNR with the scaling-factor Asnr = 1 (see Eq.(4.35)) and from a "standard" passive molecular cloud with the scaling-factor Agmc = 1 (see Eq.(4.36)), respectively. The flux of CR electrons observed in the solar vicinity is also shown. (b) The differential counts of radiation components presented in figure (a) expected after a Tobs = 104 s observation with the high altitude IACT array 5@5. The detection rates of CR electrons are shown for 3 different values of the geomagnetic cutoff: 0, 10, and 20 GeV.
Because of the limited detection area, the potential of GLAST is still limited, especially for spectroscopic measurements from regions outside of the inner Galaxy and at large galactic latitudes. Planned imaging atmospheric Cherenkov detectors like CANGAROO-III, H.E.S.S. and VERITAS will have very good angular resolutions of about 0.1° and detection areas 104 — 105 m2. Even so, above the energy threshold of these instruments around 100 GeV, the Y-ray fluxes drop significantly, thus spectroscopic studies in this energy regime will be limited by the low photon fluxes. In the energy region from several GeV to several 100 GeV an adequate potential for studies of the diffuse galactic background may require future low-threshold IACT arrays like 5@5 installed at very high mountain altitudes (see Sec. 2.3.3). A challenge for such instruments would be the spectroscopy of the diffuse Y-radiation on 1/3° or perhaps even smaller angular scales. The number of Y-rays detected by 5@5 at given energy E with
(i.e. E(dN/dE) within 10-3 sr solid angle and for an exposure time 104 s, are shown in Fig. 4.22b.It is seen that the number of detected Y-rays in each 0.3° x 0.3° bin
toward the galactic center could be as large as 103 at 30 GeV and 250 at 100 GeV. Although the detection rate of CR electrons which constitute the main source of background for 5@5, is an order of magnitude higher, the signal-to-noise ratio,
is sufficiently high for the detection of statistically significant signals for just several hours observations by this instrument.
Fig. 4.23 The number of Y-rays above an energy E expected per 1 deg2 from the directions of the galactic center and anti-center, after 1 year of operation of GLAST in the scanning mode.
For the effective field of view of about 3 degree (in diameter), these observations may allow a simultaneous probe of 25 "0.3° x 0.3° " bins. This should be sufficient to resolve point-like sources with luminosities several times 1033(d/10 kpc)2 erg/s, and thus to separate the flux of truly diffuse Y-ray emission from contributions of discrete sources. Note that the 1/3° angular scale corresponds to 50(d/10 kpc)2 pc linear size, thus these observations may reveal the sites of CR production in the Galaxy even when the accelerators themselves are not visible in Y-rays. Remarkably, this could be a quite widespread case, for example due to the lack of adequate targets in accelerators and/or fast escape of accelerated particles from their production sites. In any case, the study of <100 pc proximity of CR accelerators should allow correct estimates of the overall energy released in accelerated relativistic particles and an important study of CR propagation effects (e.g. the diffusion coefficient) in the (presumably) very active and turbulent regions surrounding the CR accelerators.
Concluding remarks
The diffuse galactic Y-ray emission carries unique information, a proper understanding of which should eventually result in a quantitative theory for the origin of galactic cosmic rays. The problem is complicated and confused by the operation of several competing Y-ray production mechanisms. Although the data obtained by the COMPTEL and EGRET detectors aboard the Compton GRO allow rather definite conclusions concerning the relative contributions of different Y-ray production mechanisms in the energy region from 1 MeV to 30 GeV, many details concerning both the spatial distribution of CRs and their energy spectra in different parts of the Galactic Disk remain unresolved. The next generation of space- and ground-based Y-ray detectors with significantly improved performance should be able to provide a framework for a coherent understanding of many aspects of the origin and propagation of galactic cosmic rays.
Gamma-rays below 100 MeV. In this energy region the diffuse y-radiation has an electronic origin, namely the observed Y-ray fluxes from 10 MeV to 100 MeV can be well explained by superposition of the bremsstrahlung and IC components of radiation . At lower energies, a non-negligible flux can be contributed by the annihilation of relativistic positrons with the ambient thermal electrons, and perhaps also by superposition of prompt Y-ray lines from interaction of sub-relativistic protons and nuclei with the ambient interstellar gas. The detailed spectroscopic studies in the region between several 100 keV and 10 MeV by detectors of the INTEGRAL mission could reveal the spectral features associated with these radiation channels. The detection of prompt Y-ray lines would allow determination of presently highly uncertain flux of sub-relativistic CRs in the ISM, and thus should give a definite estimate of the proton bremsstrahlung contribution to the nonthermal hard X-ray emission of the galactic ridge. The direct measurements of hard X-rays, in particular the mapping and spectroscopy of radiation from 20 keV to several 100 keV by the detectors of the INTEGRAL mission may distinguish between two models relating this radiation to the bremsstrahlung of sub-relativistic particles (electrons and/or protons) and to the synchrotron radiation of extremely high energy electrons. The second model predicts also IC Y-radiation extending well beyond 1 TeV at the flux level marginally detectable by the next generation of IACT arrays. The detailed spectroscopic studies of diffuse radiation by GLAST, in particular the identification of spectral features in the "electron-dominated" to the "nucleon-dominated" transition region around 100 MeV, should allow determination one of the crucial parameters characterising the production and propagation of low-energy CRs, the ratio of the CR electron density to the proton density in the Galactic Disk.
The "GeV bump" and beyond. Above 100 MeV,
Y-rays dominate the diffuse radiation at low galactic latitudes for any reasonable set of parameters characterising the electron-to-proton ratio in CRs and the ambient photon and gas densities in the Galactic Disk. Moreover, the excess emission detected by EGRET at energies of several GeV can be naturally explained by Y-rays of nucleonic origin, assuming that the spectrum of CR protons in the inner Galaxy is harder than the spectrum of directly observed CRs. In particular, the results presented in Figs. 4.19a and 4.20 show that the proton spectrum given by Eq.(4.31) with
which could be formed due to a certain combination of diffusive and convective escape time-scales, is able to explain reasonably well the observed excess GeV emission. In the total
spectrum the contribution of
Y-ray component gradually decreases, however, this decline is compensated for by the hard IC component, which at energies above 100 GeV becomes the dominant contributor to the overall Y-ray flux (see Figs. 4.20 and 4.21). The "GeV bump" can be explained also by a single power-law spectrum of CR protons with rp ~ 2.5 (Fig. 4.19a), but then we should assume strong suppression of the IC contribution to the overall Y-ray flux. These two scenarios predict essentially different origins of Y-rays in the VHE domain. While in the case of the proton spectrum given by Eq.(4.31), the Y-ray emission at E > 100 GeV is contributed mainly by IC scattering of multi-TeV electrons on the 2.7 K CMBR, in the case of a single power-law spectrum of protons the VHE Y-ray flux is dominated by the n0-decay component. The upper limits for the diffuse y-ray fluxes at TeV energies shown in Fig. 4.21 are significantly higher than the predicted fluxes. Moreover, the upper limits reported by the Whipple (LeBohec et al., 2000) and HEGRA, collaborations are derived for galactic longitudes around 40° , and thus are irrelevant to the radiation of the inner Galaxy. This part of the Galactic Disk can be much better surveyed by IACT arrays located in the Southern Hemisphere. These instruments should be able to detect the VHE diffuse Y-ray emission of the Galactic Disk, and thus to provide crucial information about the character of propagation of > 110 TeV cosmic rays in the Galactic Disk.
Resolving small-scale features of the diffuse background. The removal of contributions from unresolved Y-ray sources is a key condition for detailed study of truly diffuse radiation, in particular its spectral and spatial variations which carry direct information about the character of propagation of GCRs. If the "unresolved source component" is contributed by objects with fluxes of more than 10 per cent of the minimum detectable flux by EGRET, GLAST will be able to resolve the truly diffuse component from the overall diffuse Y-ray background of the Galactic Disk, and probe its spatial distribution on an angular scale « 0.3°. This corresponds to linear scales of less than 100 pc even in remote galactic regions. This implies that GLAST can reveal the sites of enhanced CR density expected within 100 pc around strong cosmic ray accelerators. The potential of GLAST for spec-troscopic measurements is, however, limited by photon statistics, especially for energies beyond 10 GeV. In this energy region a unique spectroscopic performance on the same angular scales of about « 0.3° may demonstrate the future sub-10 GeV IACT arrays like 5@5. Before then, the forthcoming IACT arrays should be able to detect the diffuse galactic background at TeV energies. In particular, a deep survey of the inner Galaxy by H.E.S.S. may provide the first observational probe of the average density of TeV cosmic rays and, hopefully, allow the study of their variations in the inner Galaxy on 1° angular scales.
