Giant Molecular Clouds as Tracers of Cosmic Ray (Cosmic Gamma Radiation) Part 2

Gamma rays from a cloud near the accelerator

One of the principal parameters determining the Y-ray visibility of GMCs is

is the diffuse mass of a GMC in units of 105 solar masses, andAssuming that Y-rays are produced by interactions of CRs with the ambient gas,

whereis the Y-ray emissivity. In a "passive" GMC, i.e. in a cloud submerged in the "sea" of GCRs, assuming that the level of the latter is the same as the proton flux measured at the Earth, given by Eq.(4.30), the Y-ray emissivity above 100 MeV is equal towhere the parametertakes into account the contribution of nuclei both in CRs and in the interstellar medium (Dermer, 1986; Mori, 1997). A "passive" cloud could be detectable by GLAST, iftaking into account the large angular size (typically1 degree or more) of relatively close clouds. At energies

thus even for

(there are only several clouds in the Galaxy with such a large value ofdetection of TeV Y-rays from passive clouds is extremely difficult. Nevertheless, searches for VHE Y-rays from GMCs are of a great interest because of the possible existence of high-energy cosmic ray accelerators nearby or inside GMCs.

Indeed, since the density of CRs in the regions up to 100 pc around the accelerators at some stages may exceed the average level of the "sea" of GCRs,we may expect significantly enhanced Y-ray emissivities in these regions. This is demonstrated in Fig. 4.7, where the emissivities, in terms ofare presented for an impulsive proton accelerator at two different instants t and two different distances R from the accelerator. For comparison, the Y-ray emissivity of the "sea" of galactic cosmic ray protons is also shown.

The expanding "bubble" of cosmic rays penetrating the nearby molecular clouds initiates intense Y-ray emission. The right-hand side axis in Fig. 4.7 shows the differential Y-ray fluxes expected from a cloud with The temporal evolution of the integral Y-ray fluxes in the energy intervals between 0.3-3 GeV and 1-10 TeV from a cloud with located at 10 pc, 30 pc, and 100 pc distances from an impulsive proton accelerator withare shown in Fig. 4.8. For the diffusion coefficient, the values ofare assumed.

Fig. 4.7 The differential emissivities and fluxes of Y-rays at different times t and different distances R from an impulsive proton accelerator withThe left-hand side axis shows the Y-ray emissivities, in terms ofThe right-hand side axis shows the Y-ray fluxes,which are expected from a cloud with parameterfor the given emissivity . The curves 1 and 3 correspond to timesand the curves 2 and 4 toThe emissivities at the distance R = 10 pc are plotted by solid lines (curves 1 and 2), and the emissivities at R = 30 pc are shown by dashed lines (curves 3 and 4). The primary proton spectrum and the diffusion coefficients are the same as in Fig. 4.4 withThe curve shown by the full dots corresponds to the Y-ray emissivity for the locally observed proton flux.

The emissivities and fluxes of Y-rays from the "sea" of galactic cosmic rays interacting with the cloud, are also shown.

The comparison of the expected Y-ray fluxes with the sensitivities of GLAST (for approximately 1 year observation time), and the future IACT arrays (for « 10 h of observation time), show that at certain (not necessarily same) epochs the cloud could be visible at GeV and/or TeV energies, up to distances to the accelerator R ~ 30 pc even for the source size of about 1°, provided that

Fig. 4.8 Time dependence of theY-ray emissivities (the left-hand side ordinate axes) and the fluxes (the right-hand side ordinate axes) from a cloud in the energy intervals 0.3-3 GeV and 1-10 TeV at three different distances from an impulsive accelerator: 10 pc, 30 pc, and 100 pc. The fluxes are calculated for a GMC with and a proton accelerator withThe horizontal lines indicate the corresponding emissivities and fluxes of 7-rays expected from the "sea" of GCRs. The expected sensitivities of GLAST and the next generation of IACT arrays in the same energy intervals are shown for the range of the 7-ray source size between 0.1° and 1°.

 

Typical estimates of distances to most of the unidentified EGRET sources, based on their spatial distribution in the galactic plane, is between 1.2 and 6 kpc. The corresponding Y-ray luminosities can be explained by the CR irradiation of GMCs with reasonable values of the parameterbetween 0.1 and 1, provided that powerful and relatively young particle accelerators withoperate in the vicinity of these clouds.

The remarkable feature of Y-radiation of GMCs is the strong evolution in time of both the absolute fluxes and the spectra of Y-rays. The character of the evolution is different for impulsive and continuous injection of cosmic rays into the ISM, and essentially depends on the diffusion coefficient D(E) and distance R between the target and accelerator (see Fig. 4.7 and Fig. 4.8). Depending on the combination of the diffusion coefficient D(E), distance R, as well as the age of the accelerator t, one should expect quite different Y-ray spectra from source to source. Namely, in the case of a cloud near a relatively young accelerator the differential Y-ray spectrum is expected to be much harder than the primary spectrum of the accelerated particles, i.e.Meanwhile, the Y-ray spectra from clouds located near old accelerators would be soft, with a spectral indexDepending on the energy of Y-rays under consideration, the accelerator may be classified as "young" for a cloud at the given distance i.e. during the times untilNote that in the case of energy-independent propagation of cosmic rays the spectra of Y-rays are the same at all epochs, and atthey repeat the spectrum of the parent protons, though the evolution of the absolute fluxes is strong.

Thus, the detection of Y-rays from different clouds located at different distances from the accelerator may provide unique information about the diffusion coefficient D(E) as well as about the age of the accelerator. Similar information may be obtained detecting Y-rays from the same cloud, but in different energy domains, e.g. at GeV and TeV energies. However, in the case of energy-dependent propagation of cosmic rays the chance of simultaneous detection of a cloud in GeV and TeV Y-rays could be not very high, because the maximum fluxes at these energies are reached at different epochs. Since the higher energy particles propagate faster and therefore reach the cloud earlier, the maximum of GeV Y-radiation appears at an epoch when the maximum of the TeV Y-ray flux has already passed. In the case of energy-independent propagation (e.g. due to strong convection) the ratio of fluxesis independent of time,therefore the clouds which are visible at GeV energies would be detectable also at TeV energies.

Accelerator inside the cloud

The second interesting possibility for enhanced cosmic ray density in GMCs is the existence of an accelerator inside the cloud (see e.g Ginzburg and Ptuskin, 1984; Morfill et al., 1984; Ormes et al., 1988; Atoyan, 1996a). For a constant gas density and power-law CR spectrum, the Y-ray flux at energies above 1 GeV reduces to

where W50 is the total kinetic energy of CR protons in the cloud at instant t of observation in units of for r between 2.0 and 2.8.

This equation allows us to understand qualitatively the energy budget of cosmic rays which is required to make a cloud visible in Y-rays. However, for quantitative calculations one needs to take into account the effects of the spectral modification due to energy-dependent propagation (end escape) of relativistic particles in the cloud. The Y-ray fluxes expected from a cloud with an impulsive and continuous accelerator in its center are shown in Fig 4.9a,b. For the chosen radius of the cloud,a mean gas densityis assumed, which corresponds to the mass of the cloudThe distance to the cloud is taken to be d =1 kpc.

At initial epochs,when all relativistic protons remain inside the cloud, the Y-ray fluxes repeat the hard power-law spectrum of protons with an index• the Y-ray spectrum gradually steepens due to the escape of high energy particles from the cloud. For the chosen gas density ofthe cloud with the continuous accelerator inside becomes visible at GeV energies, i.e.only at late epochs,when the total energy output in accelerated protons becomes of order of 3 x 1048 erg. On the other hand, because of the hard source spectrum of accelerated protons, the cloud may already be visible in TeV Y-rays at epochswhen

In the case of an impulsive accelerator the expected GeV-TeV correlations look quite different. In this scenario Y-ray fluxes monotonically decrease with time because of proton losses, especially due to the escape of particles from the cloud. The effect is especially strong at TeV energies. While, for the chosen radius, density and the diffusion coefficient, the flux of Y-raysat 1 GeV remains almost stable untilthe flux of TeV

drops to a very low (although still detectable) level. Remarkably, this feature is quite different from the one which is expected if the accelerator is outside the cloud. In this case the low energy particles need more time to reach the cloud, therefore the cloud becomes visible at GeV Y-rays later than at TeV Y-rays (compare Figs. 4.7 and 4.9a).

Atfluxes are suppressed not only due to the escape of the particles from the cloud, but also due to their energy losses. At stages when the energy losses of protons become important, i.e.a significant fraction of the total energy of accelerated protons is deposited in the secondary electrons from thewhich results in additional Y-ray production due to the bremsstrahlung of these electrons. This component of radiation, together with the bremsstrahlung associated with the primary (i.e. directly accelerated) electrons, may have a significant impact on the

Fig. 4.9 Gamma-ray fluxes expected from a cloud with an accelerator in its center. The parameters of the cloudand the diffusion coefficient are: Rci = 20pc, n = 130 cm-3, d = 1 kpc,(a) – impulsive accelerator; the curves 1, 2, 3, 4 correspond to the ages t = 103, 104, 105, 106 yr, respectively. (b) – continuous accelerator; the curves 1, 2, 3, 4 correspond to the ages t = 102, 103, 104, 105 yr, respectively.Y-ray spectrum below 1 GeV.

On the level of the "sea" of galactic cosmic rays

It is generally believed that the local CR flux (hereafter LCRs), i.e. that directly measured at the Earth, gives a correct estimate for the level of the "sea" galactic cosmic rays. However, strictly speaking, this is an ad hoc assumption. In fact, it is not obvious that LCRs should be taken as being representative of the whole galactic population of relativistic particles. In other words, we cannot exclude the possibility that the flux of LCRs could be dominated by a single or few local sources, especially given the fact that the Solar system is located in a rather extraordinary region – inside active star formation complexes which constitute the so-called Gould Belt. This statement is certainly true for the observed > 1 TeV electrons which suffer severe synchrotron and inverse Compton losses, and thus reach us, for any reasonable diffusion coefficient, from regions no farther than a few hundred parsecs (see Sec. 4.3).

Because of possible contamination of the "sea" of GCRs by nearby sources, we may expect a non-negligible deviation of both the spectrum and the energy density of LCRs from the spectrum and density of GCRs. Therefore, the "GCRs=LCRs" hypothesis needs a reliable observational confirmation. This can be achieved by observations of high energy Y-rays from "passive" GMCs, i.e. from clouds located in environments free of strong CR accelerators. If the flux of LCRs does reflect the level of the "sea" of GCRs, the shape and the absolute flux of Y-rays from "passive" clouds can be predicted with reasonable accuracy. The standard spectral shape of Y-radiation would be an important indicator of quietness of Y-ray emitting clouds, although the absolute Y-ray fluxes from individual clouds can be quite different because of different values of the parameter M5/d2pc. Therefore this method requires detailed spectroscopic measurements for an ensemble of GMCs with known distances dkpc and masses M5. Also, detection of enhanced Y-ray fluxes, compared with the "standard" Y-ray flux calculated for LCRs, would imply a presence of nearby CR sources. Although these clouds cannot be used for precise determination of the level of the "sea" of GCRs, a reliable detection of Y-radiation from even a single under-luminous GMC, i.e. a cloud emitting Y-rays below the expected "standard" flux, would imply that the CR flux we observe at the Earth is our local "fog" which obscures the genuine flux of GCRs. Below we argue that the Y-observations of the Orion complex contain evidence for such a drastic conclusion with important astrophysical implications for the origin of cosmic rays.

The extensive study of the high energy diffuse emission towards Orion by EGRET allowed an accurate measurement of the emissivity in the Orion region aboveand, more importantly, a derivation of the differential emissivity in a broad energy region from 30 MeV to 10 GeV (Digel et al., 1999). These measurements, together with Y-ray emissivities calculated under different assumptions about the CR spectrum and flux, are shown in Figs. 4.10a,b and Fig. 4.11.The emissivity ofy-rays that corresponds to the local proton flux represented by Eq.(4.30), assuming an additional 50 per cent contribution from a-particles and other nuclei, is shown in Fig. 4.10a (curve 1). Although the predicted integral emissivity above 100 MeV,

almost coincides with the measured emis-sivity, it is difficult to fit the derived Y-ray spectrum without assuming an additional, low energy component, e.g. a power-law with a photon index r = 2.4 (dotted line). This component could be naturally attributed to the bremsstrahlung of primary (i.e. directly accelerated) and partly also secondaryelectrons.

Fig. 4.10 Gamma-ray emissivity in the Orion region. The spectra of7-rays are shown by solid lines. The power-law (p-l) components at low energies, with the photon index r = 2.4, are shown by dotted lines. The dashed lines correspond to the total,spectra. (a)7-ray emissivity is calculated for the flux of LCRs (curve 1), and a flux lower by a factor of 1.5 (curve 2). The dashed curve corresponds to the sum of the latter and the low energy p-l component; (b)7-ray emissivity (solid curve) is calculated for a proton spectrum with power-low index index r = 2.1 and energy densityThe dashed curve corresponds to the superposition of the n0-decay and low energy p-l components.

It is seen from Fig. 4.10a that the superposition of the ‘power-law’ andcontributions (dashed line) satisfactorily fits the derived emissivity, if one ignores the last point measured by EGRET between 1 and 10 GeV. Note that such a fit is achieved assuming a somewhat reduced, by a factor of 1.5, CR flux in Orion compared with the local CR flux (curve 2).

One should probably not overemphasise this difference, taking into account possible systematic errors in measurements of the CR flux, as well as uncertainties in the CO measurements used for derivation of the column density of the molecular hydrogen. However, the discrepancy becomes quite significant if we include in the fit the measured highest energy point at 1-10 GeV. This point apparently requires a harder CR spectrum. In particular, Fig. 4.10b shows that a good fit to the EGRET data could be achieved assuming a flat spectrum of protons with power-law index r = 2.1, and energy densitywhich is by a factor of 1.7 less than the energy density of LCRs. The lack of y-ray measurements above 10 GeV do not allow a robust constraint on the power-low index, but, most probably, it cannot exceed 2.4.

Fig. 4.11 Differential y-ray emissivities in the Orion region. The curves 1, 2 and 3 correspond to emissivities calculated for CR spectra with the same power-law index r = 2.1, but with exponential cutoff at 3 different energies, .and 10 TeV, respectively. The corresponding energy densities of CR protons are: wp = 0.55, 0.7, and 0.85 eV/cm3. At low energies an additional power-law component of radiation is also assumed (dotted curve). The superpositions ofand power-law components are shown by dashed curves.

This almost excludes the possibility that Orion is a passive Y-ray source (i.e. its Y-radiation is merely contributed by the "sea" of GCRs interacting with massive molecular clouds). A more plausible interpretation of this result would be a scenario when the bulk of the observed Y-ray flux is produced by particles accelerated within the Orion complex, with a less (although unavoidable) contribution from GCRs homogeneously distributed throughout the Galactic Disk, and freely passing through the molecular clouds. Indeed, such an extra contribution by GCRs around 1 GeV would lead to an overproduction of Y-rays, unless we assume that the level of the "sea" of GCRs at energies ~ 1 — 10 GeV does not exceed « 1/3 of the directly measured flux of LCRs.

This rather dramatic conclusion formally could be avoided by speculating that the low-energy CRs cannot freely penetrate the dense clouds (see, however, Cesarsky and Volk, 1978). For example, assuming that the coefficient of reflectivity of CRs from a cloud decreases with energy, e.g. approximately as E-K, with k ~ 0.6 — 0.7, one can obtain the required hard spectrum of particles in Orion without invoking additional nearby accelerators . Both these possibilities do not agree, to a certain extent, with the current concepts of origin and propagation of GCRs. Therefore, more careful analysis is needed before claiming any deviation from the conventional models of GCRs. Note that the conclusion about the hard CR spectrum in Orion is essentially based on the reported Y-ray flux above 1 GeV. This indicates the importance of future accurate spectrometric measurements of Y-radiation of Orion, as well as of other individual Y-ray emitting clouds detected by EGRET towards Cepheus, Monoceros, and Ophiuchus (Digel et al., 1999). These measurements should allow an effective separation of the contributions from the "sea" of GCRs and from the local CR accelerators. It is especially important to extend the measurements to higher energies. If the "excess" flux at 1-10 GeV is indeed due to the acceler-ator(s) nearby or inside the Orion complex, we may expect continuation of this hard spectrum well beyond 10 GeV, depending on the high energy cutoff in the CR spectrum (see Fig. 4.11). On the other hand, the hypothesis of the energy-dependent reflection of CRs from dense clouds (assuming that GCRs=LCRs), predicts an essentially different spectrum of Y-rays – a flat part below a few GeV, with a quite steep power-law tail with r ~ 2.75 at higher energies. This part of the spectrum is produced by particles of the "sea" of GCRs which freely enter the cloud. Such standard high energy Y-ray tails should be observed from other local clouds as well.

Large-scale CO surveys of molecular clouds in the Milky Way by Dame et al. (1987) revealed two dozen local GMCs within 1 kpc. The study of high energy Y-rays from these clouds with a broad-distribution of distances from ~ 100 — 200 pc (like the Taurus dark clouds or Aquila Rift) to 800 pc (like Cyg OB7 and Cyg Rift), which should be visible for GLAST, is of great interest for the derivation of the spatial and spectral distribution of CRs in our local environment.