DE-EXCITATION NUCLEAR GAMMA-RAY LINE EMISSION FROM LOW-ENERGY COSMIC RAYS IN THE INNER GALAXY

The component below about 1 GeV nucleon⁻¹ of the interstellar cosmic-ray (CR) spectrum is probably least well known. Direct observations are not conclusive because CRs with these energies are effectively deflected by the action of the outstreaming solar wind such that the energy spectra measured inside the heliosphere are strongly altered with respect to the interstellar one. It results in an uncertainty of the particle flux, which is increasing toward lower energies and below a few hundred MeV nucleon⁻¹ the CR composition and the spectrum are essentially unknown. Indirect evidence for an important low-energy component comes from observations of the interstellar ionization rate. In particular, observations of the molecule H⁺₃ in diffuse interstellar clouds point to a CR-induced ionization rate, which exceeds by more than an order of magnitude the one that is calculated for the standard CR flux thought to be produced by diffuse shock acceleration in supernova remnants (Indriolo et al. 2009; Indriolo & McCall 2012). However, neither the nature—electrons or nuclei—nor the spectrum of the low-energy component can be deduced from these observations. An independent argument for the existence of a significant component of low-energy CR nuclei comes from the observed quasi-linear increase of Be with metallicity (Tatischeff & Kiener 2011).

The most compelling indirect observation of this component would be the detection of nuclear γ-ray lines from the galactic disk. In fact, the strongest lines from the most abundant nuclei are preferentially produced in the CR energy range below a few hundred MeV in collisions of protons and α-particles with interstellar matter. They are expected to be the same as those frequently observed from strong solar flares, i.e., lines from the de-excitation of the first few levels in ¹²C, ¹⁶O, ²⁰Ne, ²⁴Mg, ²⁸Si, and ⁵⁶Fe (Ramaty et al. 1979). Indriolo et al. (2009) constructed CR spectra, which produce the observed ionization rate in diffuse clouds by adding a low-energy component to the standard CR spectrum. With that they estimated fluxes in the 4.4 MeV line of ¹²C and the 6.1 MeV line of ¹⁶O from the central radian of the Galaxy close to the sensitivity limits of the International Gamma-Ray Astrophysics Laboratory (INTEGRAL). Besides strong narrow lines, the nuclear line emission is composed of broad lines produced by the CR heavy-ion component and of thousands of weaker lines that together form a quasi-continuum in the E_γ ∼ 0.1–10 MeV range.

In this paper, we calculate this total nuclear γ-ray line emission from the inner Galaxy by making use of the work of Indriolo et al. (2009), new developments in nuclear reaction cross sections (Murphy et al. 2009; Benhabiles et al. 2011), and recent observations of CR-induced high-energy γ-ray emission with Fermi-LAT (Abdo et al. 2009; Strong 2011; Ackermann et al. 2012). Finally, the possibilities for a detection of this emission with existing and eventual future space-borne γ-ray instruments are discussed.

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Following the method of Indriolo et al. (2009), the interstellar CR spectra for the calculation of the nuclear γ-ray line emission have been divided into two distinct components.

• 1.  
  Standard CRs, whose origin and acceleration are widely attributed to massive stars through the action of their stellar winds followed by their explosions as supernova. Their composition and energy spectra are relatively well known above several GeV nucleon⁻¹ from direct measurements while the extrapolation to lower energies can be done with propagation and demodulation calculations. An important indirect constraint on the CR spectra above several hundred MeV nucleon⁻¹ is the diffuse interstellar high-energy γ-ray emission due to π⁰ production and decay. This emission has been observed from several Galactic sources by Fermi-LAT, as, for example, from the local gas and dust (Abdo et al. 2009) and from the inner Galaxy (Strong 2011), which are of particular interest to the present study. These standard CRs produce an ionization rate well below the mean ionization rate deduced from H⁺₃ column densities observed in diffuse molecular clouds.
• 2.  
  A distinct low-energy component added to the standard CRs to reach the observed ionization rate. For this we adopt the values deduced from recent observations of the molecule H⁺₃ in diffuse interstellar clouds pointing to a mean molecular hydrogen ionization rate of ζ₂ = 3–4 × 10⁻¹⁶ s⁻¹ (McCall et al. 2003; Indriolo et al. 2009; Indriolo & McCall 2012). Another requirement of this component is that the total interstellar CR spectra stay compatible with the observed CR spectra above 1 GeV nucleon⁻¹, ensuring also that the high-energy γ-ray emissions stay compatible with the above cited Fermi-LAT observations.

2.1. Standard CRs

In the most important energy band for comparison with Fermi-LAT data, between about 1 GeV and a few hundred GeV nucleon⁻¹, data from some 10 balloon-borne and satellite-borne instruments exist. We adopted the most recent observations of CR fluxes from the PAMELA detector onboard the Russian Resurs-DK1 spacecraft, which provides high-precision data for protons and helium nuclei in the rigidity range of R ∼ 1–1000 GV (Adriani et al. 2011). Their proton fluxes agree in the kinetic energy range above E ∼ 30 GeV, where solar modulation effects should be negligible, with other recent data typically at the 20% level or better. The agreement is slightly worse for the helium fluxes, where differences up to 40% can be observed (see, e.g., Figure 1 in Adriani et al. 2011).

To obtain the local interstellar (LIS) proton and helium fluxes, the observed fluxes have been demodulated with the force-field model of Gleeson & Axford (1968) with a solar modulation parameter of Φ = 450 MV (Adriani et al. 2011). This yields LIS proton fluxes in the range of E = 0.89–1010 GeV and LIS helium fluxes in the range of E = 0.36–505 GeV nucleon⁻¹. For the LIS helium fluxes, we supposed a pure α-particle composition, ignoring an eventual small contribution of ³He nuclei.

The extrapolation of the proton fluxes to lower energies was done with a standard leaky-box model for Galactic CR propagation. An unbroken power law in particle momentum as it results from diffuse shock acceleration (Jones & Ellison 1991; Dermer 2012) has been used for the source spectrum: F(p)∝p^−s. Using dF/dE = dF/dp dp/dE = dF/dp 1/v, the corresponding energy spectrum is F(E) = F₀p^−s/β, where v, p mean the particle velocity and momentum and β = v/c. F₀ and the spectral index s were then adjusted such that the propagated spectrum reproduces the LIS proton fluxes obtained from the PAMELA measurements. In the propagation calculation, the escape length distribution was taken from the disk-halo diffusion model of Jones et al. (2001) and the proton inelastic cross sections from Moskalenko et al. (2002). The best adjustment was achieved with a source index of s = 2.35. Figure 1 (left panel) shows the propagated proton spectrum together with the Pamela data and some other recent measurements (Menn et al. 2000 [IMAX]; Shikaze et al. 2007 [Bess]; Alcaraz et al. 2000a, 2000b [Alpha-Magnetic Spectrometer AMS-01]; Boezio et al. 1999 [Caprice]).

For the LIS helium spectrum we took the demodulated helium data of PAMELA from E = 0.36–300 GeV nucleon⁻¹ only; the two data points above that energy suffer a large uncertainty. Extrapolation of the LIS helium spectra to lower energies was done, as in the proton case, with the leaky-box model with the same parameters for the escape lengths. The inelastic cross section for α + ⁴He was taken from the model of Tripathi et al. (1999) except below E_α = 15 MeV, where a transition to the experimental values around 10 MeV was operated. Here the best adjustment of the Pamela He data in the range E = 1–100 GeV nucleon⁻¹ was found with a source index of s = 2.32. As shown in Figure 1, the propagated helium spectrum misses the relatively steep fall of the LIS spectrum below about 0.4 GeV nucleon⁻¹. This part is certainly subject to large demodulation uncertainties, the force-field model being only an approximation and may especially fail at these low energies. In the case of electrons, Strong et al. (2011) recently showed through constraints on the interstellar electron spectrum from synchrotron radiation that modulation may be significantly overestimated for them and that their true interstellar spectrum shows a sharp turnover below ∼1 GeV. However, as this part has only a minor influence on high-energy γ-ray emission calculations for standard CRs, we simply opted for the values of the propagated spectrum. Above 300 GeV nucleon⁻¹ we used the data of the ATIC-2 experiment (Panov et al. 2009), which have smaller uncertainties than the Pamela data there and agree with them at lower energies. The spectra of heavier nuclei were taken identical to the helium spectrum with relative CR abundances given in Table 9.1 of Longair (1992), averaged over the three energy bands.

With these CR spectra, the γ-ray emissivity due to the π⁰ decay has been calculated with the model of Kamae et al. (2006) for the differential γ-ray emission cross section in the π⁰ → 2γ decay. Cross section data for π⁰ production in p + p reactions have been taken from the parameterization of Dermer (1986). For the p + ⁴He reaction, the inclusive cross section displayed in Figure 4 of Murphy et al. (1987) up to 2 GeV has been used. Above 6.3 GeV the cross section has been obtained by multiplying the p + p cross section with the multiplication factor m_He p of Mori (2009), and a linear interpolation was applied in the energy gap. All other reaction channels (α + ⁴He and p,α + H i) were calculated with Mori's multiplication factors relative to the p + ⁴He cross section. Here, H i stands for elements C, N, O, Ne, Mg, Al, Si, S, Ar, Ca, Fe, and Ni. For the ambient LIS composition, solar photospheric abundances have been used. In the CR composition we added ¹¹B, ⁵²Cr, and ⁵⁵Mn as representatives of Sc-Mn, which are relatively abundant in CRs. The result of the calculation is shown in Figure 2 together with the Fermi-LAT data for the local diffuse γ-ray emissivity of Abdo et al. (2009) and their estimate of the bremsstrahlung component. The calculated curve reproduces remarkably well the observed emissivity in shape and absolute normalization, very close to the calculation of Abdo et al. (2009) albeit with slightly different CR spectra and composition.

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The Galactic CR electron spectrum is constrained by its electromagnetic emissions induced during propagation in the Galaxy and by direct data from many balloon and satellite experiments (see, e.g., Strong & Moskalenko 2009). The emissions span a wide range from the Radio band for the synchrotron radiation to MeV and TeV energies for bremsstrahlung and inverse Compton scattering. For the standard CR electron spectrum we rely on results from the GALPROP model, which has been developed to calculate numerically the Galactic propagation of hadrons and leptons including secondary-particle production and propagation (Strong & Moskalenko 1998). The model also makes detailed calculations of the electromagnetic emissions, which are induced by primary and secondary particles. From the different CR electron spectra and propagation models studied in Strong et al. (2000), we adopt the conventional model. It fits the direct data above several GeV and agrees simultaneously with the Galactic synchrotron emission. The latter constraint requires a spectral break of the CR electron spectrum below several GeV, which was confirmed in a recent study by Strong et al. (2011).

2.2. Low-energy Part

The previously described standard hadronic CRs yield an ionization rate for molecular hydrogen of ζ₂ = 4.3 × 10⁻¹⁷ s⁻¹ integrated in the CR energy range E = 0.002–10³ GeV nucleon⁻¹, about a factor of 10 below the most recent observed mean rates in diffuse molecular clouds ζ₂ = 4 × 10⁻¹⁶ s⁻¹ (Indriolo et al. 2009) and ζ₂ = 3.5^+5.3_−3.0 × 10⁻¹⁶ s⁻¹ (Indriolo & McCall 2012). For a direct comparison with Indriolo et al. (2009), who first proposed a distinct low-energy CR (LECR) component above 2 MeV nucleon⁻¹ to account for a high ζ₂, we adopted the first value in the following calculations and figures.

Using the conventional model electron spectrum of Strong et al. (2000) extrapolated down into the eV range, Padovani et al. (2009) found a negligible contribution of electrons to the ionization rate in molecular clouds (ζ₂ ∼10⁻¹⁹ s⁻¹). There could still be an important CR electron component below 200 MeV to produce the observed ionization rate. Such a LECR electron component has, for example, been studied by Strong et al. (2000) and Porter et al. (2008) in order to reproduce the Comptel MeV excess. But this is beyond the scope of this paper and we will concentrate on the hadronic component. Supposing that the extra ionization in these clouds is entirely due to low-energy nuclei, we explored a range of spectra and compositions for such an LECR component.

Scherer et al. (2008) proposed that a CR population of anomalous cosmic rays (ACRs) accelerated in astrospheres of stars similar to the Sun makes up a significant part of the interstellar CR spectrum below E = 0.3 GeV, and when adding the contributions of other stars those ACRs may be the dominant component of LECRs. Such a scenario was discussed by Indriolo et al. (2009) for their low-energy power-law spectrum (dubbed "carrot" spectrum) with the power-law index and normalization adjusted to produce the observed ionization rate. We adopted this model in the first scenario for our low-energy part of the interstellar spectrum.

The spectra and composition were derived in the following way: LECR source spectra were constructed from the ACR proton spectra at the helio- and astropause of Scherer et al. (2008), which were constrained by recent data of the Voyager spacecraft. These spectra are well described by a power-law function with an exponential cutoff at $E_{c}: F(E) = F_0 E{^{-s}} {E}^{-E/E_{c}}$ with a spectral index of s = 2.4. We explored ACR spectra for this index and an upper and a lower limit of s = 2.7 and s = 2.0, respectively. For α particles and heavier nuclei, the same index was used and the cutoff energy was taken following the species scaling of Steenberg (2000): E_c(A, Q)/E_c(p) = (A/Q)^{−2γ/(γ + 1)} with energies expressed in energy per nucleon and A, Q being the mass number and the charge state, respectively. For the sake of simplicity, we used γ = 1 and considered only singly charged ions, which represent the majority of ACR ions in the heliosphere, reducing the scaling to E_c(A, Z)/E_c(p) = A⁻¹. E_c was varied from 5 MeV to an upper limit, where the particle fluxes are still compatible with the observed CR helium and proton fluxes above 0.5 and 1 GeV nucleon⁻¹, respectively. The upper limits were found to be E_c = 600, 1200, and 4800 MeV for spectral indices s = 2.0, 2.4, and 2.7, respectively. The ACR composition was taken from Cummings et al. (2002).

For the second scenario, we used source spectra resulting from shock acceleration (SA-LECRs) as for standard CRs, but with an energy cutoff of $E_c: F(E) = F_0 R^{-s}/\beta e^{-E/E_c}$. R is the particle rigidity; spectral index s and E_c, expressed in energy per nucleon, were taken identical for all species. For the source spectral index we used s = 2.35, which is the index found for the standard CRs as our central value, and s = 2.0 and s = 2.7 falling in the typical range of models of diffuse shock acceleration (see, e.g., Jones & Ellison 1991; Schlickeiser 2002). The energy cutoff E_c, which in this scenario may be considered arising from a truncation in space or time in the acceleration process, was varied from 5 MeV to an upper limit compatible with the observed CR helium and proton fluxes above 0.5 and 1 GeV nucleon⁻¹, respectively. It was found to be E_c = 150 MeV for s = 2.7 and E_c = 120 MeV for s = 2.35 and s = 2.0. For the composition of the source spectra we took the CR source abundances of Lund (1989) from Table 9.1 in Reames (1999).

These spectra were then propagated for both scenarios with the leaky-box model to obtain the interstellar LECR spectra. All propagated LECR spectra were normalized to produce an ionization rate of ζ₂ = 3.6 × 10⁻¹⁶ s⁻¹ in diffuse clouds, yielding ζ₂ = 4 × 10⁻¹⁶ s⁻¹ when added to the standard CRs. We calculated the ionization rate as Indriolo et al. (2009), assuming in particular that CRs with kinetic energy below a threshold energy of 2 MeV nucleon⁻¹ cannot penetrate diffuse clouds and thus do not affect the ionization rate there.

Examples of LECR proton and α-particle spectra are shown in Figure 3 together with the standard CRs alone. The curves with s = 2.35 and E_c = 120 MeV, and s = 2.4 and E_c = 1.2 GeV for SA-LECRs and ACR-LECRs, respectively, represent upper limits still compatible with the demodulated proton and helium data. The ionization rates of LECRs added to the standard CRs in dense clouds, taking a low-energy threshold of 10 MeV as proposed in Indriolo et al. (2009), are displayed in Figure 4. Nearly all spectra yield rates above the recommended value of van der Tak & van Dishoeck (2000) for molecular cloud cores and, with the exception of ACR-LECRs where s = 2.7, cross their upper limit for the higher cutoff energies. We note, however, that the energy threshold of 10 MeV is an approximation based on stopping range calculations and is certainly subject to considerable uncertainties. Furthermore, magnetic mirroring can decrease the CR ionization rate in molecular cloud cores by a factor of ∼3–4 (Padovani & Galli 2011), which would bring all rates, if not into the recommended range, at least below the upper limit discussed in van der Tak & van Dishoeck (2000).

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Nuclear line emission was calculated for the same reaction channels as for the calculation of π⁰ production, except for the p + p channel which produces no γ-ray lines. Cross sections have been taken from the recent compilation of Murphy et al. (2009), which contains cross section excitation functions of about 140 relatively strongly produced γ-ray lines by energetic proton and α-particle reactions in astrophysical phenomena like solar flares. The excitation functions extend from the reaction threshold to typically 1 GeV nucleon⁻¹, which in most cases is amply sufficient for the present study where the nuclear γ-ray line emission is dominated by the low-energy part. Above that range, constant cross sections were supposed.

For all other γ-ray lines we relied entirely on calculations with the reaction code TALYS (Koning et al. 2008), as was done in Murphy et al. (2009), with some slight parameter changes for ¹⁴N, ^{20, 22}Ne, and ²⁸Si which gave an improved reproduction of new experimental γ-ray data for proton and α-particle-induced reactions with these nuclei (Benhabiles et al. 2011). This code works in the range up to 250 MeV for proton reactions and 62.5 MeV nucleon⁻¹ for α-particle reactions. Above these energies a constant cross section was supposed. Lines emitted during the decay of radioactive nuclei were included in these calculations, but not the 511 keV line and continuum emissions resulting from β⁺ decay and subsequent positron annihilation. Also, emission induced by π⁺-decay positrons was not included in the calculated spectra.

As described above, the CR spectra were normalized such that an ionization rate of ζ₂ = 4 × 10⁻¹⁶ s⁻¹ was obtained and the calculated high-energy emission due to π⁰ decay reproduced the Fermi observations of the diffuse γ-ray emission of the inner Galaxy (Strong 2011). For the composition of the ambient medium in the inner Galaxy, we took solar abundances with, however, twice the solar metallicity. The Fermi-LAT data and calculations for ACR-LECR spectra with s = 2.4 and two extreme cases of energy cutoffs E_c = 5 MeV and E_c = 1.2 GeV are shown in Figure 5. When adding the inverse Compton component from high-energy leptons and the estimated emission due to unresolved point sources as presented in Strong (2011), the reproduction is quite good for both cases. The π⁰ production is apparently completely dominated by the standard CRs, even for LECRs with E_c = 1.2 GeV, which add only a small component below E ∼ 1 GeV.

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Examples of nuclear γ-ray line emission for the three cases of ACR-LECRs with s = 2.4 and the case with the strongest emission s = 2.0, E_c = 120 MeV of SA-LECRs are shown in Figure 6. Emission due to the standard CRs alone, as described in Section 2.1, is also shown for comparison. The total γ-ray line intensity for the latter is dominated by interactions of the heavy-ion content due to their enrichment in standard CRs with respect to the interstellar medium. It accounts for about 70% of the total nuclear line emission. Some outstanding narrow lines produced in proton- and α-particle-induced reactions are nevertheless present. The emissions of ACR-LECRs with cutoff energies E_c = 5 MeV and 25 MeV add practically only a narrow-line component, the quasi-continuum being completely dominated by the standard CR component of the CR spectra. In fact, this is mainly because heavy ions play a completely negligible role in low-energy cutoff ACR-LECRs due to their very low cutoff energies (E_c(A,Z)/E_c(p) = A⁻¹; see Section 2.2). Their contribution is less than 10⁻³ at E_c ⩽ 8 MeV, ∼6% at E_c = 80 MeV and rises to ∼50% at E_c = 1.2 GeV.

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The overall emission is stronger for SA-LECRs because more particles above the reaction thresholds are present with respect to ACR-LECRs of the same cutoff energy. ACR-LECR spectra with their steep rise toward low energies contain many low-energy particles that contribute strongly to ionization but are very inefficient for γ-ray line production. This is true for the narrow lines induced by light ions and slightly more pronounced in the quasi-continuum, which furthermore reflects the importance of energetic heavy ions in SA-LECRs. They contribute between ∼50% at E_c = 5 MeV and ∼60% at E_c = 120 MeV to the nuclear γ-ray emission.

The strongest narrow lines in decreasing order are the 4.4 MeV line (essentially from ¹²C and ¹¹B, produced in reactions with ¹²C and ¹⁶O), the 6.1 MeV line (a mainly inelastic scattering off ¹⁶O and spallation reaction products ¹⁵O and ¹⁵N), and the 1.63 MeV line (mainly from inelastic scattering reactions with ²⁰Ne). Integrated fluxes of these narrow lines and the integrated fluxes in energy ranges 1–3 MeV and 3–8 MeV are shown in Figure 7. Although the continuum fluxes increase steadily with cutoff energy, the narrow-line fluxes tend to level or even slightly decline above E_c ∼50 MeV. The latter can be explained by the cross section excitation functions of the dominant line-producing reactions, which have their maxima generally well below 50 MeV. An exception is 6.13 MeV fluxes for SA-LECRs, which include an important contribution of ¹⁶O spallation reactions with higher thresholds.

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Narrow-line and continuum fluxes have also been calculated with two spectra and compositions as proposed by Indriolo et al. (2009). The flux values for their "carrot" spectrum are within 20% of the values for ACR-LECRs with s = 2.7 and E_c = 8 MeV, while the values for their power-law spectrum agree with better than 15% of the ones for SA-LECRs with s = 2.0 and E_c = 14 MeV. The 4.4 MeV and 6.1 MeV narrow-line fluxes are smaller by about a factor of 10 than the fluxes predicted by Indriolo et al. (2009) for the central radian of the Galaxy (330° < l < 30°, ∣b∣ < 10°), probably mainly because of the method of absolute normalization. In Indriolo et al. (2009) it was based on the column density of the target material in the central radian assumed to be 10²³ cm⁻². By normalizing the nuclear line emission to the π⁰-decay flux from the inner Galaxy as determined by Fermi-LAT (Strong 2011), our 4.4 MeV and 6.1 MeV line fluxes are independent of the column density. They depend only on the spectral shape and composition of CRs and the metallicity of the inner Galaxy. Supposing that the intensity of the CRs, which are responsible for the bulk of the π⁰ production (E ∼0.5–20 GeV nucleon⁻¹), is the same throughout the Galaxy, the Fermi-LAT data imply a mean column density of about 2 × 10²² cm⁻² in the inner Galaxy (300° < l < 60°, ∣b∣ < 10°). This explains at least a large part of the difference.

Our estimations of nuclear cross section uncertainties can roughly be divided into two categories. (1) Strong lines whose cross section excitation functions are explicitly listed in the compilation of Murphy et al. (2009). They are at least partly based on experimental data whose uncertainties are of the order of 15% or less. For the 1.63, 4.4, and 6.1 MeV lines, the bulk of the emission is induced by particles in the energy range where a wealth of experimental data exist, and the nuclear uncertainties on the narrow-line fluxes should be less than 20%. (2) The weak-line quasi-continuum taken from TALYS (Koning et al. 2008) calculations. The predictions of this code have been extensively compared to experimental γ-ray cross sections in several studies (Benhabiles et al. 2011; Murphy et al. 2009; Tatischeff et al. 2006) and a typical agreement of a factor of two or better for individual lines was found. As this quasi-continuum consists of thousands of individual lines, the overall uncertainty on the integrated cross section in the two energy bands 1–3 and 3–8 MeV should be smaller than that. A conservative estimate would be less than 50%. This weak-line emission component is maximal for the high-energy CR component (∼70%), while for the LECRs it represents ∼50% at the highest energy cutoffs and at E_c = 5 MeV drops to ∼20% and ∼25% for ACR-LECRs and SA-LECRs, respectively. It results in nuclear uncertainties of the 1–3 and 3–8 MeV fluxes of less than ∼40%.

Another uncertainty of the narrow-line fluxes comes from the metallicity of the ambient medium. For the average metallicity at the Galactocentric distance of the Sun, measurements are generally equal or slightly below the solar system value (Daflon & Cunha 2004; Lemasle et al. 2007; Pedicelli et al. 2009; Rolleston et al. 2000). The radial gradients, however, especially toward the Galactic center (R = 0), appear less well defined. Using the available extracted radial gradients, and assuming they stay constant toward the center, extrapolation of element abundances to the center yields values ranging from [O/H] = 0 (Daflon & Cunha 2004) to [Fe/H] = 1 (Pedicelli et al. 2009), where [O/H] = log10((O/H)_{R = 0}/(O/H)_☉), with (O/H)_☉ being the solar system value. The fact that the inner Galaxy largely dominates the γ-ray emission and positive metallicity gradients, however, makes a metallicity higher than the solar value reasonable in this case. Our choice of taking [X/H] = 0.3, X = C-Ni for the average metallicity toward the inner Galaxy is only a guess with a conservative estimated uncertainty of a factor of two. This uncertainty affects less, however, the quasi-continuum fluxes, which are to a great part due to the CR heavy-ion component. Adding that to the nuclear uncertainties, a typical overall uncertainty of a factor of two is expected for the calculated narrow-line fluxes and between 50% and a factor of two for the continuum fluxes.

The explored parameter space for LECR spectra and composition spans a wide range in spectral forms and composition, from extremely metal-poor for ACRs with low E_c to the metal-rich-propagated CR source abundances for SA-LECRs. All spectra are compatible with the high-energy diffuse emission of the inner Galaxy observed by Fermi-LAT, the ionization rate of diffuse clouds, and recent satellite and balloon data of the CR proton and helium spectra. Estimated ionization rates of dense clouds, however, are for all CR spectra, except for the low cutoff-energy ACR-LECRs somewhat higher than the recommended value. These estimations are very uncertain, however, as they neglect the effects of magnetic fields on the CR propagation. Padovani & Galli (2011) recently found that magnetic mirroring always dominates over magnetic focusing, implying a reduction of the CR ionization rate in molecular cloud cores by a factor of ∼3–4.

It would, of course, be very surprising if the LECR component could be described by a single distribution with one definite spectral shape, index, cutoff energy, and composition, and be exclusively composed of nuclei. However, whatever the nature of LECRs, they can probably be approximated by a combination of the spectra and compositions studied here, and we believe that the nuclear γ-ray line emission falls into the range that we have explored and which is presented in Figures 6 and 7. It is therefore interesting to compare our predictions with γ-ray instrument sensitivities.

Integrating over the solid angle of the inner Galaxy (300° < l < 60°, ∣b∣ < 10°) yields flux values (in cm⁻² s⁻¹) 0.73 times the values presented in Figure 7. These values are unfortunately far below the narrow-line sensitivities of SPI/INTEGRAL for diffuse emissions: ∼5 × 10⁻⁴ cm⁻² s⁻¹ for the 4.4 and 6.1 MeV lines with FWHM widths ΔE ∼ 100 keV and ∼2 × 10⁻⁴ cm⁻² s⁻¹ for the 1.63 MeV line with ΔE ∼ 20 keV (Teegarden & Watanabe 2006). An important fraction of the 6.1 MeV line may be very narrow if much of the interstellar oxygen is locked up in dust grains (Tatischeff & Kiener 2004). It would result in a sensitivity gain of a factor of five at maximum, but even that is still far from the highest estimated fluxes. In summary, no constraints on LECRs can be inferred from SPI/INTEGRAL observations of the inner Galaxy.

A definite detection of CR-induced nuclear γ-ray line emission or stringent constraints on the nature of LECRs in the case of non-detection probably has to wait for next-generation telescopes with an expected increase in sensitivity of typically a factor of 10–100. We therefore compare the calculated fluxes of instrument proposals to the last call (2010) of ESA's 2015–2025 Cosmic Vision program. Of the three instruments with similar estimated sensitivities in the 0.1–10 MeV range that have been presented, we focus on the CAPSiTT proposal (Lebrun et al. 2010) for which some of us participated substantially in the performance estimates.

The most promising narrow line comparing CAPSiTT sensitivities with predicted fluxes is the 4.4 MeV line; the sensitivity gain for an eventual very-narrow-line component of the 6.1 MeV line is less significant for this instrument with an estimated energy resolution at 6 MeV of ∼30 keV. Assuming a uniform emission in the defined region, the CAPSiTT 3σ five year survey line sensitivity for the 4.4 MeV line (ΔE = 100 keV FWHM) is ∼7 × 10⁻⁶ cm⁻² s⁻¹ for such an extended emission, using only Compton events in the CAPSiTT instrument. This is at the limit for ACR-LECR spectra and would allow detection for SA-LECRs with cutoff energies above 15 MeV. Pair-creation events, which have not been considered for the proposal to ESA below E_γ = 10 MeV, can improve significantly the sensitivity for such extended emissions, increasing, e.g., the effective detection area threefold at E = 5 MeV. This would allow a detection for nearly all considered LECR scenarios.

The broadband 1–3 and 3–8 MeV sensitivities in five years amount to ∼2 × 10⁻⁵ cm⁻² s⁻¹ and ∼1 × 10⁻⁵ cm⁻² s⁻¹, respectively. The flux expected from the standard CRs alone is already slightly higher than the sensitivity in the 1–3 MeV band and well above the sensitivity in the 3–8 MeV band. A detection looks, therefore, very promising for all LECR scenarios. It may, however, be difficult to disentangle from other emissions like inverse Compton scattering of CR electrons and unidentified point sources, which probably dominate the diffuse flux of the inner Galaxy in the 1–10 MeV range. Analysis and discussion of the diffuse interstellar emission as measured by SPI/INTEGRAL and by COMPTEL/CGRO in this energy range can be found in Bouchet et al. (2011).

The nuclear γ-ray line emission probably has a latitude and a longitude profile similar to that of the high-energy diffuse emission observed by Fermi-LAT (Strong 2011). This emission is approximately constant along 320° < l < 40° and concentrated on the Galactic plane, where about 60% of the emission is in a band with b = ±15. Differences may arise because of the metallicity dependence of narrow-line fluxes, which is negligible for π⁰-decay emission, essentially produced in reactions with ambient H and He. Differences of ionization rates in diffuse interstellar clouds, sometimes observed for sight lines with small angular separation, indicate a non-uniform localized distribution of LECRs (Indriolo & McCall 2012). This is not surprising since low-energy particles have shorter ranges than the standard CRs resulting certainly also in an inhomogeneous distribution of LECRs in the inner Galaxy concentrated around the acceleration sites. This would probably only slightly affect the integrated fluxes since they are tied to the mean ionization rate, but the spatial distribution of the nuclear line emission would then be different from the high-energy emission from π⁰ decay.

These effects would be favorable for an eventual observation by a Compton-imaging telescope like CAPSiTT, whose estimated angular resolution at 5 MeV (08) is about a factor of three better than that of COMPTEL/CGRO and SPI/INTEGRAL. The point-source sensitivities of CAPSiTT in five years amount to ∼2 × 10⁻⁷ cm⁻² s⁻¹ and ∼3 × 10⁻⁷ cm⁻² s⁻¹ for the 4.4 MeV line and the 3–8 MeV band, respectively. Our calculated fluxes of the 4.4 MeV line from the inner Galaxy are typically 10–10² times higher than that. If, e.g., the spatial extension of the inhomogeneities is of the order of the angular resolution, a detection becomes very probable. Assuming that the large scatter of observed ionization rates in diffuse clouds (see, e.g., Indriolo & McCall 2012) reflects the LECR density, the 4.4 MeV flux variations may reach a factor of 10. This would be very favorable for a detection by a future instrument with the characteristics of CAPSiTT. Our calculated fluxes in the 3–8 MeV band are a factor of 10²–10³ higher than the point-source CAPSiTT sensitivity, and a concentration of this flux by a few percentages in a point source would be detectable. Following the scatter of ionization rates, a factor-of-few variations in the fluxes are probable although a non-negligible part of the 3–8 MeV band is produced by standard CRs. That inevitably would be detected by a future instrument with good angular resolution.

The presented nuclear line and continuum fluxes from the inner Galaxy induced by interactions of CRs in the interstellar medium were calculated for a large variety of LECR spectra and composition, and it is probable that the real values fall somewhere inside the obtained ranges. The total nuclear γ-ray emission from the inner Galaxy is predicted to be in the range of (0.1–2.0) × 10⁻⁵ cm⁻² s⁻¹ for the 4.4 MeV line, (0.1–1.0) × 10⁻⁵ cm⁻² s⁻¹ for the 6.1 MeV line, and (0.3–3.7) × 10⁻⁶ cm⁻² s⁻¹ for the 1.63 MeV line. For the broadband emissions we find (0.2–1.3) and (0.3–2.1) × 10⁻⁴ cm⁻² s⁻¹ for the 1–3 and 3–8 MeV bands, respectively. An eventual observation of narrow nuclear γ-ray lines with future γ-ray space telescopes based on actually available technology appears to be in reach for a large range of LECR scenarios, although it will be challenging for scenarios with low-energy cutoffs where fluxes do not exceed a few 10⁻⁶ cm⁻² s⁻¹ from the inner Galaxy. It may also be promising for the continuum, especially the 3–8 MeV continuum flux, which exceeds the estimated future instrument sensitivities by up to a factor of 20. This is especially true for an instrument with good angular resolution, which allows the separation of this emission from other diffuse emissions, and a very inhomogeneous spatial distribution of LECRs in the inner Galaxy could not be missed by such an instrument.