Nuclear de-excitation lines as a probe of low-energy cosmic rays
aa r X i v : . [ a s t r o - ph . H E ] J a n Astronomy & Astrophysicsmanuscript no. ms © ESO 2021January 12, 2021
Nuclear de-excitation lines as a probe of low-energy cosmic rays
Bing Liu , , , , Rui-zhi Yang , , † , and Felix Aharonian , , Department of Astronomy, School of Physical Sciences, University of Science and Technology of China, Hefei, Anhui 230026,China † [email protected] CAS Key Laboratory for Research in Galaxies and Cosmology, University of Science and Technology of China, Hefei, Anhui230026, China School of Astronomy and Space Science, University of Science and Technology of China, Hefei, Anhui 230026, China Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210093, China Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Ireland Max-Planck-Institut für Kernphysik, P.O. Box 103980, D 69029 Heidelberg, Germany National Research Nuclear University MEPhI, Kashirskoje Shosse, 31, 115409 Moscow, RussiaJanuary 12, 2021
ABSTRACT
Low-energy cosmic rays (LECRs) contribute substantially to the energy balance of the interstellar medium. They play also significantrole in the heating and chemistry of gas, and, consequently, on the star formation process. Because of the slow propagation coupledwith enhanced energy losses of subrelativistic particles, LECRs are concentrated around their acceleration sites. LECRs e ff ectivelyinteract with the ambient gas through nuclear reactions. Although these processes are energetically less e ff ective compared to heatingand ionization, they are extremely important from the point of view of nuclear de-excitation lines, which carry unique informationabout LECRs. We present results on production of de-excitation lines combining the numerical treatment of nuclear reactions usingthe code TALYS, with the propagation and energy losses of LECRs. Key words. cosmic rays - γ -rays: ISM
1. Introduction
The energy density of Galactic cosmic rays (CRs), w CR ≈ / cm , is comparable to the energy density contributed bythe interstellar magnetic fields and thermal gas. CRs play an es-sential role in the process of star formation through the heatingand ionization, initiating several crucial chemical reactions in thedense cores of molecular clouds (Papadopoulos 2010).The flux and spectra of CRs inside the Solar System havebeen measured with unprecedented accuracy by space detec-tors such as PAMELA (Adriani et al. 2013, 2014), AMS-02 (Aguilar et al. 2015a,b), CREAM (Yoon et al. 2017), DAMPE (An et al. 2019), and CALET (Maestro et al. 2020). Most ofthese direct measurements from Earth focus on the CR spectraabove a few GeV / nuc, below which the fluxes are strongly af-fected by solar modulation. A few years ago, the Voyager1satel-lite passed through the termination shock and measured the low-energy CR (LECR) spectra (from several MeV / nuc up to hun-dreds of MeV / nuc) beyond the Solar System (Cummings et al.2016). The measurements outside the heliosphere are thought tobe free of solar modulation and thus may represent the LECRspectra in the local interstellar medium. However, this informa-tion cannot be extrapolated to other parts of the Galaxy, in whichthe CRs are not homogeneously distributed (Aharonian et al.2018; Jóhannesson et al. 2018; Baghmanyan et al. 2020). Fur- A Payload for Antimatter Matter Exploration and Light-nuclei Astro-physics The Alpha Magnetic Spectrometer The Cosmic Ray Energetics and Mass experiment The Dark Matter Particle Explorer The CALorimetric Electron Telescope thermore, the flux of LECRs can vary dramatically on a smallerscale because of higher energy losses and propagation e ff ects,and the flux is usually much higher around possible CR accelera-tion sites. This is indirectly supported by studies of the interstel-lar ionization rates (in particular, see, e.g., Indriolo et al. 2009;Indriolo & McCall 2012; Indriolo et al. 2015). These researchesalso argued for an LECR component in addition to the standardcontribution by supernova remnants (SNRs), which is also sup-ported by the observation of primary Be (Tatische ff & Kiener2011).In this regard, γ -rays produced in interactions of CRs withthe ambient gas can be used as a unique tool to study the spec-tral and spatial distributions of CRs throughout the Milky Way.For CRs whose kinetic energy exceeds the kinematic thresh-old of π -meson production, E th ≃
280 MeV / nuc, the best γ -ray energy band for exploration is 0.1 - 100 GeV because ofthe copious production of π -decay γ -rays and the potential ofthe currently most sensitive detector, Fermi LAT (Atwood et al.2009). At energies below this kinematic threshold, the nuclearde-excitation lines provide the most straightforward informationabout the LECR protons and nuclei (e.g., Ramaty et al. 1979;Murphy et al. 2009).In this paper, we treat the production of nuclear de-excitationlines by combining the recent advances in the modeling of nu-clear reactions with the propagation and energy losses of subrel-ativistic and transrelativistic CRs. In Sec. 2 we calculate the dis-tributions of LECRs near the sources, taking the processes of dif-fusion and energy losses into account. In Sec. 3 we describe themethod for calculating the emissivity of de-excitation γ -ray linesusing the code TALYS (Koning et al. 2008). We then present the Article number, page 1 of 8 & Aproofs: manuscript no. ms results and discuss their implications. Finally, we summarize themain results in Sec. 4.
2. Propagation of LECR protons
The energy losses of CR protons with kinetic energies above ∼ ff ect on the initially in-jected CR spectral shape. At lower energies, the losses are dom-inated by the ionization and heating of the ambient medium. Inthis regime, as shown in Fig.1, the cooling time is energy de-pendent, thus the propagation can significantly distort the initialspectrum. On the other hand, because of the energy-dependentparticle di ff usion, LECRs propagate more slowly than relativis-tic CRs. Consequently, the spatial distribution of LECRs shouldbe much more inhomogeneous than that of high-energy CRs.LECRs are expected to be concentrated in the vicinity of theiraccelerators with energy distributions that strongly depend onthe distance to their production sites. The propagation of LECRsin the proximity of their sources should therefore be treated withgreat care and depth.As introduced in Padovani et al. (2009), L = − dE / dN H ,represents the energy loss-rate per column density dN H , thenthe ionization cooling time for protons colliding with a mediumatomic hydrogen density n can be estimated by τ ∼ EL n β c , where β = v/ c . For protons with kinetic energy 10 MeV that collidewith H , L ≃ × − eV cm (see Fig.7 in Padovani et al. 2009).The cooling time of 10 MeV protons in a dense environmentwith n ≥
100 cm − therefore is about several thousand years,much shorter than the duration of typical CR accelerators suchas SNRs. Therefore we adopt the steady-state solution for con-tinuous injection to estimate the spectra of LECRs. To be morespecific, we assume a continuous injection of protons from a sta-tionary point source. Then the steady-state energy and radial dis-tribution distribution of the LECR protons is obtained by appli-cation of the analytical solution derived by Atoyan et al. (1995), F p ( r , E ) = π / P ( E ) Z ∞ E Q ( x )[ ∆ u ( E , x )] / × exp − r ∆ u ( E , x ) ! d x . (1)Here Q ( E ) represents the CR injection rate, P ( E ) is the energyloss-rate of CR protons summarized in Padovani et al. (2009), r represents the radial distance to the source, and ∆ u ( E , x ) = R xE D ( E ′ ) P ( E ′ ) dE ′ , where D ( E ) is the energy-dependent di ff usion co-e ffi cient of CRs. In general, this is a quite uncertain parame-ter that depends on the level of turbulence in the environment.In the Galaxy, it is derived from observations of secondaryCRs. We adopted the di ff usion coe ffi cient derived for Galac-tic CRs at energies above 1 GeV (Strong et al. 2007) and as-sumed that it can be extrapolated to low energies down to 1 MeV: D ( E ) = × χ ( E / . cm s − . Because the turbu-lence level near the CR sources is high, the di ff usion could bemuch slower (Malkov et al. 2011; D’Angelo et al. 2018). E ff ectslike this have previously been observed in the γ -ray band. Theelectron halos near pulsars reveal a small di ff usion coe ffi cient(Abeysekara et al. 2017; Di Mauro et al. 2019). To take this ef-fect into account, we considered a broad range of the parameter χ = , . , .
01. Here the total proton injection rate Q , integratedfrom 1 MeV to 100 MeV, and the distance of the source d , arefixed by the value of parameter Q / d = erg s − kpc − . −1 Proton Energy (MeV) −13 −12 E n e r g y l o ss r a t e ( M e V s − ) totalnuclear interactionsheating and ionization Fig. 1: Energy loss-rate as a function of kinetic energy for pro-tons colliding with atomic hydrogen. The number density ofatomic hydrogen n is assumed to be 1 cm − . The dashed blueline indicates the loss rate due to p-p inelastic interactions, andthe dotted red line represents the energy losses caused by heatingand ionization.The injection spectrum of CRs depends on the accelerationmechanism and the conditions inside the accelerator such as theturbulence level and the magnetic field. Typically (although notalways), in the case of di ff usive shock acceleration, for instance,the distribution of accelerated particles can be presented as apower law in momentum p , Q ( p ) = Q p − s (see, e.g., Amato2014). In this paper, it is more convenient to write the distribu-tion in terms of kinetic energy E , Q ( E ) = Q p − s /β , where Q isthe normalization parameter derived from the power of the CRsource. By solving Eq.1, we obtain the steady-state distributionof protons at di ff erent radial distances r to the source.The energy spectra of CR protons di ff using from the site oftheir acceleration are shown in Fig.2. In the left panel of Fig.2,the curves are calculated for four injection spectra of protonswith power-law index s = r =
10 pc, the medium density n = − , andthe parameter χ =
1. In the right panel of Fig.2, we present theCR spectra for the injection spectrum with s = . r = ff usion coe ffi cient, that is, the parameter χ =
1, 0.1, and 0.01,we find that for a small di ff usion coe ffi cient, the energy spectraof protons become very hard, especially at large distances fromthe source.In Fig. 3 we show the radial dependence of proton fluxes. Inthe left panel, we show the e ff ect of the di ff usion coe ffi cient onthe flux of 10 MeV protons. At small distances from the source,their proton flux is significantly higher for slow di ff usion, but atlarge distances, the flux drops as the cooling becomes an impor-tant factor. The contrast of the spectra under di ff erent assump-tions of n (the red and black lines in the left panel of Fig.3) alsoshows the e ff ect of the ambient gas density on the CR spectrum.As expected, because of enhanced energy losses, the radial dis-tribution of the CR fluxes become sharper than 1 / r at larger dis-tances, r ≥
10 pc. In the right panel, we show the r -profiles fordi ff erent CR energies calculated for the parameter χ =
1. Forthe radial profile of the CR, the flux at 1 GeV is close to 1 / r .This is consistent with predictions for the continuous injection inAtoyan et al. (1995), as long as the energy losses are negligible.At low energies, E ≤ Article number, page 2 of 8ing Liu et al.: Nuclear de-excitation lines as a probe of low-energy cosmic rays and slow propagation, we see a stronger radial dependence ofthe CR flux. Namely, at small distances, the flux follows the 1 / r profile, but at larger distances the cooling starts to play signifi-cant role and causes the radial distribution to become as steepas 1 / r . For 1 MeV protons, the transition between 1 / r and 1 / r takes place at just several pc. Last but not least, we note that thehardening of the spectrum of CR protons at low energies in thelocal interstellar medium, as shown by the gray line in Fig. 2,fitted by Phan et al. (2018) using data from Voyager1 and AMS-02 detectors), can be naturally explained by the propagation andenergy losses.In the derivation of Eq.(1), only the di ff usion and energy lossof protons are taken into account. Meanwhile, the advection mayalso play a non-negligible role in the vicinity of CR sources. Inthis case, an advection term V ∂ F p ( r , E ) ∂ r should be added to the prop-agation equation, where V is the advection velocity. By dimen-sional analysis, the advection dominates di ff usion in the region r > D / V ∼
30 pc D cm s − / V
100 km / s . The Alfv´ e nic velocity in theinterstellar medium is estimated as several km / s assuming thedensity of ∼ − and magnetic fields of about 3 µ G (see, e.g.,Han 2017). In this case the advection can be neglected close tothe source. However, for a strong outflow of gas or a stellar windnear the source, with a speed as as high as 1000 km / s (see, e.g.,Domingo-Santamaría & Torres 2006), at distances r ≥ . ff usion, resulting in the steady-state solution F p ( r , E ) = Q ( E )4 π r β c , (2)where E is obtained from the equation rV = R E E dE ′ P ( E ′ ) . The cor-responding CR fluxes are shown in Fig.4. The fast advection re-sults in the strong suppression of CR flux even compared withthe fast di ff usion case ( χ =
1) in the vicinity of the source.Moreover, in the calculation above we assumed that thepower-law di ff usion coe ffi cient extends to low energy. Recentanalyses show indications of a low-energy break in the di ff usioncoe ffi cient in the ISM (Vittino et al. 2019; Weinrich et al. 2020),which was also predicted in Ptuskin (2006) because the dampingof CRs terminates the cascade of turbulence and induces fasterdi ff usion for LECRs. However, it is not straightforward to adoptthis scenario in the vicinity of the CR sources, where the exter-nal turbulence is also stronger by an order of magnitude. The de-tailed calculation requires a self-consistent treatment of the CRpropagation and magnetic turbulence development and dampingnear the CR sources, which need further investigations.
3. Rates and spectral features of the de-excitation γ -ray line emission γ -ray lineemission The interactions of LECRs with the surrounding gas excite nu-clei that belong to LECRs and to the ambient medium. The al-most prompt de-excitation of these nuclei leads to the MeV γ -ray line emission. The main production of γ -ray lines proceedsthrough (1) energetic protons and α -particles as projectiles inter-acting with heavier elements of the ambient gas, that is, directreactions, and (2) interactions of heavy nuclei of LECRs withthe hydrogen and helium of the ambient gas, that is, inverse re-actions. Both channels were taken into account in the calcula-tions of the γ -ray emission. For simplicity, we only consideredthe most abundant stable isotope of elements, including C, N, O,Ne, Na, Mg, Al, Si, S, Ca, Ar, Fe, and Ni, and disregarded the isotopes with lower abundance, such as He, C , and Ne. Theabundance of these element species in the LECRs were extractedfrom Table 3 of Cummings et al. (2016). For the composition ofthe ambient medium, we used the recommended present-day so-lar abundances of Lodders (2010). These data are compiled inTab.1. Moreover, we assumed that the injected energy spectraof energetic α and other species have the same shape as that ofCR protons, F i ( r , E ) ∝ F p ( r , E ), where E is expressed as kineticenergy per nucleon, and we calculated their propagated spectrausing the same method as described in Sec.2. The energy loss-rate of heavy nuclei can be significantly di ff erent from that ofprotons. To account for these di ff erences, the energy loss-ratefor each nucleus species including ionization and nuclear inter-action were derived from formulae in Mannheim & Schlickeiser(1994) and cross sections in Sihver et al. (1993).To calculate emissivities of the de-excitation γ -ray line lines,we used the code TALYS (version 1.95) , which is a flexi-ble and user-friendly program aimed at a complete and accu-rate simulation of nuclear reactions (Koning et al. 2008). Thenewly updated version of TALYS provides adequate precisionof cross sections at projectile energies < N, Ne, and Si using the re-sults of Benhabiles-Mezhoud et al. (2011). Then, following theapproach of Murphy et al. (2009), we divided the γ -ray emis-sion into three categories: the explicit lines, the quasi-continuumconsisting of discrete lines, and the continuum. All the discretelines with the TALYS-calculated cross sections with >
10 mbarnwere selected as explicit lines. Those with smaller cross sectionswere treated as quasi-continuum. The continuum component pro-duced by the so-called direct, pre-equilibrium, and compoundreactions (see the TALYS user manual for a detailed descrip-tion) was considered as well. Because in the updated version ofTALYS the projectile energy relevant to reactions with involve-ment of α -particles is limited to 250 MeV / nuc, we extrapolatedthese line production cross sections to 1 GeV / nuc and assumedthat the continuum production cross section remains constantwhen the projectile energies exceed 250 MeV / nuc. The produc-tion cross sections of the specific lines listed in the compilationof Murphy et al. (2009) were extracted from Table 3 therein. Foreach explicit line, we derived the line profile according to themethod proposed in Ramaty et al. (1979). For the given compositions of LECRs and the ambient gas, thedetectability of the γ -ray lines, that is, their flux integrated overthe entire region occupied by LECRs, depends on several pa-rameters. First of all, the LECR injection rate of source Q ver-sus its distance d , which could be represented by the parame-ter Q / d , the density of the ambient gas n , the speed of prop-agation of LECRs, and their original spectral shape. With themethod described above, we first calculated the emissivity of the γ -ray line emission at di ff erent radial distances r to a hypothet-ical CR source that continuously injects CRs with a power-lawindex s = Q / d = erg s − kpc − into the surroundingmedium of n =
100 cm − . The results, as shown in Fig.5, show asignificant e ff ect of the propagation process on the emissivitiesof the γ -ray line emission. We then integrated the intensity ofseveral representative narrow lines along the line of sight at dif-ferent angular distances θ , assuming the distance of the source d is 1 kpc. As shown in Fig.6, the fluxes drop sharply with θ https://tendl.web.psi.ch/tendl_2019/talys.html Article number, page 3 of 8 & Aproofs: manuscript no. ms −3 −2 −1 E (GeV) −3 −1 d N / d E ( c m − s r − s − G e V − ) s=1.0s=2.0s=3.0s=4.0Voyager + AMS 10 −3 −2 −1 E (GeV) d N / d E ( c m − s r − s − G e V − ) χ=1.0χ=0.1χ=0.01Voyager + AMS Fig. 2: Calculated proton spectra under di ff erent assumptions. Left panel: Proton spectra at the radical distance r =
10 pc from thehypothetical CR source with various injection spectral indices, in which s = ff usion coe ffi cient parameter χ = .
0. Right panel: Proton spectra with injection spectral index s = . ff usion coe ffi cients (solid lines for χ = .
0, dashed lines for χ = .
1, and dotted lines for χ = .
01) at di ff erent radial distances, where r = Q / d = × erg s − kpc − and n = − are assumed, and the gray lines represents the fit of the CR proton intensity from Phan et al. (2018) based on themeasured fluxes of local CRs reported by Voyager1 (Cummings et al. 2016) and AMS-02 (Aguilar et al. 2015a). −1 r (pc) d N / d E ( c m − s r − s − G e V − ) χ=1.0χ=0.1χ=0.01 10 −1 r (pc) d N / d E ( c m − s r − s − G e V − ) E p =1MeVE p =10MeVE p =100MeVE p =1000MeV ∝1/r∝1/r ∝1/r∝1/r Fig. 3: Radial distribution of protons with certain kinetic energies. Left panel: Flux of 10 MeV protons as a function of radialdistance r under di ff erent assumptions of medium density (black lines for n = − , and red lines for n =
100 cm − ) and di ff usioncoe ffi cient (solid lines for χ = .
0, dashed lines for χ = .
1, dotted lines for χ = . ff erentkinetic energies E p as a function of radial distance r , assuming n = − , and χ =
1. For comparison, two radial profiles 1 / r (dashed gray line) and 1 / r (dotted gray line) are also shown. In both panels, we assume s = . Q / d = × erg s − kpc − .and become almost negligible at θ ∼ . ◦ , which correspondsto a radial distance r ∼
25 pc. Unfortunately, the angular reso-lution of MeV γ -ray detectors, including those planned for theforeseeable future, such as e-Astrogam (de Angelis et al. 2018)and AMEGO (McEnery et al. 2019), is quite limited, about 1 . ◦ , thus the angular distribution of these lines can be detected onlyfor very nearby objects, d ≪ γ -ray emission around the injection pointas a point-like source, and calculate the di ff erential flux of this γ -ray source by integrating the γ -ray emission within 25 pc fromthe injection site, F γ ( E γ ) = π d Z r π r I ( E γ , r )d r , (3)where I ( E γ , r ) is the γ -ray emissivity at the distance r . In the left panel of Fig. 7, we show the di ff erential fluxes of γ -rayscalculated for s = . Q / d = erg s − kpc − , n = − ,and χ =
1. The brightest lines are 0.847, 1.634, 4.44, and 6.13MeV lines resulting from the de-excitation of Fe, Ne, C,and O, respectively, from their first or second excited state toground state. The direct (narrow) and inverse (broad) compo-nents linked to the nuclei of LECRS and the ambient gas bothcontribute substantially to the total flux. The direct processescontribute to the narrow line structures, while the inverse pro-cesses are responsible for the broad lines and thus contributemostly to the continuum emissions. In the right panel of Fig. 7,we compare the fluxes of γ -ray emission integrated within 25 pcradial distance from the source for two di ff erent gas densities n = − and n =
100 cm − and di ff erent di ff usion coe ffi cientparameters ( χ = Article number, page 4 of 8ing Liu et al.: Nuclear de-excitation lines as a probe of low-energy cosmic rays −3 −2 −1 E (GeV) d N / d E ( c m − s r − s − G e V − ) n=1s=2.0 r=1pcr=10pc Fig. 4: Proton spectra at di ff erent radial distances, in which r = s = . n = − , and Q / d = × erg s − kpc − , the solid ( χ = .
0) and dotted lines( χ = .
01) are calculated for the di ff usion using Eq.(1), and thedash-dotted lines are calculated for advection using Eq.(2) for V = / s. −1 E (MeV) −25 −24 −23 −22 −21 E m i ss i v i t y ( M e V − c m − s − ) r=1pcr=5pcr=25pc Fig. 5: Calculated γ -ray emissivity at di ff erent radial distancesfrom the hypothetical CR source, in which r = Q / d = × erg s − kpc − , d = s = .
0, and n =
100 cm − .di ff usion coe ffi cient can enhance the flux of γ -ray line emission.The integrated fluxes of the narrow 4.44 MeV line emission, cal-culated for di ff erent combinations of n and χ , are presented inTable 2. The 4.44 MeV γ -ray line flux sensitivity of the pro-posed telescopes e-ASTROGAM (de Angelis et al. 2018) andAMEGO (McEnery et al. 2019) is ∼ − ph cm − s − for the ob-servation time T obs = n ≥
100 cm − and slowparticle di ff usion, the LECR sources can be revealed through γ -ray lines provided that the parameter Q / d is not significantlysmaller than 10 erg s − kpc − . In all figures above, the composi-tion of the ambient medium is fixed to the solar abundance. How-ever, in certain astronomical locations, the composition mightbe di ff erent, in particular, it might be enhanced by heavy ele-ments in metal-rich environments, such as the Galactic center(Benhabiles-Mezhoud et al. 2013), or in the young SNR Cas A(Summa et al. 2011). The higher abundance can dramatically en- −2 −1 θ (∘∘ −4 −3 −2 I n t e n s i t y ( c m − s r − s − ∘ r (pc∘ Fig. 6: Integrated flux of strong narrow lines at 4.44 MeV (solidline), 6.13 MeV (dotted line), 1.63 MeV (dashed line), and 0.847MeV (dash-dotted line), as a function of angular distance θ (orradial distance r ) from the hypothetical CR source. Q / d = × erg s − kpc − , d = s = .
0, and n =
100 cm − areassumed for the calculation.hance the γ -ray line fluxes and makes these sources prime targetsfor observations with next-generation MeV γ -ray detectors.So far, we did not include in calculations the γ -ray channellinked to pp interactions with the production and decay of π mesons. The relative contribution of this channel strongly de-pends on the proton spectrum, especially on the continuationof the proton spectrum beyond the kinematic threshold of π -meson production. Setting Q / d = × erg s − kpc − and n = − , in Fig.8 we show the di ff erential spectra of γ -radiation consisting of the nuclear de-excitation lines and the π -decay γ -rays integrated within the region of radius 25 pc aroundthe source, assuming that the initial proton spectrum has a simplepower-law distribution with index s = ff (the leftpanel) or with an exponential cuto ff at E cut =
100 MeV, 300 MeV,and 1 GeV (the right panel). The left panel of Fig.8 shows that π -decay γ -rays exceed the luminosity of nuclear lines. The rea-son is that the energy losses cause the spectrum of CRs below100 MeV to become very hard, thus the production rate of nu-clear lines is suppressed. On the other hand, the emissivity of π -decay γ -rays is dramatically suppressed when the cuto ff inthe spectrum of LECRs is close to the threshold of π -decay pro-duction around 280 MeV, as demonstrated in the right panel ofFig.8.It is also interesting to compare our results with thosein Benhabiles-Mezhoud et al. (2013), which were calculatedfor the inner Galaxy. The results in Benhabiles-Mezhoud et al.(2013) reveal a significantly sharper profile than our results. Thedi ff erences come mainly from the twice solar abundance used intheir calculation, and thus more contribution from the direct pro-cesses. Benhabiles-Mezhoud et al. (2013) moreover calculated adi ff use emission in a much larger region, in which the variationin the CR spectrum on a small scale may have only a minor ef-fect on the final results. The limited angular resolution of thecurrent and planned MeV instruments means that such di ff useemission may be a better target than point sources. On the otherhand, our calculations treated the spectral and density variationof CRs carefully and were aimed at the nearby CR sources. Article number, page 5 of 8 & Aproofs: manuscript no. ms −1 E (MeV) −9 −8 −7 d N / d E ( M e V − c m − s − ) .
847 1 .
63 4 .
44 6 . n=1,χ=1directinverse 10 −1 E (MeV) −7 −6 −5 d N / d E ( M e V − c m − s − ) n=1,χ=0.01n=100,χ=1n=100,χ=0.01 Fig. 7: Comparison of the integrated γ -ray di ff erential fluxes for di ff erent n (1 cm − or 100 cm − ) and χ (1.0 or 0.01). In the leftpanel, the solid line show the total γ -ray flux integrated within r =
25 pc from the hypothetical CR source, assuming χ = . n = − , and the dashed and dotted lines correspond to the contributions from the direct and inverse processes, respectively. Inthe right panel, the lines represent the total integrated γ -ray line emission under di ff erent assumptions of n and χ . In both panels, weassume Q / d = × erg s − kpc − , s = . −1 E (MeV) −10 −9 −8 −7 −6 −5 −4 d N / d E ( M e V − c m − s − ) .
847 1 .
63 4 .
44 6 . χ=1χ=0.1χ=0.01 10 −1 E (MeV) −14 −12 −10 −8 −6 d N / d E ( M e V − c m − s − ) .
847 1 .
63 4 .
44 6 . E cut =1GeVE cut =0.3GeVE cut =0.1GeV Fig. 8: Comparison of γ -ray fluxes resulting from de-excitation of nuclei (dotted lines) and π -decay process (dashed lines) integratedwithin 25 pc from the hypothetical CR source. In the left panel, we assume a proton spectrum F p ( E ) ∝ E − with various di ff usioncoe ffi cient parameters, in which χ = . χ = . F p ( E ) ∝ E − exp ( − E / E cut ) with various cuto ff energies, in which E cut = Q / d = erg s − kpc − and n = − are assumed in both panels.
4. Summary
Together with magnetic fields and turbulent gas motions, Galac-tic CRs play a dominant role in the energy balance of the inter-stellar medium. Although subrelativistic (suprathermal) particlessupply a substantial fraction of the CR pressure, the real contribu-tion of LECRs remains uncertain. Because of the slow propaga-tion and severe energy losses, the local LECRs make negligiblecontributions to the fluxes beyond 100 pc. For the same reason,LECRs are expected to be inhomogeneously distributed in theGalactic disk; subrelativistic protons and nuclei are expected tobe concentrated around their acceleration sites. Because all po-tential CR source populations (SNRs, stellar clusters, individualstars, etc.) are linked in one way or another to the star-formingregion, the e ff ective confinement of LECRs in these regions isexpected to produce feedback that stimulates the star formationthrough the ionization of the nearby molecular clouds. LECRs play a significant role also in the chemistry of the interstellarmedium. Thus an unbiased, observation based information aboutLECRs at the sites of their concentrations in the Milky Way iscrucial for understanding the fundamental processes linked tothe dynamics and chemistry of the interstellar medium, star for-mation, etc. The most direct channel of information is providedby nuclear de-excitation γ -ray lines resulting from the interac-tions of protons and nuclei of LECRs with the ambient gas.We explored the e ff ect of the initial spectra shape, energyloss, and di ff usion coe ffi cient on the spatial and energy distribu-tions of LECRs around the source that continuously injects accel-erated protons and nuclei into the surrounding medium. LECRs,lose much energy during propagation, especially at energies be-low 100 MeV / nuc. At large distances, depending on the di ff u-sion coe ffi cient, their radial profiles become steeper than 1 / r (see Fig.3), which is the typical radial distribution of particles athigher energies at which the energy losses can be neglected. We Article number, page 6 of 8ing Liu et al.: Nuclear de-excitation lines as a probe of low-energy cosmic rays
Table 1: Elemental compositionZ Element Local CR a Solar b . × − . × − . × − . × − . × − . × − . × − . × −
10 Ne 1 . × − . × −
11 Na 1 . × − . × −
12 Mg 2 . × − . × −
13 Al 3 . × − . × −
14 Si 1 . × − . × −
16 S 2 . × − . × −
18 Ar 4 . × − . × −
20 Ca 1 . × − . × −
26 Fe 1 . × − . × −
28 Ni 6 . × − . × − Notes. ( a ) The LECR abundance according to the Voyager 1 measurement (see Cummings et al. 2016, Table 3). ( b ) The recommended present-daysolar abundances extracted from the Table 6 of Lodders (2010)
Table 2: Integrated 4.44 MeV line flux under di ff erent assumptions of n and χ n χ Flux(cm − ) (photon cm − s − )1 1.0 5 . × − . × − . × −
100 1.0 1 . × −
100 0.1 3 . × −
100 0.01 5 . × − Notes.
The injection rate of protons Q / d = erg s − kpc − and spectral index s = . ∆ E is ∼
100 keV. Details is described in Sec.3.2. calculated that characteristics of the nuclear γ -ray line emissioninitiated by interactions of LECRs with the ambient gas using thecross sections gathered from experimental data and theoreticalmodeling with the code TALYS-1.95. We found that for the stan-dard di ff usion coe ffi cient characterizing the propagation of CRsin the interstellar medium, the γ -ray emission is mainly producedin regions around the source within ∼
25 pc. The slower di ff usionwith the parameter χ < γ -ray source more compactand brighter. The expected γ -ray fluxes are unfortunately wellbelow the sensitivity of current γ -ray detectors, however. Withthe arrival of the proposed γ -ray detectors that are dedicatedto low energies, such as e-ASTROGAM (de Angelis et al. 2018)and AEMGO (McEnery et al. 2019), the detection of nuclear γ -rays, in particular, the lines at 0.847, 1.63, 4.44, and 6.13 MeV ofnearby (within a few kpc) accelerators of LECRs would becomefeasible provided that the LECR accelerators are surrounded bydense ( ≥
100 cm − ) gaseous regions in which LECRs propagatesignificantly more slowly than in the interstellar medium, χ ≪ Acknowledgements.
Bing Liu thanks Jurgen Kiener for providing very helpfulinformation on the modification of TALYS structure files, and is supported bythe Fundamental Research Funds for the Central Universities. Ruizhi Yang issupported by the NSFC under grants 11421303 and the national youth thousandtalents program in China.
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