The Important Role of Cosmic-Ray Re-Acceleration
RReview
The Important Role of Cosmic-Ray Re-Acceleration
Martina Cardillo
Istituto Nazionale di Astrofisica-Istitituto di Astrofisica e Planetologia Spaziali, Via del Fosso del Cavaliere 100,00133 Roma, Italy; [email protected]; Tel.: +39-06-4993-4462Received: 1 March 2019; Accepted: 17 April 2019; Published: 24 April 2019 (cid:1)(cid:2)(cid:3)(cid:1)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8) (cid:1) (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)
Abstract:
In the last decades, the improvement of high energy instruments has enabled adeeper understanding of the Cosmic Ray origin issue. In particular, the γ -ray satellites AGILE(Astrorivelatore Gamma ad Immagini LEggero) and Fermi-LAT (Fermi-Large Area Telescope) havestrongly contributed to the confirmation of direct involvement of Supernova Remnants in CosmicRay energization. Despite several attempts to fit experimental data assuming the presence of freshlyaccelerated particles, the scientific community is now aware that the role of pre-existing Cosmic Rayre-acceleration cannot be neglected. In this work, we highlight the importance of pre-existing CosmicRay re-acceleration in the Galaxy showing its fundamental contribution in middle aged SupernovaRemnant shocks and in the forward shock of stellar winds. Keywords: cosmic-rays; re-acceleration; supernova remnants; stellar wind
1. Introduction
Cosmic Ray (CR) particles are mainly protons (90%) and nuclei with a spectrum that extends over15 orders of magnitude in energy ( E = [ ÷ ] eV). Such a large energy range can be explainedwith different kinds of sources, both galactic and extragalactic. CR origin is one of the most discussedtopics of high energy astrophysics, with γ -ray astronomy playing a critical role in this field of research.Indeed, neutral pions π , produced by CR proton-target proton interaction decay in two γ -rays withthe same spectral behavior of parent population but with lower energies and fluxes. Particle and γ -rayspectra revealed several tricky characteristics that questioned theoretical models and leave open veryimportant questions.The first issue is CR spectral composition at E ∼ × eV (the so called knee ), where thespectra steepens probably because of the transition from CR light component (hydrogen, helium andCNO) to CR heavy component (mainly Iron) ([1,2] for a review). However, in the last years, ARGO(Astrophysical Radiation with Ground-based Observatory) [3] and YAC1-TIBET Array (Yangbajing Airshower Core TIBET array) [4] measurements showed a steepening of the light component spectrum at650 TeV, well below the PeV knee detected by KASCADE-Grande (KArlsruhe Shower Core and ArrayDEtector Grande) [5] and all previous instruments. If, on the one hand, ARGO results could solve thecomplex Pevatron problem of CR Galactic component, on the other hand, it makes the understandingof transition energy location harder [1,6].Another important issue was introduced by PAMELA (Payload for Antimatter Matter Explorationand Light-nuclei Astrophysics) and AMS-2 (Alpha Magnetic Spectrometer) satellite measurements.Their data revealed a hardening of proton and helium spectra above a rigidity of 200 GV, and a rising inthe positron fraction in an energy range from a few GeV to 100 GeV [7–12]. Several theoretical modelswere developed to explain these spectral features, taking into account different possible explanations:differential diffusion and turbulence [13–17] or possible contribution from local sources [18,19] forspectral hardening, and dark matter [20] or Pulsar Wind Nebula (PWN) [21] for positron fraction rising([1,2] and reference therein). However, a final explanation is still missing. Galaxies , a r X i v : . [ a s t r o - ph . H E ] A p r alaxies , , 49 2 of 16 From the γ -ray point of view, AGILE [22] and Fermi-LAT [23] satellites, together with largeCherenkov telescopes HESS (High Energy Stereoscopic System) [24] MAGIC (Major AtmosphericGamma-ray Imaging Cherenkov Telescope) [25] and VERITAS (Very Energetic Radiation ImagingTelescope Array System) [26], have collected a large amount of data from young ( t age < t age > γ -ray spectra showed some peculiarities, such as energy spectral index steeperthan 2, deviating from linear and Non Linear Diffusive Shock Acceleration (DSA and NLDSA) theorypredictions [1,2]. In spite of the several models developed to explain these features, which introduced“ad hoc” broken power-law distribution, low-energy cut-off (e.g., [27,29]), or turbulence damping [31],we are still looking for a more consistent interpretation of experimental data.Until a few years ago, contribution from re-acceleration of pre-existing CRs was totally neglectedbecause it was considered sub-dominant with respect to a possible particle acceleration at the source.However, some recent works showed how stochastic re-acceleration in Galactic turbulence [32]could effectively contribute to the overall CR spectrum [33,34] or explain γ -ray emission fromFermi-Bubbles [35]. Moreover, theoretical models [36–40] and very recent numerical simulations [41]proved that the Diffusive Shock Re-Acceleration (DSRA) at the source, like in an SNR shock, can give adominant contribution to CR particle and γ -ray spectra. Here we point out the importance that DSRAcould have to understand the observed gamma -ray spectra. Indeed, DSRA of pre-existing CRs canwell explain the γ -ray emission from two different galactic sources, the SNR W44 [37] and the OB-star κ -Ori stellar wind [42].This brief review is focused only on the Galactic component of the CR spectrum. In Section 2, wesummarize the most important features of stochastic and diffusive particle re-acceleration. In Section 3we describe an analytical model used to model experimental data from γ -ray sources. In Section 4we briefly show results obtained in the case of SNR W44 and κ -Ori star wind. Then we write ourconclusions in Section 5.
2. The Re-Acceleration Contribution
CR particles fill our Galaxy almost isotropically. During their propagation, they interact withan interstellar magnetic field and gain energy through scattering on random magnetic perturbationswith scale of order of their Larmor radius. This process is a second order Fermi acceleration [43],also called stochastic re-acceleration, and could explain some CR particle spectrum features, such asspectral hardening or electron-positron fraction rising (see Section 2.2).However, pre-existing CRs could be re-accelerated not only during their propagation but also incorrespondence of local sources (e.g., SNR shocks). Indeed, CR re-acceleration at the source, as is thecase for the pure acceleration, is a first order Fermi energization mechanism, which is more efficientthan stochastic re-acceleration. This could explain the overall particle CR spectrum features wherestochastic re-acceleration fails (see Section 2.3). Moreover, in recent years, analysis of γ -ray spectrafrom some middle-aged SNRs pointed out some peculiar features not easily explained by typical DSAmodels but in agreement with re-acceleration at the source. Because of solar modulation, the first direct measurement of a low-energy CR very Local InterStellar (LIS) spectrum was in 2013 when the Voyager 1 spacecraft entered in the heliopause, wheremodulation effects are negligible [44,45]. New data collected by Voyager I strongly contributes to themost important results obtained in a re-acceleration context. alaxies , , 49 3 of 16 A parametrization of CR-sea in our Galaxy was done in [44,46,47], for protons, helium andelectrons, separately [37]. The spectrum of protons and He nuclei can be described as: J LIS , n = A h (cid:32) E a β p (cid:33) (cid:32) E d + k d + k d (cid:33) − b , (1)where E is particle kinetic energy per nucleon in units of [ GeV / n ] , and J LIS , n is in units of [ particles / m / s / sr / ( GeV / n )] . Parameter values in Equation (1) are: a = b = d = k = A h = J LIS , p ; and a = b = d = k = A h = J LIS , He .The LIS electron flux, instead, can be described as J LIS , e = (cid:18) E β e (cid:19) (cid:18) E + (cid:19) − + (cid:16) (cid:104) − ( E ) − E − (cid:105)(cid:17) (2)in units of [ particles / m / s / sr / MeV ] [44]. Here E is the electron kinetic energy expressed in units ofGeV, whereas the last term fits the PAMELA (and AMS-02) data in the [ − ] GeV range.Data from Voyager I, together with data at higher energies ( E ≥ CRs propagate in our Galaxy through scattering by resonant magnetic perturbations, movingwith Alfvén velocities V A = B √ ( πρ ISM ) , which is strictly correlated with the static average magneticfield, B , and the medium density, ρ ISM . During propagation, CRs gain energy through stochasticre-acceleration [43,48]. This physical process was introduced in [32] to explain low-energy secondaryto primary ratio decrement with energy. They found that re-acceleration due to perturbations with aKolmogorov spectrum (scaling with k − where k is the wave number) could provide the behaviorshown by experimental data. About ten years later, in [49] the authors confirmed that result, provinghow diffusive re-acceleration model was in good agreement with data without introducing furtherescape mechanisms.In the last years, in [48] and [33] the authors gave a qualitative estimation of transferred powerfrom inter-stellar turbulence damping to CRs. Assuming a power-law momentum distribution witha spectral index α = γ -ray emission from Fermi-Bubbles [52,53] as shownin the work of [35]. This extended γ -ray emission above and below the Galactic Center implies a largenumber of high energy particles at about 10 kpc from Galactic disk. Numerical simulations pointed outthat electrons from SNR shocks penetrating the bubbles cannot provide the electron density requiredto explain the observed γ -ray flux and the microwave spectrum detected by the Planck satellite [54]. alaxies , , 49 4 of 16 Hence, the authors developed a model that considers both stochastic re-acceleration and convectivetransport inside the bubble due to the effect of Galactic wind [55–57]. The combined effect of thesetwo mechanisms is more efficient (about one order of magnitude) than the acceleration and canexplain both γ -ray and microwave data. In [58] the authors confirmed this scenario, revealing thatmulti-wavelength spectral and morphological behavior of Fermi Bubbles could be explained by ICand synchrotron emission from electrons re-accelerated by Rayleigh-Taylor-like turbulence generatedin a supersonic outward flowing shell.Based on these results, we conclude that stochastic re-acceleration is fundamental in theunderstanding of CR behavior and the same is valid for diffusive shock re-acceleration, as we will seein the next section. After the first detection of γ -ray emission below 200 MeV from a SNR, SNR W44 [27–29], followedby similar detections in other middle aged SNRs, like IC443 [27] and W51c [59], the whole CRcommunity was excited by the chance to have an unambiguous evidence of CR acceleration in a SNRshock. Indeed, direct evidence of CR acceleration in a source is possible in the γ -ray band wherewe can distinguish the electronic component to the CR hadronic one. From one hand, a detectionof 100 TeV photons would imply hadronic origin of the emission because the electronic InverseCompton (IC) is sub-dominant at that energy due to Klein-Nishina cross section suppression. On theother hand, a detection of the “pion bump” signature at about 70 MeV, due to neutral pion rest mass( ∼
135 MeV), could also allow us to distinguish hadronic contribution from the leptonic Bremsstrahlungone. However, all γ -ray detected middle-aged SNRs not only have a cut-off at very low-energy butalso have γ -ray spectra with features difficult to understand considering linear and non-linear DSAtheory. They revealed a very steep high energy index, α ≥
3, that can be fitted only by adding an“ad hoc” low-energy cut-off at a parent power-law distribution [29] or using a broken power-lawdistribution [27,28]. Moreover, middle-aged SNRs have a slow shock velocity ( v s ∼ km/s) thatcould hardly explain efficient CR acceleration.The possibility of pre-existing CR re-acceleration contribution at the W44 shock was introducedby [60] in order to explain the steep spectrum detected by Fermi-LAT [61]. This model takes intoaccount the possible formation of a thin compressed adiabatic shell due to Molecular Cloud (MC)/SNRinteraction that enhances γ -ray emissivity after re-acceleration (the “crushed-cloud” model from [62]).In [38], the authors developed an analogous model analyzing even its temporal evolution. Both worksfound similar results: re-accelerated pre-existing CRs can explain the SNR W44 spectral behavior.However, there was an open issue: in both models, “ad hoc” spectral features are necessary to obtain agood fit of experimental data.In 2016, Voyager 1 data outside the heliosphere allowed to consider the very LIS spectrumof pre-existing CRs. This spectrum was taken into account in [37] where the authors developed are-acceleration model with a thin compressed shell but also introducing some important aspects:helium nuclei from Voyager data; radio emission only in the region of AGILE detected γ -ray emissionand not in the whole radio extension of the remnant; a simple PL distribution with high-energy cut-off.This model is briefly described in Section 3 and the results obtained for W44 in Section 4.1.The re-acceleration process could explain γ -ray emission not only from other SNRs similar toW44, as IC443, W51c and W49b, but also from different kinds of objects. At the end of December 2018,the AGILE satellite has confirmed a Fermi-LAT detected residual emission [63] from a region aroundthe OB star κ -Ori [64], in correspondence of a CO-detected star forming region. A re-accelerationmodel applied at the star wind forward shock (FS) could explain this emission as described forward inSection 4.2 [42].DSRA was then considered in [36] to explain some features of the overall CR spectrum, because ofthe very stringent conditions required by stochastic re-acceleration [34]. In that work, the authorinvestigates the hardening, detected by PAMELA and AMS02 [7,11,12,65], of protons, helium nuclei alaxies , , 49 5 of 16 and other heavier elements, validating his model with new collected data on B/C ratio [51]. Heshowed that re-acceleration models can explain primary (Carbon and Oxygen) spectra, regardlessof diffusion coefficient changes and without further amount of grammage, as provided by othermodels [66]. However, the author highlights that re-acceleration cannot explain the enhancementof positron fraction [1]. This conclusion is important because points out that re-acceleration processmust be considered in all CR models but it cannot replace the main contribution from freshlyaccelerated particles.Finally, recent numerical simulations developed by [41] prove that pre-existing CRs withsufficiently high energy can be reflected at the shock. This mechanism generates turbulence throughstreaming instability (both resonant [67] and non-resonant [68]), affecting shock inclination. In thisway, even quasi-perpendicular shocks (with an angle ≥ ◦ ) can efficiently accelerate thermal particles,despite of the results obtained in simulations without re-acceleration [69]. Moreover, in determined andphysically plausible conditions, CR seed current is constant, regardless of shock Mach number, shockinclination and CR velocities. A quantitative estimation of re-acceleration effect in SNRs provides anefficiency of a few percent, that can be higher in presence of high density target, in perfect agreementwith the W44-like cases.In the following, we will focus on the two different cases of γ -ray emission seen above, introducingsome fundamental aspects of the model of re-acceleration at the source used to fit data.
3. A DSRA Model
Particle re-acceleration at the shock of a source is a Fermi first order acceleration process ofpre-existing CRs, without a “real” thermal injection [70]. The critical condition is that, in the upstreaminfinity, particle distribution equals the Galactic one, f ( x = − ∞ , p ) = f ∞ ( p ) . Solving CR transportequation with this requirement [37,71], we obtain reaccelerated particle spectral distribution: f ( p ) = α (cid:18) pp m (cid:19) − α (cid:90) pp m dp (cid:48) p (cid:48) (cid:18) p (cid:48) p m (cid:19) α f ∞ ( p (cid:48) ) (3)with α = r sh r sh − , where r sh = u d u u is the compression ratio at the shock and u d and u u are downstream andupstream velocities, respectively. p m is the minimum momentum in Galactic CR spectrum. f in f ty ( p ) isthe Galactic CR spectrum obtained from the fluxes described in Section 2.1, using the usual expression4 π p f ∞ , i ( p ) dp = π v ( p ) J LIS , i ( E ) dE .The main effects of re-acceleration can be summarized as follows: • enhancement of particle momentum up to a maximum value dependent on time scales of thesystem (SNR age, acceleration time, energy losses); • hardening of parent spectra steeper than p − α Freshly accelerated particles could be present even if re-acceleration is the dominant process.They can be described as a simple power-law particle distribution, according to the DSA model: f i ( p ) = k i (cid:32) pp inj (cid:33) − α (4)where the index i indicates protons or electrons and p inj is the injection momentum correspondingto an injection energy E inj ∼ E sh , with E sh = m p v sh [70]. The normalization value for protons, k p ,is computed from balance between CR pressure, P CR , and ram pressure of the shock, ξ CR ρ v sh [37]. ρ is upstream density in the assumption of a totally ionized medium at the shock, and ξ CR is CRacceleration efficiency. Normalization of electron distribution, k e , is then fixed by assuming the mostconservative CR electron/proton ratio, k ep ≈ − . Normalization strongly depends on target medium alaxies , , 49 6 of 16 density and on shock velocity. Consequently, in middle aged SNRs like W44, with a slow shock velocity( ∼
100 km/s), the chance to have freshly accelerated particles is very low. Acceleration can enhancenormalization of total γ -ray spectrum and, if dominant, it modifies its shape. Since most of SNRs detected in γ -ray band are interacting with a MC, the effect of a SNR/MCinteraction on CR spectrum has to be considered. In 1982, the authors of [62] introduced the “crushedcloud” model: if the pre-shock medium density is sufficiently high (as in a MC), a thin compressedradiative shell forms behind the shock, ionizing all its propagation region [37]. Shell compression canbe stopped by magnetic or thermal pressure and we can obtain an estimation for compressed density, n m , from their balance with shock ram pressure: n µ H v sh = (cid:40) B m π Magnetic pressure; n m K B T Thermal Pressurewhere B m = (cid:113) (cid:16) n m n (cid:17) B is compressed magnetic field, µ H is the mass per hydrogen nucleus, B = b (cid:112) n / cm − µ G is unperturbed magnetic field upstream of the shock, where b depends onAlfvén velocity V a and can vary in the range [0.3–3] in MCs [72,73]. K B is the Boltzmann constant and T is shell temperature. According to the approach described in [74], compressed shell temperature isstable around 10 K, because cooling efficiency drops abruptly for higher temperatures.Computation of compressed density is critical because strictly correlated with spectral changesdue to adiabatic compression. Indeed, due to this further compression, the final spectrum will be: f (cid:48) ( p ) = f ( s − p ) , (5)where s is the compression factor is equal to s ≡ (cid:18) n m n d (cid:19) = (cid:18) n m r sh n (cid:19) (6)where n d is density immediately downstream of the shock, n m / n d is compression ratio due to radiativecooling and r sh = n d / n is the shock compression ratio due to the shock that we have already seen.The whole scenario can be summarized as follows: • Galactic Cosmic Rays are re-accelerated by first order Fermi energization mechanism in theinteraction region between shock and its environment. Their spectrum, if steeper than the slope α due to shock compression ratio, will become hard as α . Initial density of the upstream medium, n , is compressed of a factor r sh ; • in the right conditions, freshly accelerated particles can be injected at the shock through the firstorder Fermi mechanism; • with sufficiently high density, a thin adiabatic shell forms behind the shock. There, energizedparticles undergo to a further compression before escape, with a consequent enhancement of theirenergy. The density is enhanced by a further factor s . Finally we have to consider energy losses. Protons lose energy through pp-interaction [75] andionization, at high and low energies, respectively. Electrons are affected by synchrotron, InverseCompton and Bremsstrahlung losses [76] at the highest energies, and by ionization at the lowestenergies. The kinetic equation becomes: ∂ N i ( E , t ) ∂ t = ∂∂ E [ b ( E ) N i ( E , t )] + Q i ( E ) , (7) alaxies , , 49 7 of 16 where b ( E ) = − dEdt takes into account all losses and Q i ( E ) is particle injection rate per unit energyinterval, derived from energized and compressed spectrum (see [37] for details).The fundamental condition for CR energization is that acceleration time, t acc , is lower than thelowest value between the MC/SNR interaction time, t int , and the loss time, t loss . The accelerationtime can be expressed as t acc ≈ D ( p ) / v sh [1,2], where D ( E ) = r L c (cid:16) L c r L (cid:17) k T − [77] is the diffusioncoefficient, r L is particle Larmor radius, L v is perturbation correlation length and k T is perturbationspectral index [37]. From the condition t acc < min ( t int , t loss ) , CR distribution have a cut-off at amaximum momentum equal to p max ∝ ( B ) ( v sh ) − δ ( t min ) − δ ( L c ) − δ − δ . (8)where magnetic power spectrum index, δ = k T −
1, depends on turbulence model considered [37]. γ -Ray Emission Detected γ -ray emission is produced by CR protons and electrons energized and compressed,able to overcome energy losses. Protons contribute through pp-interactions, producing neutrals andcharged pions that, in turn, produce γ -rays and secondary electrons. The produced fluxes can bedescribed following the formalism of [75]: Φ s ( E s ) = × (cid:82) ∞ E min f π ( E π ) √ E π − ( m π c ) dE π Low energies. v n (cid:82) σ inel ( E s / x ) f ( E s / x ) F s ( x , E s / x ) dxx High energies;where s refers to secondary species considered, either electrons or γ -rays, x = E s / E n , where E n is thenucleon energy, F s is an analytical function describing spectral distribution of secondaries, v is nucleonvelocity and f ( E s / x ) = f ( E n ) is our final particle distribution, that considers both protons and heliumcontributions. Inelastic cross section, σ inel , depends on particle energy and on its ratio with energythreshold for π production. At lower energies, we used δ -approximation, where the factor 2 accountsfor generation of two photons from every neutral pion and both e + and e − in the case of charged pions. E min is the pion minimum energy necessary to produce a secondary particle with energy E s , and f π isthe production rate of pions with energy E π (see [37,75] for details).Now we summarize how this model could explain γ -ray and radio emission from the SNR W44and κ -Ori stellar wind.
4. Two Important Cases: A Supernova Remnants and an OB Star Wind
For W44, DSRA was introduced [37] because this SNR is too old to explain an efficient CRacceleration. Indeed, acceleration model implies “ad hoc” features, as low-energy cut-off or brokenpower-law particle distribution, in disagreement with theoretical models [27–29]. Instead, in the caseof the κ -Ori star the γ -ray excess detected from both AGILE [64] and Fermi-LAT [63] satellites cannotbe explained neither by diffuse emission nor by contribution of “dark gas” (gas not traced by HI orCO molecules, [78]) [63,64]. This excess is correlated with a CO-detected star forming region andit could be emission due to CR energization in the interaction region between star wind FS and theCO shell. In the very slow FS of star wind ( v sh ∼
10 km/s), DSRA is probably more efficient thanacceleration [42].
The SNR W44 (G34.7-0.4) is a middle-aged SNR with a distance d ∼ γ -ray [27–29,61]wavelengths. As stressed by presence of OH masers, its shock is interacting with a high densityCO-detected MC on the SE side, in correspondence of a peak in both the energny bands (see Figure 1). alaxies , , 49 8 of 16 Figure 1.
The SNR W44. Left: AGILE γ -ray intensity map between 400 MeV–1 GeV of the W44 region.Green contours and red circle indicate the 324 MHz radio detection from [79] and the OH masersfrom [80], respectively. Right: CO data from the NANTEN2 observatory. Magenta and white contoursindicate the AGILE gamma-ray emission above 400 MeV and the VLA emission, respectively. Figurefrom [28]. γ -ray emission in correspondence with high density target and of enhanced and flat radio emissioncould be a sign of CR acceleration at the shock. However, only after AGILE detection of the SNR W44at energies below 200 MeV (see Section 2.3) energized particles were confirmed in correspondence ofthe SNR/MC interaction region. One of the first acceleration models proposed a power-law particledistribution with a low-energy cut-off and a very steep high energy index ( α =
3) [29]. Some yearslater, the authors of [27,28], instead, suggested a broken power-law distribution, with an energy indexslightly steeper than α = α = v sh ∼ γ -ray spectra of W44 using “ad hoc” spectral featuresor neglected leptonic emission and energy losses [38,39,60], new Voyager I data raised the opportunityto develop a more realistic re-acceleration model (see Section 2.1). In [37], these data were usedto compute, analytically and numerically, γ -ray emission from the SNR W44 assuming a DSRAwith crushed adiabatic shell formation, according to the model explained in Section 3. Assuming aKolmogorov-like turbulence ( k T = p max ∼ GeV / c (cid:18) B µ G (cid:19) (cid:18) v sh km / s (cid:19) (cid:18) min ( t int , t loss ) years (cid:19) (cid:18) L c pc (cid:19) − , (9)This formula clearly shows that shock velocity is the most critical parameter and, consequently,explains the low-energy value of the cut-off. In this model a filling factor ξ taking into account theSNR evolution was used, V = πξ R SN v sh t int .The best model fitting both radio and γ -ray spectra (shown in Figure 2) considers re-accelerationas the main contributor, with a smaller contribution from acceleration ( ξ CR ∼ − ) necessary to reducethe value of the filling factor compared to the one obtained using a model with only re-acceleration( ξ ∼ alaxies , , 49 9 of 16 Figure 2.
Radio and γ -ray data from W44 fitted with the best re-acceleration model. Left: VLA(red) and Planck (blue) radio data from the whole remnant and VLA radio data from the AGILEemitting region (green). Primary, secondary, and total synchrotron radio emission from the modelare indicated from cyan dashed line, magenta dot-dashed and black line, respectively. Right: AGILE(green) and Fermi-LAT (red) γ -ray points plotted with γ -ray emission from pion decay (blue dottedline), from bremsstrahlung of primary (cyan dashed line), and secondary (magenta dot-dashed line)electrons, and total emission (black line). Figure from [37]. This model, however, has some critical aspects. Such a low maximum energy does not constrainmomentum spectral index α , that can vary in a range [ ÷ ] without significant changes in themain conclusions. This implies that real spectral index could be steeper than 4, as in all the otherSNRs detected in the γ -ray band, and we do not understand the reason yet. Moreover, this model wasdeveloped assuming a totally ionized medium at the shock. If this assumption was not correct, therecould be ion-neutral damping inhibiting re-acceleration [77,81]. For this reason, in [37] the authorsshowed a model that considers only crushed cloud adiabatic compression without any first orderFermi energization. This model can still explain W44 γ -ray emission but with a worst fit.Nevertheless, the SNR W44 remains the first case in which a DSRA model account for a sourcemulti-wavelength spectrum in agreement with theory and with physically coherent parameters. κ -Ori Wind The Orion region is very interesting because it is the nearest site of star formation ( d ∼ κ -Ori star. It could havetriggered star formation in the shell through its wind.COS-B [84] and EGRET [85] satellites did the first γ -ray surveys of this region; however, onlyrecent observations from Fermi-LAT [63] and AGILE [64] revealed an interesting feature. Data fromthe two satellites characterized γ -ray diffuse emission from the Orion region, taking into accountBremsstrahlung and p-p emission from atomic and molecular Hydrogen, inverse Compton fromInterStellar Radiation Field (ISRF) and CMB, and single source contribution. The γ -ray residual mapshows an excess at the South-West side of κ -Ori, in correspondence of the high-density shell detectedby XMM-Newton (see Figure 3). alaxies , , 49 10 of 16 Figure 3.
The Orion region around κ -Ori OB star. Left: γ -ray excess detected by AGILE. Right panel:CO map from [86] with contour levels from γ -ray data in black. The figure is from [64]. A first idea to explain this excess was to add “dark gas” [78] contribution to diffusion model.This was computed through column density derived from reddening maps of IRAS and COBE andfrom Planck 353 GHz maps. The residuals of the subtraction of CO-traced MC contributions areused as “dark gas” templates [64]. However, both Fermi-LAT and AGILE analysis pointed out that“dark gas” has only a little effect on the γ -ray excess flux. Another explanation could be that apossible non-linearity in CO- H relation affects the constance of the X CO conversion factor. Thisparameter is fundamental in γ -ray diffuse models because it allows to estimate H density from CO detection [63,64]. The recent AGILE analysis of this excess revealed its relation with the high densityshell of [83] and found a spectrum with a hard index that could explain its origin in the context of CRenergization [42,64].Stellar wind shocks are considered good locations for CR acceleration [87–90] but only theTermination Shocks (TS) of star winds were taken into account so far, because of their high velocity(10 –10 km/s). In the model described in [42], instead, CR energization takes place in correspondenceof the slow FS (order of 10 km/s) of κ -Ori star, assuming that the γ -ray excess could be due topre-existing CR re-acceleration.The authors used the model described in Section 3, fixing some important parameters thanks toinformation from other wavelengths, such as distance, d ∼ t age ∼ × years,of κ -Ori and FS velocity. The average density in the region of the shell was estimated through theconversion factor X CO computed in [64] and it is equal to n ∼
30 cm − . Lack of radio and TeVdetection allowed us to constraint other parameters such as magnetic field and perturbation correlationlength [42]. We used the conservative Kolmogorov spectrum also in this case, providing δ = k T − = .In this way, we obtain an explicit expression for maximum momentum: p max ∼ GeV / c (cid:18) B µ G (cid:19) (cid:18) v sh km / s (cid:19) (cid:18) t min years (cid:19) (cid:18) L c pc (cid:19) − , (10)where normalization values are of the same order assumed (or estimated) in our best model. Lookingat the numerical value of this equation, it is clear that we expect a cut-off at low energies, excludingthe possibility of TeV emission from this region.DSRA can explain the AGILE detected γ -ray emission, regardless of presence of an adiabaticcompressed shell, because energy losses compensate for the enhancement due to higher densities(Figure 4, left). However, still considering a possible presence of neutrals at the shock, the authorshave taken into account the chance to have CR energization due to the only adiabatic compression andfound that it could be sufficient to explain the AGILE emission as well (Figure 4, right). alaxies , , 49 11 of 16 Figure 4.
Left: AGILE (red) γ -ray points plotted with the different contributions estimated inour re-acceleration model: γ -ray emission from pion decay (blue line), primary and secondaryBremsstrahlung (cyan dashed line and magenta dashed line, respectively), and total emission (blackline). Right: the same data and model curves are shown in the left panel but assuming that onlyadiabatic compression is present. Figures from [42] Unfortunately, because of the cut-off at such a low-energy, as in the SNR W44, there are nostrong constraints for momentum spectral index that can vary in a range [5 – 3.5]. Nevertheless, someimportant issues can be fixed: the model does not provide for radio or TeV emission, in agreementwith absence of detections in those energy bands, and freshly accelerated particle emission can beexcluded as the dominant contribution.
5. Conclusions
CR origin is one of the most important issues of high energy astrophysics of the last decades.Looking for CR sources, we gained a better understanding of physical mechanisms correlated tomagnetic turbulence and perturbations, and we could deeply analyze several objects, such as SNRs,extracting their peculiar spectral features.Thanks to the great improvement of high energy instrument performances, we collected a largeamount of data that have questioned theoretical models, pointing out the complexity of CR behavior.In this brief review we summarized the significant progress made introducing CR re-acceleration toexplain CR particle and γ -ray data.We verified that stochastic and diffusive shock re-acceleration can contribute in a non-negligibleway to the explanation of Boron over Carbon ratio, CR spectral hardening and anti-proton excessdetected by PAMELA and AMS in particle spectrum. In particular, we showed that DSRA couldbe the dominant energization process in middle-aged SNRs like W44, where the high age makesparticle acceleration inefficient. DSRA and adiabatic compression due to thin dense shell formationcan explain both AGILE and Fermi-LAT spectra according to theoretical models, without introductionof any “ad hoc” feature. Moreover, DSRA could be efficient in other kinds of objects, such as stellarwind. We described the case of κ -Ori stellar wind in the Orion region, where a γ -ray excess detectedby Fermi-LAT and AGILE could be explained by CR re-acceleration at the interaction region with aCO-detected star formation shell. Whereas freshly accelerated particles at TS of a stellar wind werealready predicted, this is the first time that high energy energized particle emission is detected at theslow FS of a star.The important contribution of re-acceleration mechanism does not mean that it is the dominantprocess in all sources analyzed so far or that it could explain every particular feature of CR spectrum.Fresh particle acceleration remains the main CR production process, even if we do not have directevidence yet. However, we want to highlight that, before introducing new physical mechanisms andchallenging our theoretical models, we have to consider all known physical processes in order tounderstand CR origin, as is the case for any other tricky scientific issue. alaxies , , 49 12 of 16 Funding:
This research received no external funding.
Conflicts of Interest:
The author declares no conflict of interest.
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