Gamma-rays from molecular clouds illuminated by accumulated diffusive protons. II: interacting supernova remnants
aa r X i v : . [ a s t r o - ph . H E ] N ov Mon. Not. R. Astron. Soc. , 1–9 (2008) Printed 14 August 2018 (MN L A TEX style file v2.2) γ -rays from molecular clouds illuminated by accumulateddiffusive protons. II: interacting supernova remnants Hui Li and Yang Chen , ⋆ Department of Astronomy, Nanjing University, Nanjing 210093, P. R. China Key Laboratory of Modern Astronomy and Astrophysics, Nanjing University, Ministry of Education, Nanjing 210093, China
ABSTRACT
Recent observations reveal that spectral breaks at ∼ GeV are commonly present inGalactic γ -ray supernova remnants (SNRs) interacting with molecular clouds and thatmost of them have a spectral ( E dF/dE ) “platform” extended from the break to lowerenergies. In paper I (Li & Chen 2010), we developed an accumulative diffusion modelby considering an accumulation of the diffusive protons escaping from the shock frontthroughout the history of the SNR expansion. In this paper, we improve the modelby incorporating finite-volume of MCs, demonstrate the model dependence on particlediffusion parameters and cloud size, and apply it to nine interacting SNRs (W28, W41,W44, W49B, W51C, Cygnus Loop, IC443, CTB 37A, and G349.7+0.2). This refinedmodel naturally explains the GeV spectral breaks and, especially, the “platform”s,together with available TeV data. We find that the index of the diffusion coefficient δ is in the range of 0.5-0.7, similar to the galactic averaged value, and the diffusioncoefficient for cosmic rays around the SNRs is essentially two orders of magnitude lowerthan the Galactic average ( χ ∼ Key words:
ISM: supernova remnants
Supernova remnants (SNRs) are commonly believed to beone of the most important acceleration sites for the cosmicrays (CRs) below the “knee” in our Galaxy. Diffusive shockacceleration (DSA) is the prevailing acceleration mechanism,which can naturally gain a power-law population of relativis-tic electrons/protons (Blandford & Eichler 1987). Althoughmulti-wavelength analysis has been intensively made for theemission of SNRs, it is still in hot debate whether the γ -rays from them are of hadronic or leptonic origin. Recently, γ -ray telescopes of new generation, such as Fermi -LAT andH.E.S.S., provided more and more clues that SNRs inter-acting with molecular clouds (MCs) may emit γ -rays arisenfrom π decay via proton-proton collision (e.g., Abdo et al.2009, 2010a,b,c,d; Aharonian et al. 2008a,b).Interacting SNRs, distinguished by several kinds of evi-dence such as OH masers, molecular line broadening, etc.(seeJiang et al. 2009 and references therein), represent a promis-ing class of γ -ray sources. It is seen that some of the SNRs ex-hibit a spectral break at ∼ GeV, such as W28, W44, W51C,IC443, etc. Most of them have a spectral ( E dF/dE ) “plat-form” extended from the break to low energies. By coin- ⋆ E-mail: [email protected] cidence, the γ -ray emitting SNRs which harbor OH masers(Hewitt et al. 2009) all have GeV breaks. The spectral breakcan be explained in the hadronic scenario either by differentacceleration effects in the SNR-MC system, such as Alfv´enwave evanescence in the weakly ionized dense gas (Malkov,Diamond & Sagdeev 2010), reacceleration model for crushedclouds (Uchiyama et al. 2010), and two-step accelerationmodel in the reflected shocks (Inoue, Yamazaki & Inutsuka2010), time-dependent two-zone model (Tang et al. 2011), orby diffusion effects of CRs escaping from SNR shock (Li &Chen 2010, hereafter Paper I; Ohira, Murase, & Yamazaki2011).In Paper I, we developed an accumulative diffusionmodel by considering the accumulation of the diffusive pro-tons escaping from the shock front throughout the history ofthe SNR expansion; the power-law distribution is assumedfor the escaping protons and the spectrum of the diffusiveprotons at any point near the SNR is obtained. This modelis used to explain the GeV break and GeV/TeV flux dis-crepancy for the four sources around SNR W28. Comparingwith the point source injection (Aharonian & Atoyan 1996;Gabici et al. 2009), our model is more physical when ap-plied to the finite-size accelerator, such as SNRs, and small c (cid:13) H. Li et al. distance between the accelerator and MC is allowed. Al-most meantime, Ohira et al. (2011) have also developed adiffusion model by considering finite-size MCs interacted bythe CRs escaping from the SNRs which are imbedded inMCs and used the model to fit the γ -ray spectra of fourSNRs (W28, W44, W51C, and IC443). In their model, thetime evolution of maximum particle energy is considered andmono-momentum is assumed for the escaping particles andthe spectral shape of the diffusive protons is analyticallyderived.In this paper, we improve the accumulative diffusionmodel by incorporating finite-volume of MCs (Sec. 2) andapply it to a series of interacting SNRs to reproduce theGeV-TeV spectra as well as the “platform” below the breakat around GeV (Sec. 3). In Paper I, the distribution function, at an arbitrary point(at radius R c ), of the energetic protons that escape from thespherical shock front (at radius R s ) throughout the historyof the SNR expansion is given by f cum ( E p , R c , t age ) = R t age R π R π f ( E p , R ( R c , t i , θ, φ ) , t dif ) R ( t i ) sin θ dθ dφ dt i , (1)where t age is the age of the SNR, t i the time at which theproton escapes from SNR surface, t dif the diffusion time afterescape ( t dif = t age − t i ), and f ( E p , R ( R c , t i , θ, φ ) , t dif ) thedistribution function, at point C, of the energetic protonsthat escape from unit area at an arbitrary source point Son the spherical shock front surface (see Paper I for relevantnotations). The diffusion coefficient is assumed to be in theform of D ( E p ) = 10 χ ( E p / δ cm s − , where χ is thecorrection factor of slow diffusion around the SNR (Fujitaet al. 2009) and δ is the energy dependent index of diffusioncoefficient. The distance between the SNR and MC does notneed to be larger than the size of SNR, namely condition R c ≫ R s is not required as opposed to the point sourceinjection models.Following the treatment of the dynamical evolutionof SNR in Paper I, we use the Sedov-Taylor law R s =(2 . E SNR t /ρ ) / for the adiabatic phase, where ρ =1 . m H n is the density of the interstellar (intercloud)medium, and R s = (147 ǫE SNR R t / πρ ) / for the radia-tive phase, where R t is the transition radius from the Sedovphase to the radiative phase, E SNR is the supernova explo-sion energy, and ǫ is a factor equal to 0.24 (Blinnikov et al.1982; see also Lozinskaya 1992).In Paper I, we assume that all the MC mass is concen-trated in a point. Here we take the finite-volume of cloud intoaccount and in order to describe the problem with spheri-cal coordinates, we approximate it as a truncated cone which Actually, our model in Paper I has been tested for the casethat the SNR has a very small radius (e.g., for a very high ambi-ent density), which can be approximated as a point-like source,and reproduced the results of the classical point-like continuousinjection case using the same model parameters. subtends solid angle Ω at the SNR center and has a thickness∆ R c . By averaging the distribution function f cum (Eq. (1))over the finite-volume, we obtain the mean distribution ofthe energetic protons in the MC at t age as a function of E p F ave ( E p , t age ) = Z R c +∆ R c / R c − ∆ R c / r dr Z t age Z π Z π f ( E p , R ( r, t i , θ, φ ) , t dif ) R sin θ dθ dφ dt i (cid:30) Z R c +∆ R c / R c − ∆ R c / r dr. (2)In particular, for Ω = 4 π , we have the case that the SNR isenclosed by a molecular shell (as also assumed in Ohira etal. 2011).In the calculation of the γ -rays from the nearby MC (ofmass M c ) due to p-p interaction, we use the analytic photonemissivity dN γ /dE γ developed by Kelner et al. (2006; alsosee Paper I). The gained photon energy is generally 10% ofthe energetic proton energy (e.g. Katz & Waxman 2008). We now explore the model parameters and show how thespectra of escaping protons depends on the parameters. Inthe model described above, for a certain SNR, the modelparameters are of two sorts: particle diffusion ( p , δ , χ ) andMCs ( R c , ∆ R ).Figure 1 shows the dependence of the spectral shapeof the energetic protons in the finite cloud volume on eachparameter with other parameters fixed. Here we assume amiddle-aged SNR with R SNR = 20pc, t = 27000 yr, n =1 cm − , and E SNR = 10 erg and a proton illuminated MCat R c = 25pc.The spectral dependence on the MC thickness ∆ R c ispresented in Figure 1 a , where we adopt χ = 0 . p = 2 . δ = 0 .
5. We plot three curves for different thicknesses:∆ R c →
0, ∆ R c = 8 pc, and ∆ R c = 10 pc. In the ∆ R c → R c = 10 pc case representsthe situation that the MC is in contact with the SNR shocksurface ( R c = R s + ∆ R c /
2; such case is called ‘contact’case hereafter), in which the proton spectrum does not showa low-energy cutoff/turn-over since some of the low-energyprotons can diffuse into the cloud.The spectral dependence on the escaping protons energyindex p is given in Figure 1 b , with parameters χ = 0 . R = 15pc, and δ = 0 . p are used forcomparison: p = 1 . p = 2is the typical index of Fermi-type accelerated particles, and p = 2 . R c = 10 pc), it can be seenthat the slopes (both below and above the break energy) c (cid:13) , 1–9 eV spectra break for interacting SNRs of the particle distribution increase with p . For the ‘non-contact’ case ( R c > R s +∆ R c /
2, e.g. ∆ R c = 8 pc), the slopesabove the break are very similar to those of the ‘contact’case, and the low energy cut-off becomes more prominentwith the increase of p .Figure 1 c shows the spectral dependence on the diffu-sion coefficient index δ (with χ = 0 .
01, ∆ R = 15pc, and p = 2 . δ is usually adopted in therange of 0.3–0.7 (Berezinskii et al. (1990)). Here we usethree values of δ : δ =0.3, very close to the Kolmogorov typediffusion index (0.33); δ =0.5, for the Kraichnan type dif-fusion; and δ =0.7. This parameter strongly influence thespectral pattern. The slope of the proton spectrum abovethe break conforms the relation α ∼ p + δ for the contin-uous point source injection case (Aharonian 2004). For the‘contact’ case (∆ R c = 10 pc), there exhibits a “platform”pattern extended to low energy, while for the ‘non-contact’case (∆ R c = 8 pc), the low energy cut-off becomes moresignificant with the increase of δ .As shown in Figure 1 d , different correction factor ofdiffusion coefficient χ gives different flux and width of the“platform”. With the increase of the χ value, the number ofthe low energy protons increases and the number of the highenergy protons decreases, namely, the particle distributiongets softened. This is because faster diffusing high energyprotons diffuse into farther distance and the low energy onesbecome dominant at the concerned distance. Meanwhile, thewidth of “platform” becomes narrower and the slope of theproton spectra above the break energy keeps unchanged. Extended GeV emission associated with interacting SNRshas recently been revealed by a series of Fermi-LAT obser-vations (Abdo et al. 2009, 2010a,b,c,d; Castro & Slane 2010),some of which are also spatially resolved by the H.E.S.S. TeVobservations. These SNRs form a special interesting class,which may be beneficial to unveil the enigma of the originof the Galactic CRs. One of the most conspicuous features ofsuch a class is the commonly present, often gentle, spectralbreak at around 1-10GeV, which is difficult to be reproducedby leptons via inverse Compton emission (e.g. Abdo et al.2010a). In addition, the TeV spectra are mostly steep, withthe photon indices sometimes as high as ∼ .
0, which is alsohard to be explained by the primary accelerated protons,but can be done by the proton diffusion scenario (e.g. Aha-ronian & Atoyan 1996; Torres et al. 2008; paper I; Ohira etal. 2011). Here we apply our improved accumulative diffu-sion model to the nine SNRs currently available of the class(W28, W41, W44, W49B, W51C, Cygnus Loop, IC443, CTB37A, and G349.7+0.2) and reproduce the GeV-TeV spectralpatterns as aforesaid.The basic parameters of each SNR studied here arelisted in Table 1 with E SNR = 10 erg and η = 10% as-sumed. Since they are all interacting SNRs, we only considerthe MC which is in touch with the shock surface (i.e., the‘contact’ case, although in some cases not all the γ -rays iscoming from a contact MC). Thus we adopt the value of thelower-limit of the integration of Eq. (2) just the same as thevalue of the current shock radius, i.e., R c − ∆ R c / R s .In the γ -ray spectral fit, the parameters are adjusted in the following way. Given a certain cloud mass (chieflyadopted from observation), the γ -ray flux can be roughlydetermined by changing the diffusion correction factor χ (e.g., for point-like injection case, F γ ∝ χ − / (Gabici etal. 2010)). The broadness of the platform is fitted by adjust-ing the cloud thickness ∆ R c for the fixed χ and the slope ofthe “platform” and the slope above the break together withthe TeV data can in turn be obtained with proper values of p and δ . W28 is one of the prototype thermal composite (or mixed-morphology) SNRs, characterized by shell-like radio emis-sion and centre-brightened thermal X-rays. It is an evolvedSNR in the radiative phase, with an age estimate rangingfrom 35 to 150 kyr (Kaspi et al. 1993). In γ -rays the strongestTeV source is located at the northeastern edge of the rem-nant and positionally coincident with the well studied MCwith which the remnant shock interacts (Aharonian et al.2008a). In this γ -ray emitting region, there are some of theOH masers points detected in W28 (Frail et al. 1994). Re-cently, Fermi
LAT observation found that the GeV source1FGL J1801.3-2322c coincides with the TeV source and thusdemonstrates a broken power-law for the γ -ray spectrumwith a break at ∼ ∼ .
09 belowthe break and ∼ .
74 above the break (Abdo et al. 2010c).Three molecular clumps (Aharonian et al. 2008a) locatedoutside the southern boundary of the remnant have differ-ent GeV and TeV brightness. In Paper I, we have explainedthe γ -ray spectra of the four sources via hadronic processof the diffusive protons, assuming different distances for thefour sources. Here we also fit the spectrum of the north-eastern source, taking the cloud volume into account. Theresult is very similar to that in Paper I. Unlike the sources inother SNRs studied in this paper, the “platform” below thebreak is unapparent (Figure 2(a)), entailing a large value of χ and a small cloud thickness ∆ R c . The evaluation of χ alsosensitively depends on the cloud mass. HESS J1834-087 used to be representative of a class of“dark” γ -ray sources, which was not thought to be firmly co-incident with any detected sources (Aharonian et al. 2006).New H.E.S.S. analysis has revealed that the TeV emissioncan be divided into two components: the compact and ex-tended ones. While the TeV compact component compatiblewith pulsar candidate does not seem to have GeV coun-terparts, the extended one, with index 2.7, may spatiallymatch the GeV emission detected by Fermi -LAT from theSNR W41 region (M´ehault et al. 2011), making this SNRa promising candidate for generating the observed extended γ -rays. The γ -ray spectrum in Fermi regime can be fittedby a single power-law with index 2.1, which causes a breakbetween GeV and TeV.This field is also observed in radio with VLA, CO, andX-rays with XMM-Newton. The high-resolution CO obser-vation reveals its association with a giant molecular cloudwith mass > M ⊙ (Tian et al. 2007). The strong ab-sorption in X-rays together with the high the γ -ray to X-ray luminosity ratio ( ∼
11) indicates that the γ -rays may c (cid:13) , 1–9 H. Li et al. p R=0pc R=8pc R=10pc E dF / d E ( e V c m - ) Proton Energy (GeV) (a) p=1.8 p=2.0 p=2.2 E dF / d E ( e V c m - ) Proton Energy (GeV) (b) =0.3 =0.5 =0.7 p E dF / d E ( e V c m - ) Proton Energy (GeV) (c) p E dF / d E ( e V c m - ) Proton Energy (GeV) (d)
Figure 1.
Spectra of the diffusive protons in the MCs for R SNR = 20pc, t = 27000 yr, n = 1 cm − , E SNR = 10 erg, and R c = 25pc.In panel (a), ∆ R c = 0pc (blue), 8pc (black), and 10pc (red) are adopted, respectively. In panels (b)-(d), the black curves represent thecase for ∆ R c = 8pc and the red curves for ∆ R c = 10pc. Table 1.
Dynamical evolution parameters for interacting SNRsSNR age(kyr) distance(kpc) angular size R SNR (pc) ReferenceG6.4-0.1(W28) 42 1.9 48 ′ ′ ′ ′ ′ ′ ′ ′ ′ be of hadronic origin from energetic protons colliding withshocked GMC (Tian et al. 2007; Yamazaki et al. 2006).The GeV “platform” of this source is the broadest ( ∼ − χ . − ) andlarge thickness of cloud (∆ R c comparable to R s ). With theparameters used (see Table 2), the well-determined TeVslope is also reproduced. W44 is also a paradigm of “mixed-morphology” SNR, withsemi-symmetric shape in radio with ∼ ′ in size (Rho &Petre(1998)). It is considered to interact with a dense molec-ular cloud, with evidences including OH maser (Hoffman etal. 2005), molecular line broadening, CO line ratio (Castel-letti et al. 2007), etc.The γ -ray spectral energy distribution of W44 repre-sents a broken power-law, which breaks at 1.9GeV, with c (cid:13) , 1–9 eV spectra break for interacting SNRs Table 2.
Fitted parameters for the γ -rays of interacting SNRsSNR p δ χ ∆ R(pc) M cl (10 M ⊙ )G6.4-0.1(W28) 2.2 0.5 0.05 0.5 5 a G23.3-0.3(W41) 2.1 0.6 0.004 17 7 b G34.7-0.4(W44) 2.4 0.7 0.02 7 3 c G43.3-0.2(W49B) 2.4 0.6 0.03 3 1 d G49.2-0.7(W51C) 2.2 0.5 0.04 7 1 e G74.0-8.5(Cygnus Loop) 2.2 0.7 0.04 8 0 . f G189.1+3.0(IC443) 2.3 0.65 0.01 7 0 . g G348.5+0.1(CTB 37A) 2.1 0.6 0.02 5 5 . h G349.7+0.2 2.1 0.7 0.02 3 1 . i References.–(a) Aharonian et al. 2008a (b) Seta et al. 1998; (c) Seta et al. 2004; (d) Assumed; (e) Koo & Moon 1997 a,b; (f) Assumed(g) Cornett et al. 1977; (h) Reynoso & Mangum 2000; (i) Reynoso & Mangum 2001 photon indices 2.06 at low energy and 3.02 at high energy.Most of the γ -ray emission is inferred to arise from the SNRother than from the unresolved pulsar based on the resem-blance between the γ -ray and infrared ring morphologies(Abdo et al. 2010a). Most recently, AGILE observation hasalso been reported with the γ -ray spectral down to 50 MeV.(Giuliani et al. 2011)Figure 2(c) shows the fitting results of W44 using pa-rameters listed in Table 2. Our fitting not only well repro-duce the GeV “platform” spanned from 0.3 to 1.9 GeV, butalso the spectrum with energy as low as 50 MeV, whichis a robust advantage for hadronic origin of the γ -rays. Itis noteworthy that the photon index above the break en-ergy (3.02) is the largest among the 8 studied SNRs; weadopt the upper limit (0.7) of the usual range for δ so as for p (=2.4) not to deviate too much from the common values(1.8-2.2). Although the VHE spectrum of W44 is the verysteep, we predict that the flux around TeV energy is slightlyhigher than the H.E.S.S. detection limit and much higherthan the expected sensitivity of new generation TeV tele-scope Cherenkov Telescope Array (CTA) (de Cea del Pozoet al. 2009). W49B is a “mixed-morphology” SNR at a young age. Near-infrared shocked H emission suggests that W49B is an inter-acting SNR (Keohane et al. 2007). Particularly high abun-dances of hot Fe and Ni, and relatively metal-rich core andjet regions are interpreted as evidence that W49B is origi-nated inside a wind-blown bubble inside a dense molecularcloud (Keohane et al. 2007).Recently, Fermi
LAT reported a GeV source spatiallycoincident with W49B (Abdo et al. 2010d). The spectrum,again, exhibits a broken power-law shape with break energy ∼ . σ . More interestingly, the best-fit spatialposition of the LAT source which seems coincident with thebrightest part of the Spitzer
IRAC 5.8 µ m image stronglysupports the scenario that the GeV emission is linked withthe shocked gas. Recently, the H.E.S.S. collaboration hasreported its detection in TeV and the photon spectrumis smoothly connected with GeV data points (Brun et al.2010).Due to the lack of definite value of the molecular mass around this SNR, we assume M cl ∼ M ⊙ for fitting the γ -ray spectrum. The spectral slope below the break energy( < . ∼ .
2) and, consequently, alarge value of p (= 2 .
4) is inferred.
W51C is also a member of “mixed-morphology” type ofSNRs. A partial shell ∼ ′ in diameter with a breakout fea-ture in northern part appears in the radio continuum (Moon& Koo 1994). A shock-MC interaction was shown by the ob-servations of the shocked atomic and molecular gases (Koo& Moon 1997 a,b).In the γ -rays, the H.E.S.S. collaboration has detectedan extended VHE source coincident with W51C (Fiasson etal. 2009), and the Milagro observation reported a possibleexcess in this direction (Abdo et al. 2009). Recently, Fermi
LAT detects the flux in this field and shows that the GeVspectrum has a “platform” below the break energy ∼ γ -rays arise from the acceleration region.Considering the protons diffusion into the adjacent MC,we perfectly reproduce the GeV-TeV spectrum with typicalparameters (e.g., p = 2 . , δ = 0 .
5) as shown in Figure 2(e).
The Cygnus Loop is one of the most famous and well-studiedmiddle-aged SNRs. The γ -ray emission mapped by Fermi-LAT is along the SNR limb and appears to be broken intofour parts, three of which are essentially in correspondencewith H α bright patches (Katagiri et al. 2011). Actually, therehave been some evidence of the presence of dense gas alongthe SNR boundary. In the west, CO emission in −
25– +30km s − interval seems to be adjacent to the SNR (Dame2001, see Katagiri et al. 2011) and two CO emission clumpsat ∼ +9 . − (with a mass ∼ M ⊙ ) seems to be wellin contact with the optical filament (Scoville et al. 1977).Shock excited near-IR H line emission associated with theSNR is detected from the northeastern boundary (Grahamet al. 1991a,b). Also, according to the X-ray studies, dense c (cid:13) , 1–9 H. Li et al. wall of cavity is suggested to be along the eastern edge (Lev-enson et al. 1997; Levenson, Graham & Snowden 1999) andshock-cloud interaction is thought to be taking place there(e.g., Miyata & Tsunemi 2001; Zhou et al. 2010). Such amolecular-rich environment may act as a reasonable site forthe hadronic origin of γ -ray emission from shock acceleratedCRs, which is pointed out by Katagiri et al. (2011). Fermi
LAT observation in the energy band 0.2–100 GeVshows a spectral break in the range 2–3 GeV. The γ -rayluminosity is ∼ × erg s − , which is lower than thoseof other GeV-emitting SNRs. The γ -ray spectrum can bereasonably fitted by our model.The fitting result is shownin Figure 2(f) with parameters listed in Table 2. To specify∆ R c , we adopt the inner and outer radii 0 . ′ and 1 . ′ of the γ -ray ring-like structure (Katagiri et al. 2011). IC 443 is one of the most thoroughly studied interactingSNRs, with rich evidence including the OH masers from thecentral and southeast regions (Hewitt et al. 2006), CO lineratio (Seta et al. 1998), molecular line broadening (Dickmanet al. 1992), near-infrared shocked H emission (Rosado etal. 2007), etc.In γ -rays, there are several sources coincident with IC443 as observed by EGRET (Hartman et al. 1999), AGILE(Tavani et al. 2010), and Fermi (Abdo et al. 2010b) in GeVand MAGIC (Albert et al. 2007) and VERITAS (Acciariet al. 2009) in TeV. The spectrum can be represented by abroken power law with slopes of 1.93 and 2.56 and with abreak at 3.25GeV and show very broad “platform” belowthe break (Figure 2(f)).The multi-band photon spectra, with only the EGRETdata then available in GeV band, was explained by using atime-dependent model for non-thermal particles emitting inthe acceleration region (Zhang & Fang 2008). Torres et al.used the point source diffusion model assuming two clouds(with volumes ignored) in the vicinity of IC443 to explainthe GeV-TeV connection (Torres et al. 2010).As shown in Figure 2(f), the γ -ray spectrum of IC443is fitted assuming one cloud with geometric volume. Thebroad GeV “platform” is reproduced with a low diffusioncoefficient ( χ ∼ − ) and a large thickness of cloud re-quired. SNR CTB 37A has a partial shell with a extended breakoutto the south (Kassim et al. 1991). The 1720 MHz OH masers(Frail et al. 1996) and morphologically correspondent COemission (Reynoso & Mangum 2000) demonstrate that thisSNR is interacting with MCs.In high energy γ -rays , H.E.S.S. has detected TeV emis-sion in the field of CTB 37A. For the absence of X-ray syn-chrotron emission, it is unlikely that the leptonic scenariocould explain these VHE emission and a hadronic originwould be favorable (Aharonian et al. 2008b). Recently, anunresolved source lies within the eastern shell of CTB 37Awas detected by Fermi
LAT, and the spectrum in
Fermi regime, too, shows a “platform” below 4 . G349.7+0.2 is one of the radio and X-ray brightest SNRs inthe Galaxy, with an blowout morphology (Slane et al. 2002).It has been shown to be an interacting SNR, with numerousevidences including the OH masers (Frail et al. 1996), COline ratio of different transitions, molecular line broadening(Dubner et al. 2004), near-infrared(IR) shocked H emission(Reach et al. 2006), etc.The Fermi
LAT observation shows a bright γ -ray sourcein its field with a significance from the evaluation of the teststatistic ∼ σ . The spectrum exhibits a broken power lawwith break energy ∼ In this paper, the accumulative diffusion model for CRs es-caping from SNR shock (Paper I) is refined by consideringthe finite-volume clouds in the vicinity of SNRs. The vari-ation of the proton spectra with different model parame-ters are also shown for exploring the parameter space. Thisrefined model is applied to nine Galactic SNRs which arethought to be interacting with the ambient dense material,and their GeV spectral breaks/“platform”s, together withavailable TeV data, are naturally fitted.For the four SNRs (W51C, W28, W44 and IC443),Ohira et al. (2011) obtain the momentum breaks of protonspectra and successfully explain the γ -ray spectral shapes.In our model, in addition to fitting the spectral shapes, thereal differential fluxes in γ -rays are also calculated, with thecloud masses considered. For all nine SNRs, the parameter δ , which gives the energy dependence of the diffusion coeffi-cient, is used in an interval from 0.5 to 0.7, which is in thecommonly favored range 0.3-0.7. The difference of the spec-tral fit parameters between our model and Ohira et al.’s(2011) ( δ = 0 . − .
62) may be primarily caused by twofactors. The first factor is the different assumption of escap-ing spectrum of protons: in their model, the time evolutionof maximum energy and the delta-function momentum ofthe escaping protons are assumed, and in our model, typi-cal power-law distribution for escaping protons is used (e.g.,Aharonian & Atoyan 1996; Torres et al. 2008). The secondfactor is the relative positions between the shock and the γ -ray emitting MC: in their calculation, the MC is placedon the wall of stellar wind bubble separated from the shock(namely, the ‘non-contact’ case), while in our calculation,the ‘contact’ case is considered.For fitting the GeV-TeV spectra of these interactingSNRs, the diffusion coefficients (see Table 2) are requiredto be much smaller ( χ ∼ − ) than the averaged Galac-tic value ∼ χ have been noticed in observation byseveral authors (e.g., Fujita et al. 2009; Giuliani et al. 2010;Paper I; Gabici et al. 2010; Torres et al. 2011) when apply-ing the proton diffusion to the γ -ray sources in the vicinity c (cid:13) , 1–9 eV spectra break for interacting SNRs -1 -1 Fermi HESS E dF / d E ( e V c m - s - ) Photon Energy (GeV) (a) W28 -1 -1 Fermi HESS E dF / d E ( e V c m - s - ) Photon Energy (GeV) (b) W41 -1 -2 -1 Fermi AGILE E dF / d E ( e V c m - s - ) Photon Energy (GeV) (c) W44 -1 Fermi HESS E dF / d E ( e V c m - s - ) Photon Energy (GeV) (d) W49B -1 -1 Fermi HESS MAGIC E dF / d E ( e V c m - s - ) Photon Energy (GeV) (e) W51C -1 -2 -1 Fermi (f) Cygnus Loop E dF / d E ( e V c m - s - ) Photon Energy (GeV) -1 -1 Fermi MAGIC VERITAS E dF / d E ( e V c m - s - ) Photon Energy (GeV) (g) IC443 -1 -2 -1 Fermi HESS E dF / d E ( e V c m - s - ) Photon Energy (GeV) (h) CTB 37A -1 -2 -1 Fermi E dF / d E ( e V c m - s - ) Photon Energy (GeV) (i) G349.7+0.2
Figure 2. γ -ray spectral data of the eight interacting SNRs and the model spectra. The black square and red dot show the data pointsobserved by Fermi and H.E.S.S., respectively. The sensitivity curves for MAGIC (green), H.E.S.S. (red), and CTA (black) are also shownin (c), (f) and (i). Panels from (a) to (h) represent the spectra fit of SNRs W28, W41, W44, W49B, W51C, Cygnus Loop, IC443, CTB37A, and G349.7+0.2, respectively. (See text in Sec. 3) of SNRs. Theoretically, this phenomenon is also studied byMonte-Carlo simulation, in which the CR streaming insta-bility can generate Alfv´en waves. The waves strongly scat-ter the particles and make the particle diffusion in the ISMaround the SNR remarkably slow, and the diffusion coef-ficient is therefore strongly suppressed (Fujita et al. 2010;Fujita et al. 2011). This kind of suppression is significant ifthe ambient ISM is well ionized for the cosmic rays aroundthe SNRs, because the neutral damping of Alfv´en waves isnot effective.For small χ , the typical diffusion velocity for certainparticle energy may be smaller than the shock velocity, andthe low energy cosmic rays will be continuously overrunby the SNR and reaccelerated. When considering particleacceleration, one needs a small Bohm diffusion coefficient( D bohm ) to ensure particles to be proximate to the shock andrepeatly cross it efficiently. The reason why particles escapeis that their diffusion coefficient in the ISM ( D esc ) is muchlarger than the one near the shock, namely D esc ≫ D Bohm .In our paper, even if the diffusion coefficient is about twoorders of magnitude smaller than the Galactic average, thiscondition is satisfied well. Even if some of the escaping par-ticles will be overrun by the shock, these particles only fill amuch smaller volume near the shock surface than the volume of the particles diffusion region. Therefore, the probabilityof reacceleration process is quite small.Our accumulative diffusion model proves successful inexplaining the γ -rays from the nine interacting SNRs, whichis again indicative of the contribution of the protons escapingfrom SNR shocks to the diffusive CRs. This model showsits advantage in treating the hadronic emission which arisesfrom the clouds near the SNR shocks. As a matter of fact, ifthe distance between the SNR and MC is considerably largethan the SNR size, our result will be similar to the point-likeinjection case. Acknowledgments
We thank the anonymous referee for valuable comments andStefano Gabici for the helpful advice on diffusion coefficient.Y.C. acknowledges support from NSFC grants 10725312 andthe 973 Program grant 2009CB824800.
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