TeV cosmic ray nuclei acceleration in shell-type supernova remnants with hard γ-ray spectra
DDraft version February 9, 2021
Typeset using L A TEX default style in AASTeX63
TeV cosmic ray nuclei acceleration in shell-type supernova remnants with hard γ -ray spectra Houdun Zeng , Yuliang Xin, Shuinai Zhang, and Siming Liu Key Laboratory of Dark Matter and Space Astronomy, Purple Mountain Observatory, Chinese Academy of Sciences Nanjing 210034,People’s Republic of China School of Physical Science and Technology, Southwest Jiaotong University, Chengdu 610031, People’s Republic of China
ABSTRACTThe emission mechanism for hard γ -ray spectra from supernova remnants (SNRs) is still a matterof debate. Recent multi-wavelength observations of TeV source HESS J1912+101 show that it isassociated with an SNR with an age of ∼
100 kyrs, making it unlikely produce the TeV γ -ray emissionvia leptonic processes. We analyzed Fermi observations of it and found an extended source with ahard spectrum. HESS J1912+101 may represent a peculiar stage of SNR evolution that dominatesthe acceleration of TeV cosmic rays. By fitting the multi-wavelength spectra of 13 SNRs with hardGeV γ -ray spectra with simple emission models with a density ratio of GeV electrons to protons of ∼ − , we obtain reasonable mean densities and magnetic fields with a total energy of ∼ ergs forrelativistic ions in each SNR. Among these sources, only two of them, namely SN 1006 and RCW 86,favor a leptonic origin for the γ -ray emission. The magnetic field energy is found to be comparable tothat of the accelerated relativistic ions and their ratio has a tendency of increase with the age of SNRs.These results suggest that TeV cosmic rays mainly originate from SNRs with hard γ -ray spectra. Keywords:
Galactic cosmic rays (567); Gamma-ray sources (633); Non-thermal radiation sources(1119); Gamma-ray astronomy (628); Supernova remnants (1667) INTRODUCTIONAlthough it is generally accepted that soft γ -ray spectra of supernova remnants interacting with molecular clouds(SNRs) result from decay of π produced via inelastic collisions of high-energy ions with nuclei in the background dueto evolution of SNR shocks in a high-density environment (Abdo et al. 2010; Giuliani et al. 2011; Zeng et al. 2019),the nature of hard γ -ray spectra has been a subject of extensive investigations (Yuan et al. 2012; Gabici & Aharonian2014; Zhang & Chen 2016; H. E. S. S. Collaboration et al. 2018a; Celli et al. 2019). In the leptonic scenario for the γ -ray emission, the model parameters are well constrained and appear to be consistent with expectation of diffusiveshock particle acceleration mechanism (Zhang & Liu 2019a). Hadronic models require stronger magnetic fields andless efficient electron acceleration (Butt et al. 2008). These results have profound implications on the origin of cosmicrays (CRs), especially those with energies lower than the CR spectral knee energy of ∼ γ -ray spectra (Butt et al. 2008). One ofthe challenges facing hadronic models is that ion spectra need to cut off at tens of TeVs to account for the observed γ -ray spectral cutoffs, suggesting that SNRs are not PeVatrons. Recent CR proton spectral measurement by theDAMPE shows that there appears to be a spectral hump at tens of TeVs (DAMPE Collaboration et al. 2019), whichhas been attributed to a nearby SNR, such as Geminga (Qiao et al. 2019), implying indeed that shocks of SNRs can Corresponding author: Siming [email protected], [email protected] a r X i v : . [ a s t r o - ph . H E ] F e b Zeng et al. only accelerate protons up to a few tens of TeV (Lagage & Cesarsky 1983; Bell et al. 2013). Observations of youngSNR Cas A and γ -Cygni SNR also imply a high-energy cutoff of the ion distribution in the TeV energy range (Zhang& Liu 2019b; Abeysekara et al. 2020; MAGIC Collaboration et al. 2020).HESS J1912+101 was first discovered in 2008 by the H.E.S.S. collaboration with a shell structure (Aharonian et al.2008). However its radio counterpart had not been identified until very recently with polarization measurement (Reich& Sun 2019), implying presence of large scale strong magnetic field. Interestingly, observations of molecular clouds inthe direction of HESS J1912+101 suggest that it is associated with an SNR with an age of 70 −
200 kilo-years (kyrs)(Su et al. 2017), which is consistent with the characteristic age of 170 kyrs for pulsar J1913+1011 inside it (Morriset al. 2002). SNR G279.0+1.1 has similar properties with γ -ray emission up to 0.5 TeV detected recently (Araya 2020).A recent population study of SNRs shows that higher energy particles are preferentially accelerated in younger SNRswith higher shock speeds (Zeng et al. 2019). In the absence of continuous TeV particle acceleration in old SNRs, it isvery challenging to produce the TeV emission from HESS J1912+101 via leptonic processes.In section 2, we show challenges to reproduce γ -ray emission from HESS J1912+101 and SNR G279.0+1.1 vialeptonic processes. Section 3 is dedicated to the study of G296.5+10.0 for its hard γ -ray spectrum similar to HESSJ1912+101. In section 4 we fit the multi-wavelength spectra of another 10 SNRs with hard γ -ray spectra in thehadronic and leptonic scenarios and discuss the model implications. Our conclusions are drawn in section 6. HESS J1912+101Recent radio observations of HESS J1912+101 revealed strongly polarized emission at 6 cm from the northeast halfof the shell (Reich & Sun 2019). Due to strong radio emission from the surrounding, a shell structure cannot beidentified in the total intensity maps. The total polarized flux density at 6 cm is about 0.5 ± ± µ G for the interstellar medium.Via CO and HI observations, Su et al. (2017) showed that HESS J1912+101 is likely associated with an old SNRwith an age of 0 . − . × years at a distance of ∼ γ -ray emission.Recently Zeng et al. (2019) studied a sample of γ -ray SNRs and found that in general high-energy particles in thesesources have a broken power-law distribution with the break energy and the low-energy spectral index decreasing withthe increase of SNR age. These results imply that higher energy particles are mostly accelerated in younger SNRswith relatively higher shock speeds. The acceleration of TeV particles quenches for SNR with an age greater than 10kyrs. This challenges a leptonic origin for the TeV emission from HESS J1912+101.Figure 1 shows the energy loss timescale of electrons due to the synchrotron and inverse Compton (IC) processes.It can be seen that for a typical value of the interstellar magnetic field, the maximum energy of electrons in HESSJ1912+101 should be about 10 TeV. The γ -ray produced via IC by such electrons should cut off below 10 TeV. The leftpanel of Figure 2 shows the evolution of electron distribution under the influence of energy loss due to synchrotron andIC processes for an injected broken power-law spectrum with a maximum energy of 1 PeV at the beginning. Comparedto the age of this SNR, TeV and higher energy particles are assumed to be accelerated instantaneously in the earlystage of the SNR evolution (Bell et al. 2013).Recent analyses of Fermi data by Zhang et al. (2020) uncovered a compact GeV source with a soft spectrum withinthe shell of HESS J1912+101, and there appears to be extended diffuse emission. Here we re-analyzed the Fermi -LATdata around HESS J1912+101. In the region of HESS J1912+101, there are four 4FGL sources (4FGL J1913.3+1019,4FGL J1914.7+1012, 4FGL J1911.7+1014, 4FGL J1912.7+0957). Among them, 4FGL J1913.3+1019 is associatedwith PSR J1913+1011 (Morris et al. 2002; Smith et al. 2019; Zhang et al. 2020) and others are unidentified sourceswith soft spectra. We removed these three unidentified 4FGL sources from the model file and treated them as partsof the diffuse emission around HESS J1912+101. Using the data above 1 GeV with the
Fermipy package version0.19.0 (Wood et al. 2017), we tested several spatial templates for HESS J1912+101, including an uniform disk, a 2DGaussian model, and the HESS image. The uniform disk model (R.A., decl.=288 . ◦ ± . ◦ , 10 . ◦ ± . ◦ with σ = 0 . ◦ ± . ◦ ) is favored, while the 2D Gaussian template (R.A., decl.=288 . ◦ ± . ◦ , 10 . ◦ ± . ◦ with σ = 0 . ◦ ± . ◦ ) gives an equally good representations of the data. We produced a TS map above 1 GeV aftersubtracting the γ -ray emission from 4FGL J1913.3+1019, which is shown in the left panel of Figure 3. eV cosmic ray acceleration Electron [GeV] T c oo li n g [ y e a r ] U IR =1.0 ev/cm , T IR = 30 K T syn with B=3.0 G T syn with B=5.0 G T IC with CMB using Thomson cross section T ICNK with CMB using full K-N cross section T ICNK with IR using full K-N cross sectionThe age region of HESS J1912+101
Figure 1.
Electron cooling time due to synchrotron and inverse Compton emission. The magnetic fields and properties of thebackground soft photons are indicated. The grey band indicates the age range obtained via molecular cloud observations (Suet al. 2017). E [GeV] E d N d E the injected accelerated electron distribution with =1.7 =1.0, E br =50 GeV and E max =1 PeV B=3 G, T age =100.0 ky B=3 G, T age =10.0 ky B=3 G, T age =1.0 ky E [MeV] E d N / d E [ M e V c m s ] B=3 G, T age =100.0 ky B=3 G, T age =10.0 ky B=3 G, T age =1.0 kyReich & Sun (2019)Chang et al. (2008)H.E.S.S. Collaboration et al. (2018)This work Figure 2.
Left: evolution of electron distribution due to synchrotron and IC losses. The initial distribution is a broken power-law with a high-energy cutoff with parameters indicated in the figure. Right: evolution of the corresponding emission spectracompared with the spectral energy distribution (SED) of HESS J1912+101. The radio data are taken from Reich & Sun (2019).The lower limit is for the polarized emission. The X-ray upper limit is from Chang et al. (2008), and the blue data points arefrom the H.E.S.S. collaboration (H. E. S. S. Collaboration et al. 2018b).
In the energy range of 1 GeV - 500 GeV, the TS value of HESS J1912+101 is fitted to be 469.0, and the spectralindex of a power-law model is 2.54 ± . ± . × − photon cm − s − . For the point source 4FGL J1913.3+1019, the TS value and the power-law spectral index are fittedto be 24.2 and 1.90 ± γ -ray SEDs of HESS J1912+101 and 4FGL J1913.3+1019 shown in the right panel ofFigure 3 were produced by dividing all data between 1 GeV and 500 GeV into 10 bins with identical width on thelogarithmic of energy. And the 95% upper limits are for energy bins with the TS value of HESS J1912+101 smaller Zeng et al. . . . . . . . . Right ascension (deg) D ec li n a t i on ( d e g ) E [GeV]10 E d N / d E [ e r g c m s ] T S V a l u e Figure 3.
Left: 4 ◦ × ◦ TS map of photons above 1 GeV around HESS J1912+101 after subtracting γ -ray emission from 4FGLJ1913.3+1019. The green crosses and circle represent the 4FGL sources and the best-fit radius of the uniform disk is marked bythe white circle. The cyan contours show the TeV γ -ray emission of HESS J1912+101 (H. E. S. S. Collaboration et al. 2018b).Right: The γ -ray SED of HESS J1912+101 (black dots) and 4FGL J1913.3+1019 (green dots). The blue dots are the HESSdata of HESS J1912+101 (H. E. S. S. Collaboration et al. 2018b).The gray histogram denotes the TS value of HESS J1912+101for each energy bin and the arrows indicate the upper limits with 95% significance level. than 4.0. The γ -ray SED shows a new spectral component below 10 GeV, which may be attributed to shock interactionwith molecular clouds. The nature of this soft extended component will be explored in a separate paper. Here wefocus on spectral modeling above 10 GeV.The right-panel of Figure 2 shows that even with a magnetic field of 3 µ G, the age of HESS J1912+101 needs to beless than 10 kyrs to reproduce the γ -ray spectrum, which contradicts molecular cloud observations (Su et al. 2017) andproperties of the associated pulsar (Smith et al. 2019). Here the γ -ray is produced via IC processes (Jones 1968), andbesides the cosmic microwave background radiation (CMB), we assume an infrared photon background with T = 30 Kand an energy density of 1 eV cm − (Porter et al. 2006). To facilitate model comparison, these values for backgroundphotons will be used in this paper unless specified otherwise. Although the γ -ray spectrum is flat, it implies an electrondistribution with an index of ∼ α = 1 . E br = 50 GeV, the spectral indexis 2.7.On the other hand, the γ -ray spectrum can be readily fitted in the hadronic scenario. For the sake of simplicity, weassume a power-law distribution with an identical index for electrons and ions. N ( R i ) = N ,i R − αi exp[ − ( E i /E i cut ) δ ]where R i = p i /q i is the rigidity of the particle, E , p and q are the particle energy, momentum and charge, respectively,and ” i ” represents different particle species. Considering that the flux ratio of TeV CR electrons and protons is lessthan 0 .
1% and high-energy electrons are subject to radiative energy loss as they propagate in the Milky Way galaxy,we fix the density ratio of electrons and protons at 1 GeV K ep = N , e /N , p = 5 × − . The total energy content ofprotons above 1 GeV ( W p ) determines the normalization of the particle distributions. We will usually consider twocases: W p = 10 and W p = 10 . The mean background density n H and magnetic field B , and the spectral index α and cutoff energy of protons E p cut can be adjusted to fit the multi-wavelength SED. The cutoff energy of electrons E e cut is obtained by requiring the corresponding synchrotron energy loss time be equal to the age of the remnant andwe assume a super exponential high-energy cutoff for the electron distribution with δ = 2 unless specified otherwise. eV cosmic ray acceleration E d N / d E [ M e V c m s ] HESS J1912+101 =1.9, E ec ( B , t )=122.5 GeV, E pc =70 TeV, =2.0, W p =10 erg, K ep =5×10 , n H =2.7 cm and B=24.5 GReich & Sun (2019)Chang et al. (2008)H.E.S.S. Collaboration et al. (2018)This work E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] HESS J1912+101 =1.9, E ec ( B , t )=5.1 GeV, E pc =70 TeV, =2.0, W p =10 erg, K ep =5×10 , n H =27 cm and B=120 GReich & Sun (2019)Chang et al. (2008)H.E.S.S. Collaboration et al. (2018)This work E [MeV] R e s i d u a l Figure 4.
Fit to the multi-wavelength SED of HESS J1912+101 in the hadronic scenario for the γ -ray emission. The totalenergy of protons above 1 GeV is 10 erg (Left) and 10 erg (Right). The model parameters are indicated on the Figures.The solid line is for γ -ray emission via hadronic processes, while the dotted, dotted-dashed, and dashed lines are for electronbremsstrahlung and IC of Infrared and CMB photons, respectively. The high-energy cutoff of ion distribution is always exponential with δ = 1. When calculating the γ -ray emission viathe hadronic processes, we only consider protons and contributions from other ions are approximated by multiplyingthe proton produced γ -ray flux by a factor of 1.84 (Mori 2009).Figure 4 shows the results of the spectral fit and the model parameters are listed in Table 2. When calculating thetotal energy of the magnetic field W B , we assume a uniform magnetic field with a volume filling factor of 1. Thismagnetic field energy therefore should be considered as an upper limit. Although both set of parameters give good fitto the radio and γ -ray spectra, the model with a weaker magnetic field and therefore more energy in energetic particles(left panel of Figure 4) is favored for the more reasonable value of the magnetic field energy. Moreover, the case witha strong magnetic field has a synchrotron spectrum cutting off in the radio band (the right panel of Figure 4), whichappears to be too low. Of course, the magnetic field is not well constrained. For the given radio emission, one canalways compensate the increase in the magnetic field with a decrease in the energetic particle energy.Araya (2020) recently carried out a detailed analyses of G279.0+1.1, a huge SNR with a radius of ∼
40 pc. It has avery hard γ -ray spectrum with a spectral index of 1 . ± .
09. Although it has not been detected in the TeV range, the γ -ray spectrum obtained with the Fermi-LAT extends to 0 . γ -ray emission. It is interesting to note that there appears to be a low energy spectral component near 1GeV, reminiscence of the spectral component below 10 GeV for HESS J1912+101. Compared with HESS J1912+101,SNR G279.0+1.1 has a similar γ -ray luminosity, a few times higher radio luminosity and radius, leading to a highermagnetic field and a large magnetic energy. However, the small volume filling factor of the radio emission region canreduce the magnetic energy significantly. G296.5+10.0G296.5+10.0 is a bilateral morphology SNR in radio and X-rays with an angular extension of 90 arcmin ×
65 arcmin,and the distance is estimated as 2.1 kpc (Giacani et al. 2000). It has relatively bright radio emission with a typicalspectral index of − . XMM-Newton observations taken in 2016 roughly cover the bright limbs of G296.5+10.0 (PI:Brian Whillianms).Here we analyze the
XMM-Newton data to estimate the flux of non-thermal emission. This emission could be fairlydim as it was not reported in the ROSAT data, and even the residual contamination from the soft proton flares mayaffect the detection. As a result, only the ID:0781720101 observation is used, which didn’t suffer apparent soft protonflares during its 28 ks exposure. The data reduction employs the standard procedure in the
XMM-Newton
ScienceAnalysis System (SAS; version: 15.0.0) and the Extended Source Analysis Software (ESAS) package. The diagnosticfile created by the ‘pn-filter’ shows a steady light curve with PN count rate of ∼ ‘eimageget’ script to generate the PN and MOS images, Zeng et al. E d N / d E [ M e V c m s ] G279.0+1.1 =1.9, E ec ( B , t )=18.6 GeV, E pc =40 TeV, =2.0, W p =10 erg, K ep =5×10 n H =2.6 cm and B=82 GDuncan et al. (1995) and Woermann & Jonas (1988)Araya 2020H. E. S. S. Collaboration et al. 2018 E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] G279.0+1.1 =1.9, E ec ( B , t )=6.0 GeV, E pc =40 TeV, =2.0, W p =5×10 erg, K ep =5×10 n H =5.2 cm and B=145 GDuncan et al. (1995) and Woermann & Jonas (1988)Araya 2020H. E. S. S. Collaboration et al. 2018 E [MeV] R e s i d u a l Figure 5.
Same as Figure 4 but for G279.0+1.1. The total energy of protons above 1 GeV is 10 erg (Left) and 5 × erg(Right). − − − − . Energy (keV) P ho t on s c m − s − k e V − unresolved AGN emission PN src spec.PN bkg spec., scaled − − − . P ho t on s c m − s − k e V − Absorbed Power Law PNMOS1: 1/2 fluxMOS2: 1/4 flux10.5 2 5 − χ Energy (keV)
Figure 6.
The left panel shows X-ray images of the northeast part of SNR G296.5+10.0, where the red, green, and blue colorsrepresent emission in the 0.2-0.5 keV, 0.5-1.0 keV, and 1.0-2.0 keV bands, respectively. The color bars in the bottom are inunits of photons cm − s − . The blue circle with a radius of 5.15 (cid:48)(cid:48) is the region for spectral extraction, while the other circlesand the square are for the ‘local background’ regions. The green box is for the PN data, and the white and the yellow circlesare for the MOS1 and MOS2 data, respectively. A few point sources are marked out with red. The middle panel shows thesource-region spectrum and the scaled ‘local background’ spectrum (according to the effective area) of the PN data, with themodel of unresolved AGN emission in the cosmic X-ray background over-plotted. The right panel shows the XMM-Newton
PNand MOS spectra with their ‘local background’ subtracted, and the best-fit models are shown in the red color. The blackcurve, as modeled by an absorbed power law, represents the non-thermal emission, which is likely caused by the cosmic X-raybackground. and the ‘eimagecombine’ to combine them and produce a background-subtracted, vignetting-corrected, and smoothedimage, where the background is based on the filter wheel closed images. This image (the left panel of Figure 6) coversthe northeast part of the SNR.The PN and MOS spectra are extracted from a circular region with a radius of 5.15 (cid:48) , well confined within thecentral CCD of the MOS1 and MOS2. A few bright point sources are manually removed when making the mask. The ‘mos/pn-spectra” scripts are used to create spectra, and the ‘mos/pn-back’ scripts to generate model quiescent particlebackground (QPB) spectra. Using the same method we also produce spectra from ‘local background’ regions at thenortheast corner of the field of view, where the SNR emission seems negligible. These regions are slightly differentfor the MOS1, MOS2, and PN as shown in the left panel of Figure 6, due to differences in the effective boundariesof different detectors. We present the PN source spectrum and the ‘local background’ spectrum in the middle panelof Figure 6 with their QPB spectra subtracted, and compared with the model of the unresolved AGN emission inthe cosmic X-ray background (De Luca & Molendi 2004; Kuntz & Snowden 2008). The model is an absorbed powerlaw component with a spectral index of 1.46 and a normalization of ∼ . − s − sr − keV − at 1 keV, andthe absorption is determined by the Galactic HI column density towards this SNR of about 1 . × cm − (HI4PI eV cosmic ray acceleration - . - . - . - . Right ascension (deg) D ec li n a t i on ( d e g ) - . - . - . - . Right ascension (deg) D ec li n a t i on ( d e g ) - . - . - . - . Right ascension (deg) D ec li n a t i on ( d e g ) - . - . - . - . Right ascension (deg) D ec li n a t i on ( d e g ) Figure 7.
TS maps of a 3 ◦ × ◦ region around G296.5+10.0. The top two panels is for photons in the range of 1 GeV - 1 TeV,and the bottom two panels is for photons from 5 GeV to 1 TeV. The magenta dashed circle and the white solid circle representthe size of spatial template of G296.5+10.0 in 4FGL and this work by Fermi -py, respectively. The white cross show the positionof the radio-quiet X-ray-emitting neutron star (1E 1207.4-5209) in it (Helfand & Becker 1984; Zavlin et al. 2000). The green(left) and cyan (right) contours describe the radio and X-ray emission of G296.5+10.0, respectively.
Collaboration et al. 2016). In the hard X-ray band (2-7 keV), the PN source spectrum is slightly under the cosmicX-ray background curve, suggesting absence of prominent non-thermal emission.Nevertheless, to estimate an upper limit of the non-thermal emission, we fit the PN and MOS spectra jointly, butusing the ‘local background’ spectra as the background spectra. A single temperature APEC model represents theSNR thermal emission, and a power law model is for the non-thermal emission. The redshift is set to zero, and the
Zeng et al.
Galactic HI column density is assigned to be the maximum column density for the foreground absorption. The best-fitspectra are shown in the right panel of Figure 6. The best-fit temperature of the thermal emission is 0.15 keV, and themetal abundances are slightly sub-solar (Table 1). The non-thermal flux in the range of 0.5–10 keV is 6 . ± . × − erg cm − s − , with a photon index of 1 . ± .
4. Since that the ‘local background’ spectra do not have a good statisticin the hard X-ray band, this component is likely from the unresolved AGN emission. Note that the photon index of1.4 for SNR is too hard if the hard tail X-ray component is synchrotron X-rays. We will treat this fitted flux as anupper limit to nonthermal emission from the SNR, which in turn suggests an upper limit of the non-thermal flux of ∼ . × − erg cm − s − for the entire SNR region (Kellett et al. 1987). Table 1.
The best-fit results for the
XMM-Newton data of G296.5+10.0Model: TBabs*(APEC+Powerlaw)TBabs n H (1 . − . × cm − APEC η apec * kT [keV] C N O Ne, Mg, Si, S Fe, Ni0 . ± .
01 0 . ± . < . . ± . . ± . . ± . . ± . flux (0 . −
10 keV) . ± . × − erg cm − s − Photon Index 1 . ± . χ / d.o.f. ∼ Note —Compared to the MOS spectra, the PN spectrum may have some systematic deficit in flux. The total flux of the PN isallowed to vary during the joint fitting, and the best-fit value here is 0 . ± . ∗ Normalization parameter of the APEC model has the physical meaning of − π [ D A (1+ z ) ] (cid:82) n e n H dV , where D A is the angulardiameter distance to the source (cm) and z is the redshift, n e and n H are the electron and the hydrogen densities (cm − ), and V is the volume. Using 52 months of Pass 7 data recorded by
Fermi -LAT, Araya (2013) detected extended γ -ray emission towardthe region of SNR G296.5+10.0 with a ∼ σ confidence level. The γ -ray spectrum of it can be fitted by a power-lawwith an index of 1.85 ± . ◦ , Dec.= − . ◦ ) with an radius of 0.76 ◦ . E [GeV]10 E d N / d E [ e r g c m s ] T S V a l u e Figure 8.
The γ -ray SED of G296.5+10.0. The red solid line shows the best-fitting power-law spectrum in the energy rangeof 100 MeV - 1 TeV, and the red dashed lines show its 1 σ statistic error. The gray histogram denotes the TS value for eachenergy bin and the arrows indicate the upper limits with 95% significance level. eV cosmic ray acceleration E d N / d E [ M e V c m s ] G296.5+10.0 =1.9, E ec ( B , t )=255 GeV, E pc =70 TeV, =2.0, W p =10 erg, K ep =5×10 n H =0.35 cm and B=70 GMilne & Haynes (1994)This work E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] G296.5+10.0 =1.9, E ec ( B , t )=9.7 GeV, E pc =70 TeV, =2.0, W p =10 erg, K ep =5×10 n H =4.2 cm and B=360 GMilne & Haynes (1994)This work E [MeV] R e s i d u a l Figure 9.
Same as Figure 4 but for G296.5+10.0.
With the latest
Fermi -LAT Pass 8 data collected from 2008 August 4 to 2018 August 4, we updated the γ -raymorphology and spectrum of G296.5+10.0. Figure 7 shows the TS maps of a 3 ◦ × ◦ region around G296.5+10.0. Ineach panel, the magenta dashed circle is the size of spatial template of G296.5+10.0 in 4FGL (Abdollahi et al. 2020).As can be seen, the γ -ray emission of G296.5+10.0 has a significant deviation with this spatial template. Therefore,we use the Fermi -py tool to refit the data and get the updated centered position and radius of the uniform disk, whichis shown as the white solid circle in Figure 7. The best-fit position and radius of the uniform disk are (R.A.= 182 . ◦ ,Dec.= − . ◦ ) and 0.79 ◦ , respectively. With this spatial template, the TS value of G296.5+10.0 is fitted to be 203.68,and the spectrum can be well fitted by a power-law with an index of 1.90 ± . ± . × − photon cm − s − with statistical error only. Moreover, toderive the γ -ray SED of G296.5+10.0, all of the data from 100 MeV to 1 TeV are divided to be 14 equal logarithmicbins. And for any energy bin with TS value of G296.5+10.0 smaller than 5.0, an upper limit at 95% confidence levelis calculated. The SED and fit results are shown in Figure 8.G296.5+10.0 has an age of ∼
10 kyrs (Vasisht et al. 1997) and a GeV γ -ray spectrum similar to that of HESSJ1912+101. Adopting the hadronic model for HESS J1912+101, one can fit the radio and γ -ray spectra of G296.5+10.0.Due to the absence of TeV observations, the high-energy cutoff of the proton distribution is not well constrained andwe adopt a value of 70 TeV derived from the spectral fit of G296.5+10.0. Figure 9 shows the spectral fit, and themodel parameters are listed in Table 2, which are very similar to those for HESS J1912+101 except for a slightlystronger magnetic field. As we will see below, this is due to the higher radio to γ -ray flux ratio of G296.5+10.0 thanthat of HESS J1912+101. Similarly, we favor the model with a weaker magnetic field (left panel of Figure 9). HADRONIC AND/OR LEPTONIC MODELS FOR HARD GEV SPECTRA OF OTHER 10 SNRSWe now extend the above study to all SNRs with hard γ -ray spectra. Figure 10 shows the multi-wavelength non-thermal spectra of 12 SNRs with hard GeV spectra. The spectra have been normalized at γ -ray band by fitting the γ -ray spectra with a hadronic model. The model assumes that protons have a single power law with an exponentialhigh energy cutoff. The normalization of the SED of each source is adjusted to minimize the χ of the γ -ray data ofall sources. We then have an index of 1.74 and E p cut = 47 TeV. Then we may classify these sources based on theirradio and/or X-ray spectra.Based on the radio flux, these SNRs may be divided into three categories. SN 1006, RCW 86, G296.5+10.0,G78.2+2.1 and N132D have strong radio emission, while the radio emission from G150.3+4.5 and HESS J1534-571are very weak. Their normalized radio flux densities can differ by about two orders of magnitudes. The famous TeVbright SNRs RX J1713-3946, RX J0852.0-4622, HESS J1731-347, and HESS J1912+101, RCW 103 have normalizedradio flux densities between the above two categories. In Table 2, we use double horizontal lines to separate thesecategories and give the estimated age, distance, radius of these SNRs and the related references. Non-thermal X-rayemission is detected from five relatively young SNRs: SN 1006, RCW 86, RX J1713-3946, RX J0852.0-4622, and HESSJ1731-347. As will be shown below, a broken power-law spectrum is needed to explain their multi-wavelength non-thermal emission spectra, while for other sources, the above hadronic model for HESS J1912+101 and G296.5+10.0with a single power-law high-energy particle spectrum is sufficient (See Table 2).0 Zeng et al. E [MeV] E d N / d E [ M e V c m s ] = = 3.06 for gamma-ray dataFitted SEDs by using decay p = 1.74, E pc = 47 TeVRX J0852.0 4622RX J1713.7 3946HESS J1731 347RCW 86 SN 1006G150.3+4.5G296.5+10.0HESS J1534 571HESS J1912+101 RCW 103G78.2+2.1G279.0+1.1N132D Figure 10.
The multi-wavelength spectral data of 13 SNRs with hard γ -ray spectra. The γ -ray spectra are fitted with ahadronic model with the normalization of individual spectrum as free parameters. The model assumes that protons have asingle power-law energy distribution with an exponential high-energy cutoff. Note that the TeV spectra of G78.2+2.1 (HAWC)and N132D (HESS) cut off at relatively lower energies, and the soft spectral component of GeV of HESS 1912+101 may be fromother contributors, and are not considered in SED fitting. The best-fit model parameters are indicated on the Figure. Referencesfor the observational data are as follows. RX J0852.0 − − − . .
5: radio (Gerbrandt et al. 2014), X-ray and GeV (Devin et al. 2020); G296 . . − For the two SNRs with very weak radio emission, G150.3+4.5 is similar to G296.5+10.0 in the sense that there is noTeV data. We therefore set the high-energy cutoff of the proton distribution at 70 TeV. The spectral fits are shownin the upper panels of Figure 11. We favor the model with a low value of 10 erg for the total proton energy W p (left panel) with a magnetic field of 32 µ G. An even lower value of W p is disfavored since it implies an even strongermagnetic field and therefore an energy ratio of the magnetic field to the high-energy electrons greater than 3500. Forhigher values of the total proton energy, the electron cutoff energy needs to be lower than that determined by requiringthe synchrotron energy loss time being equal to the age of the SNR. Otherwise the IC emission will dominate the γ -ray emission with a harder spectrum than the observed one. The right panel shows such a case with the electron eV cosmic ray acceleration E d N / d E [ M e V c m s ] G150.3+4.5 =1.75, E ec ( B , t )=2.0 TeV, E pc =70.0 TeV, =2.0, W p =10 erg, K ep =5×10 , n H =4.2 cm and B=32 GGerbrandt et al. (2014)Devin et al. (2020)ROSAT from Devin et al. (2020) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] G150.3+4.5 =1.75, E ec =200 GeV, E pc =70.0 TeV, =2.0, W p =10 erg, K ep =5×10 , n H =0.48 cm and B=6.0 GGerbrandt et al. (2014)Devin et al. (2020)ROSAT from Devin et al. (2020) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] HESS J1534 571 =1.45, E ec ( B , t )=591 GeV, E pc =20 TeV, =2.0, W p =10 erg, K ep =5×10 , n H =1.2 cm and B=46 GMaxted et al. (2018)H.E.S.S. Collaboration et al. (2018)Araya. (2017)H.E.S.S. Collaboration et al. (2018) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] HESS J1534 571 =1.45, E ec ( B , t )=14 GeV, E pc =20 TeV, =2.0, W p =10 erg, K ep =5×10 , n H =12.0 cm and B =300 GMaxted et al. (2018)H.E.S.S. Collaboration et al. (2018)Araya. (2017)H.E.S.S. Collaboration et al. (2018) E [MeV] R e s i d u a l Figure 11.
Same as Figure 4 but for G150.3+4.5 (upper) and HESS J1534 −
571 (lower) with very weak radio emission. cutoff energy of 200 GeV to suppress contributions to the γ -ray via the IC processes. Equating the synchrotron energyloss time to the SNR age will lead to a cutoff energy of electron E ecut greater than 50 TeV for the relatively weakermagnetic field of 6 µ G.We notice that there are some degeneracies among W p , n H , B and K ep . The product of W p and n H is determinedby the γ -ray spectrum. The total proton energy discussed above should be re-scaled by the actual value of the meannumber density of the background n H . We fix K ep to 5 × − in the spectral fit above. For a given radio flux and W p , an increase of K ep will lead to more energetic electrons and a weaker magnetic field.The lower panels of Figure 11 show the spectral fits for HESS J1534 − −
571 is well constrained by TeV observations. However, Table 2 shows that the cutoff energy of 20TeV is much lower than the value of 70 TeV for the three sources studied above. Similar to G296.5+10.0 and HESSJ1912+101, we favor the model with a higher value of W p (left panel) for the weaker magnetic field and highersynchrotron cutoff energy. The ratio of W B /W e = 1600 is also more reasonable. However, the magnetic field is not aswell constrained as for G150.3+4.5. We also notice that with a spectral index of 1.45, HESS J1534 −
571 has a muchharder energetic particle spectrum than other sources. Such a hard spectrum is needed to fit the γ -ray spectrum.More radio flux density measurements are needed to test this model.Among the 5 SNRs with intermediate radio emission, RCW 103 does not have non-thermal X-ray emission, similarto HESS J1912+101. There is also no TeV data, we then fix the proton cutoff energy at 70 TeV. Although RCW103 is relatively young with an age of 4.4 kyrs, radio and GeV observations lead to a high-energy particle spectrumslightly softer than that for HESS J1912+101. The GeV flux of RCW 103 is actually about 3 times higher than thatof HESS J1912+101. Since the distance to the two source is comparable, the γ -ray luminosity of RCW 103 of about2 times higher. For the same proton energy W p and comparable radio flux densities, RCW 103 therefore has a higherbackground density n H and stronger magnetic field. However, the radius of RCW 103 is more than 3 times smallerthan HESS J1912+101, leading to a factor of 30 difference in the volume. We therefore have a much lower value of W B /W e . Even the case with a W p of 10 erg (left panel of Figure 12) has a very low value of 0.034 for W B /W e ,2 Zeng et al. E d N / d E [ M e V c m s ] RCW 103 =2.05, E ec ( B , t )=1.14 TeV, E pc =70 TeV, =2.0, W p =10 erg, K ep =5×10 n H =6.5 cm and B=50 GDickel et al. (1996)Xing et al. (2014) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] RCW 103 =2.05, E ec ( B , t )=0.56 TeV, E pc =70 TeV, =2.0, W p =10 erg, K ep =5×10 n H =65 cm and B=226 GDickel et al. (1996)Xing et al. (2014) E [MeV] R e s i d u a l Figure 12.
Same as Figure 4 but for RCW 103. E d N / d E [ M e V c m s ] RX J1713.7 3946 =1.60, =1.0, E ebr =82 GeV, E ec =38 TeV, E pc =40 TeV, =2.0, W p =10 erg, K ep =5×10 , n H =0.6 cm and B=62 GLazendic et al. (2004)Tanaka et al. (2011)H.E.S.S. Collaboration et al. (2018)H.E.S.S. Collaboration et al. (2018) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] RX J1713.7 3946 =1.89, =1.0, E ebr =1.8 TeV, E ec =70 TeV, E pc =70 TeV, =2.0, W p =7.7×10 erg, K ep =5×10 , n H =0.1 cm and B=22 GLazendic et al. (2004)Tanaka et al. (2011)H.E.S.S. Collaboration et al. (2018)H.E.S.S. Collaboration et al. (2018) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] RX J1713.7 3946 =1.60, =1.0, E ebr ( B , t )=25.8 GeV, E ec =13.5 TeV, E pc =40 TeV, =2.0, W p =6×10 erg, K ep =5×10 , n H =11.7 cm and B=550 GLazendic et al. (2004)Tanaka et al. (2011)H.E.S.S. Collaboration et al. (2018)H.E.S.S. Collaboration et al. (2018) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] RX J1713.7 3946 =1.55, =1.75, E ebr ( B , t )=0.39 TeV, E ec =40 TeV, E pc =40 TeV, =2.0, W p =5×10 erg, K ep =5×10 , n H =1.20 cm and B=142 GLazendic et al. (2004)Tanaka et al. (2011)H.E.S.S. Collaboration et al. (2018)H.E.S.S. Collaboration et al. (2018) E [MeV] R e s i d u a l Figure 13.
Several spectral fits to the SED of RX J17137.7 − γ -ray emission. Although the model shown in the lower left has fewer parameters,the magnetic field appears to be too strong. The model in the lower right panel has a relatively weaker magnetic field but givesa poorer fit to the SED. we still favor this model for its relatively higher cutoff energy of the synchrotron spectrum. To increase the value of W B /W e , one needs to consider lower values for W p as discussed above (See right panel of Figure 12).The other 3 SNRs with intermediate radio emission RX J1713.7 − − −
347 havebeen studied extensively for their prominent non-thermal X-rays and TeV emission. There are still debates on thenature of the γ -ray emission. Detailed TeV observations of RX J17137.7 − γ -ray spectrum in both the leptonic and hadronic scenarios for the γ -ray emission eV cosmic ray acceleration Table 2.
Physical and fitting parameters for our sample.Source Age Distance Radius W p n H α E pcut ∆ α δ E ebr E ecut B W B W B /W e kyr kpc pc 10 erg cm − TeV GeV TeV µ G 10 erg 10 G150.3+04.5 6.0 1.0 24 1.0 4.2 1.75 70 − − a
32 6 . − − .
24 0.26HESS J1534 −
571 10.0 3.5 22.4 1.0 12 1.45 20 − − a
300 496 7 . × G323.7 − − − a
46 11.6 HESS J1912+101 170 4.1 15 1.0 27 1.9 70 − − a
120 23.9 6 . × G044.5 − − − a G279.0+1.1 100 3.0 41.5 5.0 5.2 1.9 40 − − a
145 7 . × . × − − a
82 2 . × RCW 103 4.4 3.3 4.8 1.0 65 2.05 70 − − a
226 2.8 12G332.4 − − − a
50 0.14
RX J1713.7 − a . × a
40 142 6.5 14G347.3 − . (Leptonic) 7.7 0.1 1.89 70 1.0 2.0 1800 70 22 0.16 RX J0852.0 − . × a
20 165 29.9 2 . × a
30 100 11 14G266.2 − . (Leptonic) 350 0.001 1.5 70 1 . − −
22 11 0.13
HESS J1731 −
347 2.5 3.2 14 1.0 7.5 1.5 30 1.0 2.0 38 6.5 550 403 1 . × a . × a
25 85 9.6 8 . − . (Leptonic) 55 0.05 1.5 70 1.0 2.0 170 25 32 1.05 0.29(Leptonic) 5.5 0.05 1.95 70 − −
13 23 0.71
G296.5+10.0 10.0 2.1 24.1 1.0 4.2 1.9 70 − − a
360 8 . × . × − − a
70 33.7 SN 1006 1.0 2.2 9.6 1.0 1.0 1.90 70 1.0 1.0 386 a − − . RCW 86 1.8 2.5 15.3 1.0 6.5 1.45 20 0.85 1.0 0.048 a . × . × . × G315.4 − a
30 31 1.68
Gamma Cygni 8.25 2.0 17 1.0 29 2.00 10 − − a
650 1 . × . × G78.2+01.2 10 2.9 2.00 10 − − a
140 47.2 N132D 2.5 50 11.4 10.0 32 2.10 70 − − a
423 1 . × N132D 2.5 50 11.4 50.0 6.4 2.10 70 − − a
148 15.9
Note —References of physical parameters − HESS J1912+101 (Su et al. 2017; Zhang et al. 2020); RCW 103 (Reynoso et al.2004; Braun et al. 2019); RX J1713.7 − − −
347 (Tian et al. 2008; H. E. S. S. Collaboration et al. 2011b); G150.3+4.5 (Cohen 2016; Devin et al.2020); HESS J1534 −
571 (Maxted et al. 2018); G279.0+1.1 (Duncan et al. 1995; Araya 2020); G296.5+10 (Vasisht et al. 1997;Giacani et al. 2000); SNR 1006 (Winkler et al. 2003; Katsuda et al. 2009); RCW 86 (Bocchino et al. 2000; Helder et al. 2013); γ Cygni (Higgs 1977; Leahy et al. 2013); N132D (Dickel & Milne 1995; Vogt & Dopita 2011). a : Determined by requiring the synchrotron energy loss time being equal to the SNR age; Zeng et al. (H. E. S. S. Collaboration et al. 2018a). In general, for sources with strong non-thermal X-ray emission, a singlepower law particle distribution will lead to a poor fit to the multi-wavelength SED. But for the sake of simplicity andconsidering the overall quality of γ -ray data, we will still adopt a single power-law distribution with an exponentialhigh-energy cutoff for the rigidity of ions. The electron distribution, however, can be a broken power law with anexponential ( δ = 1) or super exponential ( δ = 2 .
0) cutoff. Since the acceleration of low energy particles are not affectedby radiative energy loss, we assume that the electrons and ions have the same spectral index at low energies.The upper-right panel of Figure 13 shows a leptonic scenario for the γ -ray emission. The corresponding modelparameters are given in the fourth row for RX J1713.7 − − for the infrared background photons and ion processes also have significantly contribution to the γ -rayemission (solid line), a high value of 22 µ G is inferred for the magnetic field. However, the total energy of the magneticfield is on the order of 10 ergs, which is still much lower than that for ions. Since the ion spectral cutoff is notwell-constrained by the data, we set it at 70 TeV as we did above for other sources. An increase of the magnetic fieldwill lead to a shift to the dominance of γ -ray fluxes by the hadronic processes. The upper left panel of Figure 13 showsour favored hadronic model for the γ -ray emission. The corresponding model parameters are given in the third rowfor RX J1713.7 − γ -rayobservations (H. E. S. S. Collaboration et al. 2018a) for the adoption of a single power-law ion distribution here. Thespectral index of 1.6 is comparable to the low energy spectral index inferred from γ -ray observations and the productof W p and n H is also compatible with these observations. For such a hard spectrum, a broken power law electrondistribution is needed to fit the radio to X-ray spectrum via the synchrotron process. For the magnetic field of 62 µ G,we find a break energy of 82 GeV and a cutoff energy of 38 TeV. Although the electron cutoff energy is very closeto the proton cutoff energy, their distributions are quite different at high energies for the differences in the spectralindex and shape of the cutoff δ . The total energy of the magnetic field is comparable to that of ions and is more than2 orders of magnitude higher than that of electrons. Note that although K ep = 0 . W B /W e and a slight decrease in E ebr , giving rise to a slightly higher ratio of W p /W e .To reduce the number of model parameters, one may increase the magnetic field and set the electron radiative energyloss timescale at the break energy to be equal to the age of the SNR. This leads to the fit in the lower left panel ofFigure 13. The corresponding model parameters are given in the first row for RX J1713.7 − γ -rayemission is completely dominated by the hadronic processes. However, the total energy of the magnetic field W B ismore than 5 orders of magnitude higher than that of electrons and more than 2 orders of magnitude higher than theenergy of ions W p . One may adjust the change of the spectral index ∆ α from low to high energies to reduce themagnetic field. This leads to the fit in the lower right panel of Figure 13, which is not as good as the others, especiallyin the X-ray band. The corresponding model parameters are given in the second row for RX J1713.7 − α is due to contribution to GeV γ -ray via the leptonic processes.The spectral fits to the SED of RX J0852 − − − − µ G, the magneticfield energy is about one tenth of the proton energy and about 100 times higher than the energy of electrons. Theupper right panel shows a leptonic model with the model parameters given in the fifth row for RX J0852 − γ -rays at tens of TeV. Compared with the leptonic model for RX J1713.7 − . × erg for the very hard spectrum and very high cutoff energy, which is a bit too high to bereasonable. The total energy of the magnetic field however is about 10 erg and comparable to that of the electrons.The model of the middle right panel of Figure 14 is similar to that of the lower right panel of Figure 13 for RXJ1713.7 − − − − W B /W e , ∆ α = 1 . − − W p is 10 times eV cosmic ray acceleration E d N / d E [ M e V c m s ] RX J0852.0 4622 =1.75, E ebr =55 GeV, E ec =50 TeV, E pc =70 TeV, =2.0, W p =10 erg, K ep =5×10 , n H =0.55 cm and B =31 GAharonian et al. (2007)Duncan & Green (2000)Tanaka et al. (2011H. E. S. S. Collaboration et al. (2018) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] RX J0852.0 4622 =1.5, E ebr =20 GeV, E ec =70 TeV, E pc =70.0 TeV, =2.0, W p =3.5×10 erg, K ep =5×10 , n H =0.001 cm and B =8 GAharonian et al. (2007)Duncan & Green (2000)Tanaka et al. (2011H. E. S. S. Collaboration et al. (2018) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] RX J0852.0 4622 =1.75, =1.4, E ebr ( B , t )=0.17 TeV, E ec =20 TeV, E pc =70 TeV, =1.0, W p =10 erg, K ep =5×10 , n H =5.5 cm and B =165 GAharonian et al. (2007)Duncan & Green (2000)Tanaka et al. (2011H. E. S. S. Collaboration et al. (2018) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] RX J0852.0 4622 =1.5, =2.32, E ebr ( B , t )=0.46 TeV, E ec =30 TeV, E pc =35 TeV, =2.0, W p =10 erg, K ep =5×10 , n H =0.45 cm and B =100 GAharonian et al. (2007)Duncan & Green (2000)Tanaka et al. (2011H. E. S. S. Collaboration et al. (2018) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] RX J0852.0 4622 =1.75, E ebr =28 GeV, E ec =20 TeV, E pc =70 TeV, =2.0, W p =10 erg, K ep =5×10 , n H =5.5 cm and B =165 GAharonian et al. (2007)Duncan & Green (2000)Tanaka et al. (2011H. E. S. S. Collaboration et al. (2018) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] RX J0852.0 4622 =2.2, E ec =22 TeV, E pc =70.0 TeV, =1.0, W p =6×10 erg, K ep =5×10 , n H =0.2 cm and B =11 GAharonian et al. (2007)Duncan & Green (2000)Tanaka et al. (2011H. E. S. S. Collaboration et al. (2018) E [MeV] R e s i d u a l Figure 14.
The upper two rows are the same as Figure 13 but for RX J0852 − W p and a stronger magnetic field. The bottom right panel is for a relatively simple single power-lawleptonic model. However, the cutoff of the electron distribution is exponential in this case. smaller, leading to a very strong magnetic field of 165 µ G and a very high value of 3 . × for W B /W e . The modelof the lower right panel of Figure 14 has a single power-law electron distribution with the model parameter given inthe sixth row for RX J0852 − −
347 shown in Figure 15 are very similar to those in Figure 14. The modelparameters are given in Table 2. Due to its relatively higher X-ray to γ -ray flux ratio, the magnetic fields in theleptonic scenarios are higher than those for RX J0852 − −
347 is between those for the other two sources, so is the totalenergy of protons. For the hadronic models, we first notice that the cutoff energy of protons is the lowest among these6
Zeng et al. E d N / d E [ M e V c m s ] HESS J1731 347 =1.5, E ebr =100 GeV, E ec =17 TeV, E pc =30 TeV, =2.0, W p =10 erg, K ep =5×10 , n H =0.75 cm and B=85 GTain et al. (2008)Doroshenko et al. (2017)Guo et al. (2018) and Condin et al. (2017)H.E.S.S. Collaboration et al. (2011) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] HESS J1731 347 =1.5, =1.0, E ebr =170 GeV, E ec =25 TeV, E pc =70 TeV, =2.0, W p =5.5×10 erg, K ep =5×10 , n H =0.05 cm and B=32 GTain et al. (2008)Doroshenko et al. (2017)Guo et al. (2018) and Condin et al. (2017)H.E.S.S. Collaboration et al. (2011) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] HESS J1731 347 =1.5, =0.85, E ebr ( B , t )=16.5 GeV, E ec =6.4 TeV, E pc =30 TeV, =2.0, W p =10 erg, K ep =5×10 , n H =7.5 cm and B=550 GTain et al. (2008)Doroshenko et al. (2017)Guo et al. (2018) and Condin et al. (2017)H.E.S.S. Collaboration et al. (2011) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] HESS J1731 347 =1.5, =1.82, E ebr ( B , t )=0.69 TeV, E ec =25 TeV, E pc =30 TeV, =2.0, W p =10 erg, K ep =5×10 , n H =0.6 cm and B=85 GTain et al. (2008)Doroshenko et al. (2017)Guo et al. (2018) and Condin et al. (2017)H.E.S.S. Collaboration et al. (2011) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] HESS J1731 347 =1.5, E ebr =38 GeV, E ec =6.5 TeV, E pc =30 TeV, =2.0, W p =10 erg, K ep =5×10 , n H =7.5 cm and B=550 GTain et al. (2008)Doroshenko et al. (2017)Guo et al. (2018) and Condin et al. (2017)H.E.S.S. Collaboration et al. (2011) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] HESS J1731 347 =1.95, E ec =13 TeV, E pc =70 TeV, =1.0, W p =5.5×10 erg, K ep =5×10 , n H =0.05 cm and B=23 GTain et al. (2008)Doroshenko et al. (2017)Guo et al. (2018) and Condin et al. (2017)H.E.S.S. Collaboration et al. (2011) E [MeV] R e s i d u a l Figure 15.
Same as Figure 14 but for HESS J1731 − three sources and its particle distributions are also harder than the other two sources. The γ -ray luminosity of thesethree sources are comparable as can be seen from the product of W p and n H .Compared with G296.5+10.0, SN 1006 and RCW 86 have prominent non-thermal X-ray emission and are relativelyyounger. They all have relatively strong radio emission. Figure 16 shows the spectral fits to these two SNRs with themodel parameters given in Table 2. Although both the leptonic (left panels) and hadronic (right panels) models givereasonable fits to the SEDs, the hadronic models are disfavored for their relatively stronger magnetic fields, especiallyfor RCW 86, whose hadronic model requires a magnetic field of more than 10 mG. This is because the hard GeVspectrum is not compatible to the soft radio spectrum if we assume electrons and ions have the same spectral index.To fit the spectrum, the synchrotron spectrum needs to have a spectrum break below the radio band, implying verystrong magnetic field if this break is associated with radiative energy loss processes. However, we notice that multi-wavelength images of RCW 86 reveal complicated structure (Ajello et al. 2016). Multi-zone hadronic models may stillwork. More detailed studies are warranted. For SN 1006, W p is on the order of 10 erg. A much higher value can be eV cosmic ray acceleration E d N / d E [ M e V c m s ] SN 1006 =2.1, E ec =7.3 TeV, E pc =70 TeV, =1.0, W p =1.5×10 erg, K ep =5×10 , n H =0.1 cm and B=65 GDyer et al. (2009)Bamba et al. (2008)Condon et al. (2017)Acero et al. (2010) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] SN 1006 =1.9, =1.0, E ebr ( B , t )=0.39 TeV, E ec =8.1 TeV, E pc =70 TeV, =1.0, W p =10 erg, K ep =5×10 , n H =1.0 cm and B=180 GDyer et al. (2009)Bamba et al. (2008)Condon et al. (2017)Acero et al. (2010) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] RCW 86 =2.25, =1.0, E ebr ( B , t )=7.2 TeV, E ec =30 TeV, E pc =70 TeV, =1.0, W p =10 erg, K ep =5×10 , n H =0.05 cm and B=31 mGASCA-Lemoine-Goumard et al. (2012)RXTE-Lemoine-Goumard et al. (2012)Caswell et al. (1975) and Lemoine-Goumard et al. (2012)Ajello et al. (2016)H.E.S.S. Collaboration et al. (2018) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] RCW 86 =1.45, =0.85, E ebr ( B , t )=0.048 GeV, E ec =0.85 TeV, E pc =20 TeV, =1.0, W p =10 erg, K ep =5×10 , n H =6.5 cm and B=12 mGASCA-Lemoine-Goumard et al. (2012)RXTE-Lemoine-Goumard et al. (2012)Caswell et al. (1975) and Lemoine-Goumard et al. (2012)Ajello et al. (2016)H.E.S.S. Collaboration et al. (2018) E [MeV] R e s i d u a l Figure 16.
The spectral fits for SN 1006 and RCW 86. The left panels correspond to the favored leptonic scenarios for the γ -ray emission. ruled out without reducing K ep since electrons already have significant contributions to the γ -rays via the IC emissionprocess in both scenarios. We also notice that both leptonic models for these two SNRs require an exponential cutoffinstead of the super exponential one and SNR 1006 has a single power law electron distribution while RCW 86 hasa broken one. The leptonic models for RWC 86 explored by Ajello et al. (2016) only consider the CMB for the ICprocess and have a single power law electron distribution, which is different from our favored model.Besides the three SNRs studied above, there are two more radio bright SNRs: G78.2+01.2 and N132D. Both of themhave very soft spectra in the TeV band, indicating a spectral cutoff. The latter is an SNR in the Large MagellanicCloud and is the most powerful SNR in our sample (Bamba et al. 2018). Although thermal X-ray emission has beendetected from both sources, there is no evidence for non-thermal X-rays. A simple single power-law model can readilyfit their SEDs. The model parameters are given in Table 2. For G78.2+01.2, we favor the model with W p = 10 ergfor the more reasonable value of magnetic field and W B /W e . Stronger magnetic fields are needed for lower values of W p . Considering the fact that N132D is the most powerful SNR, a value of 5 × erg appears to be reasonablefor W p . To reduce W p , the magnetic field needs to be increased to reproduce the observed radio flux. The strongmagnetic field of 423 µ G appears to be reasonable to this SNR. So both models for N132D shown in Figure 17 arefavored. N132D has a relatively soft γ -ray spectrum. The proton distribution cuts off at 70 TeV. The cutoff energyof the proton distribution for G78.2+01.2, however, is only about 10 TeV, the lowest in our sample. It is likely thatprotons above 10 TeV have already escaped from the SNR and may illuminate surrounding molecular clouds. Moreobservations in the TeV band are warranted. DISCUSSIONSIn general, all the models presented above give good fits to the SEDs. We picked up the favored ones mostly basedon the model parameters. Firstly, we favor models with a total energy of protons below 10 erg and a magnetic fieldbetween 10 to 100 µ G or as close as to this range as possible. Since these SNRs are expected to dominate the fluxof TeV cosmic rays, on average each SNR should inject less than 10 erg of energy to the cosmic rays (Zhang et al.8 Zeng et al. E d N / d E [ M e V c m s ] G78.2+2.1 =2.00, E ec ( B , t )=77 GeV, E pc =10 TeV, =2.0, W p =10 erg, K ep =5×10 n H =2.9 cm and B=140 GHAWCWendker et al. (1991); Zhang et al. (1997); Kothes et al. (2006); Gao et al. (2011)Abeysekara et al. (2018)Aliu et al. (2013) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] G78.2+2.1 =2.00, E ec ( B , t )=3.6 GeV, E pc =10 TeV, =2.0, W p =10 erg, K ep =5×10 n H =29 cm and B=650 GHAWCWendker et al. (1991); Zhang et al. (1997); Kothes et al. (2006); Gao et al. (2011)Abeysekara et al. (2018)Aliu et al. (2013) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] N132D =2.10, E ec ( B , t )=230 GeV, E pc =70 TeV, =2.0, W p =5×10 erg, K ep =5×10 n H =6.4 cm and B=148 GDickel & Milne (1995)H.E.S.S. Collaboration et al. (2015)Hughes et al. (1998)this workBamba et al. (2018) E [MeV] R e s i d u a l E d N / d E [ M e V c m s ] N132D =2.10, E ec ( B , t )=28 GeV, E pc =70 TeV, =2.0, W p =1×10 erg, K ep =5×10 n H =32 cm and B=423 GDickel & Milne (1995)H.E.S.S. Collaboration et al. (2015)Hughes et al. (1998)this workBamba et al. (2018) E [MeV] R e s i d u a l Figure 17.
Same as Figure 4 but for G78.2+01.2 (upper) and N132D (lower). W B /W e . It can be seen that most of the favoredmodels satisfies the first criteria except for SNRs G78.2+01.2 and N132D, where the magnetic field is above 100 µ G.A magnetic field below 100 µ G will require a total energy of protons exceeding 10 ergs. Most of the favored modelshave a W p of 10 erg. Only for G150.3+04.5 and SN 1006, W p is one order of magnitude lower. This is reasonablesince these SNRs are likely resulting from Type Ia SNs for their lack of compact neutron stars within the remnants.N132D is the most powerful SNR, a value of W p exceeding 10 erg is acceptable.Figure 18 shows the scatter plot between B vs n H for the favored models. The mean density of the emission regionis always less than 10 cm − except for N132D, which is consistent with the X-ray observations. It appears that n H = 0 .
21 cm − gives the dividing line between the leptonic and hadronic models with the former having a lowerdensity. Assuming a single power-law distribution with α = 2 and K ep = 5 × − , the dotted line shows the densitywhen the γ -ray flux at 1 GeV produced via the hadronic processes equals to that produced via IC of the CMB. Withthe decrease of α , this line will shift toward high densities since the GeV emission efficiency via the IC process increases.Along the dotted line, the radio to γ -ray flux density ratio increases with the increase of B , which is consistent withFigure 10 with radio brighter sources having stronger magnetic fields. The radio flux density also depends on thespectral index with weaker radio emission for sources with harder spectra. This explains the relative strong magneticfield for the two weak radio sources HESS J1534-571 and G150.3+4.5. The exact strength of the magnetic field alsodepends on contributions to the γ -ray via the leptonic processes in the hadronic scenario. Below the dotted line, theleptonic process dominates the γ -ray emission. The dashed lines indicate the correlation between n H and B if the γ -ray emission is solely produced via the hadronic scenario for 13 SNRs studied in the paper, where f R and f GeV represent the flux density at 1 GHz and 1 GeV, respectively. Equally good fits to the SEDs can be obtained alongthese lines. Note that via the CO and/or HI observations, much higher densities are obtained for some sources in oursample, e.g., ∼
130 cm − for RX J1713.7-3946 (Fukui et al. 2012), ∼
60 cm − for HESS J1731-347 (Fukuda et al.2014), ∼
100 cm − for RX J0852-4622 (Fukui et al. 2017), ∼
75 cm − for RCW 86 (Sano et al. 2019), ∼ − eV cosmic ray acceleration log ( B [ G]) l o g ( n H [ c m ]) F pp F IC at E ph = 1 GeV for K ep = 5 × 10 and = 2.0 log n H cm = + 12 log BG + log K ep - log f R f Gev + Constant filled points: for hadronicopen points: for leptonicG150.3+4.5G296.5+10.0HESS J1912+101RX J1713.7 3946RX J0852.0 4622HESS J1731 347RCW 103 SN 1006HESS J1534 571RCW 86Gamma CygniN132DG279.0+1.1
Figure 18.
Gas density n H vs magnetic field B for the favored models for the 13 SNRs studied in this paper. The open signsbelow n H = 0 . − are for the leptonic models. The dashed lines satisfy the inserted equation, which assumes synchrotronprocess for the radio flux density f R and hadronic processes for the γ -ray flux density f GeV and gives the model-predictedrelationship between n H and B in the hadronic scenario for different SNRs. The dotted line indicates the gas density that cangive a γ -ray flux density at 1 GeV via hadronic processes F pp equal to the 1 GeV flux density produced via IC scattering ofCMB F IC by energetic electrons with K ep = 0 .
005 and α = 2 . cm − for N132D (Bamba et al. 2018; Sano et al. 2020) and ∼
45 cm − for Gamma Cygni (MAGIC Collaborationet al. 2020). A higher average density in the γ -ray emission region will result in a larger magnetic field and a lowertotal energy of relativistic protons. We obtained a lower limit to the total energy of cosmic rays of 10 − ergsby adopting these densities. The number density of some individual cloud can be as high as 10 − cm − in RXJ1713.7-3946 (Sano et al. 2010; Maxted et al. 2012). Most of these high density regions are associated with local cloudswith a small volume filling factor, implying that the shock acceleration mainly operates in a low density inter-cloudmedium as we assumed (see Table 2). Under the strong magnetic field of these clouds, the broad-band SED can bewell reproduced without considering the higher value of n H due to the energy depended-penetration of cosmic-raysinto the dense clouds. Considering that the distribution of high energy particles should be more or less uniform dueto diffusion, a good spatial correspondence between TeV gamma-rays and interstellar neutral gases is expected in thehadronic scenario for the γ -ray emission.To explain the origin of hard γ -ray spectra from supernova remnants in the hadronic scenario, Gabici & Aharonian(2014) first showed that the energy dependent penetration of cosmic rays into dense emission regions can lead toa very hard γ -ray spectrum at low energies. Detailed studies of shock interaction with molecular clouds show thatthe magnetic field strength will be enhanced not only on the surface of targeted clouds, but also inside these clouds(Zirakashvili & Aharonian 2010; Inoue et al. 2012; Inoue 2019). The model was further developed by Celli et al. (2019).Detailed modeling of RX J1713.7-3946 also favors the hadronic scenario (Zhang & Chen 2016). Our results suggestthat the hard spectra may be due to very efficient particle acceleration in a low density environment (Zhang et al.2017; Zhang & Liu 2019c). A softer spectrum can be produced when shocks slow down dramatically due to interaction0 Zeng et al. with molecular clouds (Bell et al. 2013; Tang & Chevalier 2014), which may explain the low energy spectral componentseen in HESS J1912+101 and G279.0+1.1. B [ G] W e ( E > G e V ) [ e r g ] G150.3+4.5G296.5+10.0HESS J1912+101RX J1713.7 3946RX J0852.0 4622HESS J1731 347RCW 103 SN 1006HESS J1534 571RCW 86Gamma CygniN132DG279.0+1.1
Figure 19.
The total energy content of electron above 1 GeV W e vs magnetic field B for the 13 SNRs studied in this paper. Figure 19 shows the scatter plot between B and W e . The total energy of electrons W e is about 10 erg, with N132Dhaving the highest value of 1 . × erg and G150.3+04.5 having the lowest value of 2 . × erg. These resultslook reasonable. Table 2 shows that the cutoff energies of these electrons are always around 1 TeV for sources withoutnonthermal X-ray emission, which may explain the spectral break near 1 TeV in the cosmic ray electron spectrum(DAMPE Collaboration et al. 2017). For the three sources RX J1713.7 − − − K ep for the difference in their spectral shape. Theleptonic model always has a softer spectrum than the hadronic one. Better spectral measurements in the radio bandmay distinguish these models.Figure 20 shows the dependence of W B /W e on the age of the SNR. In the leptonic models, the magnetic field energyis comparable to the total energy of electrons. In the hadronic scenario, the magnetic energy is comparable to that ofprotons and W B /W e appears to increase with the age of the SNR. CONCLUSIONSIn this paper, we carried out detailed spectral modeling of 13 SNRs with hard GeV spectra. We re-analyzed theFermi data of HESS J1912+101, and found its TeV emission can not be attributed to leptonic process for the old ageof the SNR inferred from molecular cloud observations and the spin-down age of the associated pulsar. The same isfor SNR G279.0+1.1. A detailed analysis of XMM-Newton observations of G296.5+10.0 failed to uncover nonthermalemission, which in combination with Fermi data analyses also favors the hadronic scenario for the γ -ray.Of the 13 sources studied here, only SN 1006 and RCW 86 favor the leptonic scenario for their γ -ray emission. RXJ1713.7 − − −
347 can be explained with both leptonic and hadronic models. In eV cosmic ray acceleration Age [kyr] W B W e SN 1006RCW 86G150.3+4.5G296.5+10.0HESS J1912+101 RX J1713.7 3946RX J0852.0 4622HESS J1731 347RCW 103 HESS J1534 571Gamma CygniN132DG279.0+1.1
Figure 20.
The ratio of the magnetic energy W B to the total energy content of electron above 1 GeV W e for the 13 SNRsstudied in this paper. the leptonic models, the total energy of the magnetic field is comparable to that of the electrons. In the hadronicmodels, the magnetic fields and protons are close to energy equipartition. All these sources have prominent nonthermalX-ray emission. For the other 8 sources without evident nonthermal X-ray emission, the hadronic models with a singlepower-law particle distribution are favored. And in the hadronic scenario, the magnetic field of older remnants tendsto contain more energy than relativistic particles, which may be attributed to escape of high energy particles fromSNRs (Profumo et al. 2018; MAGIC Collaboration et al. 2020).Although our results do not completely address the origin of hard γ -ray spectra from SNRs, young remnants withprominent nonthermal X-ray emission favors the leptonic scenario, while absence of nonthermal X-ray emission stronglyfavors the hadronic scenario. For RX J1713.7 − − − ergfor each core collapse SNR, which indicates very efficient ion acceleration and is compatible to the relatively hardspectra inferred from observations (Zhang & Liu 2019c). G78.2+01.2 has the lowest cutoff energy indicating escape ofparticles beyond 10 TeV from the SNR. Nearby molecular clouds may be illuminated by these escaping particles andproduce γ -ray in the TeV band. HESS 1912+101 has the oldest age in our sample, yet the cutoff energy of protonsis relatively high, indicating structure of the magnetic field may play an important role on the escape process. Thestrong linear polarization of the radio emission indeed indicates presence of large scale regular magnetic field, whichmay trap high-energy particles in this source effectively. For sources with prominent nonthermal X-ray emission,the electron distribution always cuts off above 7 TeV, while those without nonthermal X-ray emission, their electron2 Zeng et al. distribution always cuts off near 1 TeV, which may explain the cosmic ray electron spectrum in the TeV range (DAMPECollaboration et al. 2017). Further exploration of this issue is warranted. Age [year] s y n ( E e , c u t ) [ y e a r ] G150.3+4.5G296.5+10.0HESS J1912+101RX J1713.7 3946RX J0852.0 4622HESS J1731 347RCW 103SN 1006 HESS J1534 571RCW 86Gamma CygniN132DG279.0+1.1W28W30 3C391Kes 79W44W49BW51CG73.9+0.9Cygnusloop HB21CTB109TychoHB3HB9G166.0+4.3S147 IC443G205.5+0.5Puppis AKes 17MSH 15-56CTB33CTB 37A CTB 37BG349.7J1745kes 27kes 41MSH11-61AMSH17-39
Figure 21.
The correlation between the electron synchrotron cooling time at the cutoff energy and the age of SNRs.
To study the acceleration of high-energy particles in SNRs, Zeng et al. (2019) plotted the synchrotron energy losstime at the cutoff energy of electron distribution vs the ages of a sample of SNRs. This figure is updated here as shownin Figure 21, confirming the early discovery that high-energy electrons are mostly accelerated in young SNRs and theradiative energy loss and escape processes dominate in old SNRs.ACKNOWLEDGMENTSWe thank the anonymous referee for very helpful suggestions that help to improve the manuscript significantly. Thiswork is partially supported by National Key R&D Program of China: 2018YFA0404203, NSFC grants: U1738122,U1931204, 11761131007, 11573070, the Natural Science Foundation for Young Scholars of Jiangsu Province, China(No. BK20191109), and by the International Partnership Program of Chinese Academy of Sciences, grant No.114332KYSB20170008. REFERENCES
Abdo, A. A., Ackermann, M., Ajello, M., et al. 2010,Science, 327, 1103, doi: 10.1126/science.1182787Abdollahi, S., Acero, F., Ackermann, M., et al. 2020, ApJS,247, 33, doi: 10.3847/1538-4365/ab6bcb Abeysekara, A. U., Archer, A., Aune, T., et al. 2018, ApJ,861, 134, doi: 10.3847/1538-4357/aac4a2Abeysekara, A. U., Archer, A., Benbow, W., et al. 2020,ApJ, 894, 51, doi: 10.3847/1538-4357/ab8310 eV cosmic ray acceleration Acero, F., Aharonian, F., Akhperjanian, A. G., et al. 2010,A&A, 516, A62, doi: 10.1051/0004-6361/200913916Aguilar, M., Aisa, D., Alpat, B., et al. 2015a, Phys. Rev.Lett., 114, 171103, doi: 10.1103/PhysRevLett.114.171103—. 2015b, Phys. Rev. Lett., 115, 211101,doi: 10.1103/PhysRevLett.115.211101Aharonian, F., Akhperjanian, A. G., Bazer-Bachi, A. R.,et al. 2007, ApJ, 661, 236, doi: 10.1086/512603Aharonian, F., Akhperjanian, A. G., Barres de Almeida,U., et al. 2008, A&A, 484, 435,doi: 10.1051/0004-6361:20078715Ajello, M., Baldini, L., Barbiellini, G., et al. 2016, ApJ,819, 98, doi: 10.3847/0004-637X/819/2/98Araya, M. 2013, MNRAS, 434, 2202,doi: 10.1093/mnras/stt1162—. 2017, ApJ, 843, 12, doi: 10.3847/1538-4357/aa7261—. 2020, MNRAS, 492, 5980, doi: 10.1093/mnras/staa244Bamba, A., Fukazawa, Y., Hiraga, J. S., et al. 2008, PASJ,60, S153, doi: 10.1093/pasj/60.sp1.S153Bamba, A., Ohira, Y., Yamazaki, R., et al. 2018, ApJ, 854,71, doi: 10.3847/1538-4357/aaa5a0Bell, A. R., Schure, K. M., Reville, B., & Giacinti, G. 2013,MNRAS, 431, 415, doi: 10.1093/mnras/stt179Bocchino, F., Vink, J., Favata, F., Maggio, A., & Sciortino,S. 2000, A&A, 360, 671.https://arxiv.org/abs/astro-ph/0005369Braun, C., Safi-Harb, S., & Fryer, C. L. 2019, MNRAS,489, 4444, doi: 10.1093/mnras/stz2437Butt, Y. M., Porter, T. A., Katz, B., & Waxman, E. 2008,MNRAS, 386, L20, doi: 10.1111/j.1745-3933.2008.00452.xCelli, S., Morlino, G., Gabici, S., & Aharonian, F. A. 2019,MNRAS, 487, 3199, doi: 10.1093/mnras/stz1425Chang, C., Konopelko, A., & Cui, W. 2008, ApJ, 682, 1177,doi: 10.1086/589225Clark, D. H., Caswell, J. L., & Green, A. J. 1975,Australian Journal of Physics Astrophysical Supplement,37, 1Cohen, J. M. 2016, PhD thesis, University of Maryland,College ParkCondon, B., Lemoine-Goumard, M., Acero, F., & Katagiri,H. 2017, ApJ, 851, 100, doi: 10.3847/1538-4357/aa9be8DAMPE Collaboration, Ambrosi, G., An, Q., et al. 2017,Nature, 552, 63, doi: 10.1038/nature24475DAMPE Collaboration, An, Q., Asfandiyarov, R., et al.2019, Science Advances, 5, doi: 10.1126/sciadv.aax3793De Luca, A., & Molendi, S. 2004, A&A, 419, 837,doi: 10.1051/0004-6361:20034421Devin, J., Lemoine-Goumard, M., Grondin, M.-H., et al.2020, arXiv e-prints, arXiv:2009.08397.https://arxiv.org/abs/2009.08397 Dickel, J. R., Green, A., Ye, T., & Milne, D. K. 1996, AJ,111, 340, doi: 10.1086/117786Dickel, J. R., & Milne, D. K. 1995, AJ, 109, 200,doi: 10.1086/117266Doroshenko, V., P¨uhlhofer, G., Bamba, A., et al. 2017,A&A, 608, A23, doi: 10.1051/0004-6361/201730983Duncan, A. R., & Green, D. A. 2000, A&A, 364, 732.https://arxiv.org/abs/astro-ph/0009289Duncan, A. R., Haynes, R. F., Stewart, R. T., & Jones,K. L. 1995, MNRAS, 277, 319,doi: 10.1093/mnras/277.1.319Dyer, K. K., Cornwell, T. J., & Maddalena, R. J. 2009, AJ,137, 2956, doi: 10.1088/0004-6256/137/2/2956Fleischhack, H. 2019, in International Cosmic RayConference, Vol. 36, 36th International Cosmic RayConference (ICRC2019), 675.https://arxiv.org/abs/1907.08572Fukuda, T., Yoshiike, S., Sano, H., et al. 2014, ApJ, 788,94, doi: 10.1088/0004-637X/788/1/94Fukui, Y., Moriguchi, Y., Tamura, K., et al. 2003, PASJ,55, L61, doi: 10.1093/pasj/55.5.L61Fukui, Y., Sano, H., Sato, J., et al. 2012, ApJ, 746, 82,doi: 10.1088/0004-637X/746/1/82—. 2017, ApJ, 850, 71, doi: 10.3847/1538-4357/aa9219Gabici, S., & Aharonian, F. A. 2014, MNRAS, 445, L70,doi: 10.1093/mnrasl/slu132Gao, X. Y., Han, J. L., Reich, W., et al. 2011, A&A, 529,A159, doi: 10.1051/0004-6361/201016311Gerbrandt, S., Foster, T. J., Kothes, R., Geisb¨usch, J., &Tung, A. 2014, A&A, 566, A76,doi: 10.1051/0004-6361/201423679Giacani, E. B., Dubner, G. M., Green, A. J., Goss, W. M.,& Gaensler, B. M. 2000, AJ, 119, 281,doi: 10.1086/301173Giuliani, A., Cardillo, M., Tavani, M., et al. 2011, TheAstrophysical Journal, 742, L30,doi: 10.1088/2041-8205/742/2/l30Guo, X.-L., Xin, Y.-L., Liao, N.-H., et al. 2018, ApJ, 853, 2,doi: 10.3847/1538-4357/aaa3f8H. E. S. S. Collaboration, Abramowski, A., Acero, F., et al.2011a, A&A, 531, A81,doi: 10.1051/0004-6361/201016425—. 2011b, A&A, 531, A81,doi: 10.1051/0004-6361/201016425H. E. S. S. Collaboration, Abramowski, A., Aharonian, F.,et al. 2015, Science, 347, 406,doi: 10.1126/science.1261313H. E. S. S. Collaboration, Abdalla, H., Abramowski, A.,et al. 2018a, A&A, 612, A6,doi: 10.1051/0004-6361/201629790 Zeng et al. —. 2018b, A&A, 612, A8,doi: 10.1051/0004-6361/201730737—. 2018c, A&A, 612, A7,doi: 10.1051/0004-6361/201630002H. E. S. S. Collaboration, Abramowski, A., Aharonian, F.,et al. 2018d, A&A, 612, A4,doi: 10.1051/0004-6361/201526545Helder, E. A., Vink, J., Bamba, A., et al. 2013, MNRAS,435, 910, doi: 10.1093/mnras/stt993Helfand, D. J., & Becker, R. H. 1984, Nature, 307, 215,doi: 10.1038/307215a0HI4PI Collaboration, Ben Bekhti, N., Fl¨oer, L., et al. 2016,A&A, 594, A116, doi: 10.1051/0004-6361/201629178Higgs, L. A. 1977, AJ, 82, 329, doi: 10.1086/112054Hughes, J. P., Hayashi, I., & Koyama, K. 1998, ApJ, 505,732, doi: 10.1086/306202Inoue, T. 2019, ApJ, 872, 46,doi: 10.3847/1538-4357/aafb70Inoue, T., Yamazaki, R., Inutsuka, S.-i., & Fukui, Y. 2012,ApJ, 744, 71, doi: 10.1088/0004-637X/744/1/71Jones, F. C. 1968, Physical Review, 167, 1159,doi: 10.1103/PhysRev.167.1159Katsuda, S., Petre, R., Long, K. S., et al. 2009, ApJL, 692,L105, doi: 10.1088/0004-637X/692/2/L105Katsuda, S., Tsunemi, H., & Mori, K. 2008, ApJL, 678,L35, doi: 10.1086/588499Kellett, B. J., Branduardi-Raymont, G., Culhane, J. L.,et al. 1987, MNRAS, 225, 199,doi: 10.1093/mnras/225.2.199Kothes, R., Fedotov, K., Foster, T. J., & Uyanıker, B. 2006,A&A, 457, 1081, doi: 10.1051/0004-6361:20065062Kuntz, K. D., & Snowden, S. L. 2008, A&A, 478, 575,doi: 10.1051/0004-6361:20077912Lagage, P. O., & Cesarsky, C. J. 1983, A&A, 125, 249Lazendic, J. S., Slane, P. O., Gaensler, B. M., et al. 2004,ApJ, 602, 271, doi: 10.1086/380956Leahy, D. A., Green, K., & Ranasinghe, S. 2013, MNRAS,436, 968, doi: 10.1093/mnras/stt1596Lemoine-Goumard, M., Renaud, M., Vink, J., et al. 2012,A&A, 545, A28, doi: 10.1051/0004-6361/201219896MAGIC Collaboration, Acciari, V. A., Ansoldi, S., et al.2020, arXiv e-prints, arXiv:2010.15854.https://arxiv.org/abs/2010.15854Maxted, N. I., Rowell, G. P., Dawson, B. R., et al. 2012,MNRAS, 422, 2230,doi: 10.1111/j.1365-2966.2012.20766.xMaxted, N. I., Braiding, C., Wong, G. F., et al. 2018,MNRAS, 480, 134, doi: 10.1093/mnras/sty1797Milne, D. K., & Haynes, R. F. 1994, MNRAS, 270, 106,doi: 10.1093/mnras/270.1.106 Mori, M. 2009, Astroparticle Physics, 31, 341,doi: 10.1016/j.astropartphys.2009.03.004Morris, D. J., Hobbs, G., Lyne, A. G., et al. 2002, MNRAS,335, 275, doi: 10.1046/j.1365-8711.2002.05551.xPorter, T. A., Moskalenko, I. V., & Strong, A. W. 2006,ApJL, 648, L29, doi: 10.1086/507770Profumo, S., Reynoso-Cordova, J., Kaaz, N., & Silverman,M. 2018, PhRvD, 97, 123008,doi: 10.1103/PhysRevD.97.123008Qiao, B.-Q., Liu, W., Guo, Y.-Q., & Yuan, Q. 2019, JCAP,2019, 007, doi: 10.1088/1475-7516/2019/12/007Reich, W., & Sun, X.-H. 2019, Research in Astronomy andAstrophysics, 19, 045, doi: 10.1088/1674-4527/19/3/45Reynoso, E. M., Green, A. J., Johnston, S., et al. 2004,PASA, 21, 82, doi: 10.1071/AS03053Sano, H., Sato, J., Horachi, H., et al. 2010, ApJ, 724, 59,doi: 10.1088/0004-637X/724/1/59Sano, H., Rowell, G., Reynoso, E. M., et al. 2019, ApJ, 876,37, doi: 10.3847/1538-4357/ab108fSano, H., Plucinsky, P. P., Bamba, A., et al. 2020, ApJ,902, 53, doi: 10.3847/1538-4357/abb469Smith, D. A., Bruel, P., Cognard, I., et al. 2019, ApJ, 871,78, doi: 10.3847/1538-4357/aaf57dSu, Y., Zhou, X., Yang, J., et al. 2017, The AstrophysicalJournal, 845, 48, doi: 10.3847/1538-4357/aa7f2aTanaka, T., Uchiyama, Y., Aharonian, F. A., et al. 2008,ApJ, 685, 988, doi: 10.1086/591020Tanaka, T., Allafort, A., Ballet, J., et al. 2011, ApJL, 740,L51, doi: 10.1088/2041-8205/740/2/L51Tang, X., & Chevalier, R. A. 2014, ApJL, 784, L35,doi: 10.1088/2041-8205/784/2/L35Tian, W. W., Leahy, D. A., Haverkorn, M., & Jiang, B.2008, ApJL, 679, L85, doi: 10.1086/589506Tsuji, N., & Uchiyama, Y. 2016, PASJ, 68, 108,doi: 10.1093/pasj/psw102Vasisht, G., Kulkarni, S. R., Anderson, S. B., Hamilton,T. T., & Kawai, N. 1997, ApJL, 476, L43,doi: 10.1086/310493Vogt, F., & Dopita, M. A. 2011, Ap&SS, 331, 521,doi: 10.1007/s10509-010-0479-7Wendker, H. J., Higgs, L. A., & Landecker, T. L. 1991,A&A, 241, 551Winkler, P. F., Gupta, G., & Long, K. S. 2003, ApJ, 585,324, doi: 10.1086/345985Woermann, B., & Jonas, J. L. 1988, MNRAS, 234, 971,doi: 10.1093/mnras/234.4.971Wood, M., Caputo, R., Charles, E., et al. 2017, inInternational Cosmic Ray Conference, Vol. 301, 35thInternational Cosmic Ray Conference (ICRC2017), 824.https://arxiv.org/abs/1707.09551 eV cosmic ray acceleration25