The Gamma-Ray Origin of RX J0852.0-4622 Quantifying the Hadronic and Leptonic Components: Further Evidence for the Cosmic-Ray Acceleration in Young Shell-type SNRs

Fukui et al. quantified the hadronic and leptonic gamma-rays in the young TeV gamma-ray shell-type supernova remnant (SNR) RX J1713.7-3946 (RX J1713), and demonstrated that gamma rays are a combination of hadronic and leptonic gamma-ray components with a ratio of ∼6: 4 in gamma-ray counts N g. This discovery, which adopted a new methodology of multi-linear gamma-ray decomposition, was the first quantification of the two gamma-ray components. In the present work, we applied the same methodology to another TeV gamma-ray shell-type SNR RX J0852.0-4622 (RXJ0852) in 3D space characterized by (the interstellar proton column density N p)-(the nonthermal X-ray count N x)-[N g], and quantified the hadronic and leptonic gamma-ray components as having a ratio of ∼5:5 in N g. The present work adopted the fitting of two/three flat planes in 3D space instead of a single flat plane, which allowed suppression of the fitting errors. This quantification indicates that hadronic and leptonic gamma-rays are of the same order of magnitude in these two core-collapse SNRs, verifying the significant hadronic gamma-ray components. We argue that the target interstellar protons, in particular their spatial distribution, are essential in any attempts to identify the type of particles responsible for gamma-ray emission. The present results confirm that cosmic-ray (CR) energy ≲100 TeV is compatible with a scheme in which SNRs are the dominant source of these Galactic CRs.


Gamma-Ray Production in the Galaxy
The origin of Galactic cosmic rays (CRs) has been a longstanding issue in astrophysics.For CRs of energy less than the knee at <10 15.5 eV, supernova remnants (SNRs) are the most promising candidates to explain CR acceleration in the Galaxy.Diffusive shock acceleration provides an effective mechanism to accelerate charged particles, which account for the acceleration of CRs in SNRs (Bell 1978).In order to verify CR acceleration in SNRs, it is essential to identify gamma rays and/or neutrinos, both of which follow the p-p reactions of CR protons.The observations of SNRs with the gamma-ray instruments, including H.E.S.S., MAGIC, VERITAS, Fermi-LAT, etc. detected gamma rays toward a number of SNRs in the last two decades.Neutrino imaging is being developed, however, it is not yet at a stage comparable to gamma-ray imaging (e.g., Madsen 2019).Most recently, the IceCube Collaboration revealed a strong concentration of neutrino emission in the Galactic plane, lending support for the SNR origin of neutrinos (IceCube Collaboration 2023).The very high-energy gamma rays in the GeV-TeV range are therefore the current best probe for CRs.In particular, young TeV gamma-ray SNRs with ages of 1000-5000 yr are the most important because their gamma-ray energy range is the highest at 100 TeV in the Galaxy, reaching fairly close to the knee, which is likely linked with the highest energy CRs in the Galaxy.These SNRs include RX J1713.7-3946(RX J1713), the brightest one in the sky, and RX J0852.0-4622(RX J0852) the second brightest.This is in contrast to middle-aged SNRs with lower gamma-ray energy by three orders of magnitude.Middle-aged SNRs do not exhibit ongoing acceleration of the highest energy CRs, but their escaping CRs are important tracers of past CR acceleration (e.g., Casanova et al. 2010;Mitchell et al. 2021).

The Two Gamma-Ray Components
CRs create gamma rays via two processes, i.e., the hadronic process (pp → π 0 → 2γ) and the leptonic process (inverse Compton (IC) scattering).Quantification of CR energy will be accomplished only by identifying both the hadronic gamma-ray components and the interstellar protons, the target for the p-p reactions.Otherwise, one cannot exclude the possibility that gamma rays are dominated by leptonic gamma-ray components that carry only a minor part of the CR energy.It was thought that the gamma-ray spectrum could offer a key signature that could discriminate the two components.This, however, turned out to be hard to achieve because the gamma-ray spectrum is dramatically changeable not only by the process but also by the properties of the CRs and the interstellar medium (ISM) in SNRs.For example, Abdo et al. (2011) claimed that the gamma rays obtained by the Fermi Collaboration in RX J1713 are due to the leptonic process by presenting a hard GeV-TeV gammaray spectrum similar to what is expected from the leptonic process.On the other hand, Inoue et al. (2012) argued that density-dependent penetration of CR protons into dense cloud cores produces a hadronic gamma-ray spectrum very similar to the leptonic gamma-ray spectrum.Such dense cloud cores were in fact observed in the gamma-ray peaks in RX J1713 by Fukui et al. (2003), (Fukui et al. 2012, Paper I hereafter), Moriguchi et al. (2005), and Maxted et al. (2012Maxted et al. ( , 2013)), and may significantly affect the gamma-ray spectrum.The hard gammaray spectrum compared with the GeV-TeV gamma-ray spectrum was calculated for uniform low-density target protons (Abdo et al. 2011), which is not realistic.Inoue et al. (2012) therefore suggested that only spatial correspondence between the interstellar protons and the gamma rays, instead of the gamma-ray spectrum, can verify hadronic gamma rays.A similar argument by Gabici & Aharonian (2007) on the spectrum was presented in terms of the CR diffusion in diffuse gamma rays, and such a modified hard hadronic spectrum was confirmed through numerical simulations by Gabici & Aharonian (2014).H.E.S.S. Collaboration (2018a, and references therein) (see also Aharonian et al. 2007a) repeatedly showed that the observed gamma-ray spectrum of RX J1713 can be fit well by using either the pure hadronic model or the pure leptonic model under a reasonable set of CR parameters, while for simplicity they assumed uniform ISM protons instead of the realistic clumpy ISM distribution (Paper I, for details see below).In summary, the spectral fit is not a tool that can by itself discriminate the two origins of gamma rays.

Gamma-Ray Imaging and Its Spatial Correspondence
Hadronic gamma rays will naturally follow the observed distribution of the target interstellar protons, and the spatial distribution of the gamma rays is an essential piece of the properties of hadronic gamma-ray.Early gamma-ray imaging was too low in spatial resolution at a degree scale (e.g., EGRET).The advent of the atmospheric Cerenkov telescopes improved the resolution, particularly in the TeV range.Among all, the H.E.S.S. obtained TeV gamma-ray images with a resolution of ∼0°. 1, which are able to resolve nearby young SNRs with ages of 1000-5000 yr having spatial extents of around a degree.These SNRs include RX J1713, RX J0852, HESS J1731-347 (HESS J1731), RCW 86, and several more in the TeV range (The H.E.S.S. Galactic plane survey, H.E.S.S.

Collaboration 2018b).
In RX J1713, the CANGAROO Cerenkov telescope detected and mapped TeV gamma rays (Enomoto et al. 2002), andFukui et al. (2003) compared the NANTEN CO observations with the partial TeV gamma-ray image.Fukui et al. (2003) revealed that one of the CO peaks, a dense molecular cloud core in the SNR, showed a good spatial match with the TeV gamma-ray peak, and suggested that the coincidence is a possible signature of the hadronic gamma-ray components.Subsequently, the H.E.S.S. Collaboration revealed good spatial correspondence between the TeV gamma-ray peaks and the NANTEN CO clouds toward the middle-aged SNR W28, indicating the presence of hadronic gamma rays (Aharonian et al. 2006).Soon after, in RX J1713 and RX J0852 H.E.S.S. revealed their shell-like TeV gamma-ray images, whereas their comparisons with NANTEN CO clouds indicated that the CO did not show an overall match with the gamma-ray shells, being unfavorable for the hadronic interpretation (Aharonian et al. 2007a(Aharonian et al. , 2007b)).In particular, it was revealed that strong gamma rays are emitted even in regions with no CO emission.
Paper I (see also Fukui 2008) renewed the total interstellar proton distribution in RX J1713 based on the CO and H I gas, where the new H I survey by McClure-Griffiths et al. (2005) at ¢ 2 resolution was employed.A new aspect of Paper I was the inclusion of the atomic hydrogen gas having densities of 10-100 cm −3 , which was neglected in the previous comparisons under the assumption that CO gas only is important as target protons.As a result, Paper I revealed that the total interstellar protons consisting of both molecular and atomic protons have good spatial correspondence with gamma rays, indicating that dense H I gas is equally important to the CO gas toward gamma-ray bright regions.Further, in RX J0852 Fukui et al. (2017, Paper II hereafter) carried out a comparative study of the total ISM protons of both atomic and molecular gas with the TeV gamma rays, and found that RX J0852 also shows good spatial correspondence with the total ISM protons, which include both molecular and atomic protons.Paper I and Paper II therefore lend support for a hadronic gamma-ray component both in RX J1713 and RX J0852 under the assumption of uniform CR energy density.
Nonetheless, the spatial correspondence alone between the gamma rays and the target ISM protons does not exclude the contribution of the leptonic components.In an extremely opposite case, suppose for instance that the leptonic gamma rays are overwhelming the hadronic gamma rays everywhere in an SNR, while the distributions of the gamma rays, nonthermal X-rays, and the ISM protons all appear shell-like.In such a case, the gamma-ray distribution is determined by the leptonic components, and the correspondence between the gamma rays and the ISM protons is fortuitous.We therefore need a more accurate quantitative method for verification of the origin of gamma rays.In this context, it helps to consider a case where the two gamma-ray components are coexistent in the gammaray counts.Such a hybrid picture was suggested in HESS J1731 and RCW 86, which exhibit that part of the gamma rays shows spatial correspondence with the ISM and the rest with the nonthermal rays (Fukuda et al. 2014;Sano et al. 2019).In the hybrid case, we expect naively that the gamma-ray counts will increase with both the ISM proton column density and the nonthermal X-ray counts, which may become obvious in scatter plots of the gamma-ray counts versus the ISM proton column density or versus the nonthermal X-ray counts.If the hybrid case is correct, the two SNRs HESS J1731 and RCW 86 imply that the two gamma-ray components may be similar to each other.However, in these cases, the number of pixels available for study is 10, limiting the precision of the conclusions.

Quantification of the Hadronic and Leptonic Gamma Rays in RX J1713
Recently, in RX J1713 H.E.S.S. gamma-ray data were updated and released after significant improvement by the H.E.S.S. Collaboration (2018a).The new TeV gamma-ray data (>1 TeV energy range) have a higher angular resolution by a factor of 3, 1.4 pc, along with a factor of 2 better sensitivity.Fukui et al. (2021, Paper III hereafter) used the data and applied a new methodology that enabled quantification of the origin of two gamma rays for the first time, and derived a hadronic-leptonic gamma-ray count ratio of ∼6:4 in RX J1713.We note that Paper III is distinguished from the previous theoretical results (e.g., H.E.S.S. Collaboration 2018a) because the ISM proton distribution adopted in Paper III is obtained directly from the CO and H I observations in Paper I, which ensures sufficiently high accuracy in calculating the hadronic gamma-ray components.This accuracy cannot be attained in the other works that assume uniform ISM distribution, which has no observational justification.
The new methodology of Paper III quantifies the leptonic and hadronic gamma-ray components as follows; the hadronic gamma-ray counts are proportional to the number product of the CR protons and the target interstellar protons in the p-p reactions and the leptonic gamma-ray counts are proportional to the product of the number of the CR electrons and the target low-energy photons, usually the cosmic microwave background (CMB) photons, in the IC scattering.These relationships allow one to formulate the gamma-ray counts [N g ] as a combination of two linear terms; one is proportional to the X-ray counts [N x ], as a proxy of the CR electrons, and the other is proportional to the ISM proton column density [N p ] under an assumption that the CR energy density and magnetic field are uniform.In RX J1713, the distributions of N p and N x are shelllike, similar to the TeV gamma-ray distribution N g , whereas, to be strict, distributions of N p and N x are spatially different.The difference is expressed by the spatial correlation coefficient between N p and N x , which is calculated to be 0.7 using pixel sizes of 0°.1 (Paper I).If the two distributions are completely identical, the coefficient is equal to 1.0.The difference produces, not vastly, but significantly different spatial distribution of the hadronic and leptonic gamma rays.Then, Paper III applied the formulation to the data pixels of RX J1713 in a 3D space subtended by N p -N x -N g and showed that N g is expressed by a flat tilted plane in the space.This regression plane is used to derive the hadronic and leptonic gamma-ray counts in each pixel, and Paper III obtained their ratio to be ∼6:4 in N g over the whole SNR.This indicates that the two gamma-ray components are comparable to each other.The next issue is to apply the methodology to the other SNRs and to acquire a broader and deeper view of CR acceleration.Obtaining a larger sample of gamma-ray SNRs will allow us to elucidate significant details of the CR acceleration.

TeV Gamma Ray SNR RX J0852
RX J0852.0−0462(RX J0852, G266.2−1.2) is an SNR with a large diameter of 2°at a distance of 750 pc (e.g., Katsuda et al. 2008;Allen et al. 2015).The SNR has nonthermal X-ray emission without thermal features with an age of (2.4-5.1)× 10 3 yr (Allen et al. 2015).The H.E.S.S. Collaboration imaged the shell-like TeV gamma-ray distribution of RX J0852, which looks similar to the X-ray shell.These properties are common to RX J1713.RX J0852 will enable testing the spatial correspondence between the gamma rays and the ISM thanks to its large apparent size, and is a second promising target where the origin of CRs can be quantified.The supernova is a core-collapse type (Aschenbach 1998;Mereghetti 2001;Pavlov et al. 2001;Slane et al. 2001).The associated interstellar gas has been revealed as part of a molecular supershell of ∼70 pc in diameter by NANTEN CO observations (Paper II, see also Appendix A, and for CO supershells see Fukui et al. 1999;Matsunaga et al. 2001).Paper II analyzed the ISM proton distribution toward RX J0852, which includes both molecular and atomic gas, and showed that the total ISM protons associated with the SNR correspond well spatially to the gamma-ray distribution.
The present paper aims at quantifying the two gamma-ray components in RX J0852 and is organized as follows.Section 2 describes the data sets of CO, H I, TeV gamma rays, and X-rays used in this paper, and Section 3 presents the formulation and the results of the 3D fitting in the N p -N x -N g space of RX J0852 along with supplementary analysis results for RX J1713.In Section 4, we discuss the CR properties shown by the results, including a comparison with RX J1713, and give our conclusions in Section 5.

Observational Data
The present work utilized three data sets of gamma rays, X-rays, and interstellar protons as described in the following.

H.E.S.S. TeV Gamma Rays
As the gamma-ray data, we used the excess count map at E > 100 GeV obtained by the H.E.S.S. Collaboration (2018c) as given in Table 1.The angular resolution is given by a point-spread function (PSF) of 0°.08 at a 68% containment radius, which translates to an FWHM of ∼0°.19 (~¢ 11. 3).We adopted a pixel size of ∼0°.20 (~¢ 11. 4) for a pixel-to-pixel comparison, which corresponds to ∼2.5 pc at a distance of 750 pc (see also Table 1).For more details see the H.E.S.S. Collaboration (2018c).

Suzaku X-Rays
We analyzed Suzaku archive data of RX J0852.0-4622 from the Data Archives and Transmission System (DARTS at ISAS/ JAXA).6 Details of the data reduction are given below.Table 2 summarizes the information on the 45 pointings in total.Part of the data has already been published by Takeda et al. (2016) and Paper II.
In the present analysis of the image, we employed the X-ray Imaging Spectrometer (XIS; Koyama et al. 2007).XIS consists of four CCD cameras, XIS0, XIS1, XIS2, and XIS3, which were installed at the focal plane of the X-ray telescopes (XRTs; Serlemitsos et al. 2007), where XIS2 was not usable due to the damage by the micrometeorite on 2006 November 9.In addition, XIS0 had an anomaly in its segment A on 2009 June 23.In the present work, we only used the data obtained with XIS0 (excluding segment A after 2009 June 23), XIS1, and XIS3.These observations utilized spaced row charge injection (SCI; Nakajima et al. 2008;Uchiyama et al. 2009) except for observation ID 500010010.In the present analysis, we used cleaned event files processed and screened by HEASoft version 6.117 and Suzaku pipeline versions 2.0, 2.2, and 2.8.In the procedure, we made images of the photon count at 2.0-5.7 keV, where non-X-ray background was calculated and subtracted from the nighttime observed data of Earth by using xisnxbgen.We also made Monte Carlo calculations of the flat-field imaging (Ishisaki et al. 2007) in order to correct for the vignetting effect by XRT.Here we considered the effect of the pixels that were not usable in SCI by using xisexpmapgen.In the exposure-corrected and background-subtracted count map (normalized in a units of ( ) - ¢  08 52 01. 4, 46 17 53 h m s (Aschenbach 1998;Aschenbach et al. 1999;Slane et al. 2001) and the pulsar wind nebula 36. 18, 46 44 13. 4 J2000 J2000 h m s (Acero et al. 2013) in the center of the image were masked by a circle of 150″ radius.The resultant image was binned in the same pixels with the H.E.S.S. gamma rays, and was used in the present study.

ISM Protons
The interstellar proton column density distribution was derived following the method of Paper II by using the NANTEN 12 CO(J = 1-0) data (Moriguchi et al. 2001) and  These data were smoothed to the same pixel sizes as the H.E.S.S. gamma rays data ~¢ 4. 8.The velocity integration range was examined and a range of 20-40 km s −1 was adopted in the present work as explained below in this subsection.The CO-to-H 2 conversion factor X CO was taken to be 1.5 × 10 20 cm −2 (K km s −1 ) −1 (Aruga et al. 2022).The H I column density N(H I) was calculated by considering the H I optical depth effect based on the submillimeter dust optical depth following Paper II.The total ISM proton column density N p is given as follows: and re-gridded to a pixel size of ¢ 11. 4.Here N(H 2 ) is the column density of molecular hydrogen H 2 .
It is generally a complicated task to identify the ISM that is associated with an SNR.In the case of RX J0852, it was obvious that the CO and H I gas at a velocity of around 25-30 km s −1 are associated with the SNR (Paper II).The gas in this velocity range shows good morphological correspondence with the X-ray shell in the southwestern part (see Figures 1(b) and 3 of Paper II).The velocity range conflicts with the gas obeying the galactic rotation at a distance near 1 kpc.The gas motion is significantly affected by the local disturbance in the order of >10 km s −1 , which is likely driven by the supershells in the region of RX J0852 as identified in Paper II.In the present work, we took a velocity range of a velocity width of 20 km s −1 , i.e., 20-40 km s −1 , which corresponds to the expanding pattern of the shell created by a stellar wind bubble as shown in Appendix A. The velocity span is the same as that of RX J1713 (Paper I; Paper III) and is consistent with that expected if it is created by the stellar wind acceleration.Paper II suggested that gas with an even larger velocity up to 50 km s −1 might contribute to the gamma-ray emission, while the increase in the H I mass for the larger velocity range is unimportant, i.e., less than ∼10% of the total H I mass.

RX J1713
We used the data of the gamma rays, X-rays, and the interstellar protons N p that were published in Paper I and The three physical quantities relevant to the analysis include the H.E.S.S. TeV gamma-ray count N g , the Suzaku nonthermal X-ray counts N x , and the interstellar proton column density N p . Figure 1(a) shows the distribution of gamma rays.Figures 1(b) and (c) show the distributions of the nonthermal X-rays and the ISM protons superposed with the TeV gamma-ray contours.Figure 2 shows the three data sets gridded to a pixel size of ¢ 11. 4, which is matched to the H.E.S.S. resolution as given in Table 1.The pixels that are analyzed are enclosed by white solid lines.We excluded the pixels toward the PWN unrelated to the SNR in the east (outlined by the dashed-line circle in Figure 2).Figure 3 shows three scatter plots of N g -N x , N g -N p , and N p -N x .Figure 3(a) shows that N g has a high correlation with N x with a correlation coefficient of 0.76.On the other hand, Figure 3(b) shows that N g -N p has a lower correlation coefficient of 0.27 with a larger scatter than in N g -N x .In Figure 3(c), N p -N x has a positive correlation coefficient of 0.14.

RX J1713
Figure 4 shows the distributions of the three physical quantities relevant to the analysis, including the H.E.S.S. TeV gamma-ray count N g , the XMM-Newton nonthermal X-ray counts N x , and the interstellar proton column density N p .Figures 4(a    and N p -N x .Figure 5(a) shows that N g has a high correlation with N x with a correlation coefficient of 0.77, and Figure 5(b) shows that N g -N p has a high correlation coefficient of 0.78.The increase in N g in both N x and N p suggests that N g increases in both N p and N x .Figure 5(c) shows that N p -N x has a positive correlation coefficient of 0.71.

Formulation
Following Paper III, we express N g by a linear combination of N x and N p as follows: The first term stands for the hadronic gamma rays via the p-p reaction, N g hadronic , and the second term for the leptonic gamma rays, N g leptonic , via the IC scattering.We assume here that the energy density of CR protons is uniform within the volume, where the energy density of the CR electrons is negligibly small due to a small electron/proton ratio or with some nonuniformity (see, Zirakashvili &, Aharonian 2010, hereafter ZA10;Brose et al. 2021).In addition, we assume that the magnetic field strength B is uniform within the volume as suggested by the numerical simulations by Inoue et al. (2012), while the simulations show a moderate variation in the field strength by ∼20% when averaged in volume.The CMB photon density is uniform and additional stellar photons are negligible in the region of RX J0852 as shown by the absence of any H II regions or OB stars around the region (Moriguchi et al. 2001).
In the following, we give approximate relationships of the quantities in Equation (2).The first term is expressed by the CR proton volume density n p (CR) times the ISM proton column density N p , where a is a constant including the p-p reaction coefficient (k 1 ) times n p (CR), and k 1 includes a branching ratio of 1/3 for the π 0 production.The second term is proportional to the lowenergy photon volume density n(CMB) times the CR electron column density N e (CR), and N x is expressed by the CR electron column density N e (CR) and the B field as follows: k 3 is the synchrotron emissivity coefficient, and N e (CR) is a sum of the CR electron volume density n e (CR) along the line of sight.

Fitting of the Hadronic and Leptonic Components in RX J0852
In order to determine the best-fit flat plane(s) in the 3D space of N p -N x -N g , we applied Equation (2) to all the data pixels in the 3D space by least-squares fitting following Paper III.
We obtained a multiple linear regression plane as summarized in the first line in Table 3, a single plane as adopted in Paper III.The distribution of the difference in N g is defined as where the 1 in brackets stands for the single-plane and the hatsymbol (  ) the predicted value by the fit plane.The spatial distribution of ΔN g (1) and ( )  N 1 g are shown in Figures 6(a) and (b), respectively.We see that ΔN g (1) tends to become large in the shell, especially in the south, and to become small in the inner part.Figure 6(c) shows a plot of ΔN g (1) as a function of  N g .Table 3 shows the fit results of a and b as well as the reduced χ 2 in the fit where, ν = n − 2 is the degree of freedom, n is the number of pixels of the data set, and σ(N g,i ) is the uncertainty of N g,i estimated from the statistical Poisson error in pixel counts.The subscript i stands for the ith pixel of the data set.We find that the reduced χ 2 is significantly large, more than 6, which is unacceptable.This is probably because the spatial variation of the observed quantities is too large to be described by a single plane.
As a next step, we adopted an approach to fit the pixels by two or three planes so as to cover their large variation.For this purpose, we chose two pixel groups by ΔN g (1) > 0 and ΔN g (1) 0, and three pixel groups with ΔN g (1) 0.1, −0.1 < ΔN g (1) < 0.1, and ΔN g (1) −0.1, for the two-plane fit and three-plane fit, respectively.This grouping yielded a nearly equal number of pixels in each pixel group, and is not biased toward the spatial distribution of the individual pixels either on the shell or in the inner part.
The distributions of ΔN g (2) and ( )  N 2 g and of ΔN g (3) and ( )  N 3 g are shown in Figures 7 and 8, respectively, where 2 and 3 in the brackets stand for the two-and three-plane fits.We see that the distributions of ΔN g are similar to those in Figure 6(a), showing a trend of decrease from the shell to the inner part.Table 3 presents the coefficients a and b.The resultant hadronic and leptonic fractions (Table 4) have similar values within a small difference of ±6% in the three-plane fit.
Table 4 also summarizes the values of N g obtained by the present analysis.Based on the present three-plane results, we calculate the hadronic and leptonic gamma-ray counts in each pixel,  N i g, hadronic and  N i g, leptonic , as given by for the three pixel groups.All the errors are calculated in the same manner as in Paper III, and are not repeated here.Consequently, we find that the hadronic component occupies (52 ± 1)% of the total gamma-ray count and the leptonic component (48 ± 1)%.Further discussion is given in Section 4. Figure 9(a) shows the hadronic fraction of gamma rays as a function of N x for two ranges of N p larger or smaller than 3.26 × 10 21 cm −2 .We see a trend in which the hadronic fraction decreases with N x and increases with N p . Figure 9(b) shows the spatial distribution of the hadronic fraction.We find that the fraction is increased in the inner part of the shell and decreased in the shell, in particular in the north and south where the X-rays are enhanced.

Fitting of the Hadronic and Leptonic Components in RX J1713
Figure 10 reproduces the results of the single-plane fit from Paper III.Following the multi-plane fit in RX J0852, we applied a two-plane fit to the data pixels of RX J1713 for the same data set in Paper III.In the present fit, the pixels were grouped into two with ΔN g (1) > 0 and ΔN g (1) < 0. The fit results are listed in Figure 11 and Table 5.The reduced χ 2 in Table 5 shows that the values in the two-plane fit decreased further from 0.41 to 0.85 as compared with the value of 1.74 in the single-plane fit.We find the present results show that the fit results have smaller errors.The distributions of ΔN g (2) of the two pixel groups are shown in Figures 11(a)-(d).We find that the ΔN g (1) > 0 pixel group and the ΔN g (1) 0 pixel group are distributed both in the inner part and the shell part.Table 6 shows the hadronic and leptonic gamma-ray components.Consequently, we obtain that the hadronic component occupies (62 ± 5)% of the total gamma-ray count and the leptonic component (38 ± 5)% in RX J1713.These indicate that the hadronic gamma rays are by 5% weaker within the systematic errors of Paper III, while the basic trend remains the same.

Hadronic/Leptonic Gamma-Ray Ratio
Paper I showed that the ISM proton distribution corresponds well to the gamma-ray distribution, whereas Paper I did not exclude the leptonic components.If we assume an extreme case where the leptonic gamma-ray counts are by more than an order of magnitude higher than the hadronic gamma rays everywhere in an SNR, the hadronic components become almost completely masked by the leptonic components.Then, it is very difficult to quantify the hadronic components from observations.However, the present work along with Paper III revealed that the hadronic components and the leptonic components are comparable in the gamma-ray counts and competing with each other in the two SNRs RX J1713 and RX J0852.A probable reason for the situation is the large mass of the target interstellar protons, which enhances the hadronic gamma rays.The two SNRs are of the core-collapse type, which is naturally associated with massive neutral gas either in atomic or molecular form.On the other hand, in Type Ia SNRs such neutral gas may not be massive enough to produce strong hadronic gamma rays, leading to insignificant hadronic components.

Quantification of the CR Energy
Quantification of the CR energy density in an SNR is crucial to verifying the acceleration of CRs.The present work along with Paper III demonstrates that the present methodology can  4): estimated regression coefficients and their standard deviations; column (5): reduced χ 2 (Equation ( 7)); column (6): variance inflation factor, less than a severe threshold of 3 indicates that multicollinearity is not a significant issue in the analysis (see Appendix C3 of Paper III).
quantify the hadronic gamma rays and the CR proton energy W p in RX J0852 and RX J1713.The energy is calculated based on the associated interstellar proton density along with the gamma-ray luminosity.The CR proton energy W p in the SNR is expressed as follows: where t pp is the cooling time of the CR protons and L g the total gamma-ray luminosity (Aharonian et al. 2006), and f is the hadronic fraction.The total CR proton energy W p above 1 GeV in RX J0852 is given as follows (H.E.S.S. Collaboration 2018c): ´--

W d n
7.1 0.3 1.9 10 750 pc ISM 1 cm erg, 11 p s t a t s y s t 49 where d is the distance, 750 pc, and n p (ISM) is the ISM proton density, ∼90 cm −3 , by adopting the shell radius of ∼11.8 pc and the thickness of ∼5.6 pc.W p is estimated to be W p = 7.7 × 10 47 erg by adopting n = 90 cm −3 , where the hadronic gamma rays are assumed to be 100% of the total gamma-ray counts.The present work has shown that a fraction of the hadronic gamma-ray counts is 52% in the whole SNR, and W p = 4.0 × 10 47 erg.
In RX J1713 W p above 1 GeV is calculated by the relationship et al. 2006).We then obtain W p = (0.5-1.4) × 10 48 erg for n = 130 cm −3 (Paper I; Paper III) and a hadronic fraction in the present work of 0.62.This energy is similar to that of RX J0852.We roughly calculate the energy density of CR protons in the two SNRs.In RX J0852, we calculate the energy density to be 2.3 × 10 −12 erg cm −3 by dividing W p by the volume of the SNR shell having an outer radius of 11.8 pc and an inner radius of 6.2 pc.We also apply the same method to RX J1713, which is modeled by a shell having an outer radius of 10.1 pc and an  inner radius of 5.9 pc (Paper I) and obtained the average density of (3.1-8.6)× 10 −12 erg cm −3 .The CR energy densities above 1 GeV in the two SNRs are inferred to be 1-5 eV cm −3 , which gives a secure lower limit for the energy density.This value is significantly greater than the energy density of the CR sea ∼1 eV cm −3 in the Galaxy, which peaked at ∼100 MeV if we take into account the volume-filling factor of the ISM protons, ∼0.1 (see below in this subsection).
Here we note that the numbers of the pixels used in the present fits were reduced by ∼70% from the original data sets because of the exclusion of the pixels with contamination by the PWN (RX J0852) and with an inaccurate ISM density (RX J1713), as well as those outside the gamma-ray shells.In the above, we did not include the corrections.We suggest the energy values above may be reduced to ∼70% if they are taken into account.
The efficiency of the gamma-ray emission via IC scattering by CR electrons is higher than that of the CR protons by two orders of magnitude (e.g., ZA10).The leptonic gamma rays then become comparable to the hadronic gamma rays, even if the electrons are ∼1/100 of the protons in number.The CR electron energy density is therefore likely in the order of 10 45 erg, a negligibly small fraction of the total CR energy density.
The CR proton energy W p calculated in the two SNRs (3-9) × 10 47 erg is smaller than the value ∼10 50 erg, which is an expected W p often quoted if SNRs are the major source of CRs in the Galaxy.This seems to be a difficulty in the SNR origin of Galactic CRs.There are however two factors that need to be taken into account.One is the volume-filling factor of the target interstellar protons.The filling factor is roughly estimated to be ∼0.1 because the dense gas is highly clumped within the shell in RX J1713 (Paper I) as well as in RX J0852 (Paper III).It is thus possible that the current W p in the SNR is an order of magnitude smaller than (3-9) × 10 47 erg derived in the present work because the majority of the CR protons are not contributing to W p via the p-p reaction.The other is the escaping CRs from the SNR shell, which lowers W p by a factor of 10 over the SNR age of >10 5 yr (Gabici & Aharonian 2007) within the SNR boundary, while an estimate of such CRs yet involves large uncertainty (Uchiyama et al. 2012, W44;Aruga et al. 2022, Puppis A; see also H.E.S.S. Collaboration 2018a).Accordingly, we argue that SNRs as the most promising sources of CRs in the Galaxy is a plausible picture.The present work as well as Paper II provides the best quantification of the CR proton energy up to 100 TeV in the two representative young SNRs that seem to be most active in particle acceleration in the solar vicinity.
A scatter plot between the SNR age and CR proton energy W p is presented for 11 SNRs by Sano et al. (2021b).The plot shows a trend that W p increases in the first several 10 3 yr of a young SNR from 10 48 erg up to 3 × 10 49 erg.The phase is followed by decreasing W p probably due to CR escape, which corresponds to the middle-aged SNRs.The trend suggests the total CR proton energy as large as 10 50 erg over the SNR lifetime is not unrealistic by considering the significant CR escape.

Possible Variation of the CR Energy Density between the Shell and the Inner Part
The fit by two to three planes instead of a single plane was required to accommodate the strong variation of the highenergy radiation of RX J0852, in particular, the steep increase in the X-rays toward the shell.The multi-plane fit allows some variation of the coefficients a and b, which tend to increase from the inner part to the shell part.A similar trend is also found in RX J1713, suggesting that the variation may be common in young shell-type SNRs.
In RX J0852, we derived the variation of a by assuming a spherical symmetry of the SNR.For the normalization, first, the separation of each pixel from the central position (α J2000 , δ J2000 ) = (−133°.0,− 46°.37) (H.E.S.S. Collaboration 2018a) was measured.Then, the SNR was divided into 12 fan-shaped segments whose apex has an opening angle of 30°at the center.In each segment, the maximum separation of pixels was chosen as the radius.The separation of a pixel was divided by the radius and determined as the normalized radius of the pixel.
Figure 12 shows a plot of a as a function of the normalized radius.We find a trend in which a becomes more enhanced by ∼30% on average at normalized radii in the shell at a normalized radius of 0.6-1.0than the inner part at a normalized radius of less than 0.6.In RX J1713, we performed the same analysis, but found no trend like in RX J0852 because the pixels fit by the two planes are more mixed up spatially than in RX J0852, resulting in a thicker shell.
The coefficient a represents the p-p reaction coefficient and the CR proton energy density.The coefficient b depends on the IC scattering, the CMB density, and inversely on the B-field energy density (B 2 ), as well as the CR electron energy spectral index for converting the nonthermal X-rays into the gamma-ray photons.
The variation of a therefore may mean an increase of the CR energy density from the inner part to the shell by ∼40%, which may be in accord with the enhanced CR acceleration in the shell where the shock speed is higher as shown by theoretical works (see Figure 2 of ZA10).The trend in b may be more complicated than in a, since b depends on the CR electron spectrum as well as the magnetic field strength.For the electron spectrum in RX J1713, Sano et al. (2015) showed that the electron spectral index becomes harder in the shell than in the inner part, which may possibly increase b in the shell.On the other hand, the magnetic field strength increases in the shell due to the turbulent amplification, causing the decrease in b near the CO clumps (Inoue et al. 2012).So, more details of the trends especially in b remain as a future issue when more reliable variations of a and b become available.At any rate, in the CR energetics of the SNR, a plays a major role as compared with b.

Origin of N p and N x
In the present methodology, the significant difference in the distribution between N p and N x is essential in quantifying the two components.It is impossible to disentangle the two components reliably if the two distributions are very similar with a correlation coefficient close to 1.0.The difference is naturally produced by the evolutionary processes of N p and N x , and can be expected to hold in the other SNRs, including HESS J1731-347 and RCW 86.The N p distribution with a central cavity is produced by the compression of the surrounding clumpy ISM by the stellar winds of the progenitor high-mass star.The timescale of the compression is in the order of ∼10 Myr.On the other hand, the N x distribution, a combined result of the accelerated CR electrons and the magnetic field, is produced via particle acceleration and shock-cloud interaction within 1000 yr after the supernova explosion; the shock front driven by the explosion accelerates particles over a few 1000 yr and amplifies the turbulence and the magnetic field around the dense clumps via shock-cloud interaction in the recent several 100 yr in the present two SNRs (Sano et al. 2010;Inoue et al. 2012).The physical processes responsible for the N p and N x distributions have therefore different origins and timescales by orders of magnitude, although some correlation between them is expected.
The reduced N g and N p correlation in RXJ0825 versus RX J1713 (Figure 3(b)) is probably because of the small mass of the CO clumps in RX J0852, ∼1000 M ☉ , which is about 10% of that in RX J1713 (Paper II).The H I mass is ∼10 4 M ☉ in the two SNRs (Paper I; Paper III).The small CO mass results in less coupling between N p and N x due to less shock-cloud interaction.Sano et al. (2013) showed that the nonthermal X-rays associated with the CO clumps are nearly proportional to the CO clump mass in RX J1713 (see Figure 11 in Sano et al. 2013).The CO mass is the condition provided prior to the supernova.A probable reason for the small CO clump mass is a smaller H 2 /H I ratio around RX J0852, which is in the outer solar circle at a high latitude (Paper II).  3).(b) Distributions of hadronic gamma-ray fraction overlaid with gamma-ray contours (identical to those in Figure 1).

Future Prospects
The present methodology has the potential to be extended to the other young SNRs, where the distributions of N p and N x are available.N x is the nonthermal X-ray, which is emitted by CR electrons in the same energy range as the gamma-ray production via IC scattering.It is however not often the case that the nonthermal X-rays of SNRs are imaged with sufficiently high quality.We expect that a few TeV gammaray SNRs, including HESS J1731 and RCW 86, are promising candidates in the future for which the present methodology is applicable.Currently, the angular resolution of the gamma-ray observations is not high enough for them because the number of independent pixels is limited to only ∼10, due to their small diameter of ∼0°. 5.In this context, we point out that simple diagnostics by using two scatter plots of N g with N p and N x like those in Figures 3 and 5 provide a useful test for the quantification of the gamma-ray components.The two scatter plots of RX J0852 and RX J1713 show good correlations among them, which are consistent with the significant contribution to N g of both N p and N x , and represent essential features of the origin of gamma rays.
Another possibility in the future is for the middle-aged SNRs.Observations of the interstellar protons have been extensively made already for tens of middle-aged SNRs (e.g., Yoshiike et al. 2013, W44;Aharonian et al. 2008, W28;   s N 2 g and σ(ΔN g (2)), respectively.The red circles and error bars denote pixel group 1 and the blue ones pixel group 2. Yoshiike et al. 2017, IC443;Sano et al. 2021a, G346.6-0.2;Kuriki et al. 2018, Kes 79;Aruga et al. 2022, Puppis A).Their X-rays are mostly of thermal origin and do not provide a measure of the CR electrons.Nonthermal radio emission may be used instead of the X-rays, while the energy range is not identical to the gamma-ray emitting electrons, causing uncertainty depending on the energy spectrum of the CR electrons.Nonetheless, it might be worth testing how the methodology works in the middle-aged SNRs.Another uncertainty here is the estimate of the mass of the target interstellar protons.Very often, the target protons are only roughly assumed to be 1 cm −3 in these SNRs in the literature (e.g., Ellison et al. 2012).Since the ISM density is a critical quantity in the CR energetics, accurate estimates of the ISM density are needed.In addition, the low spatial resolution of the <10 GeV gamma-ray emission does not allow us to extend easily our methodology to the middle-aged SNRs at present.

Conclusions
We have carried out the quantification of the hadronic and leptonic gamma rays in the SNR RX J0852 by employing the methodology that expresses the hadronic and leptonic gammaray components by linear combinations of N p and N x under an assumption of uniform CR energy density and magnetic field (Paper III).The methodology was applied to the gamma-ray data sets of RX J0852 obtained by H.E.S.S., which are combined with the Suzaku X-ray data and the NANTEN/ ATCA-Parkes ISM data.A new feature was to use a multiplane fit instead of a single-plane fit, which allowed for the accommodation of the steep spatial variation in X-rays by somewhat relaxing the assumptions of the uniform parameters.
1.The present quantification employed fitting by two/three flat planes in a 3D space subtended by N p -N x -N g .Along with RX J0852, RX J1713 was reexamined under the modification of a multi-plane fit to Paper III.The multiplane fit was required to accommodate the steep change of the X-rays, etc., in the shell of RX J0852 and was able to reduce the fit errors in the two SNRs, without significantly altering the assumptions of uniform CR energy and magnetic field strength within the SNR. 2. The results show that the gamma rays of RX J0852 consist of both hadronic gamma-ray components: the leptonic gamma-ray components = (52 ± 1): (48 ± 1)% in N g .This indicates that the two gamma-ray components are of the same order of magnitude, and are competing with each other in the SNR.This provides a second case in addition to RX J1713, where the hadronic gamma rays are significant in the SNR, proving the origin of CRs in a young SNR. 3. The CR proton energy is calculated to be (3-9) × 10 47 erg in both RX J0852 and RX J1713, about half or one-third of that calculated without the component quantification (Paper II; Paper III).The energy is still compatible with the scheme in which SNRs are the dominant source of the Galactic CRs, if we consider the volume-filling factor of the target protons on the order of 0.1 and the large energy carried out by escaping CRs.So, the CR energy stored in an SNR at a given instance is always significantly smaller than 10 50 erg, while the energy is eventually provided if the energy were integrated in space and time over the whole lifetime of an SNR.The CR electron energy is likely smaller by two orders of magnitude than the CR proton energy, where the exact value depends on the magnetic field not directly measured, as already shown by the theoretical works.4. As a consequence of the multi-plane fit, we find in RX J0852 that there is a trend of an increase in the CR energy density in the shell as compared with the inner part of the shell, which seems to be consistent with the theoretical models of CR acceleration.5.The present work as well as Paper III have demonstrated that the spatial distribution of the interstellar protons and nonthermal X-rays (as a proxy of the CR electrons) are essential in quantifying hadronic and leptonic gamma rays.The gamma-ray spectral fit is not able to achieve such quantification, due to the large freedom in the fit by tuning the physical parameters for either of the hadronic and leptonic models.The present methodology will be applicable to other TeV gamma SNRs, if the gamma-ray resolution becomes higher by more than a factor of 2 (e.g., by the Cherenkov Telescope Array; Cherenkov Telescope Array Consortium 2019).In the middle-aged GeV gamma-ray SNRs, such quantification is still not in the course of application.The low resolution in the GeV gamma rays and the lack/weakness of the nonthermal X-rays do not allow for easily extending the methodology to middle-aged SNRs at present.

Appendix B Spatial Comparisons with CO in RX J0852
Figure 14 shows a spatial comparison among the TeV gamma rays, X-rays, and CO in RX J0852.We can find that CO clouds are distributed inside or on the gamma-ray and X-ray shells.It is noteworthy that some molecular clouds, especially for A, have clear anticorrelations with X-rays, suggesting that shock-cloud interactions with the magnetic amplification occurred.In other words, these clouds are embedded within the SNR shell and act as targets for the accelerated CR protons.
the H I data obtained with ATCA and Parkes (McClure-Griffiths et al. 2005).

Figure 1 .
Figure4shows the distributions of the three physical quantities relevant to the analysis, including the H.E.S.S. TeV gamma-ray count N g , the XMM-Newton nonthermal X-ray counts N x , and the interstellar proton column density N p .Figures4(a)-(c) show the pixels of N g , N x, and N p , respectively.The analyzed pixels are enclosed by white solid lines.Figures5(a)-(c) show three scatter plots of N g -N x , N g -N p

Figure 2 .
Figure 2. Spatial distribution of (a) N g , (b) N x , and (c) N p for RX J0852.The three data sets are pixelated on an ¢ 11. 4 grid to match the H.E.S.S. resolution.The white polygon in each panel indicates the region of interest for the present analysis, and the dashed circle outlines the PWN unrelated to the SNR.

Figure 3 .
Figure 3. Scatter plots of (a) N g -N x , (b) N g -N p , and (c) N p -N x for RX J0852.The correlation coefficient is noted in the upper right corner of each panel, and the horizontal/vertical error bars in the bottom-right corner represent the median values of the uncertainties.

Figure 4 .
Figure 4. Spatial distribution of (a) N g , (b) N x , and (c) N p for RX J1713 (identical to the H.E.S.S.18 (E > 2 TeV) ¢ 4. 8 resolution data set in Paper III).The white polygon in each panel indicates the region of interest for the present analysis.The red polygon in panel (c) outlines the region where the H I absorption is corrected (see Section 2.3 of Paper III).

Figure 5 .
Figure 5. Same as Figure 3 but for RX J1713.

Figure 6 . 1 g.
Figure 6.Results of the single-plane fit for RX J0852.(a) Maps of ΔN g (1) derived from Equation (6) and (b) ( )  N 1 g derived from Equation (2).The superposed contours in both panels (a) and (b) indicate excess counts of TeV gamma rays (identical to those in Figure 1).(c) A plot of ΔN g (1) with respect to ( )  N 1 g .The horizontal and vertical error bars shown in the left bottom corner indicate the median values of ( ( ))  s N 1 g

Figure 7 . 2 g.
Figure 7. Results of the two-plane fit for RX J0852.(a)-(d) Maps of ΔN g (2) (left panels) and ( )  N 2 g (right panels) for the pixel groups 1 (ΔN g (1) > 0, top panels) and 2 (ΔN g (1) 0, middle panels).The superposed contours in each panel are identical to those in Figure 1.(e) A plot of ΔN g (2) with respect to ( )  N 2 g .The horizontal and vertical error bars shown in the left bottom corner indicate the median values of ( ( ))  s N 2 g and σ(ΔN g (2)), respectively.The red circles and error bars denote pixel group 1 and the blue ones pixel group 2.

Figure 9 .
Figure 9. (a) Scatter plot between hadronic gamma-ray fraction and N x for RX J0852.The filled circles and open squares represent the data points where N p < 3.26 × 10 21 and <3.26 × 10 21 cm −2 , respectively.The overlaid solid lines show the relationships derived by the equation aN p /(aN p + bN x ) for N p = 3.26 × 10 21 cm −2 .The red, orange, and blue lines show the shell, intermediate, and inner parts of the SNR, respectively (the a and b values for each part are in Table3).(b) Distributions of hadronic gamma-ray fraction overlaid with gamma-ray contours (identical to those in Figure1).

Figure 10 . 1 g.
Figure 10.Results of the single-plane fit for RX J1713.(a) Maps of ΔN g (1) derived from Equation (6) and (b) ( )  N 1 g derived from Equation (2).The superposed contours in both panels (a) and (b) indicate excess counts of TeV gamma rays.The lowest contour level and contour intervals are 12 and 5 counts, respectively.(c) A plot of ΔN g (1) with respect to ( )  N 1 g .The horizontal and vertical error bars shown in the left bottom corner indicate the median values of ( ( ))  s N 1 g and σ(ΔN g (1)) (see Equations (6) and (7) in Paper III), respectively.

Figure 11 .
Figure 11.Results of the two-plane fit for RX J1713.(a)-(d) Maps of ΔN g (2) (left panels) and ( )  N 2 g (right panels) for the pixel groups 1 (ΔN g (1) > 0, top panels) and 2 (ΔN g (1) 0, middle panels).The superposed contours in each panel are identical to those in Figure 10.(e) A plot of ΔN g (2) with respect to ( )  N 2 g .The horizontal and vertical error bars shown in the left bottom corner indicate the median values of ( ( ))  s N 2

Table 2
Summary of the Suzaku XIS Archive Data of RX J0852.0-4622 a All exposures indicate the effective exposure time of XIS0, XIS1, and XIS3 after processing.

Table 3
Summary of the Multiple Linear Regression for RX J0852 Note.Column (1): model name; column (2): number of pixels of the data set; columns (3) and (

Table 4
Hadronic and Leptonic Gamma-Ray Components in RX J0852