A CR-HYDRO-NEI MODEL OF MULTI-WAVELENGTH EMISSION FROM THE VELA JR. SUPERNOVA REMNANT (SNR RX J0852.0−4622)

The development of the CR-hydro-NEI code used here has been described in detail in a number of recent papers (e.g., Ellison et al. 2007, 2010, 2012; Patnaude et al. 2009, 2010), with the most recent "generalized" version given in Lee et al. (2012). Briefly, the SNR hydrodynamics are modeled with a 1D hydro simulation based on VH-1 (e.g., Blondin & Ellison 2001). The SNR simulation provides the evolving shock speed, sonic and Alfvén Mach numbers, and other quantities necessary for the shock acceleration calculation. The NL-DSA calculation is done with a semi-analytic solution based largely on the work of P. Blasi and coworkers (e.g., Blasi et al. 2005; Caprioli et al. 2009; see Lee et al. 2012 for a full list of references). With suitable parameters, the semi-analytic calculation provides the shock compression ratio, amplified magnetic field, and full proton and electron spectra which are used to calculate the broadband continuum radiation from synchrotron, bremsstrahlung, IC, and π⁰-decay emission.

The SNR evolution is coupled to the CR production by modifying the standard hydrodynamic equations through a change in the equation of state from the influence of relativistic CRs, energy loss from escaping CRs, and magnetic pressure.⁶ The changes produced in the hydrodynamics by NL-DSA also modify the evolution and ionization state of the shocked thermal plasma and these changes are self-consistently included in our non-equilibrium ionization (NEI) calculation of the thermal X-ray emission.

We thus obtain a model of an evolving SNR where the non-thermal continuum and thermal line emission are calculated self-consistently. Treating thermal and non-thermal processes consistently is required when CR production is efficient because the production of relativistic CRs can strongly influence the density and temperature of the shock-heated thermal plasma (e.g., Ellison 2000). In such a self-consistent calculation, it is not possible, for instance, to adjust parameters so that π⁰-decay matches GeV–TeV observations without modifying the fit to thermal X-ray line emission. As we have demonstrated in our fits to SNR RX J1713.7−3946 (e.g., Ellison et al. 2012; Lee et al. 2012), this coupling strongly constrains broadband emission models.

To determine the CR proton distribution function f^cr(x, p) at a certain position x in the precursor upstream of the FS, we follow the recipe described in Lee et al. (2012; see Equation (17)) and references therein. As for the electrons, we implicitly assume that they do not affect the shock structure and dynamics due to their low energy density compared to the protons, which we have checked to be the case a posteriori for all models presented here. We also assume that radiative cooling of the electrons occurs mainly in the DS region where the B-field is highest and the electrons spend most of their time scattering per shock-crossing. As a result, this allows us to calculate the electron distribution in the precursor easily using the precursor profile and the distribution function at the subshock in the same way as for the protons after the DSA solution has been obtained at every time step.

At each position x in the precursor, we read off the local environment variables such as the gas density, the B-field strength, and the temperature as provided by the DSA solution to calculate the local photon emissivity. The total emission spectrum from the CR precursor is thus obtained by an integration over the precursor volume.

Accelerated protons and heavier ions will interact with the background gas and produce charged pions through p–p interactions. These pions further decay into secondary particles such as e⁺, e⁻, and ν's. The charged secondaries can accumulate in the SNR shell and radiate as the shock propagates into the upstream medium. We have implemented this process in the CR-hydro-NEI code by following the continuous production of the secondaries in the post-shock region, as well as the adiabatic and radiative losses of the e⁺–e⁻. We only consider secondary production and radiation in the post-shock region because the density and magnetic field are considerably higher than in the shock precursor. The relevant inclusive secondary cross-sections are obtained using the parameterized model by Kamae et al. (2006), as we do for the gamma rays. Contribution from heavy ions like p-He is taken into account via an effective enhancement factor. These secondaries contribute to the photon emissivity via synchrotron, IC, and bremsstrahlung and is estimated at the end of a simulation.

We note that there is a possibility that these secondary e⁺–e⁻ can be injected into DSA and be "reaccelerated" in the same manner as the primary electrons. This is especially true for those being generated in the CR precursor. However, since most of the secondary particles are produced and accumulated in the DS region, and the probability of these populations traveling back to the shock from their production sites in order to be injected into acceleration is relatively low, we will ignore the process of reacceleration. We will show that, while the secondary particles do not contribute significantly to the volume-integrated broadband photon spectrum for all models presented in this work, the production of these particles in the shocked gas and their accumulation can have important effects on the spatial variation of synchrotron emission in some specific X-ray bands for a hadronic model. This result will be discussed in detail in Section 4.3.

Using the spatial information from the CR-hydro-NEI code, it is relatively straightforward to obtain model predictions for multi-wavelength emission profiles. Line-of-sight projection effects are calculated assuming spherical symmetry. The projected radial (i.e., outward from the SNR center) profiles, integrated over a set of chosen wavebands, are convolved with Gaussian kernels to mimic the point-spread functions (PSFs) of various instruments and facilitate direct comparison with data.

We have constructed two representative models: a "hadronic" model where the GeV–TeV emission is π⁰-decay-dominated, and a "leptonic" model where it is IC-dominated. For both models we assume: (1) the associated SN had a kinetic energy of E_SN = 10⁵¹ erg; (2) the age of the remnant is 2500 yr to match the observed size of the SNR at the distances assumed in Table 1; (3) the injection parameter which determines the acceleration efficiency of DSA is set at χ_inj ≡ p_inj/p_th + u₂/c = 3.6, corresponding to a fraction η ∼ 2–3 × 10⁻⁴ of thermal particles being injected in DSA at any time (note that our χ_inj is ξ in Blasi et al. 2005); (4) we have conservatively assumed that the electron temperature equilibrates with the proton temperature through Coulomb collisions unless otherwise mentioned; (5) the spectrum of the background photon fields that are upscattered by the relativistic electrons to gamma-ray energies (IC) is taken from Porter et al. (2006) at the position of the SNR, which contains the cosmic microwave background and the local interstellar radiation fields in the infrared and optical bands; (6) the upstream gas temperature is fixed at T₀ = 10⁴ K regardless of the gas density gradient; (7) a number fraction of helium f_He = 0.0977 is specified for the plasma, which contributes additionally to the various photon emission. However, other than this scaling, we ignore the acceleration of heavy ions in this paper; (8) we assume that the ambient B-field is oriented quasi-parallel to the shock normal over the whole surface, that is, we assume that the magnetic field geometry is unimportant as would be the case for efficient DSA where the self-generated magnetic turbulence mediating DSA is totally tangled in the CR precursor and DS from the shock, i.e., the Bohm limit for CR diffusion is obtained. For full details of the formulation, see Lee et al. (2012).

Table 1. Model Summary^a

	Hadronicb	Leptonicc	Remarks
Input parameters
dSNR (kpc)	0.74	0.88	Distance to SNR
n0 (cm−3)	0.033	0.002†	Far upstream gas density
B0 (μG)	0.5	0.14†	Far upstream B-field
dM/dt (10−6 M☉ yr−1)	...	7.5	Pre-SN mass-loss rate
Vwind (km s−1)	...	50	Pre-SN wind speed
σwind	...	0.02	Wind magnetization
Kep	1.5 × 10-4	0.015	(e−/p) ratio at pmax of e−
αcut	0.75	0.50	Exp. cutoff index d
fFEB	0.15	0.12	Width of FEB over RFSe
falf	0.10	1.00	x-dependence of vAf
Output quantities
RFS (pc)	12.7	15.2	Forward shock radius
RCD (pc)	10.3	12.5	Contact discontinuity radius
VFS (km s−1)	2130	4700	Forward shock velocity
pmax (p) (TeV/c)	26.7	5.2	Proton max. momentum
pmax (e−) (TeV/c)	13.3	5.2	Electron max. momentum
Rtot	9.30	4.69	Total compression ratio
Rsub	3.69	3.99	Subshock compression ratio
B2 (μG)	34.1	4.8	Downstream B-field
T2 (108 K)	0.16	3.62	Downstream temperature
acc	0.84	0.36	Total accel efficiency
esc	0.34	0.12	Escaped accel efficiency
ECR/ESN (fSN)	0.48	0.14	SN energy converted to CR

Notes. ^aFor all models listed in this table, Bohm diffusion is assumed in the DS and precursor region, and MFA is included. These models all have E_SN = 10⁵¹ erg, T₀ = 10⁴ K, and f_He = 0.0977. ^† Values are taken at t = t_age (= 2500 yr). ^bBest-fit model under the "hadronic-dominated" scenario with a uniform upstream medium. ^cBest-fit model under the "leptonic-dominated" scenario with a pre-SN magnetized wind. ^dSee, e.g., Equation (24) in Lee et al. (2012) for definition. ^eSee, e.g., Equation (1) and description in Ellison & Vladimirov (2008). ^fSee, e.g., Equation (14) in Lee et al. (2012) for definition.

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An important difference between our hadronic and leptonic models is that the hadronic model evolves in a uniform upstream medium, typical of a Type Ia SN, and the leptonic model evolves in a wind cavity, typical of a core-collapse SN. While the observational evidence favors a core-collapse origin for the Vela Jr. SNR, we could not find a set of core-collapse parameters that would produce a reasonable fit to the broadband data for a hadronic model radiating in a pre-SN wind. This is because the hadronic model needs a high ambient gas density and high B-field strength in order to simultaneously explain the radio/X-ray synchrotron emission and the gamma-ray flux. We thus used a uniform interstellar medium (ISM) model for our hadronic fit. On the other hand, a leptonic model requires a lower ambient gas density to suppress the π⁰-decay gamma rays, and this is naturally realized by a wind bubble environment for a remnant sitting close to the Galactic plane. More details will be given in Section 4 where we will further discuss this point. Consistent with the different SN scenarios, we assume an ejecta mass M_ej = 1.4 M_☉ for our hadronic model and M_ej = 3 M_☉ for our leptonic model.

In Table 1, we summarize the main input parameters and output quantities measured at the end of the simulation for each model. We constrain the input parameters via a satisfactory fit to the observed broadband spectrum from radio to TeV energies, as well as a general agreement of the dynamical variables (e.g., radius of the FS) with current observations. The distance to the SNR is recently constrained by Katsuda et al. (2008) using proper-motion measurements over a seven-year time period. They provided the estimate equivalent to d_SNR ≳ (750 ± 205) × (v_sk/3000 km s⁻¹) pc. We will adopt d_SNR for our models which is consistent with this limit.

We plot the time evolution of selected important physical quantities for the hadronic and leptonic models in Figures 1 and 2. The very different undisturbed upstream environments give rise to large differences in the dynamical behavior of the two models. With the lower B-field and gas density in the wind cavity for the leptonic model, the following are expected and observed compared to the hadronic model: (1) the shock sweeps up material at a much lower rate, so that the shock speed and Mach numbers decay slower, and shock radius increases faster with time; (2) the acceleration efficiency, and hence the fraction, f_SN, of SN explosion energy, E_SN, converted into CR particles at the current age is much lower (f_SN ≃ 0.14 versus 0.48) due to the slower injection rate of thermal particles from the shocked gas into DSA. This is also reflected in the much more moderate shock modification (i.e., smaller R_tot) than for the hadronic model on average. The high f_SN fraction of the hadronic model is consistent with the result of Tanaka et al. (2011); (3) the lower B-field in the DS region (B₂) results in a longer synchrotron loss timescale, in this case longer than the acceleration timescale throughout the age of 2500 yr, resulting in a common p_max for electrons and protons. On the contrary, the hadronic model has a much higher ambient B-field strength in the uniform ISM, such that p_max of electrons becomes limited by the synchrotron loss (and IC loss to a lesser extent) starting from about 200 yr. These evolutionary differences relate directly to the broadband emission of the SNR, as we will discuss in the upcoming sections.

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As mentioned in Section 3, to obtain reasonable fits to the observed photon spectra, the two models require that the SNR evolves within very different surrounding environments. For the hadronic model, in order for the π⁰-decay photons to dominate over the IC component in the gamma-ray band, the gas density has to be high and the number ratio between electrons and protons (K_ep) has to be particularly low (K_ep ∼ 10⁻⁴). The high-density requirement argues against the SNR propagating into a pre-SN wind with rapidly decreasing density and we are forced to assume that the blast wave runs into an ISM with uniform gas density and magnetic field strength.

In contrast, the leptonic model requires that the FS propagates into a magnetized pre-SN wind region. This introduces a descending gradient for the gas density and B-field. The low shocked gas density in the DS photon-emitting region suppresses the π⁰-decay and bremsstrahlung, as well as the X-ray line emission, relative to the IC component.

Figure 3 shows the corresponding fits of the broadband spectra to currently available observations. We see that both models can explain the radio and GeV to TeV gamma-ray data reasonably well under the respective choices of parameters. In the X-ray band, however, the hadronic model has difficulty reproducing the X-ray photon index observed by ASCA, mainly due to the much faster synchrotron loss rate caused by the higher B-field in the hadronic model. The higher ambient gas density required for π⁰-decay dominance in the gamma-ray band is also accompanied by a high flux from thermal X-ray lines, which exceeds the X-ray flux observed by ASCA in the soft X-ray energy range below a few keV, despite the adoption of a conservative model of electron heating via Coulomb collisions in the post-shock region. The self-consistently calculated thermal X-ray emission provides a strong additional model constraint.

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Another important difference between the two models is the overall normalization factor required for the broadband emission to match the observed flux. For the leptonic model this factor is close to unity, but the hadronic model has to be boosted by a factor ∼5 to explain the observed flux level. This factor ∼5 is included in all of the model spectra shown in the lower panel of Figure 3.

A more in-depth comparison with the currently available X-ray data is valuable to differentiate SNR models. First, to see the general agreement of the models with data, we plot the calculated non-thermal and thermal X-ray spectra against the ASCA result (e.g., Slane et al. 2001; Aharonian et al. 2007) in Figure 4. For the hadronic model, to show the possible range of variance of the thermal spectrum based on different equilibration models for the electron temperature, we also show the calculated thermal spectrum assuming that the electron temperature equilibrates instantaneously with the proton temperature behind the FS. Coulomb equilibration and instant equilibration are two extremes for electron heating and the actual heating is very likely to lie somewhere in between. For either extreme in heating, the hadronic model predicts a thermal X-ray flux substantially higher than what observation implies (especially below ∼2 keV), in addition to its failure to reproduce the non-thermal spectral index. The leptonic model, on the other hand, shows a general good fit to the data without an overprediction of the thermal emission.

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In this regard, we note that Berezhko et al. (2009) have proposed a hadronic model in which the shock is running into a wind bubble region created by the progenitor star embedded inside a high density gas cloud. We do not consider such a situation in this work since, in such a high density environment (n_gas ≫ 0.01 cm⁻³), the resultant thermal X-ray lines are expected to violate the observation data even more than is the case for our hadronic model.

Second, we consider the X-ray spectrum near the bright NW rim of the remnant. Vela Jr. was observed with the Chandra X-Ray Observatory on 2003 January 5 and 6 (ObsIDs 3446 and 4414) using the Advanced CCD Imaging Spectrometer (ACIS). Standard cleaning and data reduction were performed using CIAO version 4.4. The merged observations yielded a total exposure time of 73.9 ks. Spectra, extracted using the specextract software, were obtained from a narrow region encompassing the FS of the SNR (solid box in Figure 5) and from a background region (dashed box) used to account for projected emission from the Vela SNR as well as internal, Galactic, and extragalactic background emission.

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The predicted thermal and non-thermal emission from CR-hydro-NEI for the projected spectral region indicated was converted into a table model for use in xspec for both the hadronic and leptonic models. The tbabs model for interstellar absorption was applied, and the model was convolved with the instrument response function and fit to the data. To account for possible excess foreground emission from the Vela SNR, a thermal NEI model (nei) with a distinct tbabs absorption component was included.

The best-fit results are shown in Figure 6, where the leptonic model fit is shown as a black histogram, and the hadronic model is shown in red. The dashed histogram corresponds to the additional tbabs×nei model. It is clear that the hadronic model provides a poor representation of the X-ray data, both at low energies, where the predicted line emission is not observed, and at high energies, where the model is much steeper than the observed spectrum. The leptonic model provides an excellent fit to the data ($\chi _\nu ^2 = 1.05$ for 327 degrees of freedom). The column density is n_H = (4.3 ± 0.2) × 10²¹ cm⁻², in good agreement with previous measurements (Slane et al. 2001; Pannuti et al. 2010) and the accompanying thermal component has a temperature of $0.26^{+0.32}_{-0.08}$ keV with a column density of (0–3.3) × 10²¹ cm⁻², consistent with observed properties for soft thermal emission from the Vela SNR. The best-fit normalization for the CR-hydro-NEI component is about 15% higher than the ratio of the spectral extraction region length to the entire SNR circumference, which is reasonable given that the rim is somewhat brighter at this position (see Figure 5).

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Thanks to the high angular resolution of Chandra, it is also possible to study spatial variation of the spectral properties near the FS (see, e.g., Pannuti et al. 2010). Correspondingly, we calculate the synchrotron photon index for a series of line-of-sight projected regions from the models which have different radial distances from the FS. The results are shown in Figure 7. Besides the absolute difference of the index values, the hadronic and leptonic models show very distinct trends of the index variation as a function of distance from the FS. For our leptonic model, the synchrotron spectrum softens as we look inward from the FS, whereas our hadronic model exhibits a much weaker dependence on position.

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The major factors that determine the spectral index of the non-thermal X-rays at a certain distance from the SNR center are the following: (1) energy loss history of the primary accelerated electrons, which is critical to the high-energy cutoff of the primary synchrotron component; and (2) the relative importance of the secondary e⁺–e⁻ to the primary electrons at that position. These secondaries are produced by the trapped accelerated protons interacting with the shocked gas, which lose energy radiatively like the primaries and meanwhile accumulate in number with time. Different from the primaries, which are accelerated by the shock and then advected DS without replenishment, the secondaries at each position in the shocked gas are continuously generated by the advected high-energy protons whose spectra do not evolve with time significantly other than from adiabatic losses. The spectral shapes of the secondary and primary synchrotron components are hence typically different. For our leptonic model, the effect from secondaries is obviously small due to the very low ambient gas density in the wind bubble. As a result, the energy loss of the primaries dominates the spatial behavior of the synchrotron radiation. Since primary electrons accelerated by the shock at an earlier phase and now residing further inward in the SNR shell have suffered from synchrotron/IC and adiabatic losses for a longer period of time than those just being freshly accelerated, the cutoffs of their spectra are found at lower energies. In addition, due to the falling B-field strength with radius in our wind model, those primary electrons accelerated earlier have experienced a higher synchrotron loss rate on average than those residing closer to the FS at the current age. These lead to the softening of the synchrotron spectrum as shown by our result.

For the hadronic model, the secondaries cannot be neglected. In the volume-integrated photon spectrum (Figure 3), the primary component dominates over the secondary one until around 10 keV. However, by looking deeper toward the SNR center where the number of secondary particles is larger due to accumulation and the primaries have a lower cutoff energy from a longer period of radiative loss, the secondary spectrum can dominate over the primary spectrum at a few keV and harden the resultant total spectrum in the 1–5 keV energy range. We find that this effect can compensate the energy loss of the primaries in the SNR shell and, for the relatively moderate ambient gas density we assume, lead to a weak variation of the synchrotron index with radius after projecting our spherically symmetric model along the line of sight. With a higher ambient gas density, a spectral hardening can be expected as we look inward from the shock. Using Chandra and XMM-Newton data, respectively, Pannuti et al. (2010) and Kishishita et al. (2013) have recently discovered a trend of softening for the non-thermal spectrum as the line of sight is moved inward from the FS toward the SNR center. This trend provides further support for our leptonic scenario. For a direct comparison, we overlaid in Figure 7 the fitted photon indices given by Kishishita et al. (2013) and found a reasonable agreement with our result. Additionally, the phenomenological spectral evolution model invoked by Kishishita et al. (2013) shows that the typical DS B-field should be around a few μG in order to explain the observed softening trend, which is highly consistent with the field strength obtained in our leptonic model.

The current generation of ground-based Imaging Atmospheric Cerenkov Telescopes possesses sufficient angular resolution to discern the spatial structures of SNRs with large angular sizes in sub-TeV to multiple TeV energies. Recent HESS observations of Vela Jr. (Aharonian et al. 2007) have measured the radial surface brightness profiles of its shell-like emission from 300 GeV to 20 TeV with a resolution of about 006. We compare our model profiles with the HESS measurements for the brightest northern part in Figure 8. The profiles are extracted from the model gamma-ray image after convolution with the PSF of the observation. The results show that both models predict gamma-ray emission profiles reasonably compatible with the data, and unlike the X-ray result, closely resemble each other after PSF smoothing.

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The reason behind this relative similarity in the gamma-ray band can be explained by the following: X-ray synchrotron emission produced by relativistic electrons is highly sensitive to the radiative loss rate. Electrons experience much faster energy loss in our hadronic model than the leptonic model, as mentioned above, which results in a sharp X-ray profile close to the FS for the hadronic case, and a more spread out profile behind the FS for the leptonic case. In the gamma-ray band, however, radiative loss plays a much less important role. In the hadronic model, the gamma-ray photons mainly originate from CR protons where losses can be ignored, while in the leptonic model the electrons responsible for the IC emission are only subject to minor losses due to the low magnetic fields.

Nevertheless, the gamma rays originate from totally different mechanisms for the hadronic and leptonic cases so differences are predicted for more precise measurements. Future ground-based gamma-ray observatories, such as the upcoming Cerenkov Telescope Array (CTA), will be able to differentiate the models with unprecedented spatial resolving power and sensitivity. For illustration, we include in Figure 8 our model profiles using the advertised best angular resolution of CTA (about 002). The red curves imply that future gamma-ray observations may be able to differentiate between the predicted radial profiles of Vela Jr.

TeV-bright SNRs like Vela Jr. and RX J1713.7−3946 have shown no sign of strong thermal emission with current X-ray observations. However, with the advent of future instruments of superior spectral resolution, it is very possible that thermal X-ray lines will be discerned in the non-thermal-dominated spectrum. As a first look, we plot the calculated X-ray spectrum in Figure 9 for our leptonic model in the energy range of 0.3–12 keV, the designed energy coverage of the soft X-ray spectrometer (SXS) on board the next-generation X-ray space observatory Astro-H. The emission lines are filtered by a Gaussian kernel with an FWHM of 7 eV to mimic the target baseline spectral resolution of SXS.⁷

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For comparison, we show the leptonic model spectrum with a resolution of 60 eV (a typical ballpark value for currently operating X-ray observatories). We see that using the resolving power of SXS, the stronger sub-keV lines can be recognized very visibly on top of the synchrotron spectrum, and it is very possible that they will be detected by Astro-H. Detection of such lines will be important to further constrain our model parameters such as the local gas compositions and the ion temperatures and densities. In a follow-up paper in preparation, we will perform a more detailed study of the X-ray spectrum by performing formal Astro-H SXS spectral simulations based on our models, and take into account thermal Doppler broadening of the emission lines.⁸

We emphasize that while small variations in parameters in either of our "best-fit" models do not strongly modify the results for that model, the parameter sets for the two scenarios are well separated and it is not possible to go smoothly from one set to the other while maintaining a satisfactory fit to the observations.

To illustrate this point and see how our models respond to parameter changes, we create modified versions for each of our models in which we purposely tune a set of important parameters so that it is positioned closer to the parameter space of the competing best-fit model. Two of the most important parameters that distinguish our leptonic and hadronic scenarios include the electron-to-proton number ratio at relativistic energies K_ep, and the upstream gas density n₀ (or the mass-loss rate dM/dt and wind speed V_wind when a pre-SN wind is present). For the leptonic case with a massive star as progenitor and a wind cavity, by recalling that the IC flux f_IC∝n₀K_ep (e.g., Ellison et al. 2010), we explore an altered model where K_ep is lowered by a factor of five (i.e., 3 × 10⁻³) and the wind matter density increased by the same factor to roughly maintain the level of f_IC.⁹ The wind magnetization is fixed so as to keep the synchrotron-to-IC flux ratio f_syn/f_IC roughly unchanged. On the other hand, we explore an altered model for the hadronic case where K_ep is boosted up by a factor of five while n₀ is decreased by a factor of 1.7, so that the model is now leaning toward the leptonic parameter space. Note that since the π⁰-decay flux $f_{\pi ^0} \propto n_0^2$, this will decrease $f_{\pi ^0}$ and increase f_IC by roughly the same factor. For both cases, we also adjust the assumed age of the remnant, within the allowable range of 1700–4000 yr implied by observations, from the default age of 2500 yr in order to achieve the same SNR angular size as the original model. Other than what described above, all other parameters are kept fixed.

The effect on the total broadband spectrum is shown in Figure 10. We can see that the modified leptonic model produces a non-thermal spectrum with an acceptable fit to the data except the highest energy TeV points and an X-ray spectral index a little too soft. But most importantly, it already starts to face the difficulty of overpredicting the thermal emission in the X-ray band due to the enhanced ambient gas density, which is the same problem encountered by our hadronic model. Another surfacing problem not shown in this plot is that the spatial dependence of the synchrotron index now fails to explain the XMM-Newton data by showing a softening trend too strong toward the SNR center (see Figure 7). For the modified hadronic model, although the thermal X-ray reduces back to a flux level more compatible with data than the original model, the broadband spectral fit becomes unacceptable by failing to explain the non-thermal X-ray flux level simultaneously with the gamma rays, due to the enhanced leptonic contributions which worsen the fit. To achieve a good fit again, we find that a much lower B-field must accompany the increased K_ep and decreased n₀, which is simply what being realized in the wind model we are employing for the leptonic model. The conclusion from this analysis is hence that it is impossible to maintain a good fit to data by continuously tuning some influential parameters from the leptonic to the hadronic case (and vice versa) unless a drastic change of the underlying SNR environment is involved, i.e., a rarified wind cavity against a uniform ISM model for the ambient medium.

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