New estimation of the nuclear de-excitation line emission from the supernova remnant Cassiopeia A

Cosmic rays (CRs) with kinematic energy below $1~{}\rm GeV/nucleon$, often referred to as low-energy CRs (LECRs), are most efficient at ionizing and heating gases and play an important role in star-forming and astrochemistry processes (Papadopoulos, 2010; Gabici, 2022). In the direct measurement of CR spectra in the solar system, the flux of LECRs is highly suppressed by the solar modulation effects. Recently, the Voyager satellite has measured the LECR spectra beyond the heliopause (Cummings et al., 2016). However, it is not straightforward that the LECR spectra measured by Voyager can be a good representative of the LECRs in the Galaxy. Due to the fast cooling and slow propagation of LECRs, their flux indirectly estimated via the ionization rate of gases shows a rather inhomogeneous distribution in the Galactic plane (e.g., Indriolo & McCall, 2012).

Supernova remnants (SNRs) are thought to be the most prominent CR accelerators in our Galaxy. The $\gamma$-ray observations in the energy range of $0.1-10~{}\rm GeV$ from AGILE and Fermi-LAT have shown strong evidence that the SNRs do accelerate CR protons to a high energy range (Giuliani et al., 2011; Ackermann et al., 2013). Observations of the large ionization rates from molecular material near SNRs, such as IC 443, W28, and W49B, suggest that SNRs may also accelerate a large population of LECRs (Indriolo et al., 2010; Vaupré et al., 2014; Zhou et al., 2022). However, due to the kinetic energy threshold of the pion-decay process ($\sim 280~{}\rm MeV$), we know little about the injection spectrum of LECRs from SNRs. In addition to the ionization effects, the inelastic collisions between LECRs and interstellar gases could excite the heavy nuclei which can emit MeV $\gamma$-ray lines via de-excitation, such as the 4.44 MeV line from ¹²C and the 6.13 MeV line from ¹⁶O (e.g., Ramaty et al., 1979; Murphy et al., 2009). Thus, from observation of these line emissions, we may derive unique information about the injection of LECR nuclei from the accelerators such as SNRs, with the advantage of excluding the influence of CR electrons (e.g., Benhabiles-Mezhoud et al., 2013; Liu et al., 2021).

Cassiopeia A (Cas A, G111.7-02.1) is the remnant of a massive star explosion $\sim$340 years ago (Fesen et al., 2006; Krause et al., 2008). As one of the youngest SNRs in our Galaxy, Cas A has been thoroughly investigated from multiwavelength observations despite many open questions that remain debatable. Located about 3.4 kpc away from the solar system (Reed et al., 1995), it is one of the brightest sources in the radio band and shows a significant shell structure with an angular radius of 2.5’ (or physical size of 2.5 pc) (Kassim et al., 1995). The synchrotron radiation extends from infrared (Tuffs et al., 1997) to X-rays of about $100~{}\rm keV$ (Grefenstette et al., 2017). Although the origin of the X-ray radiation is still under debate, Laming (2001a, b) argued that non-thermal bremsstrahlung can also explain the observed X-ray flux. Early Fermi-LAT observations reveal a hint of the hadronic origin of the $\gamma$-ray emissions (Abdo et al., 2010; Yuan et al., 2013). TeV signal from Cas A was also detected (Puehlhofer, 1999), and a significant cutoff at several TeV was revealed by MAGIC and VERITAS observations (Ahnen et al., 2017; Abeysekara et al., 2020). Despite the continuous debate about whether Cas A is a PeVatron or not, a pure hadronic or hybrid origin is preferred to the pure leptonic scenario when explaining the GeV–TeV $\gamma$-ray emission from Cas A (e.g., Zirakashvili et al., 2014; Ahnen et al., 2017; Zhang & Liu, 2019; Abeysekara et al., 2020). Thus, one would expect possible MeV de-excitation line emissions arising from Cas A accelerated LECR nuclei interacting with the surrounding medium.

In this study, we investigate the potential MeV nuclear line emission from Cas A under different assumptions of the injected CR spectra which are constrained by recent observations in the GeV-TeV range. Various scenarios of the interacting medium are also considered in the calculations applying the latest estimation of the chemical abundances of the ejecta and ambient gas. Moreover, the detection capabilities of the line emissions against the continuum background are also discussed regarding the angular resolutions and energy resolutions of the next-generation MeV telescopes.

Before the calculation of the possible de-excitation $\gamma$-ray line emission from Cas A, we need to have a general idea of the spectral shape of the accelerated particles and the composition of the interacting medium. Both factors have huge impacts on the estimation results. Given the angular resolution of the next generation MeV telescopes (typically $\gtrsim 2^{\circ}$ at MeV band) and the distance of Cas A, the line emission from Cas A is very likely to be observed as a point-like source (Liu et al., 2021). Thus, the spatial distributions of the accelerated LECRs, the interacting medium, as well as the resulting line emission will not be considered in this work.

For the calculation of the $\gamma$-ray line emissions, except for the code TALYS which is the newest 1.96 version (Koning et al., 2008; Koning et al., 2014), we applied the same procedure as described in Section 3.1 of Liu et al. (2021), which followed the method developed by Ramaty et al. (1979); Murphy et al. (2009); Benhabiles-Mezhoud et al. (2013). Two main channels of the interactions are considered here. One is the direct process in which the CR protons and $\alpha$-particles as projectiles excite heavier elements of the ambient gas and generate narrow $\gamma$-ray lines, and the other is the inverse process in which the hydrogen and helium of the ambient gas excite the heavy nuclei of LECRs and produce $\gamma$-ray line emission that is broadened.

Given the large difference in the elemental compositions between the ejecta and the CSM, here we consider three cases to study the possible influence of various interacting materials. One case (hereafter referred to as case 1) is that the $\gamma$-ray emission is generated from the shock-accelerated nuclei interacting only with the ejecta. The second one (case 2) is that the emission is produced by the accelerated nuclei colliding with the CSM. Moreover, a hybrid case (case 3) in which half of the accelerated CRs interact with the ejecta while the other half of the CRs interact with the CSM is also calculated. An estimation of the $\gamma$-ray lines from the same population of CRs colliding with the gas medium of solar abundance is also made for further comparison.

For each case, we tested possible proton spectra with different assumptions of $\alpha_{1}$ ranging from 2.0 to 2.7 while setting $\alpha_{2}=\alpha_{1}$, 3.0, and 4.0, respectively. Meanwhile, the GeV-TeV $\gamma$-ray spectral data from recent research of Abeysekara et al. (2020) are used to constrain the overall flux of the accelerated particles, which provides us a maximum for $N_{0}$ given a certain density and composition of the interacting medium. Here we applied the Eq.(20) in Kafexhiu et al. (2014) to calculate the nuclear enhancement factor $\epsilon$, then derived the effective density $\epsilon n_{\rm p}n_{\rm H}$ for the pion-decay process, in which $n_{\rm p}$ represents the density of the accelerated protons and $n_{\rm H}$ is hydrogen density of the interacting medium. Examples of the pion-decay emissions derived from the above spectral parameter settings are shown in Fig.1.

Considering the uncertainty of the relative density of H and He in the ejecta, we varied their number ratios from 0.01 to 0.05 and from 0.1 to 0.5, respectively, for the calculation of case 1. We found that such changes have very little impact ($\lesssim 3\%$) on the overall line flux under the premise of oxygen domination. For a more realistic estimation, we also considered the Doppler effect caused by the movement of the ejecta (e.g., Milisavljevic & Fesen, 2013), and adopted an $\Delta V$ of $\sim 6000~{}{\rm km\,s}^{-1}$ from the recent study of Picquenot et al. (2021) for all the elements. The resulting MeV nuclear de-excitation line emissions for case 1 are exemplified in Fig. 2. As shown in Fig. 2, the line fluxes increase with the spectral index and the presence of a concavity in momentum space will lead to much stronger line emissions. In addition, the same trend is also found for case 2 and case 3. However, assuming the same CR spectral shape, the line fluxes of case 2, are much lower compared to that of case 1, and the morphological difference of the MeV $\gamma$-ray emission is also very obvious, as illustrated by the solid lines in Fig. 3. Such contrast reflects the much more abundant heavier nuclei in the oxygen-dominated ejecta compared to those in the CSM. Taking the possible Doppler broadening into account, for case 1 and case 3, the FWHM widths ($\Delta E$) of the 4.44 MeV line and the 6.13 MeV line are $\sim 0.19$ MeV and $\sim 0.22$ MeV, respectively. The integrated narrow-line fluxes of the 4.44 MeV and the 6.13 MeV lines of these three cases are summarized in Table 2, in which the minimum and maximum are obtained when setting $\alpha_{1}=\alpha_{2}=2.0$ and $\alpha_{1}=2.7$, $\alpha_{2}=4.0$, respectively. As shown in Table 2, the integrated line flux ranges are $\sim(1\times 10^{-10}-1\times 10^{-6}){\rm\,cm^{-2}\,s^{-1}}$ for the 4.44 MeV narrow line and $\sim(4\times 10^{-11}-2\times 10^{-7}){\rm\,cm^{-2}\,s^{-1}}$ for the 6.13 MeV narrow line, respectively.

Our estimation of the integrated 4.44 MeV line flux assuming $\alpha_{1}=\alpha_{2}=2.1$ for case 1 is $\sim 1.4\times 10^{-8}{\rm\,cm^{-2}\,s^{-1}}$, much lower compared to the estimation of Summa et al. (2011). Indeed, the target density, composition of the medium, and the LECR flux can vary dramatically with the distance to the forward shock. Using a uniform density and composition can be quite biased in estimating the MeV line emission. This is also the motivation that we consider three cases in the discussions above.

Regardless of the uncertainties from the experiment data and the simulation data from TALYS, as shown in Sect.3, the de-excitation line fluxes resulting from the interaction between the Cas A accelerated CR nuclei and the medium are highly model-dependent: for certain cases, the predicted line fluxes vary by two orders of magnitude due to different settings of the spectral indexes, meanwhile, the narrow line fluxes could also differ by two orders of magnitude due to the variation in the elemental compositions of the interacting medium.

The continuum MeV $\gamma$-rays contributed from the diffuse Galactic emission and Cas A itself should be taken into account when discussing the detectability of line emission. Based on the observation of SPI aboard INTEGRAL, Siegert et al. (2022) re-analyzed the diffuse Galactic emission at 0.5 and 8.0 MeV by fitting energy-dependent spatial template GALPROP (Vladimirov et al., 2011) models within a region of $\Delta l\times\Delta b=95^{\circ}\times 95^{\circ}$ around the Galactic center. They found the above observed diffuse background is mainly contributed by IC scattering of CR electrons onto the interstellar radiation field, of which the bremsstrahlung component may account for $\sim 10\%$. We estimate the diffuse MeV emission flux in the direction of Cas A by extrapolating this newest measurement spatially. The possible diffuse background flux in the direction of Cas A within 1 $\sigma$ uncertainty is shown as the shaded area in Fig. 4 and Fig. 5, in which the angular resolutions of the telescope are assumed to be 2^∘ and 5^∘, respectively. As for the continuum MeV emission from Cas A itself, which is mainly contributed from bremsstrahlung in the hadronic scenarios, the modeled fluxes are well below or at the same level of the extrapolated diffuse background (e.g., Zhang & Liu, 2019; Abeysekara et al., 2020). Thus, the potential influence from the bremsstrahlung on the detection of the line emissions would be much weaker or similar to that of the diffuse background, and for simplicity, this was not further discussed in the following discussion.

Due to the highly model-dependent calculation of the possible nuclear $\gamma$-ray line emission from Cas A, future observations from the next-generation MeV telescopes may help us locate the interacting region(s) and constrain the injected CR spectral shape, which can be served as a diagnosis on particle acceleration and escape in Cas A. To be specific, if the interacting material is dominated by ejecta, the strong narrow line emission such as the 4.44 MeV line and the 6.13 MeV line are more likely to be detected. Moreover, the existence of a concavity in the CR injection spectra (as exemplified by the dash-dot lines in Fig. 4), would make the detection easier for case 1 (black) and case 3 (blue), even if the flux of the background continuum is very high due to the limited angular resolution. And a better angular resolution can increase the possibility of detection for case 2 (red). In general, with the possible diffuse background emission added, the detection of the MeV line emission will be more likely from instruments with better angular resolutions ($~{}2.0^{\circ}$) for the point-like source SNR Cas A. In addition, we checked the influence on the detectability regarding the energy resolutions ($\Delta E/E$, FWHM) of the telescopes. The results are shown in Fig. 5, assuming a $\Delta E/E$ of $2\%$ (solid lines) or $10\%$ (dotted lines), respectively. We found that the energy resolution is crucial for the detection of such line features. However, as calculated in the section above, we found that the narrow de-excitation lines have intrinsic Doppler broadening of about $2\%$ that is caused by the recoil of the excited nuclei, and additional broadening of about $2\%$ due to the movements of the ejecta-dominated medium. Thus the energy resolution better than this value can hardly improve the detection sensitivity.

In conclusion, we estimated the possible MeV line emission from LECRs interaction with the ambient gas in the SNR Cas A under simplified conditions. We found that if the accelerated CRs mainly interact with the ejecta, the line signal from Cas A will be more prominent due to the higher ratio of heavy nuclei therein. And the potential softening of LECR spectra caused by CR feedback to the shock would further enhance the MeV line emissions. We also found that the diffuse MeV $\gamma$-ray emissions in the Galactic plane may be the main background in the detection of such line features. Both angular resolution and energy resolution play a significant role in detecting these MeV lines from Cas A. Based on our model-dependent predication, the integrated narrow line fluxes are $\sim 1\times 10^{-10}{\rm\,cm^{-2}\,s^{-1}}$ to $1\times 10^{-6}{\rm\,cm^{-2}\,s^{-1}}$ at 4.44 MeV and from $\sim 4\times 10^{-11}{\rm\,cm^{-2}\,s^{-1}}$ to $2\times 10^{-7}{\rm\,cm^{-2}\,s^{-1}}$ at 6.13 MeV, respectively. Thus, the next generation MeV instruments with a line flux sensitivity of about $10^{-6}~{}\rm cm^{-2}s^{-1}$, such as e-ASTROGAM, AMEGO, and COSI (de Angelis et al., 2018; McEnery et al., 2019; Tomsick & COSI Collaboration, 2022) may have chances of detecting these unique spectral features in Cas A, but detectors with sensitivities exceeding the capability of projects mentioned above would be more promising for the research of such kind of individual CR sources. The recently proposed large-scale Space Projects like MeGaT (Zhang et al. 2023, private communication) and MeVGRO (Peng et.al 2023, private communication) give optimism that the probes of low-energy particles from Cas A could be realized through the detection of prompt nuclear de-excitation line emission.

Bing Liu acknowledges the support from the NSFC under grant 12103049. Rui-zhi Yang is supported by the NSFC under grants 12041305, and the national youth thousand talents program in China.

To calculate emissivities of the de-excitation $\gamma$-ray line lines, we used the code TALYS (version 1.96,Koning et al. (2008)), which could be downloaded from https://tendl.web.psi.ch/tendl_2019/talys.html. For a better match with the experiment data, we modified the deformation files of ¹⁴N, ²⁰Ne, and ²⁸Si using the results of Benhabiles-Mezhoud et al. (2011). We also used the production cross sections of the specific lines listed in the compilation of Murphy et al. (2009).