Another, probably more plausible, explanation for the systematic trend in Figure 5 might be that, in deriving SN explosion energy from the global parameters, it is difficult to take into account the complex environments of SNRs, and this is compounded by the parameter sensitivity of Equation (10) (and to a lesser extent, Equation (8)). As we have already seen in many observed SNRs (e.g., Figure 1) and simulated SNRs (e.g., Figure 3), the real ISM provides a very complex environment for SNRs. In this case, the background medium density parameter 





 for describing SNR evolution is not well-defined. Fortunately, as demonstrated in 3D simulations considering inhomogeneous background medium (e.g., Figure 4; see also Cho et al. 2015; Iffrig & Hennebelle 2015; Kim & Ostriker 2015; Li et al. 2015; Martizzi et al. 2015; Walch & Naab 2015; Zhang & Chevalier 2019), the evolutionary tracks of integrated quantities such as total momentum and kinetic energy in the radiative SNRs (i.e., after the shell formation) are not sensitive to the complexity of the background medium. In particular, the total momentum does not evolve in time after reaching a terminal value. The model uncertainty due to the ISM inhomogeneity is less than a factor of two. However, a unitary background medium density 





 does not seem be applicable to both 





 and 





. In our TS models, where the ambient medium has a large-scale nonuniformity, the thermal energy is considerably smaller than that of the uniform medium case with the same mean density (Figure 4(e)). This also happens for some SNRs in TI models (see Section 4.2). On the other hand, the observed thermal energies of the SNRs appear to be generally larger than those of the uniform medium cases with the same mean densities (Figure 4(f)). For the two prototypical SNRs interacting with MCs, W44 and IC 443, for example, Table 5 shows that 





/





 = 6–8 when we adopt the mean ambient density 





(H i+H2)(=50–70 cm−3). It is, however, clear that this density is much higher than the density of the material filling most of the volume of the ISM where the SN blast wave propagates. For example, the ambient density derived from an analysis of the X-ray surface brightness profile of W44 is ∼3 cm−3 (Harrus et al. 1997). An overestimated ambient density would predict a smaller 





 or a larger 





 to match the observed 





 (see Equation (10)). On the other hand, Equation (10) is based on 1D simulations. In real SNRs in inhomogeneous/nonuniform media, the cooling could be significantly enhanced due to the mixing and diffusion between the engulfed dense material and the hot plasma, in which case the thermal energy of real SNRs might be smaller than the 





 predicted from 1D simulations. Therefore, it is not obvious whether Equation (10) with 





(H i+H2) would overpredict or underpredict 





 for SNRs in complex environments (see also Section 4.2). High-resolution simulations of SNRs in realistic environments, including the complex physics at the hot/cool interface, are needed in oder to understand the environmental dependency of the evolution of thermal energy.
Citation: Li et al. 2015
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