The γ-ray emission of star-forming (SF) galaxies is attributed to hadronic interactions of cosmic ray (CR) protons with the interstellar gas and contributions from CR electrons via bremsstrahlung and inverse Compton (IC) scattering. The relative importance of these processes in different galaxy types is still unclear. We model these processes in three-dimensional magnetohydrodynamical (MHD) simulations of the formation of isolated galactic discs using the moving-mesh code arepo, including dynamically coupled CR protons and adopting different CR transport models. We calculate steady-state CR spectra and also account for the emergence of secondary electrons and positrons. This allows us to produce detailed γ-ray maps, luminosities, and spectra of our simulated galaxies at different evolutionary stages. Our simulations with anisotropic CR diffusion and a low CR injection efficiency at supernovae (SNe; $\zeta_\mathrm{SN}=0.05$) can successfully reproduce the observed far-infrared (FIR)–γ-ray relation. Starburst galaxies are close to the calorimetric limit, where CR protons lose most of their energy due to hadronic interactions and hence, their γ-ray emission is dominated by neutral pion decay. However, in low SF galaxies, the increasing diffusive losses soften the CR proton spectra due to energy-dependent diffusion, and likewise steepen the pionic γ-ray spectra. In turn, IC emission hardens the total spectra and can contribute up to ∼40 per cent of the total luminosity in low SF galaxies. Furthermore, in order to match the observed γ-ray spectra of starburst galaxies, we require a weaker energy dependence of the CR diffusion coefficient, $D\propto E^{0.3}$, in comparison to Milky Way-like galaxies.

中文翻译：

---

模拟星系中的宇宙射线和非热辐射——II。γ射线图、光谱和远红外-γ射线关系

恒星形成 (SF) 星系的 γ 射线发射归因于宇宙射线 (CR) 质子与星际气体的强子相互作用以及 CR 电子通过轫致辐射和逆康普顿 (IC) 散射的贡献。这些过程在不同星系类型中的相对重要性仍不清楚。我们使用移动网格代码 arepo 在孤立星系盘形成的三维磁流体动力学 (MHD) 模拟中对这些过程进行建模，包括动态耦合 CR 质子和采用不同的 CR 传输模型。我们计算了稳态 CR 光谱，并考虑了二次电子和正电子的出现。这使我们能够生成我们模拟星系在不同演化阶段的详细 γ 射线图、光度和光谱。我们在超新星（SNe；$\zeta_\mathrm{SN}=0.05$）处的各向异性 CR 扩散和低 CR 注入效率的模拟可以成功地再现观察到的远红外（FIR）-γ 射线关系。星暴星系接近量热极限，其中 CR 质子由于强子相互作用而失去大部分能量，因此，它们的 γ 射线发射主要由中性介子衰变决定。然而，在低 SF 星系中，由于能量依赖性扩散，不断增加的扩散损失软化了 CR 质子光谱，同样使 pionic γ 射线光谱变陡。反过来，IC 发射强化了总光谱，在低 SF 星系中可以贡献高达 40% 的总光度。此外，为了匹配观测到的星暴星系的 γ 射线光谱，我们需要 CR 扩散系数的能量依赖性较弱，