CRESCENDO II: Spectral cosmic rays with improved energy losses and realistic supernova seeding

Context. Cosmological simulation codes with subgrid models for cosmic rays (CRs) help us better understand their impact on baryonic feedback and non-thermal radiation in galaxies and galaxy clusters. An accurate numerical description requires a spectrally resolved treatment of the CR population, because virtually all transport, acceleration and loss processes depend on energy. Aims. We advance the treatment of CR electrons and protons in the on-the-fly spectral CR solver CRESCENDO in OpenGadget3. Methods. We implement several new energy loss processes for both protons and electrons and improve the computation of their energies and pressures beyond the ultra-relativistic approximation. Moreover, we present a subgrid model for CR seeding by supernova remnants, in which physically motivated spectra are injected at sites of ongoing star formation. Results. We test the newly implemented loss processes and the coupling between CR injection and star formation in idealized setups. We also highlight numerical subtleties, such as the differences arising when hadronic losses are modelled as continuous or catastrophic process, and the advantages of using a flexible spectral cut-off and abandoning the ultra-relativistic approximation. Furthermore, we show that using analytical approximations to compute energy fluxes can cause the slope reconstruction to fail. Conclusions. Future applications of our spectral cosmic-ray model in large-scale, full-physics cosmological simulations will represent an important step towards building a robust and observationally verifiable link between the microphysical and macrophysical aspects of the CR component in the modern paradigm of galaxy evolution.