Extended Data Fig. 4: Cosmic ray calorimetry in the E - Σ_g plane.

Mean calorimetry fraction f_cal(E) in the surface gas density Σ_g, cosmic ray energy E plane, binned in redshift intervals. This figure is constructed by deriving the gas surface density and energy dependent calorimetry fraction for each galaxy in the CANDELS sample using our model. The colour of each pixel gives the mean calorimetry fraction of all the galaxies within that particular range of Σ_g, E, and redshift. The horizontal white stripes correspond to ranges of Σ_g into which no CANDELS galaxies fall for the corresponding redshift range. Several physical processes contribute to the behaviour visible in the plot. At low Σ_g, galaxies have low f_cal at all energies E because there are few targets for hadronic collisions with CRs. As Σ_g increases, the increased ISM density results in efficient calorimetry and conversion of CR energy into γ-rays for low CR energies; however, at higher energies the CR number density is low, yielding a high CR streaming velocity and rapid escape, resulting in low f_cal. As Σ_g increases further, the increasing density results in the streaming instability being suppressed efficiently by ion-neutral damping towards lower energies, reducing the calorimetry fraction further. Finally, at the highest Σ_g, the streaming instability is suppressed completely by ion-neutral damping, but streaming is still limited to the speed of light. Consequently, increasing Σ_g further only results in increased collisions, and thus a higher calorimetry fraction.