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tokens: off free electrons (Heitler 1954 ; Chen Kamionkowski 2004 ), and at high enough energies undergo electron–positron pair production (PP). We here distinguish the cross-section for PP off of the CMB (Agaronyan, Atoyan Nagapetyan 1987 ; Ferrigno, Blasi De Marco 2005 ), atomic and ionized hydrogen and helium, as well as free electrons (Joseph Rohrlich 1958 ; Motz, Olsen Koch 1969 ; Zdziarski Svensson 1989 ). Photons also undergo photon–photon scattering where the injected photon transfers part of its energy to a CMB photon (Svensson Zdziarski 1990 ); however, this process is highly subdominant in the redshift range considered here. The mean free paths (mfp) at mean gas density for selected processes undergone by injected electrons, positrons, and photons are outlined in Fig. 2 for a neutral 10 7 M ⊙ halo at redshift 40. Solid and dot–dashed lines show interactions for the leptons while the dashed show those for photons. The dashed red, magenta, and orange lines show photoionization, Compton scattering, and pair creation off of the gas field, respectively. Electroionization and excitation are shown in green and blue, IC scattering in black, and annihilation via positronium for positron in purple. For a fully ionized halo, the yellow line shows the mfp for Coulomb interaction. For each process, the lines indicate the mfp at the average density of the halo while the shading either side of the curves shows the mfp at r vir and r vir/100 . Figure 2. mfpin units of the virial radius for the various interactions undergone by injected particles within a neutral gas 10 7 M ⊙ halo at redshift 40. Solid lines show interactions for charged particles and dashed for photons. The grey line indicates the virial radius of the halo. Processes shown are photoionization (red), Compton scattering (magenta), and pair creation off of the gas (orange) for photons and ionization and excitation (green and blue) for electrons, as well as IC scattering (cyan) and annihilation via positronium for positrons (purple, dot–dashed line). In all cases, lines show the mfp for the process at the average density of the halo, while the shaded regions either side indicate the mfp at r vir and r vir /100. For reference, the yellow curve shows the mfp for Coulomb scattering in an equivalent, fully ionized halo. The grey line is indicative of the halo's virial radius. Particles with energies such that their interaction mfp are no longer smaller than or comparable to the virial radius will readily escape the halo without either interacting with the gas and/or depositing energy. For the DM annihilation products considered here, the primary interaction of the injected electrons and positrons is IC scattering (injected photons first undergo electron/positron pair creation off of the gas field). The actual energy transfer process occurs via the secondary particle produced in those interactions, in this case, the upscattered IC photons. Therefore, the energy spectrum of the secondary cascade