Difference between the dark halo mass estimated as the halo mass where 50% cumulative SFR (Mh SFR 50%) is achieved and the halo mass calculated by converting the beff, which is obtained using the LIR (replacing SFR with LIR in Eq. (16)) to the corresponding halo mass using Eq. (17) (Mh LIR weighted). This difference has been calculated and is shown here for all the redshift bins. The dashed line shows the mean of these values: around 0.16 dex. This is the offset applied to the halo mass derived from beff to obtain the mean mass of dark matter halos contributing to CIB.
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