Combining high-z galaxy luminosity functions with Bayesian evidence

Galaxy formation during the first billion years of our Universe remains a challenging problem at the forefront of astrophysical cosmology. Although these z ≧ 6 galaxies are likely responsible for the last major phase change of our Universe, the epoch of reionization (EoR), detailed studies are possible only for relatively rare, bright objects. Characterizing the fainter galaxies that are more representative of the population as a whole is currently done mainly through their non-ionizing UV luminosity function (LF). Observing the faint end of the UV LFs is nevertheless challenging, and current estimates can differ by orders of magnitude. Here we propose a methodology to combine disparate high-z UV LF estimates in a Bayesian framework: Bayesian Data-analysis Averaging (BDA). Using a flexible, physically motivated galaxy model, we compute the relative evidence of various z = 6 UV LFs within the magnitude range -20 ≤ MUV ≤ -15 which is common to the data sets. Our model, based primarily on power-law scalings of the halo mass function, naturally penalizes systematically jagged points as well as misestimated errors. We then use the relative evidence to weigh the posteriors obtained from disparate LF data sets during the EoR, 6 ≤ z ≤ 10. The resulting LF posteriors suggest that the star formation rate density (SFRD) integrated down to a UV magnitude of - 17 represent 60.9-09.6+11.3 per cent / 28.2-10.1+9.3 per cent / 5.7-4.7+4.5 per cent of the total SFRD at redshifts 6 / 10 / 15. The BDA framework we introduce enables galaxy models to leverage multiple, analogous LF estimates when constraining their free parameters.