tokens: (See Also Section 2.7 ) Note. The motivation behind each assumption is described in the corresponding sections. We briefly summarize (column 4) the effect produced by each assumption to help the reader distinguish the genuine trends from those induced by our prior hypotheses. The reference BHAR/SFR trends are taken from Mullaney et al. ( 2012 , M12), Rodighiero et al. ( 2015 , R15), and Aird et al. ( 2019 , A19). (∗∗) The relative normalization is chosen to fit the corresponding data points of Figure 4 . 2.3. Galaxy Stellar Mass Function The first step displayed in Figure 1 consists in setting the input galaxy M ⋆ function at different redshifts. The prescription is taken from Davidzon et al. ( 2017 ), who exploited the latest optical to infrared photometry collected in the COSMOS field over the UltraVISTA area (1.5 deg 2 , see Laigle et al. 2016 ). They provide the M ⋆ function separately between SF and passive galaxies, based on the [NUV − r ]/[ r − J ] colors (Ilbert et al. 2013 ). Throughout this work, we consider only the M ⋆ function relative to the SF galaxy population (i.e., MS and SB galaxies). Next, we split the M ⋆ function of SF galaxies among the MS and SB populations. Given that the relative fraction of the two populations has been shown not to vary with M ⋆ (e.g., Rodighiero et al. 2011 ; Sargent et al. 2012 ), we only consider how their relative fraction evolves with redshift by following the prescription of Béthermin et al. ( 2012 ). The fraction of SB galaxies ( f SB ) appears to evolve linearly, from f SB = 0.015 ( z = 0) to f SB = 0.03 ( z = 1), while it stays flat at higher redshifts. By simply scaling the SF galaxy M ⋆ function down by f SB (or 1 − f SB ), we end up with the M ⋆ function of MS and SB galaxies at each redshift (Figure 2 ). We note that the input M ⋆ function of Davidzon et al. ( 2017 ) is already corrected for the Eddington bias, which might have some impact at the high- M ⋆ end. After dissecting among MS and SB galaxies, we interpolate the corresponding M ⋆ function at redshift z = 0.5, z = 1, z = 2, and z = 3 across a M ⋆ range of 10 8 M ⋆ 10 12 M ⊙ . Figure 2. Galaxy M ⋆ function at various redshifts for SF galaxies, taken from Davidzon et al. ( 2017 ). Solid and dashed lines mark MS and SB galaxies, respectively. 2.4. The MS and the SB Loci We use the MS prescription presented in Schreiber et al. ( 2015 ), which incorporates a redshift evolution and a bending toward higher M ⋆ . Schreiber et al. ( 2015 ) studied a sample of Herschel -selected galaxies out to z ∼ 4, dissecting the observed distribution of MS offsets (=SFR/SFR MS , see their Equation (10) and Figure 19) among the MS and SB populations. By fitting that distribution via a double lognormal function, MS galaxies are centered at 0.87 × SFR MS , while SB galaxies are centered at 5.3 × SFR MS (Schreiber et al. 2015 ). Both relations were rescaled to a Chabrier ( 2003 ) IMF. The 1 σ dispersion for both the MS and SB loci is assumed to be 0.3
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Wavelength O B-Wavelength O O O O B-CelestialRegion I-CelestialRegion O O B-CelestialRegion I-CelestialRegion O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O B-Wavelength O B-Wavelength O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Telescope O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O