We present new determinations of the local sub-mm luminosity functions , solving the “ sub-mm Olbers ’ Paradox. ” We also present predictions of source counts and luminosity functions in current and future far-infrared to sub-mm surveys .
Using the sub-mm colour temperature relations from the SCUBA Local Universe Galaxy Survey , and the discovery of excess 450 \mu m excess emission in these galaxies , we interpolate and extrapolate the IRAS detections to make predictions of the SEDs of all 15411 PSC-z galaxies from 50 - 1300 \mu m. Despite the long extrapolations we find excellent agreement with ( a ) the 90 \mu m luminosity function of Serjeant et al .
( 2001 ) , ( b ) the 850 \mu m luminosity function of Dunne et al .
( 2000 ) , ( c ) the mm-wave photometry of Andreani & Franceschini ( 1996 ) ; ( d ) the asymptotic differential and integral source count predictions at 50 - 1300 \mu m by Rowan-Robinson ( 2001 ) .
We find the local 850 \mu m sub-mm luminosity density converges to 7.3 \pm 0.2 \times 10 ^ { 19 } h _ { 65 } W Hz ^ { -1 } Mpc ^ { -3 } .
Remarkably , the local spectral luminosity density and the extragalactic background light together strongly constrain the cosmic star formation history for a wide class of evolutionary assumptions .
We find that the extragalactic background light , the 850 \mu m 8 mJy source counts , and the \Omega _ { \ast } constraints all independently point to a decline in the comoving star formation rate at z > 1 .
In order to reconcile this with direct determinations , we suggest either there is a top-heavy initial mass function at high redshifts , and/or there is stronger evolution in the more luminous far-infrared galaxies than seen in the population as a whole .