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Explaining the observed number counts of submillimetre (submm) galaxies(SMGs) has been a longstanding challenge for theoretical models. Surprisingly,recent observations have suggested that the brightest SMGs are almostexclusively multiple fainter sources blended into a single source in thesingle-dish surveys. This result is in contrast with the predictions of ourpreviously presented theoretical model, which includes some effects ofblending. In this Letter, we consider the implications of an upper limit on thesubmm flux density for the demographics of the SMG population. Using a relationamongst submm flux, star formation rate (SFR), and dust mass (M_d) from ourprevious work, we infer the maximum SFR for a range of flux density limits. ForM_d = 2 x 10^9 (5 x 10^8) M_sun, the SFR limit that corresponds to an870-{\mu}m flux density (S_870) limit in the range 9 - 12.5 mJy is in the range~630 - 1400 (3600 - 7700) M_sun/yr. The SFR limit implies a correspondinglysharp, redshift-dependent cutoff in the stellar mass (M_star) function, thevalue of which we predict using the S_870-M_star relation predicted by ourmodel. The M_star limit decreases with increasing redshift: for an S_870 limitof 9 - 12.5 mJy, the M_star limit ranges from ~4 - 7 x 10^12 M_sun at z ~ 1 to~3 - 5 x 10^11 M_sun at z ~ 6. We discuss the few interferometrically detectedSMGs that may be brighter than the proposed cutoff. Although such objects arecertainly interesting, inferences based on such objects may not apply to mostSMGs.

The star formation rate and stellar mass limits for submillimetre galaxies implied by recent interferometric observations