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Sub-millimetre galaxies reside in dark matter halos with masses greater than 3x10^11 solar masses

The extragalactic background light at far-infrared wavelengths originates from optically-faint, dusty, star-forming galaxies in the universe with star-formation rates at the level of a few hundred solar masses per year. Due to the relatively poor spatial resolution of far-infrared telescopes, the faint sub-millimetre galaxies are challenging to study individually. Instead, their average properties can be studied using statistics such as the angular power spectrum of the background intensity variations. A previous attempt at measuring this power spectrum resulted in the suggestion that the clustering amplitude is below the level computed with a simple ansatz based on a halo model. Here we report a clear detection of the excess clustering over the linear prediction at arcminute angular scales in the power spectrum of brightness fluctuations at 250, 350, and 500 microns. From this excess, we find that sub-millimetre galaxies are located in dark matter halos with a minimum mass of log[M_min/M_sun ]= 11.5^+0.7_-0.2 at 350 microns. This minimum dark matter halo mass corresponds to the most efficient mass scale for star formation in the universe, and is lower than that predicted by semi-analytical models for galaxy formation.