A 2.8 millimeter survey of the Hubble deep field

We present a continuum survey of the Hubble Deep Field at a wavelength of 2.8 mm made with the BIMA array. A mosaic of seven pointings was constructed to span the entire 4.'7 x 4.'7 area observed by the Hubble Space Telescope with 4.'' 7 resolution and a nearly uniform 0.71 mJy rms sensitivity. No significant sources of emission were found (>5 sigma). We use these observations to place limits on the presence of far-infrared emission from dusty star-forming galaxies at high redshifts. The most stringent limits apply for a critically closed universe (Omega(0) = 1), dust temperatures typical of nearby starbursts (40 K), and long-wavelength dust emissivity power-law index beta = 1. For these parameters, the data rule out systems at z > 5 with far-infrared luminosities in excess of 1.3 x 10(13) L-.. The lack of a large population of such luminous systems supports the view that galaxies are assembled in a hierarchical fashion instead of forming the bulk of their stars In single bursts of short duration. For an open universe and/or substantially higher dust temperatures, the limits are higher by an order of magnitude or more and allow for undetected massive starbursts.