THE KILOPARSEC-SCALE STAR FORMATION LAW AT REDSHIFT 4: WIDESPREAD, HIGHLY EFFICIENT STAR FORMATION IN THE DUST-OBSCURED STARBURST GALAXY GN20

We present high-resolution observations of the 880 mu m (rest-frame FIR) continuum emission in the z = 4.05 submillimeter galaxy GN20 from the IRAM Plateau de Bure Interferometer (PdBI). These data resolve the obscured star formation (SF) in this unlensed galaxy on scales of 0 ''.3 x 0 ''.2 (similar to 2.1 x 1.3 kpc). The observations reveal a bright (16 +/- 1 mJy) dusty starburst centered on the cold molecular gas reservoir and showing a bar-like extension along the major axis. The striking anti-correlation with the Hubble Space Telescope/Wide Field Camera 3 imaging suggests that the copious dust surrounding the starburst heavily obscures the rest-frame UV/optical emission. A comparison with 1.2 mm PdBI continuum data reveals no evidence for variations in the dust properties across the source within the uncertainties, consistent with extended SF, and the peak star formation rate surface density (119 +/- 8M(circle dot) yr(-1) kpc(-2)) implies that the SF in GN20 remains sub-Eddington on scales down to 3 kpc(2). We find that the SF efficiency (SFE) is highest in the central regions of GN20, leading to a resolved SF law with a power-law slope of Sigma(SFR) similar to Sigma(2.1 +/- 1.0)(H2), and that GN20 lies above the sequence of normal star-forming disks, implying that the dispersion in the SF law is not due solely to morphology or choice of conversion factor. These data extend previous evidence for a fixed SFE per free-fall time to include the star-forming medium on similar to kiloparsec scales in a galaxy 12 Gyr ago.