ALMA Submillimeter Continuum Imaging of the Host Galaxies of GRB021004 and GRB080607

We report 345 GHz continuum observations of the host galaxies of gamma-ray bursts (GRBs) 021004 and 080607 at z>2 using the Atacama Large Millimeter/Submillimeter Array (ALMA) in Cycle 0. Of the two bursts, GRB021004 is one of the few GRBs that originates in a Lyman limit host, while GRB080607 is classified as a "dark burst" and its host galaxy is a candidate of dusty star forming galaxy at z~3. With an order of magnitude improvement in the sensitivities of the new imaging searches, we detect the host galaxy of GRB080607 with a flux of S_{345} = 0.31+/-0.09 mJy and a corresponding infrared luminosity of L_{IR}=(2.4-4.5)x10^{11} L_sun. However, the host galaxy of GRB021004 remains undetected and the ALMA observations allow us to place a 3-sigma upper limit of L_{IR}<3.1x10^{11} L_sun for the host galaxy. The continuum imaging observations show that the two galaxies are not ultraluminous infrared galaxies but are at the faintest end of the dusty galaxy population that gives rise to the submillimeter extragalactic background light. The derived star formation rates of the two GRB host galaxies are less than 100 M_sun yr^{-1}, which are broadly consistent with optical measurements. The result suggests that the large extinction (A_V~3) in the afterglow of GRB080607 is confined along its particularly dusty sightline, and not representative of the global properties of the host galaxy.