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ALMA Observations of the Host Galaxy of GRB090423 at z=8.23: Deep Limits on Obscured Star Formation 630 Million Years After the Big Bang

We present rest-frame far-infrared (FIR) and optical observations of the host galaxy of GRB090423 at z=8.23 from the Atacama Large Millimeter Array (ALMA) and the Spitzer Space Telescope, respectively. The host remains undetected to 3-sigma limits of Fnu(222 GHz)<33 microJy and Fnu(3.6 micron)<81 nJy. The FIR limit is about 20 times fainter than the luminosity of the local ULIRG Arp220, and comparable to the local starburst M82. Comparing to model spectral energy distributions we place a limit on the IR luminosity of L_IR(8-1000 micron)<3e10 Lsun, corresponding to a limit on the obscured star formation rate of SFR_IR<5 Msun/yr; for comparison, the limit on the unobscured star formation rate from Hubble Space Telescope rest-frame UV observations is SFR_UV<1 Msun/yr. We also place a limit on the host galaxy stellar mass of <5e7 Msun (for a stellar population age of 100 Myr and constant star formation rate). Finally, we compare our millimeter observations to those of field galaxies at z>4 (Lyman break galaxies, Ly-alpha emitters, and submillimeter galaxies), and find that our limit on the FIR luminosity is the most constraining to date, although the field galaxies have much larger rest-frame UV/optical luminosities than the host of GRB090423 by virtue of their selection techniques. We conclude that GRB host galaxies at z>4, especially those with measured interstellar medium metallicities from afterglow spectroscopy, are an attractive sample for future ALMA studies of high redshift obscured star formation.