We present rest-frame far-infrared ( FIR ) and optical observations of the host galaxy of GRB 090423 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 F _ { \nu } ( 222 { GHz } ) \lesssim 33 \mu Jy and F _ { \nu } ( 3.6 { \mu m } ) \lesssim 81 nJy .
The FIR limit is about 20 times fainter than the luminosity of the local ULIRG Arp 220 , and comparable to the local starburst M 82 .
Comparing to model spectral energy distributions we place a limit on the IR luminosity of L _ { IR } ( 8 - 1000 { \mu m } ) \lesssim 3 \times 10 ^ { 10 } L _ { \odot } , corresponding to a limit on the obscured star formation rate of { SFR _ { IR } } \lesssim 5 M _ { \odot } yr ^ { -1 } ; for comparison , the limit on the unobscured star formation rate from Hubble Space Telescope rest-frame UV observations is { SFR _ { UV } } \lesssim 1 M _ { \odot } yr ^ { -1 } .
We also place a limit on the host galaxy stellar mass of M _ { * } \lesssim 5 \times 10 ^ { 7 } M _ { \odot } ( 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 \gtrsim 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 GRB 090423 by virtue of their selection techniques .
We conclude that GRB host galaxies at z \gtrsim 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 .