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There is a well known correlation between the mass and metallicity of star-forming galaxies. Because mass is correlated with luminosity, this relation is often exploited, when spectroscopy is not available, to estimate galaxy metallicities based on single band photometry. However, we show that galaxy color is typically more effective than luminosity as a predictor of metallicity. This is a consequence of the correlation between color and the galaxy mass-to-light ratio and the recently discovered correlation between star formation rate (SFR) and residuals from the mass-metallicity relation. Using Sloan Digital Sky Survey spectroscopy of ∼180, 000 nearby galaxies, we derive “LZC relations,” empirical relations between metallicity (in seven common strong line diagnostics), luminosity, and color (in 10 filter pairs and four methods of photometry). We show that these relations allow photometric metallicity estimates, based on luminosity and a single optical color, that are ∼50% more precise than those made based on luminosity alone; galaxy metallicity can be estimated to within ∼0.05-0.1 dex of the spectroscopically derived value depending on the diagnostic used. Including color information in photometric metallicity estimates also reduces systematic biases for populations skewed toward high or low SFR environments, as we illustrate using the host galaxy of the supernova SN 2010ay. This new tool will lend more statistical power to studies of galaxy populations, such as supernova and gamma-ray burst host environments, in ongoing and future wide-field imaging surveys. [ABSTRACT FROM AUTHOR]

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 3σ limits of Fν(222 GHz) ≲ 33 μJy and Fν(3.6 μm) ≲ 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 this with model spectral energy distributions, we place a limit on the infrared (IR) luminosity of LIR(8-1000 μm) ≲ 3 × 1010L☼, corresponding to a limit on the obscured star formation rate of M☼ yr–1. For comparison, the limit on the unobscured star formation rate from Hubble Space Telescope rest-frame ultraviolet (UV) observations is SFRUV ≲ 1 M☼ yr–1. We also place a limit on the host galaxy stellar mass of M* ≲ 5 × 107M☼ (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, Lyα 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 ≳ 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. [ABSTRACT FROM AUTHOR]