Measuring Star-formation Rate and Far-Infrared Color in High-redshift Galaxies Using the CO (7-6) and [NII] 205 micron Lines

To better characterize the global star formation activity in a galaxy, one needs to know not only the star formation rate (SFR) but also the rest-frame, far-infrared color (e. g., the60-100 mu m color, C(60/100)) of the dust emission. The latter probes the average intensity of the dust heating radiation field and scales statistically with the effective SFR surface density in star-forming galaxies including (ultra-) luminous infrared galaxies ((U) LIRGs). To this end, here we exploit a new spectroscopic approach involving only two emission lines: CO(7-6) at 372 mu m and [N II] at 205 mu m([ N II](205 mu m)). For local (U) LIRGs, the ratios of the CO(7-6) luminosity (LCO(7-6)) to the total infrared luminosity (L-IR; 8-1000 mu m) are fairly tightly distributed (to within similar to 0.12 dex) and show little dependence on C (60/100). This makes LCO(7-6) a good SFR tracer, which is less contaminated by active galactic nuclei than L-IR and may also be much less sensitive to metallicity than LCO(1-0). Furthermore, the logarithmic [N II](205 mu m)/CO(7-6) luminosity ratio depends fairly strongly (at a slope of similar to-1.4) on C(60/100), with a modest scatter (similar to 0.23 dex). This makes it a useful estimator on C(60/100) with an implied uncertainty of similar to 0.15 (or less than or similar to 4 K in the dust temperature (T-dust) in the case of a graybody emission with T-dust greater than or similar to 30 K and a dust emissivity index beta >= 1). Our locally calibrated SFR and C(60/100) estimators are shown to be consistent with the published data of (U) LIRGs of z up to similar to 6.5.