Measuring Star Formation Rate and Far-infrared Color in High-redshift Galaxies Using the CO(7–6) and [N II] 205 μm 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., the 60–100 μm 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 μm and [N ii] at 205 μm([N ii]_(205μm)). For local (U)LIRGs, the ratios of the CO(7–6) luminosity (L_(CO(7–6))) to the total infrared luminosity (L_(IR); 8–1000 μm) are fairly tightly distributed (to within ~0.12 dex) and show little dependence on C(60/100). This makes L_(CO(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 L_(CO(1–0)). Furthermore, the logarithmic [N ii]_(205μm)/CO(7–6) luminosity ratio depends fairly strongly (at a slope of ~ −1.4) on C(60/100), with a modest scatter (~0.23 dex). This makes it a useful estimator on C(60/100) with an implied uncertainty of ~0.15 (or ≾4 K in the dust temperature (T_(dust)) in the case of a graybody emission with T_(dust) ≳30 K and a dust emissivity index β ≥ 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 ~6.5.