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.

Based on Herschel observations. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.