Erratum: “High‐Mass Protostellar Candidates. II. Density Structure from Dust Continuum and CS Emission” (ApJ, 566, 945 [2002])

Abstract

To derive the equations calculating the gas mass and column densities in § 3.2, we approximated the grain emissivity Qν byQν=7.5×10-4(ν/2.4 THz)β=7.5×10-4(125 μm/λ)β. This approximation stems from R. Hildebrand (ApJ, 566, 945 [2002]; Table 1, row 6, col. [4]) and was used the same way in the work of T. Hunter (ApJ, 566, 945 [2002]) and T. Hunter et al. (ApJ, 566, 945 [2002]), to which we compared our sample. This approximation implicitly assumes that the emissivity between 125 and 250 μm has the same index, β, as at submillimeter wavelengths, for which we assumed β=2. However, Hildebrand advocates β=1 for the former number. Using β=1 between 125 and 250 μm and changing the reference wavelength to 250 μm, longward of which β is left as a free parameter, we derive the following expression for Qν, which is consistent with the relation given in the Hildebrand's Table 1 (last row, col. [2]):Qν=3.75×10-4(ν/1.2 THz)β=3.75×10-4(250 μm/λ)β. At our given wavelength of 1.2 mm, assuming β=2, the newly derived value of Qν is a factor 2 higher than previously calculated. We point out that this factor 2 difference is only valid assuming β=2, and recent work has shown that β can be lower, even at the spatial scales sampled by single-dish observations. For example, S. J. Williams et al. (ApJ, 566, 945 [2002]) found a mean β of 0.9 toward the same sample of high-mass protostellar objects (in which case our old equations remain valid), and R. K. Friesen et al. (ApJ, 566, 945 [2002]) report an average β of 1.6 toward hot molecular cores (reducing the change in Qν to only 1.5). The new mass and column density equations areMgas=(2.0×10-2)/(Jν(Tdust))a/0.1 μmρ/(3 g cm-3)R/100(Fν)/Jy(D/kpc)2(ν/1.2 THz)-3-β(Msolar),Ngas=(1.25×1012)/(Jν(Tdust)Ω)a/0.1 μmρ/(3 g cm-3)R/100(Fν)/Jy(ν/1.2 THz)-3-β(cm-2). Since Qν is in the denominator of the mass and column density equations (R. Hildebrand, ApJ, 566, 945 [2002]), the derived masses and column densities are a factor of 2 lower than reported in Table 3 (cols. [3], [4], and [5]). Although this is a systematic difference, the change in mass and column density is still within the calculated error budget of a factor of 5 (§ 3.2). Therefore, we stress that the new calculations do not change the general results of the paper.