The SOFIA Massive (SOMA) Star Formation Survey. III. From Intermediate- to High-Mass Protostars

We present multi-wavelength images observed with SOFIA-FORCAST from ~10 to 40 $\mu$m of 14 protostars, selected as intermediate-mass protostar candidates, as part of the SOFIA Massive (SOMA) Star Formation Survey. We build protostellar spectral energy distributions (SEDs) with the SOFIA observations, together with archival data from Spitzer, Herschel and IRAS. We then fit the SEDs with radiative transfer (RT) models of Zhang & Tan (2018), based on Turbulent Core Accretion theory, to estimate key properties of the protostars. The SEDs generally indicate the validity of these RT models down to intermediate-mass and/or early-stage protostars. The protostars analyzed so far in the SOMA survey span a range of luminosities from ~$10^{2}$ to ~$10^{6} L_{\odot}$, current protostellar masses from ~0.5 to ~30 $M_{\odot}$, and ambient clump mass surface densities, $\Sigma_{\rm cl}$ of 0.1 - 3 g cm$^{-2}$. A wide range of evolutionary states of the individual protostars and of the protocluster environments are also probed. The 19 to 37 $\mu$m spectral index of the sources correlates with outflow cavity opening angle, ratio of this angle to viewing angle, and evolutionary stage. We have also added a sample of ~50 protostellar sources identified from within Infrared Dark Clouds and expected to be at the earliest stages of their evolution. With this global sample, most of the evolutionary stages of high- and intermediate-mass protostars are probed. From the best fitting models of the protostars, there is no evidence of a threshold value of protocluster clump mass surface density being needed to form protostars up to ~25 $M_\odot$. However, to form more massive protostars, there is tentative evidence that $\Sigma_{\rm cl}$ needs to be at least 1 g cm$^{-2}$. We discuss how this is consistent with expectations from core accretion models that include internal feedback from the forming massive star.