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Finding $η$ Car Analogs in Nearby Galaxies Using Spitzer: II. Identification of An Emerging Class of Extragalactic Self-Obscured Stars

Understanding the late-stage evolution of the most massive stars such as $η$ Carinae is challenging because no true analogs of $η$ Car have been clearly identified in the Milky Way or other galaxies. In Khan et. al. (2013), we utilized Spitzer IRAC images of $7$ nearby ($\lesssim4$ Mpc) galaxies to search for such analogs, and found $34$ candidates with flat or red mid-IR spectral energy distributions. Here, in Paper II, we present our characterization of these candidates using multi-wavelength data from the optical through the far-IR. Our search detected no true analogs of $η$ Car, which implies an eruption rate that is a fraction $0.01\lesssim F \lesssim 0.19$ of the ccSN rate. This is roughly consistent with each $M_{ZAMS} \gtrsim 70M_\odot$ star undergoing $1$ or $2$ outbursts in its lifetime. However, we do identify a significant population of $18$ lower luminosity $\left(\log(L/L_\odot)\simeq5.5-6.0\right)$ dusty stars. Stars enter this phase at a rate that is fraction $0.09 \lesssim F \lesssim 0.55$ of the ccSN rate, and this is consistent with all $25 < M_{ZAMS} < 60M_\odot$ stars undergoing an obscured phase at most lasting a few thousand years once or twice. These phases constitute a negligible fraction of post-main sequence lifetimes of massive stars, which implies that these events are likely to be associated with special periods in the evolution of the stars. The mass of the obscuring material is of order $\sim M_\odot$, and we simply do not find enough heavily obscured stars for theses phases to represent more than a modest fraction ($\sim 10\%$ not $\sim 50\%$) of the total mass lost by these stars. In the long term, the sources that we identified will be prime candidates for detailed physical analysis with JWST.