Candidate Selection

The SED of a hot dust-obscured star will generally have two peaks -- a dust obscured optical peak, which could be absent altogether given enough absorption, and a mid-IR peak whose location in wavelength depends on the radius of the dust shell around the star. In the IRAC bands, the SED will be flat or rising towards longer wavelengths. For example, $\eta$Car has a steeply rising SED towards longer mid-IR wavelengths (e.g., Robinson et al.1973) and the luminosity of the star exceeds $10^5\,$L$_\odot$ in each IRAC band (see Figure1). At extra-Galactic distances, an $\eta$Car analog would appear as a bright, red point source in IRAC images with a relatively fainter optical counterpart due to the self-obscuration.

We used the Daophot/Allstar PSF-fitting and photometry package (Stetson1992) to identify point sources in all four IRAC bands and then performed photometry at the source location using both aperture and PSF photometry. We used the IRAF ApPhot/Phot tool for the aperture photometry. The aperture fluxes were transformed to Vega-calibrated magnitudes following the procedures described in the Spitzer Data Analysis Cookbook and aperture corrections of 1.213, 1.234, 1.379, and 1.584 for the four IRAC bands. The choice of extraction aperture aperture ($R_{ap}$) as well as the inner ($R_{in}$) and outer ($R_{out}$) radii of the local background annulus are reported in Table2. We estimate the local background using a $2\sigma$ outlier rejection procedure in order to exclude sources located in the local sky annulus, and correct for the excluded pixels assuming a Gaussian background distribution. Using a background annulus immediately next to the signal aperture minimizes the effects of background variation in the crowded fields of the galaxies. We used the Daophot/Allstar package for PSF photometry. The PSF photometry fluxes were transformed to Vega-calibrated magnitudes by applying zero point offsets determined from the difference between the calibrated aperture magnitudes and the initial PSF magnitude estimates of the bright stars in each galaxy.

Table 2: Aperture Definitions

Band	Pixel Scale		$R_{ap}$	$R_{in}$	$R_{out}$
($\mu$m)	(Archive)	(Survey)
3.6-8.0	$1\farcs2$	$0\farcs75$	$2\farcs4$	$2\farcs4$	$7\farcs2$
24	$2\farcs45$	$1\farcs5$	$3\farcs5$	$6\farcs0$	$8\farcs0$
70	$4\farcs0$	$4\farcs5$	$16\farcs0$	$18\farcs0$	$39\farcs0$
160	$8\farcs0$	$9\farcs0$	$16\farcs0$	$64\farcs0$	$128\farcs0$

For the 3.6 and 4.5$\micron$ bands, after verifying consistency with the aperture magnitudes, we only use the Vega-calibrated PSF magnitudes. For 5.8$\micron$, we switch to aperture magnitudes when Allstar fails to fit the PSF to a point source at the location identified by Daophot due to the decreasing resolution. PSF photometry performs very poorly at 8.0$\micron$, leading to both inaccurate photometry and many false sources because Daophot frequently splits up extended regions of PAH emission into spurious point sources. Thus, at 8.0$\micron$ we only use aperture photometry at positions determined for sources identified in the other three bands. We do not use this band for building our initial source list.

We define our initial source list as all point sources that have $\lambda L_\lambda > 10^4$L$_\odot$ in any one of the 3.6, 4.5, and 5.8$\micron$ bands, excluding regions near saturated stars and, in the case of M81, the high surface brightness core of the galaxy. We identify sources in each of these three bands, and cross-match the catalogs using a 1pixel matching radius. We then adopt the position determined at the shortest wavelength (highest resolution) with a $>3\sigma$ detection, and we use this position for the 8.0$\micron$ aperture photometry. We fit the mid-IR SED of each object as a power law in wavelength

$$\log_{10}(\lambda L_\lambda) = a\times \log_{10}(\lambda) + b$$ (1)

to determine the slope ($a$, $\lambda L_\lambda \propto \lambda^a$) and intercept ($b$). We can crudely relate the slope ($a$) to a dust temperature as

$$a = -4 + \frac {\log_{10} \left( \frac{e^{\frac{hc}{\lambda_... ...ght)} {\log_{10} \left( \frac{\lambda_4}{\lambda_1} \right) },$$ (2)

where $\lambda_1$ and $\lambda_4$ are the shortest and longest band-centers assuming a blackbody spectrum and ignoring Planck factors. We define the total mid-IR luminosity ($L_{mIR}$) as the trapezoid rule integral of $L_\lambda$ across the band centers

$$L_{mIR} = \sum_{i=1}^{3} \frac{1}{2}\left( \lambda_{i+1} - \... ..._{i}\right) \left( L_{\lambda_{i}} + L_{\lambda_{i+1}}\right),$$ (3)

where $\lambda_i=$ 3.6, 4.5, 5.8, and 8.0$\micron$. We also calculate the fraction $f$ of $L_{mIR}$ that is emitted in the first three IRAC bands. We define $f$ as the ratio of the energy emitted between 3.6 and 5.8$\micron$ (first two terms of the integral), to $L_{mIR}$ (all three terms of the integral). The approximate values of $L_{mIR}$, $a$, and $f$ for $\eta$Car are $10^{5.65}\,$L$_\odot$, $2.56$, and $0.32$, and those for ObjectX are $10^{5.17}\,$L$_\odot$, $0.22$, $0.57$.

We defined candidates as sources with mid-IR luminosity $L_{mIR}>10^{5}\,$L$_\odot$, a mid-IR SED slope $a>0$, and $f>0.3$. Figures 2 and 3 show the distribution of point sources in M81 with $\lambda L_\lambda > 10^4$L$_\odot$ in at least one of the 3.6, 4.5, and 5.8$\micron$ IRAC bands as a function of $L_{mIR}$, $a$, and $f$. The open red triangles in these figures correspond to candidates that are known to be non-stellar in nature (see Section2.3), and the solid red triangles represent the surviving candidates. While a few hundred sources in M81 are bright enough in the mid-IR to be included in these figures, only a handful of these even remotely resemble $\eta$Car, and not a single one of them is as luminous and as red (cold) as $\eta$Car. The other targeted galaxies show similar distributions of sources. These distributions illustrate that our selection criteria for identifying potential $\eta$Car analogs are robust and allows for selecting objects that are significantly less luminous in the mid-IR and have much warmer circumstellar dust than $\eta$Car. Table5 reports the survey area and the number of candidates found for each galaxy.

We used aperture photometry to estimate the MIPS 24, 70, and 160$\micron$ band luminosities of the objects that meet our selection criteria. For point sources that do not have a flux that is $\gtrsim3\sigma$ above the local sky, we determine the $3\sigma$ detection limit for each aperture location using the local background estimate. Due to the poor spatial resolution of these bands, which forces us to choose increasingly large apertures at longer wavelengths (see Table2), these measurements have limited utility. Figure5 shows the mid-IR SEDs of the candidates we identified in M33 along with normal stars in the M33 image selected from top left region of Figure5. At 24$\micron$, the SEDs of the normal stars show the expected slope for the Rayleigh-Jeans tail of their SEDs, followed by an unphysical rise at 70 and 160$\micron$. Essentially, due to the poor resolution, the apertures used for these two bands include many objects other than the intended target, and even normal stars appear to have rising far-IR SEDs. This means that we can generally use the 24$\micron$ fluxes while the 70 and 160$\micron$ measurements should be treated as upper limits regardless of their origin. Nevertheless, the MIPS bands are useful as a qualitative constraint on an object's physical nature (i.e. if it is a galaxy, QSO, cluster etc.).