SOFIA {\it FORCAST} Photometry of 12 Extended Green Objects in the Milky Way

TL;DR

This study uses SOFIA FORCAST photometry to analyze 12 extended green objects in the Milky Way, constructing their spectral energy distributions to understand their evolutionary stage and physical properties.

Contribution

First mid-infrared imaging and photometry of 12 EGOs with SOFIA, combined with multi-wavelength data and modeling to characterize their physical parameters and evolutionary status.

Findings

Median luminosity-to-mass ratio suggests a transitional evolutionary stage.

Models indicate typical protostar radius around 10 solar radii.

Objects are likely in a cooler, younger phase of IR-bright stage.

Abstract

Massive young stellar objects are known to undergo an evolutionary phase in which high mass accretion rates drive strong outflows. A class of objects believed to trace this phase accurately is the GLIMPSE Extended Green Object (EGO) sample, so named for the presence of extended 4.5 $\mu$m emission on sizescales of $\sim$0.1 pc in \textit{Spitzer} images. We have been conducting a multi-wavelength examination of a sample of 12 EGOs with distances of 1 to 5 kpc. In this paper, we present mid-infrared images and photometry of these EGOs obtained with the SOFIA telescope, and subsequently construct SEDs for these sources from the near-IR to sub-millimeter regimes using additional archival data. We compare the results from greybody models and several publicly-available software packages which produce model SEDs in the context of a single massive protostar. The models yield typical \rstar\/$\sim$10 \rsun, \tstar\/$\sim$10$^3$ to 10$^4$ K, and \lstar\/$\sim$1~$-$~40~$\times$~10$^3$ \lsun; the median $L/M$ for our sample is 24.7 \lsun/\msun. Model results rarely converge for \rstar\/ and \tstar, but do for \lstar, which we take to be an indication of the multiplicity and inherently clustered nature of these sources even though, typically, only a single source dominates in the mid-infrared. The median $L/M$ value for the sample suggests that these objects may be in a transitional stage between the commonly described ``IR-quiet'' and ``IR-bright'' stages of MYSO evolution. The median $T_{dust}$ for the sample is less conclusive, but suggests that these objects are either in this transitional stage or occupy the cooler (and presumably younger) part of the IR-bright stage.

Figures

Tables

Table 1. Table 1 EGO Source Properties

Source	$V_{\mathrm{LSR}}^a$	Distanceb	EGOc	IRDCd	H2Oe	CH3OH Masers (GHz)f
	(km s-1)	(kpc)	Cat		Maser	6.7g	44h	95i
G10.29$-$0.13	14	1.9	2	Y	Y	Y	Y	Y
G10.34$-$0.14	12	1.6	2	Y	Y	Y	Y	Y
G11.92$-$0.61	36	3.38${}_{-0.27}{}^{}{}_{}{}^{+0.33}$ (3.5)	1	Y	Y	Y	Y	Y
G12.91$-$0.03	57	4.5	1	Y	Y	Y	?	Y
G14.33$-$0.64	23	1.13${}_{-0.11}{}^{}{}_{}{}^{+0.14}$ (2.3)	1	Y	Y	?	Y	Y
G14.63$-$0.58	19	1.83${}_{-0.07}{}^{}{}_{}{}^{+0.08}$ (1.9)	1	Y	Y	Y	?	Y
G16.59$-$0.05	60	3.58${}_{-0.27}{}^{}{}_{}{}^{+0.32}$ (4.2)	2	N	Y	Y	?	Y
G18.89$-$0.47	66	4.2	1	Y	Y	Y	Y	Y
G19.36$-$0.03	27	2.2	2	Y	N	Y	Y	Y
G22.04$+$0.22	51	3.4	1	Y	Y	Y	Y	Y
G28.83$-$0.25	87	4.8	1	Y	Y	Y	Y	?
G35.03$+$0.35	53	2.32${}_{-0.20}{}^{}{}_{}{}^{+0.24}$ (3.2)	1	Y	Y	Y	Y	Y

Table 2. Table 2 SOFIA FORCAST Observing Parameters

Source	Pointing Center (J2000)		Obs. Datea	TOSb	$\sigma$ (MAD)c
	RA	Dec		(s)	37 $\mu$m	19 $\mu$m
G10.29$-$0.13	18:08:49.2	-20:05:59.3	2016 July 13	502	0.26	0.08
G10.34$-$0.14	18:08:59.9	-20:03:37.3	2016 Sept 27	626	0.30	0.07
G11.92$-$0.61	18:13:58.0	-18:54:19.3	2016 July 12	604	0.22	0.07
G12.91$-$0.03	18:13:48.1	-17:45:41.3	2016 July 19	1000	0.18	0.04
G14.33$-$0.64	18:18:54.3	-16:47:48.3	2016 July 12	593	0.24	0.07
G14.63$-$0.58	18:19:15.3	-16:29:57.3	2016 July 13	641	0.22	0.07
G16.59$-$0.05	18:21:09.0	-14:31:50.3	2016 July 20	810	0.19	0.04
G18.89$-$0.47	18:27:07.8	-12:41:38.3	2016 Sept 27	626	0.25	0.06
G19.36$-$0.03	18:26:25.7	-12:03:56.3	2016 Sept 20	285	0.46	0.09
G22.04$+$0.22	18:30:34.6	-09:34:49.3	2016 Sept 20	642	0.21	0.05
G28.83$-$0.25	18:44:51.2	-03:45:50.3	2016 Sept 27	470	0.26	0.07
G35.03$+$0.35	18:54:00.4	+02:01:15.7	2016 Sept 22	500	0.29	0.08

Table 3. Table 3 SOFIA FORCAST 19.7  μ 𝜇 \mu m and 37.1  μ 𝜇 \mu m Fitted Flux Densities

EGO	Sourcea	Coordinates (J2000)b		Fitted Sizeb		19 $\mu$m Fluxc	37 $\mu$m Fluxc
		RA (h m s)	Dec (∘ $\prime$ $″$)	Major $\times$ Minor ($″\times ″$)	PA (∘)	Density (Jy)	Density (Jy)
G10.29$-$0.13	a	$\cdots$	$\cdots$	$\cdots$	$\cdots$	¡0.40	¡1.3
G10.34$-$0.14	a	18:09:00.001 (0.003)	-20:03:34.53 (0.04)	1.41 $\times$ 1.01 (0.31 $\times$ 0.45)	97 (31)	¡0.36	14 (3)
	b	18:09:00.02 (0.02)	-20:03:28.8 (0.2)	4.55 $\times$ 2.97 (0.71 $\times$ 0.61)	97 (15)	0.7 (0.2)	9 (2)
G11.92$-$0.61	a	18:13:58.078 (0.002)	-18:54:20.16 (0.04)	2.63 $\times$ 2.39 (0.1 $\times$ 0.05)	32 (9)	1.1 (0.4)	57 (12)
	b	18:13:58.113 (0.008)	-18:54:16.25 (0.09)	3.41 $\times$ 2.59 (0.14 $\times$ 0.13)	100 (6)	0.7 (0.3)	25 (5)
G12.91$-$0.03	a	18:13:48.227 (0.004)	-17:45:38.46 (0.06)	2.17 $\times$ 1.58 (0.26 $\times$ 0.30)	148 (17)	0.2 (0.1)	9 (2)
	b	18:13:48.276 (0.005)	-17:45:45.91 (0.09)	2.01 $\times$ 1.49 (0.40 $\times$ 0.48)	160 (29)	0.7 (0.2)	6 (1)
	c	18:13:48.44 (0.01)	-17:45:32.5 (0.2)	1.43 $\times$ 1.11 (0.84 $\times$ 0.91)	35 (140)	¡0.20	2.2 (0.6)
G14.33$-$0.64	a	18:18:54.232 (0.003)	-16:47:48.40 (0.06)	5.40 $\times$ 3.41 (0.08 $\times$ 0.06)	4.2 (1.3)	0.7 (0.3)	85 (17)
	b	18:18:53.36 (0.01)	-16:47:42.3 (0.1)	11.42 $\times$ 10.23 (0.15 $\times$ 0.13)	107 (5)	22 (5)	200 (41)
	c	18:18:54.64 (0.01)	-16:47:49.6 (0.1)	point source	pt. src.	¡0.33	7 (1)
G14.63$-$0.58	a	18:19:15.225 (0.009)	-16:30:03.3 (0.1)	3.60 $\times$ 2.91 (0.41 $\times$ 0.39)	59 (22)	¡0.34	10 (2)
G16.59$-$0.05	a	18:21:09.124 (0.002)	-14:31:48.79 (0.03)	2.47 $\times$ 2.41 (0.04 $\times$ 0.04)	89 (29)	0.7 (0.2)	67 (14)
	b	18:21:09.509 (0.001)	-14:31:55.88 (0.01)	6.14 $\times$ 5.18 (0.1 $\times$ 0.09)	141 (4)	5 (1)	68 (14)
	c	18:21:08.511 (0.001)	-14:31:57.92 (0.01)	1.91 $\times$ 1.91 (0.1 $\times$ 0.1)	167 (360)	0.8 (0.3)	6 (1)
G18.89$-$0.47	a	18:27:07.835 (0.008)	-12:41:35.1 (0.1)	1.93 $\times$ 1.85 (0.70 $\times$ 0.72)	167 (307)	¡0.31	5 (1)
	b	18:27:08.46 (0.03)	-12:41:29.8 (0.5)	5.0 $\times$ 3.3 (1.7 $\times$ 1.5)	23 (31)	¡0.31	4 (1)
G19.36$-$0.03	a	18:26:25.750 (0.005)	-12:03:52.57 (0.07)	2.69 $\times$ 2.48 (0.28 $\times$ 0.28)	70 (52)	0.3 (0.1)	24 (5)
	b	18:26:25.591 (0.009)	-12:03:47.9 (0.1)	3.78 $\times$ 2.56 (0.41 $\times$ 0.39)	84 (12)	1.7 (0.5)	20 (4)
G22.04$+$0.22	a	18:30:34.635 (0.003)	-09:34:45.74 (0.04)	2.13 $\times$ 1.57 (0.13 $\times$ 0.15)	135 (9)	0.4 (0.2)	21 (4)
	b	18:30:33.43 (0.01)	-09:34:47.9 (0.2)	4.81 $\times$ 4.34 (0.40 $\times$ 0.38)	95 (32)	1.8 (0.4)	14 (3)
G28.83$-$0.25	a	18:44:51.138 (0.001)	-03:45:48.05 (0.01)	4.41 $\times$ 2.53 (0.16 $\times$ 0.14)	87.5 (0.1)	0.3 (0.2)	32 (7)
	b	18:44:50.938 (0.008)	-03:45:56.5 (0.2)	2.61 $\times$ 1.34 (0.42 $\times$ 0.63)	159 (12)	1.1 (0.3)	8 (2)
G35.03$+$0.35	a	18:54:00.524 (0.003)	+02:01:19.16 (0.04)	3.64 $\times$ 3.10 (0.03 $\times$ 0.03)	115 (2)	1.5 (0.4)	160 (31)
	b	18:54:00.700 (0.007)	+02:01:23.2 (0.1)	5.47 $\times$ 3.91 (0.09 $\times$ 0.07)	131 (2)	0.8 (0.3)

Table 4. Table 4 IRAC Integrated Flux Densities

EGO	Source	Aperturea	Annulusa	Aperture Correctionb			Aperture-Corrected Flux Density (mJy)
		Radius ($″$)	Radii ($″$)	3.6 $\mu$m	5.8 $\mu$m	8.0 $\mu$m	3.6 $\mu$m	5.8 $\mu$m	8.0 $\mu$m
G10.29$-$0.13	a	3.6	3.6 to 8.4	1.125	1.135	1.221	0.4 (0.3)	15 (3)	22 (8)
G10.34$-$0.14	a	3.6	3.6 to 8.4	1.125	1.135	1.221	16.0 (0.8)	94 (6)	99 (14)
	b	3.6	3.6 to 8.4	1.125	1.135	1.221	11.2 (0.6)	137 (7)	350 (21)
G11.92$-$0.61	a	2.4	2.4 to 7.2	1.215	1.366	1.568	10.0 (0.4)	66 (3)	40 (2)
	b	2.4	2.4 to 7.2	1.215	1.366	1.568	22.9 (0.9)	193 (7)	152 (6)
G12.91$-$0.03	a	3.6	3.6 to 8.4	1.125	1.135	1.221	8.7 (0.4)	52 (3)	20 (5)
	b	4.8	14.4 to 24.0	1.070	1.076	1.087	1.3 (0.2)	55 (4)	130 (13)
	c	3.6	3.6 to 8.4	1.125	1.135	1.221	0.5 (0.2)	15 (2)	34 (5)
G14.33$-$0.64	a	4.8	14.4 to 24.0	1.070	1.076	1.087	6.6 (0.4)	86 (4)	136 (9)
	b	12.0	14.4 to 24.0	1.000	1.000	1.000	141 (6)	1600 (70)	4300 (180)
	c	3.6	3.6 to 8.4	1.125	1.135	1.221	2.1 (0.2)	26 (1)	31 (3)
G14.63$-$0.58	a	2.4	2.4 to 7.2	1.215	1.366	1.568	0.9 (0.1)	10.5 (0.1)	13 (2)
G16.59$-$0.05	a	3.6	3.6 to 8.4	1.125	1.135	1.221	3.3 (0.3)	108 (5)	107 (7)
	b	6.0	6.0 to 12.0	1.060	1.063	1.084	60 (3)	740 (30)	1840 (80)
	c	6.0	6.0 to 12.0	1.060	1.063	1.084	43 (2)	330 (15)	820 (40)
G18.89$-$0.47	a	4.8	14.4 to 24.0	1.070	1.076	1.087	4.6 (0.6)	46.2 (0.4)	20 (11)
	b	4.8	14.4 to 24.0	1.070	1.076	1.087	22 (1)	104 (6)	200 (15)
G19.36$-$0.03	a	4.8	14.4 to 24.0	1.070	1.076	1.087	24 (1)	151 (7)	190 (12)
	b	3.6	3.6 to 8.4	1.125	1.135	1.221	11.0 (0.5)	101 (4)	220 (10)
G22.04$+$0.22	a	4.8	14.4 to 24.0	1.070	1.076	1.087	1.4 (0.3)	30 (2)	26 (6)
	b	9.6	14.4 to 24.0	1.011	1.011	1.017	79 (4)	791 (32)	1980 (83)
G28.83$-$0.25	a	4.8	14.4 to 24.0	1.070	1.076	1.087	23 (1)	77 (5)	17 (8)
	b	4.8	14.4 to 24.0	1.070	1.076	1.087	8.0 (0.6)	91 (5)	220 (13)
G35.03$+$0.35	a	3.6	3.6 to 8.4	1.125	1.135	1.221	17.0 (0.8)	140 (6)	58 (6)
	b	3.6	3.6 to 8.4	1.125	1.135	1.221	30 (1)	121 (6)	34 (6)

Table 5. Table 5 MIPS 24  μ 𝜇 \mu m Standard Star Fitted and Catalog Fluxes, & Flux Ratios

Stara	Coordinates (J2000)b		Catalog Flux	Fitted Flux	Flux Ratio
	RA (h m s)	Dec (∘ $\prime$ $″$)	(mJy)	(mJy)
1	18:30:32.40	-09:35:47.25	1950 (39)	1220 (40)	1.60
2	18:30:12.78	-09:36:47.99	1980 (36)	1250 (38)	1.58
3	18:30:53.95	-09:39:51.27	2960 (55)	1870 (71)	1.58
4	18:30:46.32	-09:32:28.89	1230 (23)	770 (23)	1.60
5	18:30:48.45	-09:36:00.11	780 (14)	490 (17)	1.59

Table 6. Table 6 MIPS 24  μ 𝜇 \mu m Aperture-Corrected Fitted Flux Densities

EGO	Source	Coordinates (J2000)a		Fitted Fluxb	Aperture-Correctedc
		RA (h m s)	Dec (∘ $\prime$ $″$)	Density (Jy)	Fitted Flux (Jy)
G10.29$-$0.13	a	$\cdots$	$\cdots$	$\cdots$	¡0.28
G10.34$-$0.14	a	18:08:59.989 (0.004)	-20:03:34.97 (0.06)	0.77 (0.03)	1.23 (0.08)
	b	18:09:00.017 (0.003)	-20:03:28.75 (0.05)	1.51 (0.04)	2.4 (0.1)
G11.92$-$0.61	a	18:13:58.065 (0.001)	-18:54:21.26 (0.01)	2.484 (0.003)	4.0 (0.2)
	b	18:13:58.122 (0.001)	-18:54:14.97 (0.01)	2.262 (0.003)	3.6 (0.2)
G12.91$-$0.03	a	18:13:48.233 (0.002)	-17:45:38.19 (0.03)	1.11 (0.02)	1.77 (0.09)
	b	18:13:48.283 (0.001)	-17:45:46.21 (0.01)	1.50 (0.01)	2.4 (0.1)
	c	18:13:48.469 (0.004)	-17:45:31.77 (0.04)	0.28 (0.01)	0.45 (0.03)
G14.33$-$0.64	a	$\cdots$	$\cdots$	confused	$\cdots$
	b	$\cdots$	$\cdots$	saturated	$\cdots$
	c	$\cdots$	$\cdots$	confused	$\cdots$
G14.63$-$0.58	a	18:19:15.221 (0.001)	-16:30:03.26 (0.02)	0.683 (0.009)	1.09 (0.06)
G16.59$-$0.05	a	$\cdots$	$\cdots$	saturated	$\cdots$
	b	$\cdots$	$\cdots$	saturated	$\cdots$
	c	$\cdots$	$\cdots$	confused	$\cdots$
G18.89$-$0.47	a	18:27:07.82 (0.01)	-12:41:35.1 (0.2)	0.34 (0.04)	0.54 (0.07)
	b	18:27:08.45 (0.01)	-12:41:29.5 (0.2)	0.64 (0.07)	1.0 (0.1)
G19.36$-$0.03	a	18:26:25.782 (0.001)	-12:03:53.73 (0.01)	2.356 (0.005)	3.8 (0.2)
	b	18:26:25.569 (0.001)	-12:03:48.13 (0.01)	3.371 (0.006)	5.4 (0.3)
G22.04$+$0.22	a	18:30:34.627 (0.001)	-09:34:46.24 (0.02)	2.23 (0.02)	3.6 (0.2)
	b	18:30:33.432 (0.001)	-09:34:48.39 (0.01)	2.79 (0.02)	4.4 (0.2)
G28.83$-$0.25	a	18:44:51.136 (0.001)	-03:45:47.845 (0.009)	2.230 (0.008)	3.6 (0.2)
	b	18:44:50.931 (0.001)	-03:45:56.506 (0.009)	2.362 (0.008)	3.8 (0.2)
G35.03$+$0.35	a	$\cdots$	$\cdots$	saturated	$\cdots$
	b	$\cdots$	$\cdots$	saturated	$\cdots$

Table 7. Table 7 Hi-GAL 70  μ 𝜇 \mu m & 160  μ 𝜇 \mu m and ATLASGAL 870  μ 𝜇 \mu m Flux Densities

EGO	Source	Hi-GALa	70 $\mu$m Fluxb	160 $\mu$m Fluxb	870 $\mu$m Flux
		70 $\mu$m Notes	(Jy)	(Jy)	(Jy)
G10.29$-$0.13	a	$\cdots$	75 (6)	298 (30)	5.0 (0.8)
G10.34$-$0.14	a	$\cdots$	280 (20)	590 (49)	6 (1)
	b	assuming all emission from a	$\cdots$	$\cdots$	$\cdots$
G11.92$-$0.61	a	$\cdots$	640 (33)	980 (58)	11 (2)
	b	assuming all emission from a	$\cdots$	$\cdots$	$\cdots$
G12.91$-$0.03	a	$\cdots$	96 (6)	270 (52)	7 (1)
	b	assuming all emission from a	$\cdots$	$\cdots$	$\cdots$
	c	assuming all emission from a	$\cdots$	$\cdots$	$\cdots$
G14.33$-$0.64	a	$\cdots$	1130 (190)	1940 (120)	32 (4)
	b	assuming all emission from a	$\cdots$	$\cdots$	$\cdots$
	c	assuming all emission from a	$\cdots$	$\cdots$	$\cdots$
G14.63$-$0.58	a	$\cdots$	130 (8)	390 (30)	15 (2)
G16.59$-$0.05	a	$\cdots$	490 (26)	740 (48)	9 (1)
	b	assuming all emission from a	$\cdots$	$\cdots$	$\cdots$
	c	assuming all emission from a	$\cdots$	$\cdots$	$\cdots$
G18.89$-$0.47	a	sources a and b fit with imfit	48 (2)	180 (27)	10 (2)
	b	sources a and b fit with imfit	19.6 (0.2)	$\cdots$	$\cdots$
G19.36$-$0.03	a	$\cdots$	250 (14)	470 (41)	8 (1)
	b	assuming all emission from a	$\cdots$	$\cdots$	$\cdots$
G22.04$+$0.22	a	sources a and b fit with imfit	204 (10)	400 (94)	5.9 (0.8)
	b	sources a and b fit with imfit	59 (3)	$\cdots$	$\cdots$
G28.83$-$0.25	a	$\cdots$	510 (65)	870 (60)	10 (1)
	b	assuming all emission from a	$\cdots$	$\cdots$	$\cdots$
G35.03$+$0.35	a	$\cdots$	1350 (71)	1230 (84)	8 (1)
	b	assuming all emission from a	$\cdots$	$\cdots$	$\cdots$

Table 8. Table 8 Temperature & Mass From Greybody Fits and Single-dish NH 3 Observations

EGO	Distancea	Temperatures (K)		Masses (M⊙)		L${}_{}{}^b{}_{FIR}{}^{}$
	(kpc)	T${}_{}{}^c{}_{dust}{}^{}$	T${}_{N{H}_3}$	Greybody	NH3-derivedd	(103 $L_{\odot }$)
G10.29$-$0.13	1.9	24 (1)	21.19 (0.17)	76	91	0.90
G10.34$-$0.14	1.6	26 (1)	28.23 (0.38)	62	56	1.42
G11.92$-$0.61	3.38${}_{-0.27}{}^{}{}_{}{}^{+0.33}$ (3.5)	27 (1)	26.27 (0.19)	450	466	12.76
G12.91$-$0.03	4.5	23 (1)	23.56 (0.31)	649	627	5.49
G14.33$-$0.64	1.13${}_{-0.11}{}^{}{}_{}{}^{+0.14}$ (2.3)	29 (2)	25.26 (0.17)	132	159	2.84
G14.63$-$0.58	1.83${}_{-0.07}{}^{}{}_{}{}^{+0.08}$ (1.9)	22 (1)	20.76 (0.32)	234	254	1.31
G16.59$-$0.05	3.58${}_{-0.27}{}^{}{}_{}{}^{+0.32}$ (4.2)	26 (1)	20.51 (0.38)	456	636	10.57
G18.89$-$0.47	4.2	22 (1)	28.24 (0.19)	879	625	3.04
G19.36$-$0.03	2.2	26 (1)	24.90 (0.31)	147	155	2.61
G22.04$+$0.22	3.4	26 (1)	26.71 (0.49)	257	248	4.90
G28.83$-$0.25	4.8	26 (1)	28.27 (0.50)	851	761	20.62
G35.03$+$0.35	2.32${}_{-0.20}{}^{}{}_{}{}^{+0.24}$ (3.2)	33 (1)	29.54 (0.92)	119	138	9.98

Table 9. Table 9 Stellar Radius, Temperature, and Luminosity Results for SED Model Grids

Source	Robitaille (2017)a,b					Robitaille et al. (2006)a				Zhang & Tan (2018)a
Name	Model	$R_{\star }$ ($R_{\odot }$)	$T_{\star }$ (K)	$L_{\star }$ (103 $L_{\odot }$)	${\chi }^2$	$R_{\star }$ ($R_{\odot }$)	$T_{\star }$ (K)	$L_{\star }$ (103 $L_{\odot }$)	${\chi }^2$	$R_{\star }$ ($R_{\odot }$)	$T_{\star }$ (K)	$L_{\star }$ (103 $L_{\odot }$)	${\chi }^2$
G10.29$-$0.13	spubhmi	49.1	6640	4.15	0.0003	71.0	7405	13.41	0.002	7.3	4994	0.03	0.001
G10.34$-$0.14	s-pbhmi	27.5	7980	2.71	1.51	79.3	4492	2.27	1.45	21.7	6835	0.91	3.98
G11.92$-$0.61	s-pbsmi	22.8	14250	18.97	3.14	6.0	27930	19.39	3.02	5.1	33013	27.34	15.07
G12.91$-$0.03	s-pbhmi	6.4	19940	5.73	1.51	118.8	4355	4.49	2.48	11.2	16298	7.83	20.43
G14.33$-$0.64	s-pbsmi	31.4	7976	3.53	0.45	110.7	4428	4.17	0.81	11.2	16298	7.83	1.89
G14.63$-$0.58	s-pbhmi	11.8	11330	2.03	3.68	68.6	4172	1.26	1.94	18.5	6780	0.64	20.54
G16.59$-$0.05	s-pbhmi	31.8	11020	13.20	1.12	65.0	7510	11.89	0.53	5.1	33013	27.34	11.84
G18.89$-$0.47	s-pbhmi	14.6	10610	2.39	1.00	96.7	4234	2.66	4.2	7.3	4994	0.03	37.73
G19.36$-$0.03	s-pbsmi	8.4	14420	2.70	1.73	98.3	4493	3.48	1.41	13.6	14585	7.41	10.93
G22.04$+$0.22	s-pbhmi	14.3	12570	4.52	1.81	27.3	9345	5.03	1.92	11.2	16298	7.83	7.66
G28.83$-$0.25	s-pbhmi	74.3	8766	28.85	0.81	293.4	4355	27.40	1.62	42.9	12552	40.43	12.96
G35.03$+$0.35	spubhmi	69.9	8552	23.13	1.08	4.8	31560	20.23	1.31	5.1	33013	27.34	0.66
Medianc:	$\cdots$	25	10800	4.3	1.31	75	5950	4.8	1.54	11	15440	7.8	12.40

Table 10. Table 10 χ 2 superscript 𝜒 2 \chi^{2} and P(D | | | M) Scores for Robitaille ( 2017 ) Model Sets a,b

G10.29$-$0.13				G10.34$-$0.14c				G11.92$-$0.61
Model	${\chi }^2$	Model	P(D$|$M)	Model	${\chi }^2$	Model	P(D$|$M)	Model	${\chi }^2$	Model	P(D$|$M)
spubhmi	0.0003	s-u-smi	0.0519	s-pbhmi	1.51	s-pbhmi	0.0029	s-pbsmi	3.14	s-ubsmi	0.0015
spubsmi	0.002	spu-smi	0.0422	s-pbsmi	2.30	s-pbsmi	0.0028	s-pbhmi	3.69	s-pbsmi	0.0009
s-pbsmi	0.004	spubhmi	0.0408625	spubsmi	6.75	spubhmi	0.0008625	spubsmi	3.87	s-pbhmi	0.0007
s-ubsmi	0.013	s-pbhmi	0.0384	spubhmi	8.53	s-ubsmi	0.0008	spubhmi	4.73	spubsmi	0.000675
s-u-smi	0.017	s-ubhmi	0.0359	s-ubsmi	12.13	s-ubhmi	0.0359	s-ubhmi	5.02	s-ubhmi	0.0006
s-pbhmi	0.022	spubsmi	0.02725	s-ubhmi	15.52	spubsmi	0.0325	s-ubsmi	6.08	spubhmi	0.0004125
s-ubhmi	0.028	s-pbsmi	0.0261	spu-smi	21.70	spu-smi	0	s-u-smi	34.70	spu-smi	0
spu-smi	0.044	s-ubsmi	0.0217	s-u-smi	23.52	s-u-smi	0	spu-smi	40.68	s-u-smi	0
G12.91$-$0.03				G14.33$-$0.64				G14.63$-$0.58
Model	${\chi }^2$	Model	P(D$|$M)	Model	${\chi }^2$	Model	P(D$|$M)	Model	${\chi }^2$	Model	P(D$|$M)
s-pbhmi	1.51	s-pbhmi	0.0013	s-pbsmi	0.45	s-pbsmi	0.0034	s-pbhmi	3.68	s-pbsmi	0.0007
spubhmi	1.84	s-ubsmi	0.0013	s-pbhmi	0.80	s-pbhmi	0.003	s-pbsmi	4.41	s-pbhmi	0.0006
spubsmi	2.84	s-pbsmi	0.0011	spubsmi	2.30	s-ubhmi	0.0006	spubsmi	24.81	spubsmi	0.0001
s-ubsmi	3.03	s-ubhmi	0.0006	spubhmi	4.40	s-ubsmi	0.0006	spubhmi	24.87	spubhmi	0.00005
s-pbsmi	3.99	spubsmi	0.00055	s-ubsmi	4.51	spubhmi	0.000425	s-ubhmi	38.19	s-ubhmi	0
s-ubhmi	4.84	spubhmi	00003375	s-ubhmi	4.94	spubsmi	0.000425	s-ubsmi	47.43	s-ubsmi	0
s-u-smi	28.58	spu-smi	0	spu-smi	12.78	spu-smi	0.0003	spu-smi	67.87	spu-smi	0
spu-smi	31.37	s-u-smi	0	s-u-smi	12.84	s-u-smi	0.0002	s-u-smi	70.85	s-u-smi	0
G16.59$-$0.05				G18.89$-$0.47				G19.36$-$0.03
Model	${\chi }^2$	Model	P(D$|$M)	Model	${\chi }^2$	Model	P(D$|$M)	Model	${\chi }^2$	Model	P(D$|$M)
s-pbhmi	1.12	s-pbsmi	0.0011	s-pbhmi	1.01	s-pbhmi	0.0008	s-pbsmi	1.73	s-pbsmi	0.0022
s-pbsmi	1.41	s-ubsmi	0.0008	spubhmi	1.83	s-pbsmi	0.0008	s-pbhmi	2.23	s-ubhmi	0.0019
s-ubsmi	2.32	spubsmi	0.00045	s-pbsmi	4.13	s-ubsmi	0.0007	spubsmi	3.02	s-pbhmi	0.0015
spubsmi	2.59	spubhmi	0.000425	s-ubhmi	8.40	spubsmi	0.000625	s-ubsmi	3.81	spubsmi	0.000625
spubhmi	2.60	s-pbhmi	0.0003	s-ubsmi	9.51	s-ubhmi	0.0002	spubhmi	3.83	s-ubsmi	0.0005
s-ubhmi	3.40	s-ubhmi	0.0003	spubsmi	9.59	spubhmi	0.0001	s-ubhmi	10.00	spubhmi	0.000425
spu-smi	32.60	spu-smi	0	spu-smi	44.43	spu-smi	0	s-u-smi	20.86	spu-smi	0
s-u-smi	35.47	s-u-smi	0	s-u-smi	44.73	s-u-smi	0	spu-smi	22.85	s-u-smi	0
G22.04$+$0.22				G28.83$-$0.25				G35.03$+$0.35
Model	${\chi }^2$	Model	P(D$|$M)	Model	${\chi }^2$	Model	P(D$|$M)	Model	${\chi }^2$	Model	P(D$|$M)
s-pbhmi	1.81	spubsmi	0.001925	s-pbhmi	0.81	spubsmi	0.00255	spubhmi	1.08	s-ubsmi	0.0056
spubhmi	2.37	s-pbhmi	0.0019	s-ubsmi	2.36	s-ubsmi	0.0023	s-pbsmi	1.46	s-ubhmi	0.0034
s-pbsmi	2.41	s-pbsmi	0.0019	spubhmi	2.53	s-ubhmi	0.002	spubsmi	1.58	spubhmi	0.0033
s-ubsmi	2.55	s-ubsmi	0.0019	spubsmi	2.86	s-pbsmi	0.002	s-ubhmi	1.94	s-pbhmi	0.0033
s-ubhmi	2.59	s-u-smi	00017	s-pbsmi	5.06	spubhmi	0.00195	s-ubsmi	2.07	spubsmi	0.002775
spubsmi	2.61	spubhmi	0.001025	s-ubhmi	5.54	s-pbhmi	0.0011	s-pbhmi	2.45	s-u-smi	0.0019
s-u-smi	16.97	s-ubhmi	0.001	s-u-smi	18.12	s-u-smi	0.0006	spu-smi	9.47	spu-smi	0.0017
spu-smi	19.13	spu-smi	0.0005	spu-smi	20.02	spu-smi	0	s-u-smi	12.47	s-pbsmi	0.0014

Equations

$$M_{gas}=R\bigg{(}\frac{F_{\nu}D^{2}}{B_{\nu}(T_{dust})\kappa_{\nu}}\bigg{)}\bigg{(}\frac{\tau}{1-e^{-\tau}}\bigg{)}$$

Full text

**affiliationtext: A.P.M.T. is a Grote Reber Doctoral Fellow at the National Radio Astronomy Observatory.

1. Introduction

Massive young stellar objects (MYSOs) are challenging to observe due to their comparative rarity and short-lived natal phase, large distances from Earth, and highly-obscured formation environments. Early observations of suspected MYSOs were performed mostly with large beams, and probed size scales ranging from cores to clumps and clouds ($\sim$0.1 pc, $\sim$1 pc, and $\sim$10 pc, respectively; see Kennicutt & Evans, 2012). Detailed descriptions of early surveys for MYSOs and their results can be found in, e.g., Molinari et al. (1996), Sridharan et al. (2002), and Fontani et al. (2005). Follow-up observations with improved sensitivity and spatial resolution, such as interferometric radio and millimeter observations, revealed that many of the objects originally identified as “MYSOs” were actually sites in which multiple protostars were forming simultaneously (e.g. Hunter et al., 2006; Cyganowski et al., 2007; Vig et al., 2007; Zhang et al., 2007, to name just a few). This predilection for forming in clustered environments means that the study of high-mass protostars is necessarily the study of protoclusters: clusters of protostars with a range of masses and in a variety of evolutionary stages. Current theories of high mass star formation differ in their predictions of the aggregate properties of these protoclusters, such as mass segregation (if any), sub-clustering of the protostars, and stellar birth order (e.g. Vázquez-Semadeni et al., 2017; Banerjee & Kroupa, 2017; Bonnell & Bate, 2006; McKee & Tan, 2003). It is therefore necessary to consider each high-mass protostar in combination with its environment.

Extended Green Objects (EGOs) were first identified by Cyganowski et al. (2008) using data from the Galactic Legacy Infrared Midplane Survey Extraordinaire (GLIMPSE, Benjamin et al., 2003; Churchwell et al., 2009) project. EGOs are named for their extended emission in the 4.5 $\mu$m Spitzer IRAC band (commonly coded as “green” in three-color RGB images), which is due to shocked H2 from powerful protostellar outflows (e.g., Marston et al., 2004). Follow-up observations of $\sim$20 EGOs with the Karl G. Jansky Very Large Array (VLA) by Cyganowski et al. (2009) established both the presence of massive protostars (traced by 6.7 GHz Class II CH3OH masers) and shocked molecular gas indicative of outflows (traced by 44 GHz Class I CH3OH masers). The causal link between accretion and ejection (Frank et al., 2014) thus implies that these objects contain protostars undergoing active accretion, and the maser data indicate that these protostars are massive. The youth of the massive protostars within these EGOs was confirmed by deep (at that time) VLA continuum observations (Cyganowski et al., 2011b), which yielded only a few 3.6 cm detections, and by later VLA 1.3 cm continuum observations (Towner et al., 2017), which revealed primarily weak ($<$1 mJy beam*-1*), compact emission. The low detection rates and integrated flux densities of the centimeter continuum emission in these sources demonstrate that any free-free emission is weak, consistent with a stage prior to the development of ultracompact HII regions.

Given that high-mass stars form in clusters, it is likely that EGOs are signposts for protoclusters rather than isolated high-mass protostars, though the level of multiplicity of massive sources ($>$8$M_{\odot}$) and overall cluster demographics remain open questions. Millimeter dust continuum observations of EGOs with $\sim$3$\arcsec$ resolution, suggest that the number of massive protostars per EGO is typically one to a few (e.g. Cyganowski et al., 2012, 2011a; Brogan et al., 2011). However, the precise physical properties of protoclusters traced by EGO emission - such as total mass, luminosity, and massive protostellar multiplicity - remain largely unexplored in EGOs as a class.

The infrared emission from EGOs, and indeed MYSOs in general, is often challenging to characterize due to the presence of high extinction from their surrounding natal clumps (as they are still deeply embedded), and confusion from more evolved sources nearby. The latter issue has been particularly affected by the relatively poor angular resolution ($>1\arcmin$) that has heretofore been available at mid- and far-infrared wavelengths, where the high extinction can be overcome. Yet these wavelengths contain crucial information as hot dust, shocked gas, and polycyclic aromatic hydrocarbons (PAHs) all emit in this regime. Scattered light originating from the protostar itself may also sometimes escape through outflow cavities and would likewise be visible in the infrared. Thus mid-infrared wavelengths are a crucial component of the Spectral Energy Distribution (SED) which is a useful tool for constraining important source properties such as mass, bolometric luminosity, and temperature.

These properties are of particular interest for MYSOs, as recent analysis of the Herschel InfraRed Galactic Plane Survey (Elia et al., 2017) and a full census of the properties of ATLASGAL Compact Source Catalog (CSC) objects Urquhart et al. (2018) shows how the luminosity to mass ratio $L/M$ of protostellar clumps can be used to both qualitatively and quantitatively discriminate between the different evolutionary stages of pre- and protostellar objects. In theoretical terms, $L/M$ is tied to evolutionary state primarily due to abrupt changes in luminosity during different stages of MYSO/clump evolution (see, e.g., the stages described in Hosokawa & Omukai, 2009; Molinari et al., 2008).

In this paper, we present new data that directly address the questions of the multiplicity and physical properties (temperature, mass, and luminosity) of the massive protoclusters traced by EGOs. We have utilized the unique capabilities of the Stratospheric Observatory for Infrared Astronomy (SOFIA, Temi et al., 2014) to image a well-studied sample of 12 EGOs at two mid-IR wavelengths: 19.7 and 37.1 $\mu$m with the necessary sensitivity ($\sim$0.05 to $\sim$0.25 Jy beam*-1*) and angular resolution ($\sim$ 3$\arcsec$) to detect and resolve the mid-infrared emission from the massive protocluster members. By combining these results with ancillary multi-wavelength archival data, we create well-constrained SEDs from the near-infrared through submillimeter regimes. We then use three SED modelling packages published by Robitaille et al. (2006), Robitaille (2017), and Zhang & Tan (2018), to constrain physical parameters (see, e.g., Gaczkowski et al., 2013; De Buizer et al., 2017). In § 2, we describe our targeted SOFIA observations and the observational details of the archival data at each wavelength. In § 3, we describe our aperture-photometry procedures for each data set and discuss our detection rates and trends. We also present sets of multi-scale, multiwavelength images for each object in order to better demonstrate their small- and large-scale properties and overall environments. In § 4, we compare the physical parameters obtained from the various SED modeling methods, including $L/M$, which help to place EGOs into a broader evolutionary context. In § 5 we discuss the implications of our results, and outline future investigations.

2. The Sample & Observations

In this paper, we conduct a multiwavelength aperture-photometry study of 12 EGOs using the SOFIA Faint Object infraRed CAmera for the SOFIA Telescope (FORCAST Herter et al., 2012). We use new SOFIA FORCAST 19 $\mu$m and 37 $\mu$m observations in conjunction with publicly-available archival datasets from Spitzer, Herschel, and the Atacama Pathfinder EXperiment111This publication is based on data acquired with the Atacama Pathfinder Experiment (APEX). APEX is a collaboration between the Max-Planck-Institut fur Radioastronomie, the European Southern Observatory, and the Onsala Space Observatory. (APEX) telescope, to model the SED of the dominant protostar in each of our target EGOs. Details of source properties for our sample are listed in Table 1.

2.1. SOFIA FORCAST Observations: 19.7 & 37.1 $\mu$m

We used SOFIA FORCAST to observe our 12 targets simultaneously at 19.7 $\mu$m and 37.1 $\mu$m. Observations were performed in the asymmetric chop-and-nod imaging observing mode C2NC2. The measured222These FWHM are the average values in dual-channel mode for each wavelength as measured by the SOFIA team since Cycle 3. More information can be found in the Cycle 5 Observer’s Handbook on the SOFIA website at https://www.sofia.usra.edu/science/proposing-and-observing/sofia-observers-handbook-cycle-5 FWHM are 2$\farcs$5 at 19.7 $\mu$m and 3$\farcs$4 at 37.1 $\mu$m. At the nearest (1.13 kpc) and farthest (4.8 kpc) source distances, these FWHM correspond to physical size scales of 2,830 to 12,000 au at 19.7 $\mu$m and 3,840 to 16,300 au at 37.1 $\mu$m. The instantaneous field of view (FOV) of FORCAST is 3$\farcm$4 $\times$ 3$\farcm$2, with pixel size $\theta$ = 0$\farcs$768 after distortion correction. This FOV corresponds to 1.1 $\times$ 1.1 pc at a distance of 1.13 kpc, and 4.8 $\times$ 4.5 pc at a distance of 4.8 kpc. Table 2 summarizes observation information for each EGO. The project’s Plan ID is 04_0159.

Data calibration and reduction are performed by the SOFIA team using the SOFIA data-reduction pipeline333The FORCAST Data Handbook can be found on the SOFIA website at https://www.sofia.usra.edu/science/proposing-and-observing/data-products. After receipt of the Level 3 data products (artifact-corrected, flux-calibrated images), we converted our images from Jy pixel*-1* to Jy beam*-1* in order to more easily perform photometric measurements in CASA (McMullin et al., 2007). Conversion was accomplished by using the CASA task immath to multiply each image by the beam-to-pixel conversion factor $X_{\lambda}=(beam\ area)/(pixel\ area)$. This factor depends on beam size and pixel size, and therefore is different for each wavelength. The beam-to-pixel conversion factors are X19.7μm = 12.0067 pixels/beam and X37.1μm = 22.2076 pixels/beam.

2.2. Archival Data

2.2.1 Spitzer IRAC (GLIMPSE) Observations: 3.6, 5.8, & 8.0 $\mu$m

All of our EGO targets were originally selected due to their extended emission at 4.5 $\mu$m as seen in Spitzer GLIMPSE images. In order to constrain the SEDs of the driving sources themselves, we used the archival Spitzer observations at 3.6 $\mu$m, 5.8 $\mu$m, and 8.0 $\mu$m (bands I1, I3, and I4, respectively) from the GLIMPSE project (Benjamin et al., 2003; Churchwell et al., 2009). The point response function (PRF) of the IRAC instrument varies by band and position on the detector. The mean FWHM in bands I1, I3, and I4 are 1$\farcs$66, 1$\farcs 72$, and 1$\farcs$88, respectively, as detailed in Fazio et al. (2004). All archival GLIMPSE data were downloaded from the NASA/IPAC Infrared Science Archive (IRSA) Gator Catalog List. The images returned by the archive are all in units of MJy sr*-1*.

2.2.2 Spitzer MIPS (MIPSGAL) Observations: 24 $\mu$m

We utilized archival 24 $\mu$m data from the MIPSGAL survey to provide additional mid-IR constraints on our SEDs for 9 of our 12 targets. For the remaining 3 targets (G14.33, G16.59, G35.03), MIPSGAL 24 $\mu$m data could not be used for the second task due to saturated pixels in the regions of interest. MIPSGAL images have a native brightness unit of MJy sr*-1*, and were converted to Jy beam*-1* by first multiplying each image by 1$\times$106 (to convert from MJy to Jy) and then multiplying by the solid angle subtended by the 6$\farcs$0 $\times$ 6$\farcs$0 MIPS beam at 24 $\mu$m. Technical details of the MIPS instrument can be found in Rieke et al. (2004). For details of the MIPSGAL observing program, see Carey et al. (2009) and Gutermuth & Heyer (2015). All MIPSGAL data were downloaded from the IRSA Gator Catalog List.

2.2.3 Herschel PACS (Hi-GAL) Observations: 70 & 160 $\mu$m

We used archival 70 $\mu$m and 160 $\mu$m data from the Herschel Infrared Galactic Plane Survey (Hi-GAL, Molinari et al., 2016), observed with the Herschel Photoconductor Array Camera and Spectrometer (PACS; Poglitsch et al., 2010) instrument, to probe the far-IR portion of the spectrum. These data were originally observed as part of the Herschel Hi-GAL project (Molinari et al., 2010, 2016) between 2010 October 25 and 2011 November 05. The observations were performed in parallel mode with a scan speed of 60*′′/s. Beam sizes, which are dependent on observing mode, were $\theta_{70\mu m}$ = 5.8${}^{\prime\prime}\times$ 12.1′′* and $\theta_{160\mu m}$ = 11.4${}^{\prime\prime}\times$ 13.4*′′* as reported in Molinari et al. (2016). The native brightness unit of the Hi-GAL data is MJy sr*-1*. Therefore, these images were converted to Jy beam*-1* using the same method as in §2.2.2.

We chose to use the Hi-GAL data over the archival PACS data available on the European Space Agency (ESA) Heritage Archive due to the additional astrometric and absolute flux calibration performed by the Hi-GAL team, as detailed in Molinari et al. (2016). All Hi-GAL data were obtained from the Hi-GAL Catalog and Image Server on the Via Lactea web portal444http://vialactea.iaps.inaf.it/vialactea/eng/index.php.

2.2.4 APEX LABOCA (ATLASGAL) Observations: 870 $\mu$m

We used archival 870 $\mu$m observations from the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL, Schuller et al., 2009) to populate the submillimeter portion of the SED. The data were retrieved from the ATLASGAL Database Server555http://atlasgal.mpifr-bonn.mpg.de/cgi-bin/ATLASGAL_DATABASE.cgi. The ATLASGAL beam size is 19$\farcs$2 $\times$ 19$\farcs$2; additional observational details can be found in Schuller et al. (2009). These images were already in units of Jy beam*-1*, and thus required no unit conversion.

3. Results

Figures 1 through 4 show pairs of three-color (RGB) images for each source. The left-hand panels show a 5$\farcm$3 field of view with 160, 70, and 24 $\mu$m data mapped to R, G, and B, respectively, and with 870 $\mu$m contours overlaid. These panels show the large-scale structure of the cloud and overall environment in which each EGO is located. The right-hand panels all have a 1$\farcm$0 FOV with the Spitzer IRAC 8.0, 4.5, and 3.6 $\mu$m data mapped to R, G, and B, respectively; the extended green emission in these images shows the extent of each EGO. SOFIA FORCAST 19.7 and 37.1 $\mu$m contours and ATLASGAL 870 $\mu$m contours are overlaid, and 6.7 GHz CH3OH masers (Cyganowski et al., 2009) are marked with diamonds. These panels show the small-scale structure and detailed NIR and MIR emission of each EGO, how this emission relates to the larger-scale 870 $\mu$m emission, and the locations of any associated markers of MYSOs, such as 6.7 GHz CH3OH masers.

Below we discuss in detail the photometric methodology used for each band for the SED analysis. Because the angular resolution and sensitivity - and hence level of confusion - vary significantly among the different observations, we have elected to use a photometry method best suited for each particular wavelength in order to minimize (as much as feasible) contamination from unrelated sources. In the following sections we describe in some detail how the photometry was done for each wavelength.

3.1. SOFIA FORCAST Photometry

Table 3.1 shows the photometry for the 19.7 and 37.1 $\mu$m SOFIA images. In this section, we describe the SOFIA astrometry, source selection, and photometry in more detail.

Astrometry

The SOFIA images required additional astrometric corrections. While the relative astrometry between the 19.7 and 37.1 $\mu$m data was accurate to less than one pixel, the absolute astrometry of the SOFIA data varied considerably. Relative to the Spitzer MIPS 24 $\mu$m data, the positions of the SOFIA images varied by up to $\sim 3\arcsec$. In order to properly register the SOFIA images, we selected field point sources that were present in both the 24 $\mu$m images and either the 37.1 and 19.7 $\mu$m images, fit a 2-dimensional gaussian to that point source in both the 24 $\mu$m and SOFIA frame and applied the calculated position difference to both SOFIA images. In most cases, we were able to find a position match with the 24 $\mu$m data in only one of the two SOFIA frames, and relied on the sub-pixel relative astrometry between the two SOFIA images in order to correct the non-matched frame. Post-astrometric correction, we consider the absolute astrometric accuracy of the SOFIA images to be dominated by the absolute position uncertainty of the MIPS 24 $\mu$m images: $\sim$1$\farcs$4.

Mid-IR Source Selection and Nomenclature

We limit our analysis to those mid-IR sources we consider to be plausibly associated with the protocluster in which the EGO resides (with some exceptions described below). For short, we call these sources “EGO-associated.” In this context, “EGO-associated” means one of two things: a) the mid-IR source is coincident with the extended 4.5 $\mu$m emission of the EGO and is therefore likely tracing some aspect of the EGO driving source in the mid-IR, or b) the mid-IR source lies outside the 5$\sigma$ level of the 4.5 $\mu$m emission but is still near to the EGO, and it is unclear whether the source is related or is a field source. In order to create a self-consistent system for selecting sources in the latter category, we establish two criteria: i) the source must lie above the 25% peak intensity level of the ATLASGAL emission and ii) it must be detected at both 19.7 and 37.1 $\mu$m. If a mid-IR detection is not within the bounds of the 4.5 $\mu$m emission and does not meet both criteria i) and ii), then it is considered to be a field source.

One source, G14.33$-$0.64_b meets neither criteria and is likely a field source. It is coincident with the known H ii region IRAS 18159$-$1648. However, it was necessary to explicitly fit this source in order to get accurate flux density results for the EGO-associated sources.

For a given EGO field, source “a” is always the brightest EGO-associated source at 37 $\mu$m, source “b” is the second-brightest at 37 $\mu$m (of all analyzed sources for that FOV), and so on in order of decreasing brightness. The 37 $\mu$m source name designations are used for all the wavelengths analyzed in this paper.

Photometry

After source selection, we fit each source with 2-dimensional gaussian functions using the CASA task imfit in order to determine the total flux density, peak intensity, and major and minor axes. We then applied a multiplicative correction factor (an “aperture correction”) to each fitted flux in order to account for the deviation of the SOFIA PSF from a true gaussian. Our detailed procedure was as described below.

We first selected emission-free regions in each image in order to determine the background noise levels. These emission-free regions are identical for all three mid-IR data sets (SOFIA 37.1 $\mu$m and 19.7 $\mu$m, and MIPS 24 $\mu$m) for a given source. However, the SOFIA images in particular have background levels that typically do not show noise variations about zero. Therefore, we chose to use the scaled MAD as an estimate of the noise (1.482$\times$MAD, where MAD is the median absolute deviation from the median), rather than the rms or standard deviation. With the exception of the ATLASGAL data, all data sets analyzed in this work have noise variations that are not centered about zero. Therefore, we have used the scaled MAD for all data sets for the sake of consistency. From this point forward, the “$\sigma$” symbol refers to the scaled MAD whenever we are estimating or discussing background noise levels of the images.

We then performed the fitting for each source using imfit. We iteratively refined each fit (e.g. by holding certain parameters, such as source position, fixed during the fit) until we determined the fit to be satisfactory. We declared a fit to be satisfactory once the absolute value of the residual intensities of all pixels in the central Airy disk were below 4$\times$MAD of the residual image, with the majority below 2$\times$MAD. In cases where source parameters are held fixed, imfit does not return an uncertainty for those specific parameters, so the uncertainty is due entirely due to user choice of source position, size, etc. For these fits, our position uncertainties are 0.01 pixels, and uncertainties in the major and minor axes or position angles are 0.1*∘*. All the uncertainties for parameters held fixed during the fit are listed in italics in Table 3.1.

Finally, we determined a wavelength-dependent multiplicative correction factor to the imfit flux results. The SOFIA PSF is an obscured Airy diffraction pattern - its central bright disk has a slightly narrower width than a standard Airy diffraction pattern due to the effect of a central obscuration in the light path (the secondary mirror). However, imfit only fits 2-dimensional Gaussians. In effect, it fits a Gaussian to the central Airy disk and ignores the surrounding Airy rings. These correction factors are effectively serving as “aperture corrections” for our data; the only difference is that they are corrections to the fitted flux values returned by imfit, rather than corrections to direct measurements. As Airy diffraction patterns are wavelength-dependent, we calculated separate aperture corrections for our 19.7 $\mu$m and 37.1 $\mu$m data. While the best practice in aperture photometry would be to measure the PSF of an unrelated, isolated point source in each field and then apply that PSF correction to the data, we found that almost none of our fields contained an unrelated point source, much less one bright enough to measure the PSF with any confidence. Instead, we employed the procedure described below.

We first created four 100$\times$100-pixel Airy diffraction patterns using the optical properties of the SOFIA telescope (primary and secondary mirror size and separation, etc.) at each of our two wavelengths. The PSFs are sampled with 0$\farcs$768 pixels, the same as the FORCAST instrument. At this pixel size, the total grid is 76$\farcs$8 in diameter; this is $\sim$23 times the FWHM at 37.1 $\mu$m (3$\farcs$4) as quoted in the Handbook, and $\sim$31 times the FWHM at 19.7 $\mu$m (2$\farcs$5). Although Airy-disk diffraction patterns mathematically extend to infinity, on a practical level, our synthetic PSFs had to be truncated to a particular size; we considered $>$20 times the quoted FWHM to be sufficient. The four PSFs for a given wavelength are mathematically identical, but each center position is given either zero- or half-pixel offsets in both the x and y directions. This effectively gives us four different sampling scenarios for the PSF. This was done to account for the fact that the peak of a given point source might not always fall neatly onto a single pixel, but instead might be sampled relatively equally between two or even four pixels. We then used imfit to fit the central disk of each of these four PSFs, and compared the flux returned by imfit for the central disk alone to the flux measured within an aperture of radius 50 pixels (38$\farcs$4 at 0$\farcs$768 per pixel; 50 pixels was the largest aperture radius available to us for a 100$\times$100-pixel grid). We calculated the ratio of measured to fitted fluxes for each of the four PSF grids for one wavelength, and took the mean of these ratios as our aperture correction factor for that wavelength. The aperture correction at 37 $\mu$m is 1.17 $\pm$ 0.02, and the aperture correction at 19 $\mu$m is 1.11 $\pm$ 0.04, where the uncertainties are the standard deviation of the four measured-to-fitted flux ratios at each wavelength.

Table 3.1 shows the aperture-corrected imfit results for our 37 $\mu$m and 19 $\mu$m data. Non-detections are noted as upper limits. Our detection rate at 37 $\mu$m is 92%; the only target for which we did not detect any 37 $\mu$m emission is G10.29-0.13. Overall, we detect 24 separate 37 $\mu$m sources in our 12 targets. Our detection rate at 19 $\mu$m is slightly lower - we detect 19 $\mu$m emission in only 9 of our 12 targets, for a detection rate of 75%. Overall, we detect 18 separate 19 $\mu$m sources in our 12 targets.