Extension of HOPS out to 500 pc (eHOPS). I. Identification and Modeling of Protostars in the Aquila Molecular Clouds^*

The Aquila cloud complex (see Figure 1) contains several star-forming clumps concentrated in two distinct regions, Aquila-North and Aquila-South (e.g., Reipurth 2008). The Aquila-North region is located at b = 2°–6° and l = 29°–34° and harbors several star-forming regions including the Serpens Main and Serpens B cluster (Harvey et al. 2007; Winston et al. 2007; Dunham et al. 2015). Aquila-North contains ∼3.5 × 10⁴ M_⊙ gas in dense regions (>1 A_V ) and harbors ∼400 YSOs (Pokhrel et al. 2020, 2021). Aquila-South is located in the southern part of the Aquila Rift at b = 2°–5° and l = 26°–30°. There are three major star-forming regions in Aquila-South: Serpens South, W40, and MWC297 (Dunham et al. 2015; Winston et al. 2018). Discovered by the Spitzer Gould Belt survey (Gutermuth et al. 2008a), Serpens-South is a young, protostar-rich cluster forming from a dense filamentary cloud (Nakamura et al. 2011; Kirk et al. 2013). W40 is another young stellar cluster that is associated with an H ii region that has cleared much of the natal molecular gas (Kuhn et al. 2010; Broos et al. 2013; Pirogov et al. 2013). Herschel observations show ∼5 × 10⁴ M_⊙ gas at >1A_V regions in Aquila-South (Pokhrel et al. 2020, 2021).

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Past ambiguities in the distance to Aquila are now being resolved by parallax measurements (see discussions by Bontemps et al. 2010; Kirk et al. 2013; Dunham et al. 2015; Könyves et al. 2015). While stellar photometry previously suggested a distance of ∼255 pc (Straižys et al. 2003), X-ray and HR diagram analysis suggested a distance >350 pc (Winston et al. 2010). Very long baseline interferometry (VLBI) observations measured trigonometric parallaxes to stars in the Serpens Main cluster and obtained a distance of ∼415 pc (Dzib et al. 2010). The method used by Straižys et al. (2003) is sensitive toward the front wall of the extinction region with cluster-forming clumps at larger distances (e.g., Bontemps et al.2010; Dzib et al. 2010). In more recent years, further observations with VLBI and Gaia converged on even larger distances. As a part of Gould's Belt Distances Survey, Ortiz-León et al. (2017) used VLBI observations that covered an 8 yr observational span to find that the individual cluster-forming clouds such as Serpens Main, W40, and Serpens South are physically associated and form a single cloud structure at an average distance of 436 ± 9 pc. The VLBI distance is also consistent with the more recent Gaia observations (see Ortiz-León et al. 2018 and Anderson et al. 2022 for the details of Gaia observations of Aquila). For the purpose of this work, we adopt a single distance of 436 pc for all of the protostars in Aquila.

The Herschel Gould Belt Survey (André et al. 2010) modeled thermal dust emission from Herschel with a modified blackbody function to obtain the column density and temperature maps. Figure 1 shows a column density map of the Aquila molecular clouds from the Herschel Gould Belt Survey (Könyves et al. 2015; Fiorellino et al. 2021). Figure 2 shows the dust temperature map for Aquila. The protostar-rich regions such as Serpens Main, Serpens B, and Serpens South have high column densities and low temperatures. Similarly, more evolved H ii region W40 have higher dust temperatures than the surrounding regions.

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The SESNA catalog provides photometry for all point sources identified in the Spitzer images using the IDL-based interactive photometry visualization tool PhotVis (see Gutermuth et al. 2008b, 2009 for the details of the automated search and photometry using PhotVis). For each of these sources, the photometry for J (1.2 μm), H (1.6 μm), and Ks (2.2 μm) are adopted from the 2MASS point-source catalog using the NASA/IPAC IRSA. Spitzer photometry is obtained by aperture photometry on point sources, using PhotVis. A positional tolerance of 1'' is used for matching sources in 2MASS and Spitzer/IRAC, and 13 to match them with Spitzer/MIPS 24 μm sources. For the Spitzer/IRAC 3.6, 4.5, 5.8, and 8.0 μm images, the aperture size is 24 with an annulus of 2.4–72 for background subtraction. Similarly for the Spitzer/MIPS 24 μm data, the aperture size is 635 with an annulus of 76–178 for background subtraction.

We adopt the same photometric calibration zero-point magnitudes (Vega-standard magnitudes for 1 DN s⁻¹) as in Gutermuth et al. (2008b): 19.455, 18.699, 16.498, and 16.892 for the 3.6, 4.5, 5.8, and 8.0 μm bands, respectively. These values are derived from the calibration effort presented in Reach et al. (2005), adjusted by standard corrections for the aperture sizes we adopt here. The 24 μm photometric calibration value that we adopt is that of Gutermuth et al. (2008b) and adjusted in Gutermuth & Heyer (2015) for the current aperture size selections, i.e., 14.525 mag for 1 DN s⁻¹ within the apertures we adopted for this work.

SESNA includes point-source detection completeness mapping at 30'' resolution over much of its coverage and all five Spitzer bandpasses, and the SESNA source catalog provides the nearest 90% differential completeness value to each source's position for all bands covered at that position. We use these latter values as upper limits when a source is not detected in all of the available bands (see Section 4.1).

For sources with Spitzer photometry and Herschel/PACS detections, 59 have an IRS low-resolution spectrum associated with them within the positional uncertainty of 2'', all retrieved from CASSIS (Section 2). We include these in the SEDs when available. If any flux mismatches were present in the SL and LL segments of the IRS spectrum, the SL segment of the IRS data was usually scaled to match the flux level at the LL segment, the justification for which is provided in F16.

We adapt the procedure and software developed for the SESNA catalog to the PACS 70, 100, and 160 μm maps. The Herschel maps are scanned in both the parallel and large map modes. PACS 70 μm maps are scanned in the parallel mapping mode with fast scanning speed (60'' s⁻¹). PACS 100 μm maps are scanned in the large map mapping mode with medium scanning speed (20'' s⁻¹). PACS 160 μm maps are mapped in both mapping modes and are scanned at fast as well as medium speeds. We average the flux densities in both maps to obtain photometry at 160 μm. Similar to the SESNA data, we performed automated point-source detection and aperture photometry using PhotVis with the search parameters optimized for the PACS data.

To obtain calibrated photometry, we follow the recipe provided in the PACS Technical Report ¹⁵ and the associated Release Notes ¹⁶ for the PACS maps. We adjust the aperture sizes according to our science needs and recalculate the aperture correction factor. Specifically, we use aperture photometry on the FITS images of the Vesta PACS observations, ¹⁷ for the scanning speeds and observing modes that match our data, to compare the signal in our apertures to those with tabulated encircled energy fractions. The use of the FITS files with appropriate scanning speeds and observing modes is crucial, especially for the 70 and 100 μm images. This is particularly necessary for the blue filters in the parallel mode data, where the increase of the onboard frames averaging in the blue (70 μm) and green (100 μm) filters results in an elongation of the point-spread functions (PSFs) in the scan direction compared to the prime mode (especially at the fast scanning velocity of 60'' s⁻¹). In contrast, for the red camera (160 μm), the sampling is identical to the Prime mode, and thus the PSFs are the same (see the PACS release notes for further details). The values for the aperture and annulus sizes and aperture correction factors are provided in Table 1. We calculate the celestial coordinates of the sources using the astrometry in the PACS image headers; these provide adequate positional accuracy, as shown in Appendix C. The uncertainties are calculated as the rms flux on the background annulus using IDL's aper.

We do not run a source identification algorithm on the SPIRE and SCUBA-2 maps due to their coarse angular resolution and their sensitivity to the extended, structured dust emission in molecular clouds (Figure 46). Instead, we search for sources at the known locations of PACS sources using the following process.

At the location of each known source, we extract postage stamp images from the SPIRE and SCUBA-2 maps with diameters ∼3 times the outer annulus radius centered on the source, where the outer annulus radii are given in Table 1. The postage stamps contain the whole aperture and annulus regions with some extra space for visualizing the surrounding environment. For each postage stamp image, we create a radial profile plot that shows the variation of flux with distance for all pixels. We bin the radius axis of the radial profile plot by 1 pixel and compute the median flux in every bin. The median fluxes are then interpolated using a spline interpolation of third order (cubic interpolation) to show the smoothed behavior in the radial profile plot. We compute the background flux in the annulus region by first clipping fluxes above the 3σ rms flux in the annulus regions defined in Table 1, followed by a mean–median–mode background ¹⁸ (F_bkg) estimator of the form (3 × median) − (2 × mean).

Our goal is to identify compact SPIRE and SCUBA-2 point sources that are at most only marginally more extended than point sources. To do this, we compute the peak flux (F_peak) in the interpolated data near the central source and define a compact source using the following criteria:

$$\begin{eqnarray*}\mathrm{Source}=\left\{\begin{array}{cc}\mathrm{Compact}\ \mathrm{source}, & \mathrm{if}\ {F}_{\mathrm{peak}}\gt (3\times \mathrm{MAD}+{F}_{\mathrm{bkg}})\\ \mathrm{Extended}\ \mathrm{source}\ \mathrm{or}\ \mathrm{nondetection}, & \mathrm{otherwise}.\end{array}\right.\end{eqnarray*}$$

Here, MAD is the median absolute deviation of the fluxes in the central aperture, providing a nonparametric measure of dispersion about the median; it is more robust than other commonly used dispersion measures (see Feigelson & Babu 2012 for a discussion on using MAD in astronomy). As an example illustration of the MAD technique, we show in Figure 3 one of the PACS-detected sources in the SPIRE maps in 250, 350, and 500 μm and in the SCUBA-2 850 μm map. This source is detected in all three SPIRE bands but is not detected by SCUBA-2.

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We perform aperture photometry on the compact sources using IDL's aper package from the IDL Astronomy Users' Library (Landsman 1993). We use the aperture and annulus sizes from Table 1 for each respective wavelength band and divide by the corresponding aperture correction factors to account for the flux outside the aperture. For extended sources, we use an aperture size equal to the beam size and do not perform background subtraction. We treat such photometry as upper limits to the actual fluxes in that wavelength and do not include them in any calculations such as L_bol and T_bol (defined in Section 4). The upper-limit photometry in the far-IR, however, plays an important role in selecting the best-fit models (described in detail in Section 6).

For the SPIRE maps, the SPIRE Data Reduction Guide ¹⁹ provides the details of aperture photometry. The guide also provides the FITS images for the SPIRE maps of the estimated encircled energy fraction for different aperture sizes. ²⁰ The recommended values of aperture sizes for 250, 350, and 500 μm maps are 22'', 30'', and 42'', respectively, with a background annulus of 60''–90'' for all three SPIRE maps. However, for the nearby (<500 pc) clouds, such annulus sizes contain contributions from extended emission from nearby sources. We choose aperture sizes similar to the beam sizes and use a narrower annulus that is closer to the central aperture. The aperture correction factor for the adjusted sizes is recalculated using SPIRE maps of Neptune following the SPIRE Data Reduction Guide. The specific values are provided in Table 1.

We follow Dempsey et al. (2013) for selecting aperture size and the aperture correction factor for the SCUBA-2 850 μm maps and refer the readers to the paper for a detailed discussion on aperture photometry of SCUBA-2 maps. In short, Dempsey et al. (2013) used a large sample of primary (Mars and Uranus) and secondary calibrator observations to investigate the instrument beam shape and photometry methods to deduce flux conversion factors for different aperture sizes. The aperture correction factors in Table 1 are estimated following the routine in Dempsey et al. (2013) using the curve of growth calculations (see Figure 6 and Table 3 in Dempsey et al. 2013).

The photometry uncertainties in the SPIRE and SCUBA-2 maps are obtained using a quadrature sum of the measured fluctuation (standard deviation) in the background annulus and flux uncertainty in the aperture calculated using flux uncertainty maps. This accounts for both formal uncertainties and uncertainties due to the background subtraction in fluctuating background. The signal-to-noise ratio (S/N) in the SPIRE and SCUBA-2 photometry must be greater than 3. If not, the estimated flux is used as an upper limit.

We plot the fluxes of the SEDs in units of janskys. The flux units for Spitzer, Herschel, and JCMT are available in terms of janskys; however, 2MASS and WISE photometry are in units of magnitudes. To convert fluxes from magnitudes to janskys for 2MASS and WISE, we use conversion factors based on Vega-based magnitudes with zero-point fluxes from Cohen et al. (2003), Wright et al. (2010), and Jarrett et al. (2011).

We find 1102 sources that have detection in at least one of the Herschel/PACS wave bands with S/N > 5. Out of the 1102 PACS-detected sources, 272 sources are detected in only one wavelength in the 1–850 μm wavelengths. Comparing the postage images of such sources at each wavelength, we find them to be mostly artifacts instead of a real source and we filter them from our catalog. For the remaining 830 sources with at least two detections in 1–850 μm, we devise a method to detect and classify protostars as well as identify pre-MS stars with disks and galaxies.

Since our classification technique relies on mid-IR observations, Spitzer photometry and spectroscopy are important prerequisites in identifying protostars. If a source is observed by Herschel but not mapped by Spitzer, the emission behavior in the mid-IR is unknown, and hence the source cannot be classified. The most reliable classifications are for the sources that have both Spitzer and Herschel coverages. To account for different degrees of mapping coverage, we sort the 830 PACS-detected sources into five different groups.

• A.  
  IRAC + MIPS + Herschel: 492 sources are mapped both by Herschel and by Spitzer with IRAC and MIPS. Of these, 59 also have Spitzer IRS spectra.
• B.  
  WISE + MIPS + Herschel: 51 additional sources are observed by Herschel and MIPS, are not observed by IRAC, yet are detected by WISE to replace the IRAC (3.6 and 4.5 μm) bands.
• C.  
  MIPS + Herschel: 25 sources are only covered by MIPS and Herschel, but are not detected by WISE due to their faintness or due to confusion.
• D.  
  WISE + Herschel: 167 sources are not covered by the Spitzer maps. For these, we use WISE and Herschel detections.
• E.  
  Herschel-only: 95 sources are detected in Herschel observations only (≥70 μm), are not covered by Spitzer, and are not detected by WISE.

In the remainder of the paper, we classify the sources that are in group A as they are the only ones that can be properly classified using mid-IR photometry and for which the far-IR properties can be constrained. Furthermore, in Section 6 we only perform model fits for the protostars in group A since the model parameters cannot be constrained for sources that lack mid-IR Spitzer coverage. Table 2 lists the 2MASS, Spitzer, Herschel, and JCMT photometry of all group A sources classified as protostar. The column "Object" in Table 2 denotes the eHOPS designation according to their increasing R.A.. The column "Comments" provides the respective "step" where the source is classified as a protostar along with brief reasoning behind its classification. In addition, we provide photometry of pre-MS stars with disks in Appendix F and galaxies in Appendix G. We provide photometry of sources in groups B, C, D, and E in Appendix I.

Table 2. Observed Fluxes (in Millijanskys) for the eHOPS Protostars in Aquila

	2MASS						Spitzer
							IRAC												MIPS
Object	FJ	ΔFJ	FH	ΔFH	FK	ΔFK	F3.6	ΔF3.6	${F}_{3.6}^{C}$	F4.5	ΔF4.5	${F}_{4.5}^{C}$	F5.8	ΔF5.8	${F}_{5.8}^{C}$	F8.0	ΔF8.0	${F}_{8.0}^{C}$	F24	ΔF24	${F}_{24}^{C}$
eHOPS-aql-1	⋯	⋯	⋯	⋯	⋯	⋯	6.4	0.1	2.2	16.3	0.2	5.2	23.7	0.3	3.8	30.3	0.4	10.9	411.6	0.7	519.4
eHOPS-aql-2	⋯	⋯	5.8	0.2	35.3	0.9	90.8	1.2	2.9	146.2	1.9	3.0	171.9	2.3	13.3	175.4	2.3	32.1	571.2	5.3	1023.4
eHOPS-aql-3	46.3	1.0	62.7	1.3	181.9	3.9	⋯	⋯	⋯	⋯	⋯	13.9	⋯	⋯	⋯	⋯	⋯	2901.5	⋯	⋯	⋯
eHOPS-aql-4	58.7	1.2	126.6	2.7	161.4	3.1	179.1	2.4	10.9	210.6	2.8	9.0	240.1	3.1	6.0	350.1	4.6	71.4	⋯	⋯	248.6
eHOPS-aql-5	0.7	⋯	6.5	0.2	18.5	0.4	44.0	0.6	2.3	65.1	0.9	3.0	82.0	1.1	2.2	100.6	1.5	9.4	413.9	5.1	745.1

WISE								Herschel
F3.4	ΔF3.4	F4.6	ΔF4.6	F12	ΔF12	F22	ΔF22	F70	ΔF70	${F}_{70}^{S}$	F100	ΔF100	${F}_{100}^{S}$	F160	ΔF160	${F}_{160}^{S}$	F250	ΔF250	${F}_{250}^{S}$
—	—	—	—	—	—	—	—	1725.9	96.7	44.1	—	—	—	2793.3	142.3	30.9	3788.7	155.7	U
53.6	1.2	135.2	2.5	193.0	2.8	707.3	13.7	1802.3	95.7	32.2	⋯	⋯	⋯	7713.3	387.8	46.9	6401.0	195.3	208.0
691.1	44.6	1398.9	78.6	21219.3	469.1	48082.6	132.9	10816.2	582.8	217.2	⋯	⋯	⋯	2314.8	120.1	35.1	557.5	35.4	78.7
275.4	7.1	345.3	7.0	508.1	6.6	1113.8	16.4	1571.9	87.0	36.8	1755.1	88.4	10.4	1578.0	81.1	15.0	1144.4	85.2	175.7
37.8	0.9	69.3	1.4	91.4	4.7	261.6	12.0	1614.8	87.4	33.4	1984.1	99.5	7.5	7966.7	399.1	U	16716.3	36.4	U

JCMT
SCUBA2
F350	ΔF350	${F}_{350}^{S}$	F500	ΔF500	${F}_{500}^{S}$	F850	ΔF850	${F}_{850}^{S}$	Comments
6622.5	324.8	U	5902.5	189.3	U	⋯	⋯	⋯	Step 3: [3.6]–[4.5] > 0.65, α4.5,24 > − 0.3
159.9	61.6	U	208.2	57.8	U	⋯	⋯	⋯	Step 3: [3.6]–[4.5] > 0.65, α4.5,24 > − 0.3
607.0	205.1	U	5208.0	8.8	U	110.5	7.9	−0.2	Step 3: [3.6]–[4.5] > 0.65, α4.5,24 > − 0.3
13,903.5	34.2	U	11414.2	21.9	U	202.9	11.2	U	Step 3: [3.6]–[4.5] > 0.65, α4.5,24 > − 0.3

Note. For each Spitzer wave band, the third column labeled as "F^C " denotes the completeness flux limit. For the Herschel and JCMT wave bands, "F^S " denotes 1σ background flux. The letter "U" implies that the flux is used as an upper limit when fitting with models. The column "Comments" states the step in which the protostar is identified with a brief explanation. Only five sources are included in the table. The full list of sources is available online.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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4.1.1. SED-based Diagnostics of IR Sources

The characterization and classification of the protostars is based on the spectral indices, bolometric temperatures, and to a smaller extent, bolometric luminosities. We define these quantities and devise source classification criteria similar to the HOPS survey papers (Megeath et al. 2012; Stutz et al. 2013; Furlan et al. 2016; Fischer et al. 2017). The full SED spans 1–850 μm photometry, including the IRS spectrum where available. We use the photometry with S/N > 5 in all wave bands and exclude the upper limits for our calculations. If either of the Spitzer 3.6, 4.5, or 24 μm photometry is not available for any source, then we use the corresponding WISE 3.4, 4.6, or 22 μm photometry in our calculations.

We define the spectral index using the mid-IR SED slope as it probes the IR emission from the disk and inner envelope. Similar to HOPS, we use the spectral index between Spitzer/IRAC 4.5 μm and Spitzer/MIPS 24 μm to classify YSOs. Bands centered at wavelengths shorter than 4.5 μm are not used to estimate the spectral index to minimize the effects of extinction (also see Anderson et al. 2022 for a discussion on disfavoring the use of shorter wavelengths to estimate the spectral index). Since the SED between the two bands is not well approximated by a power law, we calculate the spectral index α from the two endpoints,

$$\begin{eqnarray}&&\begin{array}{l}{\alpha }_{\mathrm{4.5,24}}=\displaystyle \frac{d\,\mathrm{log}(\lambda {F}_{\lambda })}{d\,\mathrm{log}(\lambda )}\\ \ =\,\displaystyle \frac{\mathrm{log}[24\,{{\rm{F}}}_{\lambda }(24\,\mu {\rm{m}})]-\mathrm{log}[4.5\,{{\rm{F}}}_{\lambda }(4.5\,\mu {\rm{m}})]}{\mathrm{log}(24)-\mathrm{log}(4.5)}.\end{array}\end{eqnarray} \tag{ 1 }$$

Similarly, for YSOs with IRS spectrum, we also estimate the spectral index (α_IRS) using the fluxes at 5 and 25 μm. We use α_IRS to find high-confidence protostars and pre-MS stars with disks in Section 4.1.2.

Myers & Ladd (1993) defined T_bol as the effective temperature of a blackbody with the same flux-weighted mean frequency as in the observed SED. We follow Myers & Ladd (1993) to calculate T_bol, as is used by many previous literature works (e.g., Dunham et al. 2015; Furlan et al. 2016):

$$\begin{eqnarray}&&{T}_{\mathrm{bol}}\,[{\rm{K}}]=1.25\times {10}^{-11}\displaystyle \frac{{\int }_{0}^{\infty }\nu {F}_{\nu }d\nu }{{\int }_{0}^{\infty }{F}_{\nu }d\nu }.\end{eqnarray} \tag{ 2 }$$

Similarly, the bolometric luminosity (L_bol) of a source is calculated by integrating the observed flux, adopting a distance and assuming the source radiates equally over 4 π sr:

$$\begin{eqnarray}&&{L}_{\mathrm{bol}}\,[{L}_{\odot }]=4\pi {D}^{2}{\int }_{0}^{\infty }{F}_{\nu }d\nu ,\end{eqnarray} \tag{ 3 }$$

where D is the distance to the source. We use the trapezoidal summation rule to integrate over the finitely sampled SEDs in Equations (2) and (3), similar to Dunham et al. (2015) and F16.

4.1.2. Step 1: Selection of High-confidence YSOs

High-confidence sources are those identified and classified as either a protostar, a pre-MS star with disk, or a galaxy with higher certainty using the full suite of MIPS, IRAC, IRS, and Herschel data. The goal of step 1 is to catalog only the high-confidence protostars and pre-MS stars with disks; we classify the remaining sources in subsequent steps. We use the high-confidence sources to establish criteria in Section 4.1.3 for removing the extragalactic contaminants from our sample.

Protostars: The sample of protostars targeted in the HOPS survey (Megeath et al. 2012; Furlan et al. 2016) were first identified using Spitzer photometry. HOPS protostars were characterized by a steeply rising SED between 3.6 and 4.5 μm such that the color [3.6] − [4.5] > 0.65 (e.g., Megeath et al. 2004; Kryukova et al. 2012) and a flat or rising SED between 4.5 and 24 μm such that α_4.5,24 ≥ −0.3 (also see F16). For the high-confidence protostars, we adopt these criteria and require a rising spectrum (α_4.5,24 ≥ 0.3), and exclude flat-spectrum sources.

In addition, the Spitzer IRS spectra provide a viable means of identifying deeply embedded protostars F16. Many protostars are characterized by a silicate absorption feature at ∼10 μm along with ice features in the 5–8 μm range. In protostars observed at a nearly edge-on inclination, there is instead a strong dip at about 10 μm that is between the scattered light at <10 μm and the thermal emission at >10 μm (Whitney et al. 2003b). Note that the presence of a silicate absorption feature is not a unique signature of a protostar and is present in other highly reddened sources. Absorption features accompanied by ice lines are a stronger indication of a protostar as the ice features are found in only cold dense regions, but we do not require those in our current criteria.

We thus require that the high-confidence protostars are those with a positive slope between 5 and 25 μm in the IRS spectra (α_IRS), indicative of a rising SED, and/or minima at ∼10 μm due to silicate absorption or high inclinations. By excluding flat-spectrum sources, we minimize the chances of incorporating nonembedded sources in our list of high-confidence protostars. In summary, for a source with IRAC, MIPS, IRS, and PACS data to be a high-confidence protostar, it should satisfy the following requirements:

$$\begin{eqnarray}&&\begin{array}{c}{\alpha }_{\mathrm{IRS}}\geqslant 0\,\mathrm{and}/\mathrm{or}\,\mathrm{absorption}/\mathrm{minimum}\,\mathrm{at}\,\lambda \approx 10\mu {\rm{m}}\\ \mathrm{and}\\ [3.6]-[4.5]\gt 0.65\\ \mathrm{and}\\ {\alpha }_{\mathrm{4.5,24}}\gt 0.3.\end{array}\end{eqnarray} \tag{ 4 }$$

We classify 29 high-confidence protostars using Equation (4). In Figure 4, we show three example SEDs of protostars out of 29: eHOPS-aql-18, eHOPS-aql-35, and eHOPS-aql-74. After we identify and filter the extragalactic contamination, we relax the above conditions to incorporate other protostars in Section 4.1.4.

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Pre-MS stars with disks: To distinguish the pre-MS stars with dusty disks from protostars, we require a declining SED slope between 3.6 and 4.5 μm. This requirement may not be satisfied by highly reddened pre-MS stars, which we will discuss in Section 4.1.4. Additionally, we restrict ourselves to the sources that have α_4.5,24 < −0.3, thereby excluding flat-spectrum sources. For pre-MS stars with a disk, the silicate feature at ∼10 μm is often apparent in emission. The silicate emission is produced by hot dust grains in the upper layers of protostellar disks. Similar to protostars, we combine all three requirements for selecting high-confidence pre-MS stars with disks:

$$\begin{eqnarray}&&\begin{array}{c}{\alpha }_{\mathrm{IRS}}\lt 0\,\mathrm{and}/\mathrm{or}\,\mathrm{silicate}\,\mathrm{emission}\,\mathrm{at}\,\lambda \approx 10\mu {\rm{m}}\\ \mathrm{and}\\ [3.6]-[4.5]\lt 0.65\\ \mathrm{and}\\ {\alpha }_{\mathrm{4.5,24}}\lt -0.3.\end{array}\end{eqnarray} \tag{ 5 }$$

We classify 13 high-confidence pre-MS stars with disks using Equation (5). Figure 5 shows three example SEDs of the high-confidence pre-MS stars with disks.

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4.1.3. Step 2: Identification of Galaxies

In Section 4.1.2, we identify 42 high-confidence YSOs that require IRS spectra for classification (29 protostars and 13 pre-MS stars with disks). In this section, we discuss different techniques that we use to classify galaxies in the remaining 450 sources to account for extragalactic contamination in our total sample. First, we search the literature for well-studied galaxies that may be present in our sample. Second, we search the high-resolution visible and IR databases to identify nearby galaxies that are spatially resolved such that the spiral arm or elliptical morphologies of galaxies are explicit. Third, we use IRAC colors to detect star-forming galaxies, a technique used by Stutz et al. (2013). Finally, we apply a method based on fitting the observed SEDs with extragalactic model templates. This method robustly identifies the galaxies that do not show strong polycyclic aromatic hydrocarbon (PAH) emission from star-forming regions and are not resolved in the high-resolution visible/IR images.

We search the Set of Identifications, Measurements, and Bibliography for Astronomical Data (SIMBAD) database ²¹ to find galaxies that are studied previously in the literature. We find three galaxies that were studied previously in Oliveira et al. (2010). These galaxies are noted as "Literature" in column "Comments" in Table 10. Then we search the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) images (Chambers et al. 2016) to find galaxies that are resolved at optical wavelengths. We also search the UKIRT Infrared Deep Sky Survey (UKIDSS) database (Lawrence et al. 2007) in the near-IR. UKIDSS has higher angular resolution than 2MASS and thus is helpful to morphologically distinguish galaxies that are resolved at near-IR wavelengths. We use a tolerance of 2'' to match our catalog with SIMBAD, UKIDSS, and Pan-STARRS. In Appendix E, Figure 48 shows a few examples of morphologically identified galaxies. We identify 34 such galaxies in our sample. Morphologically identified galaxies are noted as "Morphology" in column "Comments" in Table 10. Using these two techniques, we still cannot identify the galaxies that are farther away and not spatially resolved.

We follow Stutz et al. (2013) to detect star-forming galaxies based on their Spitzer/IRAC color–color plots, specifically using the [3.6] − [4.5] and [5.8] − [8.0] colors, or equivalently, α_3.6,4.5 and α_5.8,8.0. Star-forming galaxies are often characterized by PAH emission around the 5–8 μm regime. Stutz et al. (2013) found that the sources with α_5.8,8.0 ≥ 3 and α_3.6,4.5 ≤ 0.5 show characteristics of star-forming galaxies where bright PAH emission results in high values of α_5.8,8.0 but the α_3.6,4.5 range is dominated by starlight. This α_5.8,8.0 criterion is higher than the criterion used by Gutermuth et al. (2008b), but that only ensures that we have star-forming galaxies with high confidence when we apply the criterion of Stutz et al. (2013). In addition, we cross-check the SEDs of all of the sources that satisfy the Stutz et al. (2013) criteria to further confirm they show PAH emission at ∼8 μm. In Table 10, the IRAC-color criterion is mentioned in the column "Comments" for the galaxies identified using IRAC colors.

Figure 6 shows SEDs for three of the star-forming galaxies with prominent PAH emission at ∼8 μm that are selected using the criterion from Stutz et al. (2013). We refine our selection using the conditions in Section 4.1.5 after selecting other galaxies in the sample. We find 41 star-forming galaxies in our sample using the IRAC-color criterion from Stutz et al. (2013). Some galaxies are found using more than one criterion, for example, from both the literature and IRAC colors. Altogether, we detect 63 high-confidence galaxies following the above-described processes.

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Extragalactic SED template fitting: The majority of the galaxies identified so far are either star-forming galaxies with PAH emission at 8 μm or the galaxies that are spatially resolved in the high-resolution near-IR images. However, other extragalactic contaminants such as active galactic nucleus (AGN)-dominated galaxies do not show PAH emission and can be missed in the previous steps. We devise a novel approach to reduce contamination by galaxies in the low-luminosity sources using the model SED templates for external galaxies of Kirkpatrick et al. (2015). Templates encompass different star formation properties, from actively star-forming to AGN-dominated to composite galaxies that are between actively star-forming and quenched galaxies. We use these extragalactic model templates to fit all 492 sources of group A to identify other galaxies in our sample. In this way, we can identify actively star-forming, non-star-forming (AGN-dominated), and composite galaxies. We use the goodness-of-fit measure for SEDs called R to measure how close the observed sources are to extragalactic templates. Sources with low R values have SEDs similar to galaxies. See Appendix D for the details of the fits.

Identification of galaxies based on R alone is not effective. There may be protostars that appear similar to galaxies particularly when they are detected in only a few photometric bands. In these cases, sources can have lower R values since they have fewer photometric bands in their SEDs. Luminosity is another way to distinguish between galaxies and protostars; most galaxies are faint across all wavelengths and have low luminosities for an assumed distance of 436 pc. A low-luminosity source with low R may not necessarily be a galaxy, however, but a low-luminosity protostar such as a VeLLO (Dunham et al. 2015). This motivates using the H₂ column density (N(H₂)) around the source as an additional criterion; low-luminosity sources in regions of low gas column density are likely to be galaxies. Hence, we combine three conditions to identify galaxies in our catalog:

$$\begin{eqnarray}&&\begin{array}{c}{L}_{\mathrm{bol}}\lt {L}_{\mathrm{bol}}^{\mathrm{crit}}\\ \mathrm{and}\\ N{({{\rm{H}}}_{2})\lt N({{\rm{H}}}_{2})}^{\mathrm{crit}}\\ \mathrm{and}\\ R\lt {R}^{\mathrm{crit}}.\end{array}\end{eqnarray} \tag{ 6 }$$

The projected column density for each source is the Herschel-derived column density, N(H₂), measured at the position of the source and smoothed to the beam size of the 500 μm SPIRE map (Figure 1), and L_bol assumes a distance of 436 pc. ${L}_{\mathrm{bol}}^{\mathrm{crit}}$, N(H₂)^crit, and R^crit are estimated by studying the variation of L_bol, N(H₂), and R for all 492 sources. Figure 7 shows the variations of L_bol, N(H₂), and R for the sources in the Aquila star-forming clouds. The horizontal and vertical dashed lines mark the critical values below which we find probable galaxies, defined as the 75th percentiles of L_bol, N(H₂), and R for the sample of previously identified galaxies. For Aquila, we find ${L}_{\mathrm{bol}}^{\mathrm{crit}}$, N(H₂)^crit, and R^crit to be 0.15 L_⊙, 5 × 10²¹ cm⁻², and 9, respectively. We choose conservative critical values for L_bol, N(H₂), and R to ensure that we do not falsely identify low-luminosity protostars as galaxies.

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Using these criteria in Equation (6), in the Aquila regions, we find 31 additional galaxies. The galaxies that are identified by fitting observed SEDs with extragalactic templates are designated "Step 2" in the "Comments" column in Table 10. We inspect the SEDs of each of these galaxies to make sure there are no obvious YSOs. Furthermore, we crossmatch our galaxy catalogs with the Gaia Early Data Release 3 (EDR3) catalog ²² to ensure that there is no source in our galaxy catalog that has a reliable Gaia distance corresponding to the distance of Aquila. We do not find any galaxies with a Gaia distance <1 kpc and distance/Δ(distance) >3, confirming that no YSO with a known Gaia distance is misclassified as a galaxy.

Figure 8 shows three examples of SEDs of galaxies that are identified by the fitting process with the best fit of the extragalactic SED template. Our fitting technique successfully identifies external galaxies, whether they are star-forming, AGN-dominated, or composites. Furthermore, we find our criteria based on a combination of L_bol, N(H₂), and R are particularly helpful in identifying galaxies that otherwise would be missed if we use only Spitzer/IRAC colors. It should be noted that although our criteria successfully identify galaxies with apparently low L_bol located in less-dense clouds, we may still miss galaxies that do not obey the criteria. For example, a galaxy with L_bol = 0.2 L_⊙ but N(H₂) < N(H₂)^crit and R < R^crit may escape our selection criteria. In subsequent steps, we deploy additional techniques to identify them.

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4.1.4. Step 3: Identification of Remaining YSOs

After identifying the sources that are extragalactic in nature, we use Spitzer photometry to classify the remaining 356 sources of group A into four categories of YSOs: protostars, pre-MS stars with disks, reddened disks, and candidate protostars (CP). To select protostars, we follow previous work by Megeath et al. (2004, 2012), Gutermuth et al. (2008b, 2009), Kryukova et al. (2012), and Dunham et al. (2015) to set the necessary conditions based on mid-IR photometry. We identify protostars using the following criteria:

$$\begin{eqnarray}&&\begin{array}{l}[3.6]-[4.5]\gt 0.65\\ \mathrm{and}\\ {\alpha }_{\mathrm{4.5,24}}\gt -0.3.\end{array}\end{eqnarray} \tag{ 7 }$$

Similarly, we use the following criteria to identify pre-MS stars with disks:

$$\begin{eqnarray}&&\begin{array}{c}[3.6]-[4.5]\lt 0.65\\ \mathrm{and}\\ {\alpha }_{\mathrm{4.5,24}}\lt 0.3.\end{array}\end{eqnarray} \tag{ 8 }$$

Note the overlapping region of −0.3 < α_4.5,24 < 0.3 between Equations (7) and (8). This narrow range of the spectral index is indicative of flat-spectrum sources that fall on the borderline between protostars and pre-MS stars with disks. Flat-spectrum sources can be a mixture of protostars observed at more face-on inclination angles, protostars with thin envelopes, and a few highly reddened pre-MS stars with disks (Calvet et al. 1994; Furlan et al. 2016; Habel et al. 2021; Federman et al. 2023. Heiderman & Evans (2015) reported that only about half of the flat-spectrum sources are true protostars using envelope tracers in a large sample of Class 0/I and flat-spectrum sources. Other studies such as Großschedl et al. (2019) reported that a substantial fraction of the flat-spectrum sources are at a younger evolutionary phase compared to Class II YSOs. F16 argued that most flat-spectrum sources in Orion have far-IR emissions from thin, dusty envelopes. To minimize any ambiguity posed by the true stage of flat-spectrum sources, we additionally require [3.6] – [4.5] > 0.65 for flat-spectrum sources in our protostellar catalog in addition to α_4.5,24 > −0.3 (see also Kryukova et al. 2012; Megeath et al. 2012). Hence, using Equations (7) and (8), a flat-spectrum source is either classified as a protostar or a pre-MS star with disk, but not both, by imposing the [3.6] − [4.5] color criteria.

We find 104 protostars and 56 pre-MS stars with disks, in addition to the high-confidence sources, using the criteria in Equations (7) and (8), respectively. Figure 9 shows SEDs of three protostars out of 104. Similarly, Figure 10 shows SEDs of three pre-MS stars with disks out of 56 sources. Out of 56 pre-MS stars with disks, five sources (Source# 72009, 561496, 602852, 1525323, and 2062387 in Table 10 in Appendix G) have either no detection in one or more IRAC channels but detect elevated emission in the 8 μm channel based on the completeness limits in the channels with nondetections, or show resolved emission in the IRAC channels. These five sources are reclassified as galaxies. The reason for their reclassification is mentioned in the column "Comments" in Table 10.

So far we detect 133 protostars, 64 pre-MS stars with disks, and 99 galaxies out of the total of 492 sources. A total of 196 sources are yet to be classified. Another category of sources is the pre-MS stars with disks that reside in high-extinction regions such that [3.6] – [4.5] ≮ 0.65. Our classification technique for pre-MS stars with disks in Equation (8) is biased toward the pre-MS stars that are located in the lower column density regions. In high column density regions, the near-IR emission from YSOs suffers from extinction and an increased [3.6] − [4.5] color. For the reddened pre-MS stars with disks, extinction may have a minimal effect on α_4.5,24 but [3.6] − [4.5] can be greater than our critical value of 0.65. We identify such reddened pre-MS stars with disks in the remaining 196 sources using the following criteria:

$$\begin{eqnarray}&&\begin{array}{c}[3.6]-[4.5]\gt 0.65\\ \mathrm{and}\\ {\alpha }_{\mathrm{4.5,24}}\lt -0.3.\end{array}\end{eqnarray} \tag{ 9 }$$

We identify 32 reddened pre-MS stars with disks using Equation (9). Out of 32 reddened pre-MS stars with disks, one (Source #1371293 in Table 10 in Appendix G) has a peak at IRAC 8 μm but does not have photometry at 5.8 μm due to its extended morphology in the 5.8 μm map. Hence the source is not classified as a galaxy by our IRAC-color based criteria. The source is also missed by our extragalactic contamination criteria (Equation (6)) because it is located at N(H₂) ∼7.8 × 10²¹ cm⁻², slightly greater than N(H₂)^crit. We reclassify it as a galaxy.

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Out of the remaining 31 reddened pre-MS stars with disks, four sources (eHOPS-aql-44, eHOPS-aql-72, eHOPS-aql-77, and eHOPS-aql-81) are reclassified as protostars. These sources have −0.5 < α_4.5,24 < −0.3 and were not previously classified as protostars as we require α_4.5,24 > −0.3 for a protostar. The source eHOPS-aql-81 has α_4.5,24 = −0.32 but has an elevated far-IR emission. The sources eHOPS-aql-44 and eHOPS-aql-72 have weak silicate absorption at ∼10 μm. Another source, eHOPS-aql-77, shows scattered light emission in the near-to-mid-IR maps. Although our strict set of classification criteria classifies these four sources as reddened pre-MS stars with disks, the above-mentioned features show their protostellar nature. Figure 11 shows three examples of SEDs of reddened pre-MS stars with disks that we identify using Equation (9).

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A similar problem arises for classifying protostars. We require both [3.6] − [4.5] > 0.65 and α_4.5,24 > −0.3 to classify protostars. However, some protostars may have [3.6] − [4.5] slightly less than 0.65 but the SED rises beyond 24 μm. The criteria based on Equation (7) will exclude them from being a protostar. Additionally, a declining [3.6] − [4.5] color and a rising α_4.5,24 value can also be the signature of a few of the outlier galaxies that are missed by our selection criteria. For now, we define all such sources as "candidate protostars." We find candidate protostars (hereafter, CP) in the remaining 168 unidentified sources using the following criteria:

$$\begin{eqnarray}&&\begin{array}{c}[3.6]-[4.5]\lt 0.65\\ \mathrm{and}\\ {\alpha }_{\mathrm{4.5,24}}\gt 0.3.\end{array}\end{eqnarray} \tag{ 10 }$$

We define CP as the sources that satisfy criteria for both the pre-MS stars with disks and for the protostars, thereby preventing a robust classification. We initially find 20 CP based on criteria in Equation (10). Further investigation of the mid-IR maps and SEDs show that four out of 20 are galaxies (sources #149381, #1154877, #1251530, and #1492533 in Table 10 in Appendix G). These four galaxies show a peak at ∼8 μm but are missed by our IRAC-color based criteria because of the incomplete IRAC detections. Another four sources are classified as protostars (eHOPS-aql-76, eHOPS-aql-109, eHOPS-aql-141, and eHOPS-aql-49) due to their rising SED in the far-IR wavelengths, scattered emission in the mid-IR maps, and/or the flux ratio plots described in Section 4.1.5.

Figure 12 shows three example SEDs of CP. The SED in the first panel is of one of the four galaxies identified from its extended emission in the near-IR maps. The remaining two are protostars, eHOPS-aql-76, and eHOPS-aql-141, respectively. At the end of this step, we have identified a total of 141 protostars, 104 galaxies, 64 pre-MS stars with disks, 27 reddened pre-MS stars with disks, and 12 CPs. There are still 144 unidentified sources that we will categorize in Section 4.1.5.

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4.1.5. Step 4: Refinement Based on Color–Color/Color–Magnitude Plots

In this step, we first assess and refine the classification of our sources using color–color and color–magnitude diagrams. In Figure 13(a), we plot α_5.8,8.0 versus α_3.6,4.5 with the classification from Steps 1–3. We see a cluster of star-forming galaxies in the upper-left corner of the plot in the α_5.8,8.0 ≥ 2 and α_3.6,4.5 ≤ 0.5 region. Similarly, in their study of Orion protostars, Stutz et al. (2013) previously reported the cluster of star-forming galaxies in the α_5.8,8.0 ≥ 3 and α_3.6,4.5 ≤ 0.5 region. The sources in the α_5.8,8.0 ≤ 2 and α_3.6,4.5 ≤ 0.5 region are mostly pre-MS stars with disks. We find most protostars in the α_3.6,4.5 > 0.5 region. We scrutinize the interlopers in the vicinity of these clusters and investigate their SEDs to find if they have been misclassified. We find that three unidentified sources (eHOPS-aql-70, eHOPS-aql-150, and eHOPS-aql-54) have no MIPS photometry at 24 μm, either due to saturation or confusion with a nearby brighter source. These sources, however, have an increasing mid-IR SED slope with the peaks of their emission in the far-IR wavelengths. Since our classification criteria require a detection at 24 μm, these three sources are not yet classified as protostars. With the help of IRAC color criteria in Figure 13(a), we classify them as protostars. Another source, eHOPS-aql-46, has α_4.5,24 < −0.3 so is not identified as a protostar but instead a reddened pre-MS star with disk. However, eHOPS-aql-46 has α_3.6,4.5 > 0.5, shows scattered light nebulae in the mid-IR maps, and has an increasing SED slope in the far-IR wavelengths suggesting its protostellar nature. We reclassify eHOPS-aql-46 as a protostar. On the other hand, three unidentified sources at α_3.6,4.5 < 0.5 region have declining mid-IR SED slopes, but due to missing 24 μm photometry, were not identified before as pre-MS stars with disks. We reclassify them as pre-MS stars with disks (source #135046, #1230147, and #1230429 in Table 9 in Appendix F).

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Figure 13(b) shows the color–color diagram of α_3.6,100 versus α_3.6,4.5. The plot is similar to Figure 3 in Stutz et al. (2013), but instead of 160 μm, we use 100 μm due to its higher angular resolution and lower contamination from extended emission. Three clusters of sources, corresponding to galaxies, protostars, and pre-MS stars with disks are again apparent. Again, we assess the individual SEDs and reclassify the sources that have been misclassified or unidentified. We identify two additional pre-MS stars with disks in this diagram (sources #1230147 and #135046 in Table 9).

In the next step, we search for the reddest protostars. The most recently formed protostars are deeply buried in a dense envelope and can be undetected in some, or even all, of the Spitzer bands at ≤24 μm. In many cases, they are detected only as extended emissions from scattered light nebulae or outflow jets instead of point sources in the 3.6 and 4.5 μm IRAC bands, and consequently, do not have measured magnitudes in the Spitzer source catalogs (Stutz et al. 2013). In some cases, they are not detected in the IRAC bands or even at 24 μm (Stutz et al. 2013). Using Herschel data, Stutz et al. (2013) identified extremely red protostars that were not previously identified in the Spitzer data. Many of these are bright in the Herschel PACS wave bands and were classified as PBRSs by Stutz et al. (2013); the PBRSs include the youngest protostars known in Orion (Karnath et al. 2020; see Section 7.1). Since the selection criteria in steps 1–3 rely on the Spitzer mid-IR photometry, we need additional criteria for identifying these deeply embedded protostars, as well as any other protostars that have been missed by Spitzer.

We adopt the following components of the technique described in Stutz et al. (2013) to identify the protostars with the Herschel data. First, they included sources that were not detected at the shorter Spitzer wavelengths such as 3.6 or 4.5 μm. We start by requiring a nondetection in at least one of these two bands; sources with detections in these bands would have already been identified in Steps 1 and 3. Second, they eliminated sources with Spitzer IRAC detections that had colors similar to galaxies. We do this in Step 2 and the first part of Step 4. Third, they eliminated the requirement of Megeath et al. (2012) that the Spitzer 24 μm for protostars be brighter than 7 magnitudes; this requirement was adopted to reduce extragalactic contamination (Kryukova et al. 2012). We never adopted a limiting magnitude at 24 μm and have identified galaxies through other means. Finally, they required that the SED slope should be increasing between Spitzer 24 μm and PACS 70 μm. Since the eHOPS sample has more sensitive 100 μm photometry, we require a rising slope between Spitzer 24 μm and PACS 70 μm or Spitzer 24 μm and PACS 100 μm. We also use the PACS 100 μm flux limit below which we detect galaxies, ${{\rm{F}}}_{100}^{\mathrm{gal}}$. We adopt ${{\rm{F}}}_{100}^{\mathrm{gal}}$ as the 95th percentile of the 100 μm flux for the 104 identified galaxies to assure that our estimate of ${{\rm{F}}}_{100}^{\mathrm{gal}}$ is not biased by outliers. Thus, for a Spitzer unidentified source to be identified as a protostar, the source should have

$$\begin{eqnarray}&&\begin{array}{c}\mathrm{No}\,\mathrm{detection}\,\mathrm{at}\,3.6\,\mathrm{and}/\mathrm{or}\,4.5\,\mu {\rm{m}}\\ \mathrm{and}\\ {F}_{100}\gt \,{F}_{100}^{\mathrm{gal}}\\ \mathrm{and}\\ \nu {F}_{\nu }(70)/\nu {F}_{\nu }(24)\gt 1\,\mathrm{or}\,\nu {F}_{\nu }(100)/\nu {F}_{\nu }(24)\gt 1.\end{array}\end{eqnarray} \tag{ 11 }$$

For Aquila, we find ${{\rm{F}}}_{100}^{\mathrm{gal}}$ = 0.6 Jy. We detect eight protostars using Equation (11)–eHOPS-aql-9, eHOPS-aql-38, eHOPS-aql-75, eHOPS-aql-108, eHOPS-aql-110, eHOPS-aql-117, eHOPS-aql-149, and eHOPS-aql-152. We defer the inclusion of sources without detections at 24 μm to Step 5.

Figure 14(a) shows the "color–magnitude" plot of ν F_ν (70) with ν F_ν (70)/ν F_ν (24). The different categories of sources are colored differently as shown in the legend. The eight newly detected protostars using Equation (11) are shown by maroon diamonds. These eight sources have incomplete Spitzer/IRAC photometry due to their deeply embedded nature but the SEDs peak in the Herschel/PACS far-IR wavelengths. Additionally, we use the ν F_ν (70) versus ν F_ν (70)/ν F_ν (24) ratio plot to detect pre-MS stars with disks that have steeply declining mid-to-far-IR slopes but were not previously detected due to sparse IRAC photometry. We find four pre-MS stars with disks in the ν F_ν (70)/ν F_ν (24) < 0.1 region (source #267898, #290129, #409790, and #1303802 in Table 9 of Appendix F).

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The eight new protostars using Equation (11) are also shown in Figure 14(b). An advantage of the ν F_ν (100) versus ν F_ν (100)/ν F_ν (24) plot is its ability to segregate faint galaxies due to the higher sensitivity at PACS 100 μm in our data. In Figure 14(b), a cluster of galaxies is apparent at a region enclosed by ν F_ν (100)/ν F_ν (24) ≳ 3 and ν F_ν (100) ≲ 2 × 10⁻¹¹ erg s⁻¹ cm⁻². We find 13 additional galaxies (source #696942, #739146, #918673, #980308, #981917, #1116822, #1117119, #1155813, #1291988, #1419621, #1450123, #1524950, #2059229, and #2063039 in Table 10 in Appendix G).

At the end of "Step 4," we identify a total of 153 protostars, 118 galaxies, 71 pre-MS stars with disks, 26 reddened pre-MS stars with disks, and 12 CPs. There are still 115 sources that need to be classified.

4.1.6. Step 5: Classification of Sources with Incomplete Photometry

The classification criteria defined so far are based on the mid-IR Spitzer and Herschel/PACS photometry with S/N > 5. There are, however, sources that may have a lower S/N in one of the wave bands of Spitzer or Herschel/PACS or may be missing a detection in one of the 3.6, 4.5, or 24 μm bands, for example, due to either lower sensitivity (for a faint source) or saturation (for a bright source). Our criteria will fail to catch such sources, and we may miss some protostars, except in the case of the most deeply embedded protostars with bright PACS emission (Section 4.1.5).

If a source is not detected at a wavelength required for classification, we use the corresponding completeness limit at that wavelength. As an example, if a source is not detected at 4.5 μm then α_4.5,24 cannot be calculated, missing out on a crucial component for the source classification. In that case, we use the completeness limit as upper limit of the 4.5 μm maps at the source position to compute α_4.5,24. Hence, in the case of pre-MS stars with disks,

$$\begin{eqnarray}&&\begin{array}{c}\{[3.6]-[4.5]\}{}^{\mathrm{lim}}\lt 0.65\\ \mathrm{and}\\ {\alpha }_{4.5,24}^{\mathrm{lim}}\lt 0.3.\end{array}\end{eqnarray} \tag{ 12 }$$

Note that from Equations (12) to (15), the superscript "lim" on middle brackets denotes that a completeness limit is used in any one of the two photometric points inside the middle brackets, but not on both. The calculation is meaningless if upper limits on both photometric points are used simultaneously. Furthermore, there are pre-MS stars with disks with steeply falling ${\alpha }_{4.5,24}^{\mathrm{lim}}$ and also rapidly falling IR emissions from 24–160 μm. Some of those sources are not detected in more than one wavelength among 3.6, 4.5, and 24 μm, and hence they cannot be identified using the above conditions. We define additional criteria to identify them using the completeness limits for the far-IR wavelengths. For the bright pre-MS stars with disks that are saturated in the Spitzer/IRAC wavelengths, a steeply declining SED slope has ratios of PACS to MIPS fluxes less than one, i.e. for any two out of three PACS wavelengths, $\nu {F}_{\nu }{(\mathrm{PACS})/\nu {F}_{\nu }(24)}^{\mathrm{lim}}\lt 1$. Figure 15 shows a few examples of pre-MS stars with disks that are identified using the following condition:

$$\begin{eqnarray}&&{\{\nu {F}_{\nu }(\mathrm{PACS})/\nu {F}_{\nu }(24)\}}^{\mathrm{lim}}\lt 1\,\mathrm{for}\,\mathrm{at}\,\mathrm{least}\,\mathrm{two}\,\mathrm{PACS}\,\mathrm{bands}.\end{eqnarray} \tag{ 13 }$$

Similar to the pre-MS stars with disks, we identify other CPs using the completeness limits for missing photometry. For the sources where one of the required Spitzer photometries for classifying a CP is not available, we again use the rising far-IR flux ratio as a proxy for a CP. Figure 12 shows a few examples of such CPs that are identified using the following conditions invoking completeness limits:

$$\begin{eqnarray}&&\begin{array}{c}\{[3.6]-[4.5]\}{}^{\mathrm{lim}}\lt 0.65\,\mathrm{and}\,{\alpha }_{4.5,24}^{{lim}}\gt -0.3\\ \,\,\mathrm{or}\\ \{[3.6]-[4.5]\}{}^{\mathrm{lim}}\lt 0.65\,\mathrm{and}\,{\{\nu {F}_{\nu }(\mathrm{PACS})/\nu {F}_{\nu }(24)\}}^{{lim}}\gt 1.\end{array}\end{eqnarray} \tag{ 14 }$$

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In Equation (14), the condition $\nu {F}_{\nu }{(\mathrm{PACS})/\nu {F}_{\nu }(24)}^{{lim}}\gt 1$ must hold true for at least one PACS wavelengths. CPs may be protostars, but they may also be nonprotostellar sources such as galaxies that were not removed by our filtering process.

In Section 4.1.5, we discuss the deeply embedded protostars with red SEDs in the far-IR wavelengths that do not show emission in shorter Spitzer wavelengths such as 3.6 and/or 4.5 μm. Using Equation (11), we find eight such protostars but the criteria fail to identify the sources that are not detected at 24 μm. To find such sources, we use the 24 μm flux completeness limit and require ${\{\nu {F}_{\nu }(70)/\nu {F}_{\nu }(24)\}}^{\mathrm{lim}}\gt 1$ or ${\{\nu {F}_{\nu }(100)/\nu {F}_{\nu }(24)\}}^{\mathrm{lim}}\gt 1$ in Equation (11). We identify six additional protostars using the completeness limit as the upper limit on the 24 μm photometry–eHOPS-aql-27, eHOPS-aql-29, eHOPS-aql-36, eHOPS-aql-53, eHOPS-aql-115, and eHOPS-aql-124.

For the remaining sources, we further update the selection criteria for protostars from Section 4.1.4 by including their completeness limits:

$$\begin{eqnarray}&&\begin{array}{c}\{[3.6]-[4.5]\}{}^{\mathrm{lim}}\gt 0.65\,\mathrm{and}\,{\alpha }_{4.5,24}^{{lim}}\gt -0.3\\ \,\,\mathrm{or}\\ {\{\nu {F}_{\nu }(\mathrm{PACS})/\nu {F}_{\nu }(24)\}}^{{lim}}\gt 1\,\mathrm{for}\,\mathrm{at}\,\mathrm{least}\,\mathrm{two}\,\mathrm{PACS}\,\mathrm{bands}.\end{array}\end{eqnarray} \tag{ 15 }$$

The emission in the far-IR wavelength region can be used to detect and identify very young protostars with weak or no mid-IR emission such as the PBRSs. But the selection criteria purely based on far-IR emission and completeness limits are also prone to select starless cores or other overdensities that do not harbor protostars. These are mostly the sources that show no emission at ≤100 μm. Due to the absence of an internal heating source, the bolometric temperature of these sources is similar to the surrounding dust temperature. We identify such sources by calculating the difference between T_bol (calculated using the SED) and T_dust (obtained from Herschel observations; Figure 2). For any source, if the difference is less than 5 K (typical uncertainty in T_dust) and there is no emission at ≤100 μm, we classify them as starless cores. Figure 16 shows the variation of the T_bol with the Herschel-derived T_dust at the position of all sources in our sample. The starless cores that have a difference of less than 5 K between T_bol and T_dust with no emission at ≤100 μm are shown by black empty circles.

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We find a total of 19 protostars, one galaxy, and five pre-MS stars with disks using the completeness limits in Step 5. At the end of Step 5, there are still five sources that are not yet classified using our classification methods. These sources have sparsely sampled photometry and cannot be robustly classified. From the remaining unidentified sources, we remove the ones that do not have a detection in the 24–100 μm range as they are unlikely to be protostars. The sources that do have at least one detection in the 24–100 μm region are classified as CPs and individually examined for signs of protostars, such as scattered light nebulae in the mid-IR region; however, no additional protostars are identified.

After following the steps from Sections 4.1.2–4.1.6, we find a total of 172 protostars (Table 2), 73 pre-MS stars with disks (Table 9), 24 reddened pre-MS stars with disks (Table 9), 118 galaxies (Table 10), and 12 CPs (Table 11).

In addition to extragalactic contamination, another prominent source of contamination is background stars with infrared excesses, such as asymptotic giant branch (AGB) stars. Previous studies (Cieza et al. 2010; Romero et al. 2012; Dunham et al. 2015) showed that AGB contamination is lower for the clouds that are farther away from the Galactic plane, such as Orion A (b = ∼−20°), and higher for the clouds that are closer to the Galactic plane, such as Aquila (b = 2°–6°). For example, using optical spectroscopy, Romero et al. (2012) found an AGB contamination rate of >40% in Class III sources in Lupus V and VI (b = 6°). The rate decreases to ∼20%–25% for Ophiuchus at b = ∼16°. However, such studies also show that AGB contamination is a significant issue only for more evolved YSOs. Dunham et al. (2015) found that the AGB contamination is almost negligible as the spectral index decreases until the Class II/III boundary, after which the AGB contamination rate steeply rises to >50% for Class IIIs in their sample. In the Aquila Main region, Oliveira et al. (2009) reported ∼62% of AGB contamination in Class III sources, with a sharp decrease to ∼5% for Class II. As the focus of this work is to produce a protostellar catalog and the envelope properties using protostellar models, AGB contamination is negligible in our protostellar catalog. However, AGB contamination can be significant for the pre-MS stars with disk sample that we present in Table 9, especially for the sources that have a high L_bol and low spectral index (Dunham et al. 2015).

Previous studies identifying protostars in Aquila primarily used mid-IR photometry with Spitzer, often with a combination of near-IR or X-ray data (Winston et al. 2007; Enoch et al. 2009; Gutermuth et al. 2009; Kryukova et al. 2012; Dunham et al. 2015; Sun et al. 2022). Recent Atacama Large Millimeter/submillimeter Array (ALMA) observations have also provided millimeter/submillimeter sources (for example Plunkett et al. 2018) and their properties such as protostellar disk mass (for example Anderson et al. 2022) that have enriched the protostar catalog in Aquila. In this section, we present a detailed comparison between the protostellar catalog that we identify in this study and five other widely used catalogs in the literature. The catalogs are from Winston et al. (2007), Gutermuth et al. (2009), Enoch et al. (2009), Kryukova et al. (2012), and Dunham et al. (2015). Table 3 lists whether a particular eHOPS source in Aquila is detected ("Y") or not ("N") in these catalogs. We use a matching tolerance of 2'' to compare the positions of eHOPS protostars to the catalogs in literature.

Winston et al. (2007) used Spitzer and Chandra observations to find YSOs in the Serpens Main region (see Figure 1). They used Spitzer/IRAC and Spitzer/MIPS to detect thermal emission from circumstellar disks and envelopes to classify YSOs using color–color diagrams and SEDs. They also used Chandra X-ray observations to study the effects of circumstellar disks on stellar X-ray properties and to identify young stars without disks or envelopes. Table 4 in Winston et al. (2007) lists their identified 137 YSOs, out of which 37 sources are either Class 0/I or flat-spectrum sources. We detect 17 out of 37 sources in the eHOPS catalog. Out of the remaining 20, 19 do not have PACS detection and are excluded by our selection criteria. We inspected the SEDs and postages in the 1–850 μm images and found that most of these 19 sources are reddened pre-MS stars with disks with no significant emission (S/N > 5) in the >24 μm wavelength bands. A source, S-ID 2 in Table 4 of Winston et al. (2007) is confused with the neighboring protostar but appears to be a reddened pre-MS stars with disk. The source is also present in Kryukova et al. (2012). The final remaining source that does have PACS detection is classified as a pre-MS star with disk in the eHOPS catalog.

Based on the mid-infrared imaging and photometric survey with 2MASS and Spitzer (1–24 μm), Gutermuth et al. (2009) surveyed two regions in Aquila. These regions include star-forming clusters in Serpens Main and MWC 297 (see Figure 1). In the two regions, Gutermuth et al. (2009) reported 27 protostars out of which 17 are identified in the eHOPS survey. The remaining 10 sources do not have a PACS detection and are not included by the eHOPs selection criteria. We inspected these 10 sources and found mostly reddened pre-MS stars with disks with no emission in the > 24 μm wavelengths.

Enoch et al. (2009) presented a catalog of protostars in Ophiuchus, Perseus, and Serpens region of Aquila-North by combining large-scale 1.1 mm Bolocam continuum and Spitzer Legacy surveys. They identified protostars based on their mid-IR properties at the positions predetermined by the 1.1 mm core positions. They determined the luminosities and T_bol for these protostars using low angular resolution Spitzer data for the 70 and 160 μm fluxes. Thus, there are differences in both the sample of identified protostars and the properties of those protostars. In Serpens, they identified 34 protostars. Out of 34 protostars from Enoch et al. (2009), 29 are identified as protostars in our eHOPS survey. The median luminosity for the matched 29 protostars is 4.5 L_⊙ from both Enoch et al. (2009) and from our eHOPS estimation. The median T_bol for the matched 29 sources is 110 K from Enoch et al. (2009) and 81 K from our study. Out of the remaining five sources in Enoch et al. (2009) that do not match with our catalog, four sources do not have detections in any of the PACS wave bands (Ser-emb 23, Ser-emb 24, Ser-emb 27, and Ser-emb 32 in Enoch et al. 2009), and one source is reclassified as a reddened pre-MS stars with disk (Ser-emb 4).

Another survey of protostars in the nearest kiloparsec was by Kryukova et al. (2012) using 2MASS and Spitzer in the 1–24 μm wavelengths. Kryukova et al. (2012) reported 40 protostars in the two clusters in the Serpens Main region, out of which 29 match with the eHOPS catalog. The remaining 11 sources do not have PACS detection despite being included inside the PACS coverage; therefore, they get excluded from the eHOPS catalog.

Dunham et al. (2015) provided a catalog of YSOs in 18 molecular clouds using the Spitzer "Cores to Disks (C2D)" and "Gould Belt" Legacy surveys. They computed the spectral index (α) using a linear least-squares fit to all available 2MASS and Spitzer photometry between 2 and 24 μm. In Aquila, the Dunham et al. (2015) catalog contains 200 sources that have extinction corrected α > −0.3, out of which 115 sources match our eHOPS survey catalog. Dunham et al. (2015) used d = 260 pc for Aquila and d = 429 pc for the Serpens region. We correct the distance in calculating L_bol for the 115 sources that are matched in both Dunham et al. (2015) and our eHOPS catalog. We find the median luminosity for these 115 matched sources of 0.7 L_⊙ from Table 2 of Dunham et al. (2015) and 1.8 L_⊙ from the eHOPS estimates. The median T_bol is 255 K and 119 K from Dunham et al. (2015) and our eHOPS estimates, respectively, for the matched 115 sources. Among the 85 unmatched sources between Dunham et al. (2015) catalog and our eHOPS catalog, 75 sources do not have at least one detection in our PACS survey despite being included inside the PACS coverage regions. Three sources are outside the PACS coverage region. Among the remaining seven sources, five are reclassified as reddened pre-MS stars with disks, one as a pre-MS star with disk, and one is a CP.

A detailed comparison between the eHOPS catalog and each of the Winston et al. (2007), Gutermuth et al. (2009), Enoch et al. (2009), Kryukova et al. (2012), and Dunham et al. (2015) studies is presented in Appendix J in Tables 13, 15, 14, 16, and 17, respectively. If a certain source in one of the previous catalogs is missing in the eHOPS catalog, Tables 13–17 also explain the reason behind its exclusion in the column "Comments." We find new protostars with Herschel that were not previously identified by Spitzer, which shows that the inclusion of far-IR data is essential to making a robust protostar catalog. We note that there are sources in the literature that are not identified by eHOPS because they lack detections of >24 μm emission. Possible explanations that would cause the sources to be below the PACS detection limits include having a very low luminosity (<0.05 L_☉), being a more evolved YSO such as a reddened pre-MS star with disk, source confusion in the far-IR data, or being a residual galaxy or AGN. Categorizing each such source that is not included in the eHOPS catalog is beyond the scope of this paper.

A physical model that includes all of the crucial components of a protostellar system is required to infer the fundamental physical properties of protostars from their SEDs. We use the model grid that was developed by F16 using the Whitney et al. (2003a, 2003b) radiative transfer code after incorporating the improvements by Ali et al. (2010) and Stutz et al. (2013). The Whitney et al. (2003a, 2003b) model of a protostellar system consists of a central luminosity source, flared disk, bipolar outflow cavities, and a rotating, collapsing envelope. In these models, the density distribution of the disk follows power laws in both the radial and vertical directions. The envelopes are described by TSC models (Terebey et al. 1984) where the density distribution corresponds to a rotating collapsing cloud core with a constant infall rate (also see Ulrich 1976). The outflow cavity in the envelope follows a polynomial shape. F16 used the dust opacities from Ormel et al. (2011), which include scattering cross sections that are required by the modified Henyey-Greenstein function in the Whitney et al. (2003b) models. This opacity law was chosen since it approximately reproduced the mid-IR extinction law measured in molecular clouds by McClure (2009). We adopt a gas-to-dust ratio of 100 in the models. The grid sampling and approach is carefully detailed in F16. Our models differ from the Robitaille et al. (2006, 2007) and Robitaille (2017) grids in the choices of grid sampling and the opacity law, which were optimized in our models for low-to-intermediate-luminosity protostars in nearby clouds.

The Whitney et al. (2003b) Monte Carlo radiative transfer code has many input parameters. These parameters are related to stellar properties (stellar mass, stellar temperature, and stellar radius), disk properties (for example, disk mass, disk outer radius, and disk-to-star accretion rate), and envelope properties (for example, envelope density and cavity opening angle). Other parameters of interest are intrinsic stellar luminosity, total (stellar+accretion) luminosity, and inclination angle. In the models, an inclination of 0° is a face-on view of the protostellar system. Because of the degeneracies involved and computational complexity, F16 fixed some of the parameters at a constant value and varied others that have the most impact on protostellar SEDs. For example, F16 fixed the stellar mass at 0.5 M_⊙, stellar effective temperature at 4000 K, and envelope outer radius at 10,000 au. The parameters that F16 varied are stellar radius (which determines the intrinsic stellar luminosity), disk outer radius (which sets the flattening of the envelope in TSC models), disk-to-star accretion rate for different R_star (which determines the accretion luminosity and together with the intrinsic luminosity sets the total luminosity), envelope density at 1000 au (ρ₁₀₀₀), cavity opening angle, and inclination angle. The specific values of the model parameters are included in Table 3 of F16, and the justification for the adopted initial parameter values are provided in Section 4.1 of F16.

The model grid contains 3040 main models that are parameterized for eight total (intrinsic+accretion) luminosities, 19 envelope densities (which for a given stellar mass, determines the infall rate), four disk radii, and five cavity opening angles. Each model is further calculated for 10 different inclination angles. In total, 30,400 different model SEDs fit the observed SEDs. In this section, we provide a brief discussion of the major components of the modeling. Readers should refer to F16 for a more detailed description of the modeling procedure, including the choice of parameter space, degeneracies and biases in the fits, and uncertainties in model parameters.

The model grids used by the HOPS collaboration F16 were designed specifically for the protostars in Orion. Since we are using the same model grid to fit the protostars in other molecular clouds, it is important to modify the models in places where the parameters are specific to Orion, such as distance to the cloud. In this section, we explain the general changes that we apply to the models so that they can be used to fit the protostellar SEDs in Aquila.

The distance affects the observed fluxes calculated from the models, which in turn affects the scaling factors of the model SEDs used to determine the luminosities of the protostars. It also affects the physical sizes of the apertures. The models were produced for 24 different apertures, from 1''–24''. At the distance of the Orion clouds, 420 pc, the apertures correspond to 420–10,080 au in steps of 420 au. The use of discrete aperture sizes in models also means that there may not be an accurate model flux that corresponds exactly to the aperture of the observed flux. For example, at the distance of Aquila, the IRAC detector has an FWHM beam of 1046 au, while the model fluxes close to 1046 au are available for apertures of 840 and 1260 au. In such cases, we do a linear interpolation of the fluxes at 840 and 1260 au to approximate the model flux at 1046 au. The interpolation ensures a more accurate comparison of the observed and modeled fluxes. For IRS fluxes, we interpolate to a 53 aperture. Since most of the sources appear as point sources in the Spitzer and PACS 70 and 100 μm data, the aperture size typically does not have a significant effect on the flux.

We have SPIRE and SCUBA-2 data points in our observed SEDs that were not included in the model grids in F16. Similarly, HOPS SEDs contained APEX/SABOCA and APEX/LABOCA observations that are not included in our eHOPS SEDs. We compute the model fluxes for SPIRE and SCUBA-2 wave bands using their respective spectral response functions. For the sources in Aquila, SPIRE 350 and 500 μm observations correspond to ∼10,500 and ∼15,700 au, respectively. Both values are greater than the maximum aperture size in the model. The models assume a 10,000 au outer envelope radius, so there is no emission from the protostar at larger radii. However, the observation will capture the actual emission at radii larger than 10,000 au, which can be from a larger envelope than the model assumes or extended emission from dense gas structures in the Aquila cloud. For consistency between model and observed SEDs, we use the observed photometry at SPIRE 350 and 500 μm wavelengths as upper limits and treat them as such when fitting the observed SEDs with models. Furthermore, for sources with L_bol < 0.1 L_☉, the emission at the far-IR wavelengths is susceptible to contamination from outer envelopes. For such cases, we use the observed photometry for ≥160 μm as upper limits.

We use a customized fitting routine initially developed by Ali et al. (2010) and F16 to fit the observed SEDs of protostars in Orion. Here we summarize the important aspects of the fitting technique and ask the readers to consult Section 5 of F16 for more details. We use photometry for the entire SED: 2MASS, IRAC, MIPS, PACS, SPIRE, SCUBA-2, and the spectrum from Spitzer/IRS (where available) to fit with the model SEDs. For many sources, photometry covering the entire near-IR to submillimeter SED is available, but for some sources, there are upper limits in the SPIRE and SCUBA-2 fluxes. Of our 172 modeled protostars in Aquila, 35 have IRS observations. We do not include any additional data from the literature to maintain uniformity in the data used in the fits.

For the sources with IRS data, the spectrum tends to dominate the fit because of the many data points in the spectrum. This causes the fit to be highly biased toward the mid-IR region when IRS data are present. Furthermore, there are ice absorption features in the IRS spectrum in the 5–8 μm region and at ∼15.2 μm that are not included in the model opacities. To mitigate these issues, we follow the approach of F16 and rebin the IRS spectrum in 16 wavelengths that avoid the ice absorption region but trace silicate absorption features at ∼10 and 20 μm. A source with a finely sampled SED can have up to 15 photometric data points from 1–850 μm and 16 spectroscopic data points from the IRS. In such cases, the mid-IR remains the most finely sampled region of the SEDs, and the IRS spectra strongly influence the resulting fit. This is particularly valuable in determining the extinction toward each protostar.

We use spectral response functions for each detector and wavelength to calculate model fluxes for the same aperture sizes as in the observations, ensuring a direct comparison between observed and model fluxes. The use of models to predict Herschel fluxes is described by Ali et al. (2010). For the model data corresponding to the IRS spectrum, the model fluxes are linearly interpolated to the same 16 wavelengths as in the observed IRS data.

The fitting is done in two steps. First, we determine a scale factor and extinction. Our model grid contains only eight values for model luminosities and does not initially account for extinction. To account for variations in luminosity and extinction, we scale the models by a scale factor, s, that usually ranges between 0.5 and 2, and apply our adopted extinction law. The modeled and observed SEDs are then related as

$$\begin{eqnarray}&&{F}_{\mathrm{obs},\lambda }={{sF}}_{\mathrm{mod},\lambda }{10}^{-0.4{A}_{\lambda }},\end{eqnarray} \tag{ 16 }$$

where A_λ is foreground extinction to the protostar at wavelength λ. We use the Herschel-derived column density maps, smoothed to the beam size of the SPIRE 500 μm maps, to calculate the projected column density at the position of a protostar. We convert the column density to a total extinction through the cloud using the conversion factor of 1 A_V = 10²¹ cm⁻² (Winston et al. 2010; Pillitteri et al. 2013). Setting this Herschel-derived extinction as an upper limit, a least-squares fit simultaneously determines s and A_λ using Equation (16). See F16 for the details.

Second, after a best-fit scale factor and the extinction are applied to each model, we assess which model best reproduces the observed SED. The proximity of the model SED to the observed SED is measured using a goodness-of-fit parameter, R, similar to the method used for fitting the galaxy SEDs calculated using Equation (D4) (F16; Fischer et al. 2014). The justification for using R as the goodness-of-fit and the inverse of the approximate fractional uncertainty as weights for the photometric data points is given in Appendix D. In short, R is approximately equal to the distance of the model from the data in units of the fractional uncertainty. As a general rule of thumb, the smaller the value of R, the better the model fit, and we identify a best-fit model for a single source as that with the minimum value of R.

In this approach, a discrepant data point does not affect the fit as strongly as it would using a least-squares fit; this is important given the potential for contamination of the photometry beyond 100 μm. Determining the values of R that are consistent with good fits and the comparison of ${R}_{\min }$ values for different sources are complex tasks, since R depends on the number of data points in the observed SED. As with other goodness-of-fit statistics, an SED with fewer data points often gives a lower value of R, whereas an SED with more data points can give a larger value of R, but the fit may still be good. We further discuss these issues in the following sections, and we further address the robustness of the fits in Appendix K.

Figure 20 shows the best fits for protostars from eHOPS-aql-1 to eHOPS-aql-15. The best-fit parameters for individual SEDs are included in Table 4. Due to the large number of protostars and possible degeneracies in the model parameters, we discuss the statistical distribution of the model parameters in this section rather than individual protostellar properties. F16 presented the statistical study of the best-fit properties in a similar manner and found that certain properties such as envelope density and total luminosity are better constrained than others. We also find degeneracies between parameters such as disk radius, cavity opening angles, and inclination (see the model uncertainties and degeneracies section in Appendix K) in our study. Thus, in this section, we only discuss the distribution of the best-constrained model parameters, but we include all of the fit parameters in Table 4 for completeness.

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Figure 21 shows the distribution of ${R}_{\min }$ values for the Herschel detected protostars in the Aquila clouds. Both the median and mean of the distribution are 2.4. This implies that, on average, the natural logarithm of the ratio between observed and modeled flux deviates by about 2.4 times the average fractional uncertainty. In general, a low ${R}_{\min }$ value implies that the modeled photometry is similar to the observed photometry. The models with fewer photometry points, however, are less restrictively constrained. Thus, as discussed in Section 6.3, a lower number of fitted data points can also yield a lower ${R}_{\min }$. We find 18 sources that have ${R}_{\min }\lt 1$, out of which 14 sources are Class 0, two sources are Class I and two sources are flat-spectrum sources. A total of 11 sources out of 18 with ${R}_{\min }\lt 1$ have only two to five data points (excluding the 350 and 500 μm data that we use as upper limits for fitting with models) and therefore yield systematically lower ${R}_{\min }$ values compared to other sources.

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Similar to F16, the discrepancy between the observed SEDs and models increases substantially when ${R}_{\min }\gt 5$. We find four protostars with ${R}_{\min }\gt 5$. Among them, eHOPS-aql-77 has a mismatch between the photometry obtained from the IRS and MIPS 24 μm, suggesting that the source may be variable at ∼24 μm. Also, eHOPS-aql-77 has a lower observed PACS 70 μm photometry compared to the modeled 70 μm data because of the bright, structured emission in the background annulus, thereby raising the estimated ${R}_{\min }$. Another source, eHOPS-aql-46 has an ${R}_{\min }$ value of ∼7 because of the lower 24 μm photometry due to the presence of a bright source in the background annulus. The source eHOPS-aql-46 has scattered dust emission in the mid-IR wave bands that affect the Spitzer/IRAC photometry leading to a mismatch with the model photometry and an increased ${R}_{\min }$ of ∼7. Another protostar, eHOPS-aql-56 has a similar discrepancy at 100 μm because of the presence of a bright source in the background, resulting in ${R}_{\min }\sim 7$. Finally, eHOPS-aql-166 has ${R}_{\min }\sim 9$ due to the discrepancy between observed and modeled photometry in the Spitzer wavelengths. The slope of the SED for eHOPS-aql-166 rises in the Spitzer/IRAC wavelengths, peaks at ∼24 μm, and falls at >24μm. The source is also located in a lower-density region, N(H₂) ∼3 × 10²¹ cm⁻². These features suggest that the source may not be a protostar but a galaxy or planetary nebula that shows a peak around 24 μm due to the [O IV] line arising from highly ionized regions (e.g., Ueta 2006). The SED classification criteria based on Spitzer photometry (Equation (7)) classifies eHOPS-aql-166 as a protostar, but the observed SED deviates substantially from the best-fit model SED leading to the largest ${R}_{\min }$ value in our sample of protostars. We currently leave this in our protostar sample; future observations are needed to determine the nature of this object.

In Figure 22, we show the distribution of ${R}_{\min }$ separately for different classes of protostars. The median ${R}_{\min }$ for the three classes are similar: 2.5, 2.4, and 2.5 for Class 0, Class I, and flat-spectrum sources, respectively. About 95% of Class 0, 98% of Class I, and all flat-spectrum sources have reasonably good fits with ${R}_{\min }\lt 5$ with a minimum of three data points in their SEDs. The slightly lower fraction of Class 0 sources with reliable ${R}_{\min }$ values could be because of more uncertain SEDs, especially in the near-IR region, noisy IRS spectra, their location in extended structures such as filaments, and variability. The higher envelope density of Class 0 protostars also places them closer to the limit of parameter space probed by the model grid.

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The fits with a smaller number of photometry points may be reliable but are not as well constrained. Examining the SEDs of the protostars and their fits, particularly for the reddest protostars without mid-IR detections, we conclude that a minimum of three data points are required in the SED for a reliable fit. Out of 172 protostars, only one source, eHOPS-aql-53, contains less than three (two) data points in its SED, so we caution that the model parameters for eHOPS-aql-53 may not be constrained. All of the other 171 protostars have a minimum of three data points in their SEDs. Furthermore, there are four sources with ${R}_{\min }\gt 5$ for which the models in the grid do not provide an adequate fit. If we consider only the best fits that have a minimum of three data points and ${R}_{\min }\lt 5$, we ascertain that 167 (97%) of the protostars have reliable and well-constrained best-fit models. We only include these 167 protostars when discussing the parameter distribution in the rest of the section.

In this section, we discuss the best-fit values for the most fundamental parameters of the models. Because of degeneracies between parameters and model pitfalls (see F16), we focus on the bulk properties of the best-fit parameters and refer the readers to Table 4 for the best-fit values for individual protostars. We concentrate on the properties that primarily determine the shape and amplitude of the SEDs: the envelope density/mass and the total protostellar luminosity. We also discuss the inclination of the envelope and foreground reddening, which have a large impact on the fits. Since previous work measuring the sizes of outflow cavities using HST imaging shows that these are not well constrained by SED fitting (Habel et al. 2021), we omit a discussion of the cavities.

6.5.1. Inclination Angle

We show the histogram of the inclination angles from the best fits in Figure 23; the bins correspond to the 10 different inclinations in the model grid. The inclinations of the grid are distributed uniformly in cos(i) so that a sample with randomly distributed inclinations would show a flat distribution, as illustrated by the gray dashed histogram. We expect protostars to be randomly inclined in the sky with an equal number of protostars in each bin. Instead, we find the distribution peaking around 55°–70°. The median i in Aquila is 63°, which is close to the median value of 60° for isotropically distributed protostars. The histogram of the inclination angle in Aquila is similar to the histogram for the HOPS protostars in Orion F16. Thus, in both clouds, the models do not recover the expected distribution of inclination. This likely indicates a bias in the models since degeneracies between inclination and other parameters can affect the determination of the fundamental parameters such as envelope density/mass and luminosity. In addition, our identification of the protostars may be biased toward those at intermediate inclinations. This may occur since sources at high inclinations may be too faint—particularly in the near to mid-IR—while sources at low inclinations may be misclassified as pre-MS stars or galaxies.

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The different SED classes also show nonuniform distributions, in this case, due to degeneracies between evolutionary class and inclination. Figure 24 shows the distribution of inclination angles for different SED classes. We use the Anderson–Darling (A-D) test to determine whether the inclination distribution for different SED classes is similar. Other nonparametric statistics commonly used in astronomy are the Kolmogorov–Smirnov test and the Cramer–von Mises test. Feigelson & Babu (2012) mentioned the A-D test as the most sensitive of the three empirical distribution functions (also suggested independently by Hou et al. 2009). The A-D test shows that the distribution of inclination angles is significantly different between Class 0 and Class I protostars, and also between Class 0 protostars and flat-spectrum sources, but not between Class I protostars and flat-spectrum sources.

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There seems to be a deficit of lower inclination angles for Class 0 sources, except for i = 18°; this is expected since protostars with face-on inclinations are likely to have higher values of T_bol. Conversely, there are relatively fewer high-inclination angle sources classified as flat-spectrum protostars; such high-inclination protostars are likely to be classified as a Class I or 0 protostar due to the concentration of mass around the midplane (e.g., Fischer et al. 2014; Habel et al. 2021). The Class 0 and Class I protostars both show a peak in the i = 18° bin. Most of these sources are deeply embedded protostars that have fewer than average data points to fit. It is likely that the inclination angle is not constrained for such sources.

6.5.2. Foreground Extinction

Figure 25(a) shows the distribution of the best-fit foreground extinction A_V for all of the protostars in Aquila. There are 13 sources that are best fit by models that do not require foreground extinction. These sources have sparse mid-IR photometry, so A_V is likely not constrained. A similar result is seen in F16 for the sources with sparse or no mid-IR data. For the remaining protostars, the distribution peaks around 10–20 mag, with a median at ∼13 mag. The distribution is slightly skewed toward the higher A_V region, which is expected due to the high column densities of the Aquila molecular cloud and since Aquila is close to the Galactic plane with high foreground extinction. In Figure 25(b), we show A_V as a function of the SED classes. Out of 13 sources with A_V = 0, seven are Class 0 sources, a majority of which have a [3.6] − [4.5] > 0.65 and declining α_4.6,24 but the emission increases sharply beyond 24 μm. This is likely due to the large contribution from scattered light at λ < 8 μm in the Class 0 protostars. We find a decreasing median A_V as a function of SED Class, with median A_V of 15.9, 11.3, and 9.9 mag for Class 0, Class I, and flat-spectrum sources, respectively. The A-D test finds a significant difference in the distribution of A_V for Class 0 and flat-spectrum sources (p < 0.01) and no significant difference in either Class I and flat, and Class 0 and Class I sources. In Section 6.5.3 we discuss whether foreground reddening is biasing protostars to earlier classes.

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Figure 26 shows the variation of the foreground extinction A_V obtained from the best fits and the projected A_V values obtained from the Herschel maps. Similar to the HOPS results in F16, the majority of sources are fit with A_V lower than the Herschel-derived A_V values used as the maximum A_V allowed by the fitter. The ratio of the best-fit A_V to the Herschel-derived A_V is <0.5 for ∼40% of the sources. This is consistent with the protostars being inside the cloud, as opposed to background objects behind the cloud. There are sources for which the best-fit foreground extinction is similar to the A_V from the Herschel maps, and also some sources for which the foreground extinction is close to zero. These sources point to a potential degeneracy between foreground extinction and the density of the envelope. We discuss this in the following section (Section 6.5.3).

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6.5.3. Envelope Reference Density

The gas and dust density distributions for the collapsing protostellar envelopes models used in our model grid are described in the original TSC model paper (Terebey et al. 1984; also see Ulrich 1976 and Cassen & Moosman 1981). In the TSC model, the initial cloud (envelope) has a solid body rotation with a radial density distribution corresponding to a singular isothermal sphere, ρ ∝ r⁻². The collapse commences near the center of the protostellar system and then propagates outward at the sound speed but the material outside the collapsing region maintains hydrostatic equilibrium. In the collapsing region, the infall velocity approaches freefall, and the density distribution takes the form ρ ∝ r^−3/2, which is the solution for a steady infall rate. In our grid of models, we assume that the entire envelope has this collapse profile, except when rotation and outflows cause deviations from spherical symmetry. In the TSC model, the material falling from the envelope accumulates in a disk that extends to the centrifugal radius (R_C). In our grid, R_C is a measure of the angular momentum of the envelope, assuming an initial solid body rotation. It influences the SED by controlling the flattening of the inner envelope due to rotation. Although the disk can extend to larger radii, the model SEDs are relatively insensitive to the actual outer radius of the disk.

To characterize the density at radii that are relatively unaffected by rotation, F16 parameterized the envelope structure by the density at 1000 au. The SED is strongly dependent on the envelope density, which is the fundamental physical parameter describing the envelope. For a given collapse model and central protostar mass, the envelope density gives the rate of mass infall. For a 0.5 M_⊙ protostar with steady, spherically symmetric infall, the infall rate is given by

$$\begin{eqnarray}&&{\dot{{M}}}_{\mathrm{env}}=\left(\displaystyle \frac{{\rho }_{1000}}{2.4\times {10}^{-18}\,{\rm{g}}\,{\mathrm{cm}}^{-3}}\right)\times {10}^{-5}\,{{M}}_{\odot }\,{\mathrm{yr}}^{-1}.\end{eqnarray} \tag{ 17 }$$

The values for ρ₁₀₀₀ that are listed in Table 3 in F16 correspond to ${\dot{M}}_{\mathrm{env}}$ from 5.0 × 10⁻⁸ to 7.5 × 10⁻⁵ M_⊙ yr⁻¹ for a protostar with 0.5 M_⊙. The reduction of the infalling mass due to removal by outflow cavities is not incorporated in these estimates of the infall rate. We also include one model with ρ₁₀₀₀ = 0 g cm⁻³ (i.e., no envelope), which describes pre-MS stars that have dispersed their envelopes but have protostellar SEDs due to extinction.

The distribution of the best-fit ρ₁₀₀₀ values for all 172 protostars in Aquila are shown in Figure 27(a). One Class I protostar, eHOPS-aql-161, has the best fit with a model with no envelope (ρ₁₀₀₀ = 0). For the remaining protostars, the median of the distribution is 1.8 × 10⁻¹⁸ g cm⁻³ with first and third quartiles at 2.4 × 10⁻¹⁹ and 5.9 × 10⁻¹⁸ g cm⁻³. Between the first and the third quartiles, the sources are fairly uniformly distributed.

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Figure 27(b) shows the distribution of the reference envelope density ρ₁₀₀₀ for different SED classes. The median ρ₁₀₀₀ for Class 0 sources is 5.9 × 10⁻¹⁸ g cm⁻³, which then decreases to 5.9 × 10⁻¹⁹ g cm⁻³ for both the Class I sources and the flat-spectrum sources. The mean ρ₁₀₀₀ for Class 0, Class I, and flat-spectrum protostars are 2 × 10⁻¹⁷, 5.7 × 10⁻¹⁸, and 2 × 10⁻¹⁸, respectively. The mean ρ₁₀₀₀ thus decreases as a function of SED Class in the eHOPS-Aquila protostars. The median ρ₁₀₀₀ decrease from Class 0 to Class I by an order of magnitude; however, no such decrease in median ρ₁₀₀₀ is noticed between Class I and flat-spectrum sources. Using the A-D test, we find that the Class 0 sample is significantly different from the Class I and flat-spectrum protostars (p-value <0.01). The A-D test, however, shows that we cannot reject the null hypothesis that the Class I and flat-spectrum protostars are drawn from the same population.

Since foreground extinction and envelope density can affect an SED in a similar way, we search for degeneracies between the best-fit envelope reference density ρ₁₀₀₀ and foreground extinction A_V . This will resolve the question posed in Section 6.5.2, does foreground extinction bias the classification of protostars and the determination of their envelope densities? If a degeneracy is present, we would expect a trade-off with foreground extinction increasing as envelope density decreases. Instead, in Figure 28 we find that sources with higher A_V often have higher ρ₁₀₀₀, particularly for the Class 0 and Class I protostars. There are four Class 0 sources that have ρ₁₀₀₀ > 10⁻¹⁶ g cm⁻³ and A_V > 50, and no sources in either the Class I or flat-spectrum group in this region. Out of four Class 0 sources with high ρ₁₀₀₀ and A_V , three sources (eHOPS-aql-78, eHOPS-aql-93, and eHOPS-aql-110) do not have measured emission shortward of 24 μm and thus are likely PBRSs. For Class I protostars, the sources are mostly confined at A_V < 50, with fewer sources in the high ρ₁₀₀₀ regime compared to Class 0 protostars. Finally, the flat-spectrum sources are more confined in the lower ρ₁₀₀₀ and lower A_V region compared to the other two classes. This is consistent with the decreasing median values for both ρ₁₀₀₀ and A_V with evolutionary class in Figures 27(b) and 25(b), respectively. In summary, we find no evidence for degeneracies between extinction and envelope density. On the contrary, the Class 0 protostars are not only embedded in higher-density envelopes, but also appear to be concentrated in regions of higher cloud column density, and thus higher extinction. A similar trend is seen in parts of Orion (e.g., F16; Stutz & Kainulainen 2015; Megeath et al. 2022).

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A potential degeneracy, however, is found between inclination and envelope density. In Figure 29, we plot one parameter as function of the other, to study their correlation. The Class 0 protostars often show high inclination angles when compared to later evolutionary classes (Figure 24). Within the sample of Class 0 protostars, the 13 Class 0 protostars that have the lowest possible inclination angle have high values of ρ₁₀₀₀. The rest of the Class 0 sample tends to have lower envelope density at higher inclination angles. A similar trend is found for Class I protostars, with those at high inclinations having lower envelope densities. Interestingly, a trend is not clearly apparent for flat-spectrum protostars. This is in tension with HST 1.6 μm imaging of Orion protostars that shows that a large fraction of flat-spectrum protostars has point-source morphologies. Habel et al. (2021) explained this morphology by the flat-spectrum protostars being populated by either protostars with low envelope densities seen at higher inclinations or protostars with high envelope densities seen at low inclinations through their outflow cavities. These correlations indicate that SED class is dependent on inclination, and other inclination-independent methods are needed to more reliably sort sources by their evolutionary stage (e.g., Federman et al. 2023). Furthermore, these degeneracies and the lack of a uniform distribution of inclinations point to likely biases in our fits and sample.

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6.5.4. Envelope Mass

In Section 6.5.3, we found that the envelope reference density decreases with evolutionary class in Aquila. Similar to the envelope density, an early and deeply embedded protostar is expected to have a high envelope mass, whereas an evolved protostar has dispersed most of its envelope with very little envelope left. The mass of the envelope inside some radius r is a useful diagnostic that traces protostellar evolution. Furthermore, the envelope mass is an intrinsic property of a protostar that is independent of the inclination angle.

The protostellar outflow carves out a section of the envelope with wider cavity angles carving out more envelope mass (see Figure 7 in Fischer et al. 2017). As a result, the envelope mass calculated by merely converting ρ₁₀₀₀ (Equation (17)) to mass assuming spherical symmetry and steady infall rate is an overestimation of the actual envelope mass. For this reason, we adopt a more accurate modeling with axisymmetric envelope models where the envelopes have a rotational flattening, and outflow cavities are included. The flattening component is characterized by the centrifugal radius (R_C ), whereas outflow cavities are characterized by cavity opening angle (θ_C ). We assume a polynomial-shaped cavity with an exponent of 1.5. Note that in Whitney et al. (2003a, 2003b), the cavity opening angles are measured from the axis of rotation, so they represent the half-angle instead of the full opening angle. The cavity opening angle is the angle from the pole to the cavity edge at a height above the disk plane equal to the envelope radius.

Since envelope mass is independent of inclination angle, the model estimates the envelope mass for a particular envelope density, centrifugal radius, and cavity opening angle for 3040 independent models. We then integrated the envelope mass out to a radius of 2500 au for two reasons. First, 2500 au is close to the FWHM of the PACS 160 μm beam at the distance of Aquila. In the observed SEDs, PACS 160 μm has the largest spatial extent near the expected SED peak, and photometry at >200 μm data is often contaminated by cooler, extended dust emission, requiring us to use upper limits at these wavelengths. The second reason is to be consistent with the HOPS survey in Orion that uses 2500 au for estimating envelope mass in Orion (F16; Fischer et al. 2017). In Section 7, we compare envelope masses for both HOPS sources in Orion and eHOPS sources in Aquila; using envelope masses within the same outer radius makes them easier to compare.

Figure 30 shows the distribution of envelope masses of the best-fit models. The median of the distribution is 0.07 M_⊙, with lower and upper quartiles at 0.01 and 0.4 M_⊙, respectively. Similar to ρ₁₀₀₀, we find one protostar (eHOPS-aql-161) that has zero envelope mass. There are eight protostars that have extremely low envelope mass (M₂₅₀₀ < 10⁻³), four of which are Class I and four of which are flat-spectrum sources. These eight protostars are likely in the later evolutionary stages where only a low-density envelope providing residual mass infall is present.

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Figure 30(b) shows the distribution of M₂₅₀₀ for different SED classes. The median M₂₅₀₀ for Class 0, I, and flat-spectrum sources are 0.27, 0.02, and 0.01 M_⊙, respectively. Similarly, the mean M₂₅₀₀ for Class 0, I, and flat-spectrum sources are 0.87, 0.19, and 0.06 M_⊙, respectively. As expected, the envelopes around Class 0 protostars are significantly more massive than the other two classes. The A-D test between Class 0 and the other two classes shows that their distribution differs significantly (p-value < < 1%). The mean M₂₅₀₀ for Class I protostars is a bit higher than those for flat-spectrum sources; however, the A-D test between the Class I and flat-spectrum protostars shows that there is no significant difference between the two distributions (p-value ∼70%). This is consistent with an analysis by Federman et al. (2023) of 870 μm continuum ALMA data, which showed that that all SED classes contain a range of envelope masses, but that Class 0 protostars are typically the sources with the most-massive envelopes.

6.5.5. Total Luminosity

The total luminosity, or L_tot, is the sum of the intrinsic photospheric luminosity from the central protostar and the accretion luminosity from accreting gas landing on the protostar. (There is also a contribution to the accretion luminosity by the disk itself, but this is typically negligible except during episodes of rapid accretion; e.g., Hartmann et al. 2016). Figure 31(a) shows the histogram of the total luminosity, L_tot, obtained from the best fits. The values for L_tot vary from 0.09–606.9 L_⊙, which is expected for maximum L_tot as the model grid spans luminosities from 0.1–303.5 L_⊙ and the scaling factor varies from 0.5–2. One protostar, eHOPS-aql-143 hits the allowed luminosity ranges at the higher end of 606.9 L_⊙. The protostar eHOPS-aql-143 is an extremely luminous Class I source with L_bol ∼ 160 L_⊙. It might be possible to obtain a better fit for eHOPS-aql-143 by expanding the luminosity range in the model grid. Overall, the histogram is strongly peaked with a median at ∼5.4 L_⊙, and the lower and upper quartiles at 1.5 and 15.7 L_⊙, respectively. We will compare L_tot for the eHOPS-Aquila protostars with HOPS-Orion protostars in Section 7. A comparison with all protostars in the nearest 500 pc region will be included in a subsequent paper.

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Upon inspecting L_tot for different classes of protostars in Aquila (Figure 31(b)), we find median L_tot of 5.7, 3.9, and 5.8 L_⊙ for Class 0, I, and flat-spectrum protostars, respectively. Due to the approximate symmetry of the distribution in log(L_tot), the mean values of L_tot are much higher: 39.1, 30.9, and 11.9 L_⊙ for Class 0, I, and flat-spectrum protostars, respectively. The range of L_tot is similar for Class 0 and Class I protostars. For flat-spectrum protostars, the minimum L_tot is the same as for other classes, but the maximum L_tot is ∼115 L_⊙ (instead of ∼607 L_⊙ such as for Class 0 and Class I sources). Despite these differences, the p-value from the A-D test indicates no significant difference in the distribution of L_tot for different SED classes. We discuss the evolution of luminosity in Section 7.6.

L_tot for the best-fit models typically differs from the observed bolometric luminosity (L_bol) due to foreground extinction and the beaming of radiation out the outflow cavities (F16; Whitney et al. 2003a). L_bol is calculated by integrating the observed SEDs and assuming the protostar radiates isotropically in all directions. At high inclination angles, the protostellar luminosity is obscured by the intervening disk and envelope material, so less flux is received, and therefore the total luminosity is higher than the bolometric luminosity. In contrast, at low inclination angle, the total luminosity is lower than the bolometric luminosity; this is due to the beaming of radiation through the outflow cavities. Since low inclination angles are unlikely for randomly oriented protostars, cases where L_tot < L_bol are less common. Furthermore, while inclination can increase or decrease L_bol, the foreground extinction always reduces the L_bol. This makes a ratio L_tot/L_bol < 1 even rarer.

For the above reasons, the ratio of L_tot to L_bol is expected to increase with both inclination angle and foreground extinction, although with a large scatter. This is demonstrated in Figure 32. The left panel of the figure shows the variation of the ratio L_tot/L_bol with inclination angles obtained from the best fits. The median L_tot/L_bol for each bin of inclination angle is shown by a blue star. The median L_tot/L_bol has an increasing trend with inclination angle. There are protostars with lower inclination angles that also have smaller cavity opening angles and therefore have higher L_tot/L_bol ratios. The middle panel shows the variation of L_tot/L_bol with foreground extinction A_V . The blue stars show the median L_tot/L_bol in logarithmic bins of A_V with the bin ranges shown by horizontal blue lines overlaid on the blue stars (median values). For the sources with best-fit A_V > 1 mag, we see mostly an increasing trend for L_tot/L_bol with A_V . The third panel is similar to the second panel, but it focuses on foreground extinction values up to 60 and shows them on a linear scale with linear bins. The trend of increasing L_tot/L_bol with A_V is apparent in this panel too, where the median L_tot/L_bol increases from 2.1–6.1 from the lowest to the highest A_V bins.

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Within the HOPS sample, Stutz et al. (2013) and Tobin et al. (2015) identified 19 protostars in the Orion molecular clouds distinguished by their high 70–24 μm flux ratios. Twelve of these protostars were not identified as protostars by the Spitzer data alone due to the faint or undetectable 24 μm emission. Most of these protostars appear to be young Class 0 protostars (Stutz et al. 2013; Tobin et al. 2015, 2016). Based on high angular resolution millimeter Very Large Array (VLA) and ALMA data, Karnath et al. (2020) argued that four of these protostars were less than 10,000 yr old. Of these four objects, two may be binary systems that include Class 0 protostars, one may contain a first-stage hydrostatic core, and the fourth may be in the process of forming a hydrostatic core. These are among the youngest protostars known.

After Orion, Aquila is the second molecular cloud complex that has been systematically searched for PBRSs using the criterion established by Stutz et al. (2013). In Section 4.1.5, we found eight extremely red protostars using Equation (11) and six protostars of a similar nature using the completeness limit for the MIPS 24 μm flux in Section 4.1.6. Stutz et al. (2013) defined the PBRSs using the ν F_ν (70)/ν F_ν (24) ratio; this was established using a grid of protostar models to determine the ratios that implied high envelope densities. We follow Stutz et al. (2013) and define the PBRSs as the protostars for which ν F_ν (70)/ν F_ν (24) > 10^1.65. Figure 33(a) shows the ν F_ν (70) versus ν F_ν (70)/ν F_ν (24) diagram. The black open boxes mark the extremely red protostars that are detected using Equation (11) in Section 4.1.5 and using completeness limits in Section 4.1.6. In this figure, there are nine sources that satisfy the Stutz et al. (2013) criterion and that are designated as PBRSs.

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We use the PACS 100 μm data to find additional PBRSs that were missed in the lower-sensitivity 70 μm data. Figure 14(b) shows the ν F_ν (100) versus ν F_ν (100)/ν F_ν (24) diagram for the eHOPS-Aquila protostars. We determine the minimum ν F_ν (100)/ν F_ν (24) ratio using the PBRSs identified in the 70 μm data. These PBRSs satisfy the criteria ν F_ν (100)/ν F_ν (24) > 10^1.85. Using this criteria, we identify one more PBRS in Figure 14(b).

In summary, using the ν F_ν (70)/ν F_ν (24) and ν F_ν (100)/ν F_ν (24) criteria in Figure 14, we identify a total 10 PBRS in the eHOPS sample (eHOPS-aql-9, eHOPS-aql-29, eHOPS-aql-36, eHOPS-aql-38, eHOPS-aql-67, eHOPS-aql-75, eHOPS-aql-108, eHOPS-aql-110, eHOPS-aql-152, and eHOPS-aql-154). Out of the 10 PBRSs, two can be identified using Spitzer photometry alone (Equation (7)), six are newly identified extremely red protostars (Equation (11)), and two are identified using the completeness limit at 24 μm (Section 4.1.6).

As an example of a PBRS in the eHOPS-Aquila catalog, Figure 34 shows the SED and postage stamp images of one of the PBRS in our sample, eHOPS-aql-29. The source is not detected in any of the Spitzer wave bands in the 3.4–24 μm wavelengths and is detected only by Herschel at ≥70 μm. This particular PBRS would not have been detected with just the Spitzer IRAC and MIPS detectors. The peak of the SED is between the PACS 100–160 μm bands.

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View figure set (10 panels)

Tarball of figure set images

As shown in Table 5, Aquila has a rich population of PBRSs. The eHOPS-Aquila protostars have a similar fraction of PBRSs as the HOPS protostars in Orion. In Orion, most of the PBRSs are found in the Orion B cloud (Stutz et al. 2013; Karnath et al. 2020). The fraction of PBRSs in Aquila is in between the low fractions of PBRSs in Orion A and the high fraction found for Orion B. To compare the properties of the HOPS and eHOPS PBRSs, Table 6 lists the average and median values of the SED-based diagnostics and best-fit parameters for the PBRSs and Class 0 protostars in Aquila and Orion. In Table 6, the PBRSs are included with the Class 0 protostars when calculating the properties of the Class 0 sample.

In both clouds, the PBRSs have a lower average and median T_bol compared to the whole sample of Class 0 protostars, as expected. The median values of T_bol, L_bol ρ₁₀₀₀, and M₂₅₀₀ are very similar between the PBRS in the Aquila and Orion clouds, and between the Class 0 protostars in those two clouds. Less agreement is seen for the average values; these may be affected by a few sources with very high luminosities or envelope masses. Interestingly, the median values of L_tot are higher in Aquila. The higher L_tot values for Aquila PBRS may result from the different angular resolutions of the submillimeter data, which may favor fits with edge-on inclinations and higher L_tot values for the eHOPS-Aquila sample. We will examine these potential biases in a future paper encompassing all of the molecular clouds in the eHOPS catalog.

In general, we find very similar populations of PBRSs in both clouds. The PBRSs are distinguished from the typical Class 0 protostars by their lower T_bol values and higher envelope masses. These are consistent with the PBRSs being young Class 0 protostars with dense envelopes and high infall/high accretion rates. Future ALMA and VLA observations are needed to search for very young (<10,000 yr) protostars similar to the four found in Orion.

The total luminosity (L_tot) of a protostar is the intrinsic luminosity of its photosphere summed with the luminosity generated from accretion onto the protostar. This can differ from the bolometric luminosity (L_bol), which is calculated assuming that the protostar radiates isotropically with no correction for extinction. As described in Section 6.5.5, the radiation of protostars is concentrated along the axis of the outflow cavities; this results in L_tot > L_bol for protostars observed a higher inclinations, and L_tot < L_bol for protostars observed near a face-on inclination. In addition, foreground extinction lowers the value of L_bol. In general, since face-on inclinations are less likely, and since foreground extinction always reduce L_bol, we expect to see L_tot > L_bol for most protostars (see Section 6.5.5).

Figure 35 compares the best-fit L_tot with the observed L_bol for the protostars in the eHOPS-Aquila (left panel) and HOPS samples (right panel, from Fischer et al. 2017). In both plots, the dashed line is the region where both L_tot and L_bol are equal. The medians of L_tot/L_bol are 2.4 and 2.5 for Aquila and Orion, respectively. The distribution of the sources is remarkably similar in both plots. In Aquila, the majority of the sources (∼70%) are between L_tot/L_bol = 1 and L_tot/L_bol = 10. There are ∼15% protostars for which L_tot/L_bol < 1; the median, best-fit inclination angle for these protostars is ∼18° (more face-on). On the other end, there are another ∼15% protostars for which L_tot/L_bol > 10; and their median, best-fit inclination angle is ∼82°. These protostars are fit by models where the protostar is viewed nearly edge-on. The similarity of these L_tot versus L_bol diagrams suggests that there are no significant biases in the determination of luminosities due to the different bands used in the eHOPS and HOPS samples.

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The protostellar luminosity function (hereafter, PLF) places important constraints on the accretion history of protostars (Dunham et al. 2010; Offner & McKee 2011). This function can be represented as the distribution of L_bol or L_tot for a population of protostars. Figures 36(a), (b), and (c) show the distribution of L_bol for the eHOPS protostars in Aquila, the HOPS protostars in the entire Orion clouds (from F16), and separately for Orion A and Orion B, respectively. The PLFs in Aquila and Orion have a similar form but with peaks at different L_bol. The PLF for Aquila peaks at ∼2 L_⊙, but for Orion the PLF peaks at ∼1 L_⊙. Similarly, the median L_bol for the eHOPS protostars in Aquila is 1.8 L_⊙, which is higher than the median L_bol of 1.1 L_⊙ for the HOPS sources in Orion. From Figure 36(c), the median of the PLF for Orion A is the same as the median for the whole Orion clouds (1.1 L_☉), while for Orion B, L_bol is higher (1.5 L_☉). However, Orion B is asymmetric and peaks at a luminosity <1 L_☉.

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The differences in the PLFs are also evident when plotting in terms of the total luminosity, shown in Figure 37. L_tot takes into account the effects of inclination and extinction; however, it is also model dependent. Moreover, biases and degeneracies in the models can affect the best-fit values. The median L_tot for Aquila and Orion are 5.4 L_⊙ and 3.0 L_⊙, respectively. The ratio of the median L_tot between Aquila and Orion is the same as the ratio of the median L_bol between those clouds (1.8 and 1.9, respectively). The median L_tot for both Orion A and Orion B is 3 L_☉.

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Comparing the PLFS of the eHOPS-Aquila and HOPS samples, the A-D test gives a p-value of 0.03, implying we can reject the null hypothesis that L_bol in Aquila and Orion are drawn from the same distribution at a 3% significance level. However, there are potentially different completeness levels in the Herschel data used in HOPS and in the eHOPS-Aquila survey, which must be considered. To mitigate differences in the completeness and to minimize any residual extragalactic contamination, we perform the tests in protostars on Aquila and Orion for which L_bol > 0.1 L_⊙. Figure 38(a) shows the cumulative distribution function (CDF) of L_bol for the protostars in Aquila and in Orion. For the PLFs with L_bol for >0.1 L_⊙, Aquila and Orion are likely drawn from the same distribution with a p-value of 0.22 using the A-D test. Thus, for the >0.1 L_⊙ protostars, we cannot rule out that the distributions of L_bol for Aquila and Orion were drawn from the same parent sample. The A-D test also shows that the distributions of L_bol in Aquila and Orion B are likely drawn from the same distribution (p-value ≥0.25) but that Aquila and Orion A are not (p-value = 0.04). Also shown in Figure 38(b) is the CDF of L_tot. Similar to L_bol, we perform the A-D test on protostars with L_tot >0.1 L_⊙ and find p-value = 0.23. Furthermore, contrary to L_bol, the distributions of L_tot for Aquila, Orion A, and Orion B are likely drawn from the same distribution.

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In summary, we see higher medium and peak luminosities for both L_bol and L_tot in Aquila compared to Orion. Statistical tests imply, however, that if we consider protostars above 0.1 L_☉—at which we have higher confidence that both data sets are complete—we cannot reject the null hypothesis that the PLFs in Aquila and Orion are drawn from the same parent distribution. There is a possible exception in that the L_bol distributions of Aquila and Orion A have a relatively small probability (4%) of being drawn from the same population.

Several SED-based diagnostics are used to track the evolution of protostars as their envelopes are accreted/dispersed. These include the slope of the mid-IR SED (Lada & Wilking 1984; Greene et al. 1994), the bolometric temperature of the SED (Myers & Ladd 1993; Chen et al. 1995), and the envelope mass derived by model fits to the SED (Fischer et al. 2017). Analyses based on Spitzer and Herschel data often use a combination of the slope and T_bol to place YSOs into an evolutionary context (e.g., Evans et al. 2009, F16). Each of these diagnostics, however, has limitations. The slope and T_bol are both strongly affected by inclination and foreground extinction (e.g., Calvet et al. 1994; Whitney et al. 2003a; Fischer et al. 2017). Model fits to the SEDs can account for inclination and extinction; however, degeneracies between parameters can result in large uncertainties in the best-fit values (F16; Fischer et al. 2017). Recent work shows a strong, linear correlation between the best-fit M₂₅₀₀ and the envelope mass estimated from the 870 μm flux measured by ALMA (Federman et al. 2023), although with significant scatter.

One way to assess potential biases between the HOPS and eHOPS-Aquila data is to compare evolutionary diagnostics. In Figure 39 we compare the α_4.5,24 and T_bol for the two samples. To minimize the effect of foreground extinction, we measure the SED slope using only the mid-IR photometry between the 4.5 and 24 μm bands, similar to F16. Since the Spitzer data are similar between both data sets, the α_4.5,24 values for Aquila and Orion are calculated in a consistent manner.

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In both the HOPS and eHOPS-Aquila data, we find a similar linear dependence between α_4.5,24 and log T_bol. (Figure 39). A linear best-fit plot in Figure 39 reveals the relation α_4.5,24 = −1.2 log T_bol + 3.2 for the protostars in Aquila, and an almost identical relation for the protostars in Orion, α_4.5,24 = −1.2 log T_bol + 3.4. The dispersion from the linear relation is larger for the younger sources in both clouds. Since the α_4.5,24 data are dependent on Spitzer data alone while T_bol requires the entire SED, this similarity of these fits and diagrams indicates no substantial biases in T_bol between HOPS and eHOPS.

In contrast, some differences are apparent when comparing envelope mass to T_bol. Figure 40 shows the variation of the envelope mass within 2500 au (M₂₅₀₀) with T_bol for Aquila (panel (a)) and Orion (panel (b)). Note that the estimates for M₂₅₀₀ are from model fits whereas we calculate T_bol directly from observations. We find the expected anticorrelation between T_bol and M₂₅₀₀. M₂₅₀₀ is lower for the more evolved protostars that have higher T_bol. The correspondence between the two clouds is strongest for the Class 0 protostars that populate the low T_bol (≲70 K) part of the plot. On the other hand, for the sources with T_bol >70 K that are Class I, flat-spectrum, and Class II, we see that the interquartile ranges and median values are shifted to lower envelope masses in Orion. This largely reflects the significant number of protostars with very low envelope masses (∼10⁻³ M_⊙) in the HOPS sample. We also find differences at the extremes of the plot, with the Aquila data extending to lower T_bol and a concentration of protostars in the highest T_bol bin for HOPS, which is not apparent for eHOPS-Aquila. We examine these differences in the distributions of T_bol and envelope mass in the next subsection.

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As protostars evolve, their bolometric temperatures increase and their envelopes masses decrease as the envelope is accreted and—simultaneously—dispersed by outflows. Thus, differences in the statistical distributions of T_bol and M₂₅₀₀ may indicate differences in star formation histories of these regions (Fischer et al. 2017). This motivates a closer look at these distributions.

Figure 41 shows the histogram of T_bol for the protostars in the eHOPS-Aquila sample (panel (a)) and the HOPS sample (panel (b)). The histograms are broadly distributed for both clouds. The distribution for Aquila is shifted toward lower temperatures; the median T_bol of the eHOPS protostars in Aquila is 88 K compared to 146 K for the HOPS protostars in Orion. This is consistent with the higher fraction of PBRS and Class 0 protostars and a lower fraction of flat-spectrum protostars in Aquila. The A-D test comparing the T_bol distribution of protostars in Aquila and Orion gives a p-value <0.01, thereby rejecting the null hypothesis that T_bol in Aquila and Orion are drawn from the same distribution. We also plot a histogram of T_bol individually for Orion A and Orion B. For Orion A, the A-D test still shows a significant difference in T_bol distribution compared with Aquila with p-value < < 0.01. However, for Orion B, the A-D test finds no significant difference in the distribution of T_bol when compared with Aquila with a p-value >0.9. In Orion B, the median T_bol is 85 K, again similar to that of Aquila.

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Similar results are found for the best-fit envelope masses to the eHOPS-Aquila and HOPS protostars. Figure 42 shows the distributions of M₂₅₀₀ for the protostars in eHOPS-Aquila (panel (a)), HOPS, (panel (b)), and HOPS separately for Orion A and Orion B (panel (c)), respectively. As in the case of T_bol, the distribution of M₂₅₀₀ is shifted to higher masses for Aquila. The median M₂₅₀₀ in Aquila and Orion are 0.073 and 0.026 M_☉, respectively. The A-D test shows a significant difference in the distribution of M₂₅₀₀ in Aquila and in Orion with a p-value <0.01. Differences in the distribution of M₂₅₀₀ are also found between the Orion A and Orion B clouds. The median M₂₅₀₀ in Orion B is 0.08 M_☉, similar to the median M₂₅₀₀ in Aquila, while the median M₂₅₀₀ in Orion A is 0.01 M_☉, lower than the median M₂₅₀₀ in the whole Orion cloud. The A-D test shows that the distribution of M₂₅₀₀ in Aquila is significantly different from Orion A (p-value <0.01), but is similar to the M₂₅₀₀ distribution in Orion B (p-value ≥0.25).

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As we saw in Section 7.4, the HOPS sample contains a significant number of protostars with very low-mass envelopes (∼10⁻³ M_⊙) that are not present in eHOPS-Aquila. This is particularly true for Orion A. This difference may be due to differences in either the identification of protostars or their fits. The HOPS protostar sample may include more reddened pre-MS stars with disks or sources transitioning from protostars to pre-MS stars. Alternatively, low-mass protostars may have been removed by the galaxy template fits in Aquila, where the lack of IRS spectra would preclude the detection of silicate features indicative of protostars. Finally, the fits to the Orion SEDs may have resulted in more protostars with low envelope masses due to the different wave bands used in the fits. Establishing whether the low envelope mass sources are the result of biases, or whether they reflect real differences in the populations of protostars between these regions, requires a reanalysis of the HOPS data and is beyond the scope of this paper.

Both eHOPS-Aquila and the HOPS protostars in Orion B show a higher fraction of low T_bol/high M₂₅₀₀ protostars than Orion A. The similarity between Orion B and Aquila suggests these differences are not due to biases in the determination in T_bol or M₂₅₀₀. Furthermore, while T_bol uses the Herschel/SPIRE band and may be affected by external dust emission from the surrounding cloud, the M₂₅₀₀ values result from fits where the SPIRE data provide only upper limits. Thus, the difference in the M₂₅₀₀ distributions cannot be explained by contamination of the SPIRE data. In total, these results suggest the differences between Orion B/Aquila and Orion A are real.

The bolometric luminosity versus temperature (BLT) diagram is used to study the evolution of protostars (Myers & Ladd 1993; Evans et al. 2009; Dunham et al. 2015). Figure 43 shows the BLT diagrams for the eHOPS protostars in Aquila and HOPS protostars in Orion (see Fischer et al. 2017). The protostars in both Aquila and Orion span similar ranges in L_bol. The maximum L_bol in the eHOPS-Aquila catalog is 160 L_⊙. There are four protostars in the HOPS-Orion catalog with L_bol > 160 L_⊙: HOPS 361, HOPS 370, HOPS 376, and HOPS 384 (L_bol = 479, 361, 218, and 1478 L_⊙, respectively).

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The PLFs of the HOPS Class 0 protostars in Orion are shifted to higher L_bol relative to more evolved protostars (see Fischer et al. 2017). This is true for both the Orion A and B clouds. Fischer et al. (2017) explained this shift as an evolution toward lower luminosities as the envelopes are depleted and infall/accretion decreases. In Figure 44, we compare the distribution of L_bol in eHOPS-Aquila and HOPS for deeply embedded protostars (PBRSs + Class 0) and more evolved protostars (Class I + flat-spectrum sources). In Orion, the median L_bol for the PBRSs and Class 0 protostars are 2.2 L_☉, and for the Class I and flat-spectrum protostars, it is 0.9 L_☉. The A-D test shows the distributions of L_bol for the combined PBRSs and Class 0 protostars, and the combined Class 1 and flat-spectrum protostars are unlikely to be drawn from the same parent distribution (p-value <0.01). However, we see no such behavior of L_bol in Aquila. The median L_bol of PBRS+Class 0 protostars in Aquila is 1.9 L_☉, and for the later evolutionary phases (Class I + flat-spectrum sources) the median is 1.7 L_☉. The A-D test shows that L_bol distributions for the PBRS+Class 0 protostars and the Class 1+flat-spectrum protostars are statistically indistinguishable (p-value >0.25). Thus, the eHOPS-Aquila protostars do not show the evolution toward lower luminosities observed in the HOPS protostars.

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Fischer et al. (2017) also compared the total luminosity (L_tot) with the envelope mass (M₂₅₀₀) for the HOPS protostars in Orion as a means to study the evolution of luminosity of protostars. The plot is known as the total luminosity and mass (TLM) diagram. The TLM diagram provides an alternative to the BLT diagram by directly comparing the physical protostellar properties from model fits. In Figure 45, we provide a TLM diagram for the eHOPS protostars in Aquila and also recreate the TLM diagram from Fischer et al. (2017) for the HOPS protostars in Orion. We divide the sample in equally spaced bins of log M₂₅₀₀ and compute the median L_bol (black diamonds) and upper and lower quartiles (bars on the diamonds) in each bin.

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For the HOPS protostars, L_tot peaks around 0.3 M_⊙, after which L_tot subsequently decreases as M₂₅₀₀ decreases. This behavior was modeled by Fischer et al. (2017) by assuming an exponentially decreasing envelope mass with time. The A-D test shows that the p-values for L_tot in the consecutive M₂₅₀₀ bins of 0.002, 0.02, 0.2, 2, and 20 M_⊙ are <0.01, implying that L_tot is drawn from a different distribution. Only for the lowest M₂₅₀₀ bins of 0.0002 and 0.002 M_⊙ is the p-value >0.25, implying a statistically similar distribution. This behavior is apparent for both the Orion A and Orion B clouds (Fischer et al. 2017). In the Aquila clouds, however, the A-D p-values for L_tot for each M₂₅₀₀ bin are consistent with being drawn from the same distribution. To minimize differences due to incompleteness, we also study the variation of L_tot with M₂₅₀₀ for protostars with L_bol > 0.1 L_⊙. We find that the AD-test results do not change by excluding L_bol < 0.1 L_⊙ protostars.

In summary, in the eHOPS-Aquila sample, we do not find the evolution of luminosity present in the HOPS sample. This is due to lower average luminosities for the Class 0 protostars and higher average luminosities for the Class I/flat-spectrum protostars in Aquila relative to Orion. In the next section, we briefly discuss the implications of this result.

A primary goal in comparative studies of protostars in nearby clouds is to establish differences in the star-forming populations. These differences may arise due to different star formation histories, or due to the influence of the environment on the evolution of protostars. Both can have significant implications. Variations in the star formation rate over the relatively short lifetimes of protostars (0.5 Myr) would provide new information on how star formation is induced and regulated in clouds. Variations with the environment would provide constraints on how environmental factors mediate protostellar evolution, which may prove useful in extrapolating our understanding of low-mass star formation in the nearest 0.5 kpc to the more active (and more representative) star-forming regions such as those found in the inner region of our galaxy (Megeath et al. 2022).

In our cursory comparisons, we have established two differences. The first is the higher fraction of low T_bol/high M₂₅₀₀ protostars in Orion B and eHOPS-Aquila. Orion B has been known to have an unusual concentration of Class 0 protostars and PBRSs (Stutz et al. 2013; Karnath et al. 2020). If these differences are real, the shift to lower T_bol and higher M₂₅₀₀ in Aquila (and Orion B) may suggest that the star formation rate is increasing with time (Fischer et al. 2017). Consistent with this picture, the two clusters that dominate star formation in Aquila, the Serpens Main and Serpens South clusters, have high fractions of protostars compared to all YSOs (57%–71%; Gutermuth et al. 2008a).

The second difference is the lack of luminosity evolution in the eHOPS-Aquila. Such evolution in luminosity is apparent in both the Orion A and B clouds. Previous work has suggested that the luminosities of protostars depend on the environment (Kryukova et al. 2012, 2014; Dunham et al. 2014; Elmegreen et al. 2014). These previous works, however, did not examine luminosity as a function of evolution. If the difference in luminosity evolution is real, there are a few possible explanations. First, if the star formation rate is rapidly increasing, many of the Class I and flat-spectrum sources may be younger protostars seen at favorable inclinations (Federman et al. 2023). Alternatively, the infall and accretion rate in Aquila may be systematically lower than those in Orion, lengthening the duration of the Class 0 phase. This, however, is in tension with the higher fraction of high M₂₅₀₀ values in eHOPS-Aquila; protostars with higher M₂₅₀₀ values have higher envelope densities, shorter freefall times, and higher infall/accretion rates. Alternatively, there may be differences in how much of the energy from accretion is radiated into space and the radii of the resulting protostars (e.g., Hosokawa et al.2011).

Future work is needed to rigorously establish that such differences are not due to biases in the data. We will reexamine these differences in a future publication, in which we expand the eHOPS sample to include all of the clouds within 500 pc except Taurus.