# The Herschel -PACS Legacy of Low-mass Protostars: The Properties of Warm and Hot Gas Components and Their Origin in Far-UV Illuminated Shocks

Agata Karska, Michael Kaufman, Lars Kristensen, Ewine van Dishoeck, Gregory J. Herczeg, Joseph Mottram, Łukasz Tychoniec, Johan Lindberg, Neal Ii, Joel Green, et al.

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## To cite this version:

Agata Karska, Michael Kaufman, Lars Kristensen, Ewine van Dishoeck, Gregory J. Herczeg, et al. The Herschel -PACS Legacy of Low-mass Protostars: The Properties of Warm and Hot Gas Components and Their Origin in Far-UV Illuminated Shocks. The Astrophysical Journal Supplement, 2018, 235 (2), pp.30. 10.3847/1538-4365/aaaec5. hal-02268365

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# The Herschel-PACS Legacy of Low-mass Protostars: The Properties of Warm and Hot Gas Components and Their Origin in Far-UV Illuminated Shocks

Agata Karska¹,²,³ Ⓓ, Michael J. Kaufman⁴ Ⓓ, Lars E. Kristensen⁵ Ⓓ, Ewine F. van Dishoeck²,⁶ Ⓓ, Gregory J. Herczeg⁷ Ⓓ, Joseph C. Mottram⁸, Łukasz Tychoniec⁶ Ⓓ, Johan E. Lindberg⁹ Ⓓ, Neal J. Evans II¹⁰, Joel D. Green¹⁰,¹¹ Ⓓ, Yao-Lun Yang¹⁰ Ⓓ, Antoine Gusdorf¹², Dominika Itrich¹, and Natasza Siódmiak¹³

¹ Centre for Astronomy, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Torun, Poland
agata.karska@umk.pl

² Max-Planck Institut für Extraterrestrische Physik (MPE), Giessenbachstr. 1, D-85748 Garching, Germany

³ Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands

⁴ Department of Physics and Astronomy, San Jose State University, One Washington Square, San Jose, CA 95192-0106, USA

⁵ Centre for Star and Planet Formation, Niels Bohr Institute and Natural History Museum of Denmark, University of Copenhagen, Øster Voldgade 5-7, DK-1350 Copenhagen K, Denmark

⁶ Leiden Observatory, Leiden University, Niels Bohrweg 2, NL-2333 CA Leiden, The Netherlands

⁷ Kavli Institute for Astronomy and Astrophysics, Peking University, Yi He Yuan Lu 5, Haidian Qu, 100871 Beijing, People's Republic of China
⁸ Max Planck Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany

⁹ NASA Goddard Space Flight Center, Astrochemistry Laboratory, Mail Code 691, 8800 Greenbelt Road, Greenbelt, MD 20771, USA

¹⁰ Department of Astronomy, The University of Texas at Austin, Austin, TX 78712, USA

¹¹ Space Telescope Science Institute, Baltimore, MD, USA

¹² LERMA, Observatoire de Paris, Ecole normale supérieure, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, F-75231, Paris, France
¹³ N. Copernicus Astronomical Center, Rabianska 8, 87–100 Torun, Poland

Received 2017 September 21; revised 2018 February 7; accepted 2018 February 8; published 2018 March 28

## Abstract

Recent observations from Herschel allow the identification of important mechanisms responsible both for the heating of the gas that surrounds low-mass protostars and for its subsequent cooling in the far-infrared. Shocks are routinely invoked to reproduce some properties of the far-IR spectra, but standard models fail to reproduce the emission from key molecules, e.g., H₂O. Here, we present the Herschel Photodetector Array Camera and Spectrometer (PACS) far-IR spectroscopy of 90 embedded low-mass protostars (Class 0/I). The Herschel-PACS spectral maps, covering ~55–210 µm with a field of view of ~50′′, are used to quantify the gas excitation conditions and spatial extent using rotational transitions of H₂O, high-J CO, and OH, as well as [O I] and [C II]. We confirm that a warm (~300 K) CO reservoir is ubiquitous and that a hotter component (760 ± 170 K) is frequently detected around protostars. The line emission is extended beyond ~1000 au spatial scales in 40/90 objects, typically in molecular tracers in Class 0 and atomic tracers in Class I objects. High-velocity emission (≥90 km s⁻¹) is detected in only 10 sources in the [O I] line, suggesting that the bulk of [O I] arises from gas that is moving slower than typical jets. Line flux ratios show an excellent agreement with models of C-shocks illuminated by ultraviolet (UV) photons for pre-shock densities of ~10⁵ cm⁻⁵ and UV fields 0.1–10 times the interstellar value. The far-IR molecular and atomic lines are a unique diagnostic of feedback from UV emission and shocks in envelopes of deeply embedded protostars.

**Key words:** infrared: ISM – ISM: jets and outflows – ISM: molecules

## 1. Introduction

Complex physical processes are at play during the earliest stages of low-mass star formation, when high accretion rates translate to significant feedback from a protostar on its surroundings (e.g., Frank et al. 2014). The launching of collimated jets and wide-angle winds leads to the formation of outflow cavities and generates shock waves that compress and heat the envelope material to hundreds or thousands of K (Neufeld & Dalgarno 1989; Arce et al. 2007). Ultraviolet (UV) photons, produced as a result of accretion onto the protostar and created in shocks, penetrate to large distances due to the low densities and scattering by dust in the outflow cavities (Spaans et al. 1995; van Kempen et al. 2010b; Visser et al. 2012). As a result, the gas around low-mass protostars is heated to hundreds of K, altering the chemistry and physics of the available mass reservoir and lowering the efficiency of star formation (e.g., Offner et al. 2009; Drozdovskaya et al. 2015).

Previous studies of feedback from low-mass protostars concentrated on the low-temperature ($T_{\text{kin}} < 100$ K) gas probed

by low-J (J ≤ 10) rotational transitions of CO at submillimeter wavelengths (e.g., Bachiller & Tafalla 1999; Arce et al. 2007; van der Marel et al. 2013; Dunham et al. 2014; Yıldız et al. 2015). Those transitions trace the entrained outflow gas but show significant differences in spatial extent of emission and line profiles with respect to the more highly excited lines (Nisini et al. 2010; Kristensen et al. 2013, 2017b; Santangelo et al. 2014b). Thus, the energetic processes seen in high-J CO lines (J > 10) are likely to be different and need to be characterized separately.

The most efficient cooling of hot and dense gas occurs in the far-infrared (IR) domain, and thus the best tracers of the heating mechanisms are rotational lines of H₂O, high-J CO, OH, and forbidden transitions of [O I] and [C II] (Goldsmith & Langer 1978; Hollenbach et al. 1989). The first multi-line surveys of low-mass protostars were performed using the Long-Wave-length Spectrometer onboard the Infrared Space Observatory (Clegg et al. 1996; Kessler et al. 1996). The line spectra showed rich molecular emission that is spatially extended along the outflow direction and excited in relatively dense
~(~10⁴~10⁵ cm⁻³) and warm (~500 K) gas (Giannini et al. 2001; Nisini et al. 2002). A combination of a slow, non-dissociative shock and a fast, dissociative shock from the jet was invoked to explain the observed molecular and [O I] emissions, respectively. However, the low sensitivity of the instrument and the large telescope beam (~80′′) covering the entire extent of young stellar objects prevented study of the location of the far-IR emission.

Far-IR spectral maps from the Photodetector Array Camera and Spectrometer (PACS; Poglitsch et al. 2010) onboard the *Herschel Space Observatory* (Pilbratt et al. 2010)<fnref n="14" /> are well-suited to revisit the *ISO/LWS* results, due to their enhanced sensitivity and improved spatial and spectral resolution. The array of 5 × 5 elements covered a total field of view of ~47″ with 9.4 pixels, corresponding to spatial resolution scales on the order of ~1000 au at the typical distances to nearby protostars (~200 pc).

Three large surveys of nearby low-mass protostars were carried out using *Herschel*. The “Water in Star-forming regions with *Herschel*” (WISH) survey focused on H₂O and related species in order to characterize the physical and chemical processes in about 80 low-, intermediate-, and high-mass young stellar objects from pre-stellar cores to disks (van Dishoeck et al. 2011), using mostly high-resolution spectra from the Heterodyne Instrument for the Far-Infrared (HIFI, de Graauw et al. 2010). The PACS spectra centered at protostar position were obtained for 18/29 deeply embedded low-mass protostars, typically at selected transitions (Karska et al. 2013). The “Dust, Ice, and Gas in Time” (DIGIT) open time program obtained complementary, full PACS spectra toward 30 Class 0/I protostars in order to quantify the dust and gas evolution in the far-IR (Green et al. 2013, 2016), including eight overlap sources from the WISH survey. Finally, the “William Herschel Line Legacy” (WILL) open time survey (Mottram et al. 2017) obtained PACS and HIFI spectra toward about 50 additional low-mass protostars from the recent *Spitzer* and *Herschel* Gould Belt imaging surveys (e.g., Evans et al. 2009; André et al. 2010; Dunham et al. 2015). The WILL survey balances the samples of the WISH and DIGIT surveys, both in the evolutionary stage (Class 0/I) and luminosities of protostars, thus ensuring that the combined sample of these three surveys is more representative of the general population of low-mass protostars (see Mottram et al. 2017, for details).

Additional surveys focused on populations of protostars in specific clusters, located at similar distances. As part of the “*Herschel Orion Protostar Survey*,” CO emission covering the full PACS range was characterized for 21 protostars in Orion (Manoj et al. 2013, 2016). Far-IR emission maps for the eight youngest protostars identified in this survey (the PACS Bright Red Sources, henceforth PBRSs; Stutz et al. 2013) were analyzed by Tobin et al. (2016a). The “Herschel Study of Star Formation Feedback on Cloud Scales” (PI: H. Arce) obtained PACS and HIFI maps of the entire NGC1333 region in Perseus in the selected atomic ([O I], [C II]) and molecular lines (e.g., CO 10-9, H₂O 557 GHz), respectively (Dionatos & Güdel 2017). Riviere-Marichalar et al. (2016) provide a catalog of H₂O and [O I] lines observed with PACS for 362 young stellar objects from Class 0 to Class III.

The above programs have proven H₂O as an important tracer of energetic physical processes in the earliest stages of star formation. Line profiles of H₂O are complex, but dominated by gas moving at several tens of km/s (Kristensen et al. 2012; Mottram et al. 2014, 2017). The spatial extent of H₂O resembles the emission from H₂ and follows the outflow direction (Nisini et al. 2010; Santangelo et al. 2012). The far-IR gas-cooling budget is dominated by H₂O and high-*J* CO lines, following the predictions from models of non-dissociative C-shocks (Karska et al. 2013). Thus, H₂O emission is closely linked to the outflow shocks, and its excitation is in agreement with stationary (1D plane-parallel) shock models (e.g., Paris-Durham code, Flower & Pineau des Forêts 2015). However, these models cannot reproduce the chemistry: low abundances of H₂O and O₂ and low H₂O/CO and H₂O/OH flux ratios (Karska et al. 2014b; Melnick & Kaufman 2015). UV photons can photodissociate H₂O and reconcile the models and observations, but the models of shocks irradiated by UV have not been available for detailed comparisons until now.

In this paper, we analyze the far-IR PACS spectra of a large and uniform sample of low-mass YSOs obtained as part of the WISH, DIGIT, and WILL surveys, and compare them to the stationary shock models from Flower & Pineau des Forêts (2015), models of photodissociation regions (PDRs) from Kaufman et al. (1999), and UV irradiated C-shock models from Melnick & Kaufman (2015), to address the following questions: What is the typical far-IR spectrum of a low-mass protostar? Are the emissions in various far-IR atomic and molecular species linked? What is the spatial extent of the line emission? What are the typical rotational temperatures of CO, H₂O, and OH, and the corresponding physical conditions of the gas? What is the gas cooling budget in the far-IR? What is the origin of the far-IR emission? In particular, what kinds of shocks and densities of pre-shock material are involved? What is the strength of UV radiation, and does it affect the chemistry of low-mass protostars? Finally, how do the far-IR line properties evolve during the Class 0/I phases, and what are the corresponding changes in the physical processes (shocks, UV radiation)?

The paper is organized as follows. Section 2 describes our sample selection, observations, and data reduction. Section 3 compiles results on detection statistics, spatial extent of line emission and resolved profiles. Section 4 shows analysis of molecular excitation and far-infrared line cooling. Comparisons of absolute line emission of atomic lines to shocks and PDRs models are presented in Section 5, along with comparisons to UV-illuminated shock models. Section 6 discusses the results obtained in previous sections, and Section 7 presents the summary and conclusions.

## 2. Observations

### 2.1. *Sample Selection*

The low-mass embedded protostars analyzed here were initially observed as part of the WISH (van Dishoeck et al. 2011) and “Dust, Ice, and Gas In Time” (DIGIT, Green et al. 2013) surveys, which comprised 18 and 29 protostars targeted with PACS, respectively, including eight overlap sources. This sample was subsequently expanded by the WILL survey (Mottram et al. 2017), where a further 49 sources were observed, including 37 Class 0/I objects. Three additional sources were located in the PACS spectral maps of the primary

<footnote n="14">¹⁴ *Herschel* was an ESA space observatory with science instruments provided by European-led Principal Investigator consortia, with important participation from NASA.</footnote>
<table><caption>Table 1
Luminosities and Bolometric Temperatures of Embedded Protostars</caption><thead><tr><th>ID</th><th>R.A. (J2000)<br>(h m s)</th><th>Decl. (J2000)<br>(°′′)</th><th>Cloud</th><th>D<sup>a</sup><br>(pc)</th><th>L<sub>bol</sub><br>(L<sub>☉</sub>)</th><th>L<sub>submm</sub><br>L<sub>bol</sub><br>(%)</th><th>T<sub>bol</sub><br>(K)</th><th>Class</th><th>Other Names</th><th>Survey<sup>b</sup></th></tr></thead><tbody><tr><td>1</td><td>03 25 22.33</td><td>+30 45 14.0</td><td>Per</td><td>235</td><td>4.5</td><td>2.7</td><td>44</td><td>0</td><td>L1448 IRS2, Per-emb 22, PER 01</td><td>WL</td></tr><tr><td>2</td><td>03 25 36.48</td><td>+30 45 22.3</td><td>Per</td><td>235</td><td>9.2</td><td>1.7</td><td>54</td><td>0</td><td>L1448 IRS3/N(A), Per-emb 33, PER 02</td><td>WL</td></tr><tr><td>3</td><td>03 25 38.82</td><td>+30 44 06.3</td><td>Per</td><td>235</td><td>5.5</td><td>0.4</td><td>49</td><td>0</td><td>L1448 MMS/C(N), Per-emb 26</td><td>D</td></tr><tr><td>4</td><td>03 25 39.10</td><td>+30 43 58.0</td><td>Per</td><td>235</td><td>1.7</td><td>2.1</td><td>80</td><td>I</td><td>L1448 C(S), Per-emb 42</td><td>D</td></tr><tr><td>5</td><td>03 26 37.46</td><td>+30 15 28.0</td><td>Per</td><td>235</td><td>1.2</td><td>4.2</td><td>60</td><td>0</td><td>I03235+3004, Per-emb 25, PER 04</td><td>WL</td></tr><tr><td>6</td><td>03 27 39.09</td><td>+30 13 03.0</td><td>Per</td><td>235</td><td>6.6</td><td>1.3</td><td>48</td><td>I</td><td>L1455-IRS1, I03245+3002, Per-emb 17</td><td>D</td></tr><tr><td>7</td><td>03 28 00.40</td><td>+30 08 01.3</td><td>Per</td><td>235</td><td>0.3</td><td>6.3</td><td>236</td><td>I</td><td>L1455-IRS3, I03249+2957, Per-emb 46</td><td>D</td></tr><tr><td>8</td><td>03 28 37.09</td><td>+31 13 30.7</td><td>Per</td><td>235</td><td>11.1</td><td>0.6</td><td>84</td><td>I</td><td>NGC1333 I1, Per-emb 35, PER 05</td><td>WL</td></tr><tr><td>9</td><td>03 28 55.56</td><td>+31 14 36.6</td><td>Per</td><td>235</td><td>36.8</td><td>0.5</td><td>50</td><td>0</td><td>NGC1333 I2A, Per-emb 27</td><td>WH</td></tr><tr><td>10</td><td>03 28 57.36</td><td>+31 14 15.7</td><td>Per</td><td>235</td><td>7.1</td><td>...</td><td>82</td><td>I</td><td>NGC1333 I2B, Per-emb 36, PER 06</td><td>WL</td></tr><tr><td>11</td><td>03 29 00.52</td><td>+31 12 00.7</td><td>Per</td><td>235</td><td>0.7</td><td>3.9</td><td>37</td><td>0</td><td>HRF 65, Per-emb 3, PER 07</td><td>WL</td></tr><tr><td>12</td><td>03 29 01.57</td><td>+31 20 20.7</td><td>Per</td><td>235</td><td>16.9</td><td>1.3</td><td>129</td><td>I</td><td>HH 12, Per-emb 54, PER 08</td><td>WL</td></tr><tr><td>13</td><td>03 29 07.76</td><td>+31 21 57.2</td><td>Per</td><td>235</td><td>22.7</td><td>...</td><td>129</td><td>I</td><td>I03260+3111(W), Per-emb 50, PER 09</td><td>WL</td></tr><tr><td>14</td><td>03 29 10.50</td><td>+31 13 31.0</td><td>Per</td><td>235</td><td>9.1</td><td>3.0</td><td>34</td><td>0</td><td>NGC1333 I4A, Per-emb 12</td><td>WH</td></tr><tr><td>15</td><td>03 29 10.68</td><td>+31 18 20.5</td><td>Per</td><td>235</td><td>6.0</td><td>2.2</td><td>47</td><td>0</td><td>HRF 46, Per-emb 21, PER 10</td><td>WL</td></tr><tr><td>16</td><td>03 29 12.04</td><td>+31 13 01.5</td><td>Per</td><td>235</td><td>4.6</td><td>4.0</td><td>28</td><td>0</td><td>NGC1333 I4B, Per-emb 13</td><td>WH</td></tr><tr><td>17</td><td>03 29 13.52</td><td>+31 13 58.0</td><td>Per</td><td>235</td><td>1.1</td><td>8.7</td><td>31</td><td>0</td><td>NGC1333 I4C, Per-emb 14, PER 12</td><td>WL</td></tr><tr><td>18</td><td>03 29 51.82</td><td>+31 39 06.1</td><td>Per</td><td>235</td><td>0.7</td><td>5.0</td><td>40</td><td>0</td><td>I03267+3128, Per-emb 9, PER 13</td><td>WL</td></tr><tr><td>19</td><td>03 30 15.12</td><td>+30 23 49.2</td><td>Per</td><td>235</td><td>1.8</td><td>1.6</td><td>88</td><td>I</td><td>I03271+3013, Per-emb 34, PER 14</td><td>WL</td></tr><tr><td>20</td><td>03 31 20.96</td><td>+30 45 30.2</td><td>Per</td><td>235</td><td>1.6</td><td>5.8</td><td>36</td><td>0</td><td>I03282+3035, Per-emb 5, PER 15</td><td>WL</td></tr><tr><td>21</td><td>03 32 17.95</td><td>+30 49 47.6</td><td>Per</td><td>235</td><td>1.1</td><td>13.3</td><td>29</td><td>0</td><td>I03292+3039, Per-emb 2, PER 16</td><td>WL</td></tr><tr><td>22</td><td>03 33 12.85</td><td>+31 21 24.1</td><td>Per</td><td>235</td><td>4.5</td><td>0.5</td><td>349</td><td>I</td><td>I03301+3111, Bolo76, Per-emb 64</td><td>D</td></tr><tr><td>23</td><td>03 33 14.40</td><td>+31 07 10.9</td><td>Per</td><td>235</td><td>0.2</td><td>...</td><td>71</td><td>I</td><td>B1 SMM3, Per-emb 6, PER 17</td><td>WL</td></tr><tr><td>24</td><td>03 33 16.45</td><td>+31 06 52.5</td><td>Per</td><td>235</td><td>0.5</td><td>...</td><td>38</td><td>0</td><td>B1 d, Per-emb 10, PER 18</td><td>WL</td></tr><tr><td>25</td><td>03 33 16.66</td><td>+31 07 55.2</td><td>Per</td><td>235</td><td>1.5</td><td>0.4</td><td>113</td><td>I</td><td>B1 a, I03301+3057, Per-emb 40</td><td>D</td></tr><tr><td>26</td><td>03 33 17.85</td><td>+31 09 32.0</td><td>Per</td><td>235</td><td>3.2</td><td>0.2</td><td>46</td><td>0</td><td>B1 c, Per-emb 29</td><td>D</td></tr><tr><td>27</td><td>03 33 27.28</td><td>+31 07 10.2</td><td>Per</td><td>235</td><td>1.1</td><td>1.7</td><td>93</td><td>I</td><td>B1 SMM11, Per-emb 30, PER 19</td><td>WL</td></tr><tr><td>28</td><td>03 43 56.53</td><td>+32 00 52.9</td><td>Per</td><td>235</td><td>2.2</td><td>6.3</td><td>27</td><td>0</td><td>HH 211 MMS, Per-emb 1, PER 20</td><td>WL</td></tr><tr><td>29</td><td>03 43 56.85</td><td>+32 03 04.6</td><td>Per</td><td>235</td><td>1.9</td><td>3.8</td><td>35</td><td>0</td><td>IC348 MMS/SW, Per-emb 11, PER 21</td><td>WL</td></tr><tr><td>30</td><td>03 44 34.94</td><td>+32 01 36.1</td><td>Per</td><td>235</td><td>2.4</td><td>3.4</td><td>45</td><td>0</td><td>IC348 a, Per-emb 8, PER 22</td><td>WL</td></tr><tr><td>31</td><td>04 04 42.9</td><td>+26 18 56.3</td><td>Tau</td><td>140</td><td>3.5</td><td>0.7</td><td>248</td><td>I</td><td>L1489</td><td>D, WH</td></tr><tr><td>32</td><td>04 19 58.4</td><td>+27 09 57.0</td><td>Tau</td><td>140</td><td>1.5</td><td>3.3</td><td>136</td><td>I</td><td>I04169+2702, TAU 01</td><td>WL</td></tr><tr><td>33</td><td>04 21 11.4</td><td>+27 01 09.0</td><td>Tau</td><td>140</td><td>0.5</td><td>0.8</td><td>282</td><td>I</td><td>I04181+2654A, TAU 02</td><td>WL</td></tr><tr><td>34</td><td>04 21 56.9</td><td>+15 29 45.9</td><td>Tau</td><td>140</td><td>0.1</td><td>2.0</td><td>15</td><td>0</td><td>IRAM 04191+1522</td><td>D</td></tr><tr><td>35</td><td>04 22 00.6</td><td>+26 57 32.0</td><td>Tau</td><td>140</td><td>0.4</td><td>0.2</td><td>196</td><td>II</td><td>FS Tau B, TAU 03</td><td>WL</td></tr><tr><td>36</td><td>04 27 02.6</td><td>+26 05 30.0</td><td>Tau</td><td>140</td><td>1.4</td><td>1.5</td><td>161</td><td>I</td><td>DG Tau B, TAU 04</td><td>WL</td></tr><tr><td>37</td><td>04 27 57.3</td><td>+26 19 18.0</td><td>Tau</td><td>140</td><td>0.6</td><td>2.7</td><td>80</td><td>I</td><td>I04248+2612 AB, TAU 06</td><td>WL</td></tr><tr><td>38</td><td>04 29 30.0</td><td>+24 39 55.0</td><td>Tau</td><td>140</td><td>0.6</td><td>0.2</td><td>169</td><td>II</td><td>I04264+2433, TAU 07</td><td>WL</td></tr><tr><td>39</td><td>04 31 34.1</td><td>+18 08 04.9</td><td>Tau</td><td>140</td><td>22.9</td><td>0.7</td><td>108</td><td>I</td><td>L1551 IRS5</td><td>D</td></tr><tr><td>40</td><td>04 35 35.3</td><td>+24 08 19.0</td><td>Tau</td><td>140</td><td>1.0</td><td>1.7</td><td>82</td><td>II</td><td>I04325+2402 A, TAU 09</td><td>WL</td></tr><tr><td>41</td><td>04 39 53.9</td><td>+26 03 09.8</td><td>Tau</td><td>140</td><td>1.6</td><td>3.1</td><td>79</td><td>I</td><td>L1527, I04368+2557</td><td>D, WH</td></tr><tr><td>42</td><td>04 39 13.9</td><td>+25 53 20.6</td><td>Tau</td><td>140</td><td>4.0</td><td>0.5</td><td>151</td><td>I</td><td>TMR 1, I04361+2547 AB</td><td>D, WH</td></tr><tr><td>43</td><td>04 39 35.0</td><td>+25 41 45.5</td><td>Tau</td><td>140</td><td>2.6</td><td>0.8</td><td>189</td><td>I</td><td>TMC 1A, I04365+2535</td><td>D, WH</td></tr><tr><td>44</td><td>04 41 12.7</td><td>+25 46 35.9</td><td>Tau</td><td>140</td><td>0.7</td><td>3.0</td><td>161</td><td>I</td><td>TMC 1, I04381+2540</td><td>D, WH</td></tr><tr><td>45</td><td>08 25 43.9</td><td>-51 00 36.0</td><td>Core</td><td>450</td><td>26.5</td><td>1.5</td><td>107</td><td>I</td><td>HH 46</td><td>WH</td></tr><tr><td>46</td><td>11 06 47.0</td><td>-77 22 32.4</td><td>Cha</td><td>178</td><td>2.0</td><td>0.1</td><td>54</td><td>0</td><td>Ced110 IRS4</td><td>WH</td></tr><tr><td>47</td><td>11 09 28.51</td><td>-76 33 28.4</td><td>Cha</td><td>150</td><td>1.6</td><td>...</td><td>189</td><td>II</td><td>ISO-Chal 192, CaINa2, CHA 01</td><td>WL</td></tr><tr><td>48</td><td>12 01 36.3</td><td>-65 08 53.0</td><td>Core</td><td>200</td><td>11.4</td><td>2.5</td><td>45</td><td>0</td><td>BHR71</td><td>D, WH</td></tr><tr><td>49</td><td>12 53 17.23</td><td>-77 07 10.7</td><td>Cha</td><td>178</td><td>28.3</td><td>0.2</td><td>605</td><td>II</td><td>DK Cha, I12496-7650</td><td>D</td></tr><tr><td>50</td><td>12 59 06.58</td><td>-77 07 39.9</td><td>Cha</td><td>178</td><td>1.8</td><td>0.6</td><td>236</td><td>I</td><td>ISO-ChalII 28, CHA 02</td><td>WL</td></tr><tr><td>51</td><td>15 43 01.29</td><td>-34 09 15.4</td><td>Lup</td><td>130</td><td>1.3</td><td>1.5</td><td>51</td><td>0</td><td>I15398-3359</td><td>WH</td></tr><tr><td>52</td><td>16 26 21.48</td><td>-24 23 04.2</td><td>Oph</td><td>125</td><td>10.6</td><td>0.2</td><td>172</td><td>I</td><td>GSS30 IRS1, Elias 21, Oph-emb 8</td><td>D</td></tr><tr><td>53</td><td>16 26 25.80</td><td>-24 24 28.8</td><td>Oph</td><td>125</td><td>3.3</td><td>4.3</td><td>27</td><td>0</td><td>VLA 1623, Oph-emb 3</td><td>D</td></tr><tr><td>54</td><td>16 26 44.2</td><td>-24 34 48.4</td><td>Oph</td><td>125</td><td>1.6</td><td>1.8</td><td>236</td><td>I</td><td>WL 12</td><td>D</td></tr><tr><td>55</td><td>16 26 59.1</td><td>-24 35 03.3</td><td>Oph</td><td>125</td><td>4.3</td><td>...</td><td>69</td><td>II+PDR?</td><td>WL 22, ISO-Oph 90, OPH 01</td><td>WL</td></tr><tr><td>56</td><td>16 27 09.36</td><td>-24 37 18.4</td><td>Oph</td><td>125</td><td>15.2</td><td>0.2</td><td>310</td><td>I</td><td>Elias 29, WL 15, Oph-emb 16</td><td>D</td></tr><tr><td>57</td><td>16 27 28.1</td><td>-24 39 33.4</td><td>Oph</td><td>125</td><td>5.1</td><td>...</td><td>213</td><td>I</td><td>IRS 44, Oph-emb 13</td><td>D</td></tr><tr><td>58</td><td>16 27 29.4</td><td>-24 39 16.1</td><td>Oph</td><td>125</td><td>0.5</td><td>...</td><td>352</td><td>I</td><td>IRS 46</td><td>D</td></tr><tr><td>59</td><td>16 31 35.76</td><td>-24 01 29.2</td><td>Oph</td><td>125</td><td>1.5</td><td>3.0</td><td>287</td><td>I</td><td>IRS 63, Oph-emb 17</td><td>D</td></tr><tr><td>60</td><td>16 32 00.96</td><td>-24 56 42.7</td><td>Oph</td><td>125</td><td>8.6</td><td>0.1</td><td>80</td><td>I</td><td>Oph-emb 10, OPH 02</td><td>WL</td></tr><tr><td>61</td><td>16 34 29.3</td><td>-15 47 01.4</td><td>Core</td><td>125</td><td>2.4</td><td>0.5</td><td>333</td><td>I</td><td>RNO 91</td><td>WH</td></tr><tr><td>62</td><td>16 46 58.27</td><td>-09 35 19.8</td><td>Sco</td><td>125</td><td>0.5</td><td>0.6</td><td>201</td><td>II</td><td>L260 SMM1, SCO 01</td><td>WL</td></tr><tr><td>63</td><td>18 17 29.9</td><td>-04 39 39.5</td><td>Core</td><td>200</td><td>11.1</td><td>0.5</td><td>56</td><td>0</td><td>L 483 MM</td><td>WH</td></tr></tbody></table>
<table><caption>**Table 1**
(Continued)</caption><thead><tr><th>ID</th><th>R.A. (J2000)<br>(h m s)</th><th>Decl. (J2000)<br>(°′′)</th><th>Cloud</th><th>D<sup>a</sup><br>(pc)</th><th>L<sub>bol</sub><br>(L<sub>☉</sub>)</th><th>L<sub>submm</sub><br>L<sub>bol</sub> (%)</th><th>T<sub>bol</sub><br>(K)</th><th>Class</th><th>Other Names</th><th>Survey<sup>b</sup></th></tr></thead><tbody><tr><td>64</td><td>18 29 03.82</td><td>-01 39 01.5</td><td>Aqu</td><td>436</td><td>2.6</td><td>11.8</td><td>24</td><td>0</td><td>Aqu-MM2, AQU 01</td><td>WL</td></tr><tr><td>65</td><td>18 29 08.60</td><td>-01 30 42.8</td><td>Aqu</td><td>436</td><td>9.0</td><td>7.8</td><td>33</td><td>0</td><td>Aqu-MM4, I18265-0132, AQU 02</td><td>WL</td></tr><tr><td>66</td><td>18 29 49.56</td><td>+01 15 21.9</td><td>Ser</td><td>429</td><td>108.7</td><td>1.5</td><td>39</td><td>0</td><td>Ser-emb 6, Ser SMM1, FIRS1</td><td>WH</td></tr><tr><td>67</td><td>18 29 56.7</td><td>+01 13 17.2</td><td>Ser</td><td>429</td><td>13.6</td><td>2.5</td><td>28</td><td>0</td><td>Ser SMM4</td><td>D, WH</td></tr><tr><td>68</td><td>18 29 59.3</td><td>+01 14 01.7</td><td>Ser</td><td>429</td><td>27.5</td><td>0.3</td><td>37</td><td>0</td><td>Ser SMM3</td><td>D, WH</td></tr><tr><td>69</td><td>18 29 37.70</td><td>-01 50 57.8</td><td>SerS</td><td>436</td><td>17.4</td><td>3.9</td><td>46</td><td>0</td><td>SerpS-MM1, SERS 01</td><td>WL</td></tr><tr><td>70</td><td>18 30 04.13</td><td>-02 03 02.1</td><td>SerS</td><td>436</td><td>73.2</td><td>4.6</td><td>34</td><td>0</td><td>SerpS-MM18, SERS 02</td><td>WL</td></tr><tr><td>71</td><td>18 30 25.10</td><td>-01 54 13.4</td><td>Aqu</td><td>436</td><td>3.5</td><td>5.3</td><td>246</td><td>II</td><td>Aqu-MM6, I18278-0156, AQU 03</td><td>WL</td></tr><tr><td>72</td><td>18 30 28.63</td><td>-01 56 47.7</td><td>Aqu</td><td>436</td><td>6.5</td><td>4.5</td><td>320</td><td>I</td><td>Aqu-MM7, I18278-0158, AQU 04</td><td>WL</td></tr><tr><td>73</td><td>18 30 29.03</td><td>-01 56 05.4</td><td>Aqu</td><td>436</td><td>2.4</td><td>9.2</td><td>37</td><td>0</td><td>Aqu-MM10, AQU 05</td><td>WL</td></tr><tr><td>74</td><td>18 30 49.94</td><td>-01 56 06.1</td><td>Aqu</td><td>436</td><td>1.3</td><td>8.2</td><td>40</td><td>0</td><td>Aqu-MM14, AQU 06</td><td>WL</td></tr><tr><td>75</td><td>18 31 09.42</td><td>-02 06 24.5</td><td>W40</td><td>436</td><td>13.3</td><td>7.4</td><td>40</td><td>0+PDR</td><td>W40-MM3, W40 01</td><td>WL</td></tr><tr><td>76</td><td>18 31 10.36</td><td>-02 03 50.4</td><td>W40</td><td>436</td><td>32.6</td><td>3.7</td><td>46</td><td>0</td><td>W40-MM5, W40 02</td><td>WL</td></tr><tr><td>77</td><td>18 31 46.54</td><td>-02 04 22.5</td><td>W40</td><td>436</td><td>8.3</td><td>20.6</td><td>15</td><td>PS?+PDR</td><td>W40-MM26, W40 03</td><td>WL</td></tr><tr><td>78</td><td>18 31 46.78</td><td>-02 02 19.9</td><td>W40</td><td>436</td><td>6.1</td><td>9.4</td><td>16</td><td>PS?+PDR</td><td>W40-MM27, W40 04</td><td>WL</td></tr><tr><td>79</td><td>18 31 47.90</td><td>-02 01 37.2</td><td>W40</td><td>436</td><td>5.9</td><td>27.3</td><td>14</td><td>PS?+PDR</td><td>W40-MM28, W40 05</td><td>WL</td></tr><tr><td>80</td><td>18 31 57.24</td><td>-02 00 27.7</td><td>W40</td><td>436</td><td>4.1</td><td>2.2</td><td>33</td><td>PS?+PDR</td><td>W40-MM34, W40 06</td><td>WL</td></tr><tr><td>81</td><td>18 32 13.36</td><td>-01 57 29.6</td><td>W40</td><td>436</td><td>3.6</td><td>3.3</td><td>36</td><td>0</td><td>W40-MM36, W40 07</td><td>WL</td></tr><tr><td>82</td><td>19 01 48.03</td><td>-36 57 22.2</td><td>CrA</td><td>130</td><td>1.7</td><td>0.8</td><td>209</td><td>I</td><td>RCrA IRS 5A</td><td>D</td></tr><tr><td>83</td><td>19 01 48.47</td><td>-36 57 14.9</td><td>CrA</td><td>130</td><td>0.7</td><td>1.9</td><td>63</td><td>0</td><td>RCrA IRS 5N</td><td>D</td></tr><tr><td>84</td><td>19 01 55.33</td><td>-36 57 22.4</td><td>CrA</td><td>130</td><td>9.1</td><td>1.0</td><td>79</td><td>I</td><td>RCrA IRS 7A (+ SMM 1C)</td><td>D</td></tr><tr><td>85</td><td>19 01 56.42</td><td>-36 57 28.3</td><td>CrA</td><td>130</td><td>4.6</td><td>2.1</td><td>89</td><td>I</td><td>RCrA IRS 7B</td><td>D</td></tr><tr><td>86</td><td>19 02 58.67</td><td>-37 07 35.9</td><td>CrA</td><td>130</td><td>2.4</td><td>2.2</td><td>55</td><td>0</td><td>CrA-44, IRAS 32c, CRA01</td><td>WL</td></tr><tr><td>87</td><td>19 17 53.7</td><td>+19 12 20.0</td><td>Core</td><td>300</td><td>3.8</td><td>2.0</td><td>65</td><td>0</td><td>L 723 MM</td><td>WH</td></tr><tr><td>88</td><td>19 37 00.9</td><td>+07 34 09.6</td><td>Core</td><td>106</td><td>0.8</td><td>5.0</td><td>33</td><td>0</td><td>B335</td><td>D</td></tr><tr><td>89</td><td>20 39 06.3</td><td>+68 02 16.0</td><td>Core</td><td>325</td><td>6.7</td><td>3.3</td><td>35</td><td>0</td><td>L1157</td><td>D</td></tr><tr><td>90</td><td>21 24 07.5</td><td>+49 59 09.0</td><td>Core</td><td>200</td><td>0.3</td><td>11.1</td><td>47</td><td>0</td><td>L1014</td><td>D</td></tr></tbody></table>

Notes. Numbered Per-emb and Oph-emb names come from Enoch et al. (2009). Aqu, SerpS, and W40 numbered names are from Maurv et al. (2011). Chamaeleon names come from Spezzi et al. (2013) and Winston et al. (2012). The final entries are other names used by the WILL program, and therefore also in the Herschel archive.

a Distances come from van Dishoeck et al. (2011) for the WISH sources, Green et al. (2013) for the DIGIT sources, and Mottram et al. (2017) for the WILL sources with the exception of sources in Serpens, which have been updated to use the latest distance by Ortiz-León et al. (2017). PS refers to possible pre-stellar cores and PDR to photodissociation regions.

b Survey names refer to: D—DIGIT, WH—WISH, and WL—WILL programs on Herschel.

targets, increasing the sample to 90 sources in total (for details, see Table 1).

Most of the sources are located in the Perseus (30 sources), the Aquila Rift complex (seven sources in W40, six sources in Aquila, and two sources in Serpens South), and Taurus (12 sources). The remaining sources are from Ophiuchus (nine sources), Corona Australis (five sources), Serpens Main (three sources), and other molecular clouds. All protostars are located at distances ≲450 pc (for distance references see Kristensen et al. 2012; Green et al. 2013; Mottram et al. 2017).

The selection procedures for the WISH and DIGIT sources are discussed in detail in van Dishoeck et al. (2011) and Green et al. (2013), with a general rule that all of them are well-known and extensively studied protostars. The WILL sources were selected based on unbiased mid-IR and millimeter continuum observations with *Spitzer* and various ground-based telescopes (Mottram et al. 2017).

The sources are divided into classes based on the shapes of their spectral energy distributions (SEDs), constructed using flux densities obtained with *Herschel*-PACS (see Karska et al. 2013 for WISH, Green et al. 2016 and Manoj et al. 2016 for DIGIT, and Mottram et al. 2017 for WILL). Sources with bolometric temperatures $T_{bol} \le 70$ K are classified as Class 0, and those with $70 \text{ K} < T_{bol} < 650$ K are classified as

Class I. However, 12 sources in the original WILL sample were re-classified as either Class II or pre-stellar, based on the absence of an entrained molecular outflow (identified by broad line wings in CO 3–2 maps and HIFI H$_2$O and CO 10-9 spectra), as well as on the morphology and intensity of HCO$^+$ 4–3 and C$^{18}$O 3–2 emission (see Mottram et al. 2017 and the description of the method in van Kempen et al. 2009b and Carney et al. 2016). Additionally, in five out of those 12 sources, as well as one Class 0 source, Mottram et al. (2017) detected a narrow, bright CO 10–9 emission indicative of PDRs that are not associated with young stellar objects. Excluding pre-stellar, Class II, and PDRs, the final sample consists of 42 Class 0 and 35 Class I sources, covering a broad range of bolometric luminosities, $L_{bol}$ (see Figure 1). The comparison with the global *Spitzer* Gould Belt sample shows that the sample here is representative for the Class 0 and young Class I sources (Mottram et al. 2017).

We note that in the three sources (ID numbers 4, 82, 85), the separation of protostars is large enough to decompose the continuum emission from PACS spectral maps into distinct objects (see Lee et al. 2013 for L1448 MM and Lindberg et al. 2014 for sources in Corona Australis). The rest of the sources are treated as single objects, even though some of them are close multiples (e.g., Tobin et al. 2016b). The impact of this
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Distribution of bolometric luminosities and temperatures for the Class 0 (in red) and Class I (in blue) protostars. Different symbols show objects observed as part of the WISH survey (filled circles), the DIGIT survey (filled diamonds), and the WILL survey (open squares). Sources observed as part of both WISH and DIGIT surveys are shown only once, as filled diamonds.</figcaption></figure>

treatment depends on the evolutionary stage and relative brightness of the respective components. Murillo et al. (2016) distinguish three cases: (i) the combined SED is simply doubled when the two components have similar SEDs; (ii) the SED appears odd and double-peaked when the two components are non-coeval; (iii) the brightest component dominates the combined SED when the other one is notably dimmer and younger. Similar cases are expected to apply for the emission lines. However, without a strong indication that the sources are co-eval, the calculated luminosities cannot be properly corrected (Murillo et al. 2016), and the sources are therefore treated as single sources in the following.

## 2.2. Observations and Data Reduction

Single-footprint spectral maps of all sources were obtained with the PACS instrument onboard Herschel. Each map consists of 25 spatial pixels (spaxels) of $9''_4 \times 9''_4$, arranged in a $5 \times 5$ array with a total field of view of $\sim 47'' \times 47''$. Each spaxel contains a (sub-)spectrum observed in the first (red) or second (blue) order, within the wavelength ranges of 102–210 µm and 51–105 µm, respectively. Due to flux calibration issues at the extreme ends of the spectra, the ranges from $\sim 55$ to 100 µm and 104 to 190 µm are used in the analysis. The spectral resolving power increases with wavelength, from about 1000 to 2000 (corresponding to velocity resolutions of $\sim 140$ to $320 \text{ km s}^{-1}$) in the first order and from about 1500 to 3000 ($\sim 100$ to $210 \text{ km s}^{-1}$) in the second order.

Two main observing schemes were used: line spectroscopy mode for the WISH and WILL sources, and range spectroscopy mode for the DIGIT sources and four sources from the WISH survey (Serpens SMM1 and NGC1333 IRAS 4A, 4B, and 2A). The line spectroscopy mode yields observations of small spectral regions ($\Delta\lambda \sim 0.5–2 \mu\text{m}$) around selected lines and is particularly suited for deep integrations. The range spectroscopy mode provides the full spectrum from $\sim 50$ to $210 \mu\text{m}$, but the spectral sampling within a resolution element is about 3–4 times coarser than in the line spectroscopy mode. For both

schemes, the chopping/nodding observing mode from the source was used to subtract the background emission within 6'.

Data reduction for both observing modes was performed with the Herschel Interactive Processing Environment (HIPE, Ott 2010) version 13. The flux was normalized to the telescopic background and calibrated using observations of Neptune. Spectral flatfielding within HIPE was used to increase the signal-to-noise ratio (S/N) (for details, see Herczeg et al. 2012; Green et al. 2013; Sturm et al. 2013). The overall flux uncertainty is about 20%, based on cross-comparisons of sources in common within our programs.

A 1D spectrum is obtained for each source by summing a custom number of spaxels chosen after investigation of the 2D spectral maps (Karska et al. 2013), using the technique applied to the “CDF” (COPS-DIGIT-FOOSH protostar) archive (Green et al. 2016). This archive is freely available as a User Provided Data Product in the Herschel Science Archive.<fnref n="15" /> Most notably, the 2016 update in PACS spectroscopy includes a correction for pointing and jitter offsets during observations.

For sources with extended line emission, the co-addition of spaxels with detected emission increases the S/N, smooths the continuum, and enables correction for significant differences in beam sizes over the wide spectral range covered by PACS. For sources with point-like emission in all lines, only the central spaxel spectrum is used, but the line fluxes are multiplied by the wavelength-dependent instrumental correction factors ($\sim 1.4$ at $70 \mu\text{m}$ and $\sim 2.3$ at $180 \mu\text{m}$; see PACS Observer’s Manual).<fnref n="16" />

Because the lines are spectrally unresolved (except [O I], see Section 3.3), line fluxes are calculated by fitting Gaussians to the final 1D spectrum. Single Gaussians are used for well-isolated lines, and double or triple Gaussians for close-by lines, including blends. The line width of the Gaussians is fixed to the instrumental value for unresolved lines—except for the [O I] line at $63 \mu\text{m}$, which in several sources shows high-velocity wings (van Kempen et al. 2010b; Karska et al. 2013; Riviere-Marichalar et al. 2016). In that case, integration and/or broad Gaussian fitting are applied. All Gaussian fits were visually inspected to avoid possible confusion.

On the other hand, the analysis of spatial extent of line and continuum emission required spaxel-by-spaxel information about the fluxes (see Section 3.2). For that purpose, we used the CDF archive (Green et al. 2016), where the line-fitting process was automated and performed for the WISH and DIGIT sources.<fnref n="17" /> The main steps of the process included taking the lines from a pre-compiled database, establishing the threshold for detection, and then generating tables of line flux, width, centroid, and uncertainties for every detected line, along with an upper limit to the flux for every undetected line. After producing a line detection database, the integrity of the line fits was tested in order to better characterize the S/N and decouple any blended lines. We performed a similar automatic line fitting for the WILL sources.

We note that the line spectra for protostars analyzed here have been presented in previous survey papers: in Figures 1 and 2 of Karska et al. 2013 (the WISH survey), Figures 11–13 of Green et al. (2013) (L1014, L1551 IRS5, and Elias 29), and in Figure 4 of Mottram et al. (2017) (the WILL survey). Mini-surveys or individual sources have been analyzed by van

<footnote n="15">¹⁵ https://www.cosmos.esa.int/web/herschel/user-provided-data-products</footnote>

<footnote n="16">¹⁶ http://herschel.esac.esa.int/Docs/PACS/html/pacs_om.html</footnote>

<footnote n="17">¹⁷ https://www.cosmos.esa.int/web/herschel/user-provided-data-products</footnote>
Kempen et al. (2010b) (HH 46), van Kempen et al. (2010a) (DK Cha), Herczeg et al. (2012) (NGC1333 I4B), Lindberg et al. (2014) (CrA sources), Lee et al. (2013) (L1448-MM), Lee et al. (2014a) (Taurus sources), Je et al. (2015) (GSS30 IRS1), and Yang et al. (2017) (BHR 71). Any differences between the sources' physical parameters ($L_{bol}$, $T_{bol}$) and line fluxes given in those papers and the current work stem from the adopted distances to the sources and re-reduction of the spectra with the newer version of HIPE.

## 3. Results

### 3.1. Line Detections

PACS spectra of low-mass protostars show exclusively rotational lines of CO, H₂O, and OH, as well as forbidden transitions of [O I] and [C II]. CO, H₂O, and OH lines are seen in emission, consistent with velocity-resolved profiles obtained with HIFI, which are dominated by emission components and only very narrow absorptions from the envelope (Mottram et al. 2017). The exception in PACS data is the H₂O 2₁₂–1₀₁ line at 179 µm, seen in absorption in a few fields with multiple outflows, probably because of the significant extent of the emission and possible contamination of the off position.

The [O I] lines are seen in emission, in the majority of cases, except where the off position is contaminated due to extended emission from PDRs associated with the cloud surface. The [C II] line at 158 µm is even more sensitive to the cloud emission, and is often also detected in the nod positions, leading to the appearance of negative emission (Benz et al. 2016). In total, the CO 16–15 line targeted in the WISH, DIGIT, and WILL programs is detected in 64 out of 77 sources (Class II, PS, and PDRs excluded), the OH doublet 2Π₃/₂ J = 7/2 – 5/2 at 84 µm in 57 sources, and the H₂O 2₁₂–1₀₁ line in 49 sources. Atomic emission associated with a YSO is detected in at least<fnref n="18" /> 65 sources in the [O I] 63 µm line and in 10 sources in the [C II] line.

In addition to the CO 16–15 ($E_{up}$ = 752 K) and H₂O 2₁₂–1₀₁ ($E_{up}$ = 114 K) lines, higher-excitation transitions of these molecules are also detected. CO transitions with upper energies above 2400 K ($J_{up}$ > 29) are detected in 35 objects, with transitions up to $J = 49 – 48$ detected in the most remarkable Class 0 source, NGC1333 IRAS4B (see Herczeg et al. 2012). The H₂O 8₁₈–7₀₇ line at 63 µm ($E_{up}$ ~ 1000 K) is seen in 25 objects, where—in all cases—the highly excited ($J_{up}$ ≳ 30) CO emission is also present.

Self-absorption may have a small effect on the H₂O 2₁₂–1₀₁ fluxes (Mottram et al. 2014), but not on the higher-excitation H₂O lines, nor the CO and OH lines (Wampfler et al. 2011; Kristensen et al. 2017b). The OH lines primarily trace the outflow and their self-absorption is not expected to be significant (Wampfler et al. 2011), but the ground-state lines at 119 µm have not been accessible to HIFI. The [O I] line at 63 µm shows some self-absorption toward more massive sources (Leurini et al. 2015), but the same is not expected for the low-mass low-luminosity sources (Kristensen et al. 2017a). Thus, self-absorption is not likely to play an important role in the analysis presented here.

The detections and line fluxes of various species are related to each other (see Figure 2). There is a significant correlation, at

~6σ, between the flux in the CO 16–15 lines and the H₂O 2₁₂–1₀₁ lines, as well as the CO 16–15 lines and the OH 84.6 µm lines. A weaker, yet significant correlation is obtained between the CO and [O I] line, OH and [O I] line, and H₂O and OH lines (~4–5σ). The H₂O and [O I] lines correlate at the lowest level, 3.6σ.

Class 0 and Class I sources show similar distributions in Figure 2, except that the OH lines are brighter for the Class I sources with respect to CO and H₂O lines (see CO–OH and H₂O–OH plots). The only outlier is L1448 C(S), which contains ice features that indicate a dense envelope (Lee et al. 2013). Similar correlation strengths between the OH and [O I] lines in Class 0/I sources suggest that the fraction of OH associated with the component traced by the [O I] line increases for more evolved sources. The different origin of the [O I] emission is further supported by its strong correlation with $L_{bol}$, whereas molecular tracers correlate more strongly with the envelope mass (Mottram et al. 2017).

In summary, rich molecular line emission is seen in ~70% of the targeted sources, allowing a statistical analysis of the largest sample of protostars so far. In Section 2.2, multiple lines of molecular species are used to constrain the excitation of molecules and to calculate the cooling budget of the gas in the far-infrared.

### 3.2. Spatial Extent of Line Emission

Fully sampled maps of far-infrared line emission exist for a handful of Class 0/I protostars in a few lines and show extended emission along the outflow direction (Nisini et al. 2010, 2015; Herczeg et al. 2012). While these observations clearly associate the emission in H₂O and [O I] with jets and outflows, statistical properties of the far-IR emitting gas could not be established. Thus, the single footprint maps from PACS (FOV ~ 47 × 47", see Section 2) provide a unique data set to link the emission in various species and to test whether the extended far-IR emission is indeed common among protostars.

In order to study the prevalence and shape of any extended line emission, we remove the point-source emission associated with the continuum peaks, i.e., the position(s) of the protostar (s). For that reason, we first calculate the line (or continuum) emission from the point sources located on the map and then subtract them from the entire PACS map after convolution with the simulated point-spread function (PSF) of Herschel (the POMAC method; see Section 3.1 in Lindberg et al. 2014). The residual emission is thus not associated with any known point source, and likely originates in extended structures. Because the PACS maps are sparse, the method relies on predefined source coordinates (e.g., from infrared photometry or sub-millimeter interferometric observations) and is sensitive to pointing errors. Comparison of the residual line and continuum emission is thus useful to double-check whether the pattern of emission differs and truly indicates that line emission extends beyond the continuum peaks.

Figure 3 illustrates the above procedure for the case of Elias 29. The observed line emission (left column) appears to be extended in all lines, but that is due to the compact emission from the point source being enlarged and distorted in shape by the non-circular PSF of Herschel (central column). Subtraction of the simulated emission yields negligible residuals in the CO, H₂O, and OH lines. The emission is extended only in the [O I] line, where the residual emission shows two peaks corresponding to the blue and red outflow lobes (right column; see

<footnote n="18">¹⁸ We exclude the cases where we observe significant contamination by the off position or the other outflows.</footnote>
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Top: correlations between the line luminosities in units of $L_\odot$ for the CO 16-15 line and the H$_2$O $2_{12}-1_{01}$ line at 179 µm, the OH line at 84.6 µm, and the [O I] 63 µm line (from left to right). Bottom: correlations between the line luminosities of the H$_2$O line at 179 µm, the [O I] 63 µm line, and the OH line at 84.6 µm, as well as between the [O I] 63 µm line and the OH line at 84.6 µm. Class 0 sources are shown as red circles and Class I sources as blue diamonds. Solid lines show the best power-law fits obtained with a least-squares method. The dashed line shows the weakest correlation, with $\sigma < 4$. Correlation coefficients ($r$), significance of the correlations ($\sigma$), and the number of sources with line detections ($N$) are shown on the plots.</figcaption></figure>

Yıldız et al. 2015 for outflow directions). The continuum emission is point-like in the vicinity of the considered lines (not shown here).

We applied a similar procedure for all sources in our sample and list the sources with extended line emission in at least one species in Table 2. There are 37 sources with the extended [O I] emission at 63 µm, 23 with extended CO emission (typically 14–13 at 186 µm, see Table 2), 19 with extended H$_2$O emission in the $2_{12}-1_{01}$ line at 179 µm, and 8 with extended OH emission at 84.6 µm. These statistics include the sources where the line emission is clearly spatially offset from the continuum and the line emission is likely linked to the outflows (see Figure 19 in Mottram et al. 2017). The remaining sources, where line and continuum emission is well-aligned, may be caused by an off-center location of the source. Thus, the residual extended emission might be a result of imperfect subtraction of the PSF from the maps for this small subset of sources (with ID 39–42, 49, 52, 63).

Patterns of emission are often similar in certain species. Out of 40 sources in Table 2, both CO and H$_2$O emission are extended in 17 objects and not extended in 12 sources. Out of 37 sources with extended [O I] emission, 20 also show extended CO emission. The exceptions are, for example, NGC1333 I4A and I4B, which show very weak and compact

[O I] emission but clearly extended emission in the molecular species. Conversely, there are 13 sources where [O I] is extended, but the CO emission is compact (Figure 3). Many of these sources are located in Taurus and form a uniform group with compact molecular emission and prominent [O I] emission associated with jets (Podio et al. 2012).

The OH emission is typically compact, apart from a few sources with very bright extended emission in H$_2$O and CO (e.g., NGC1333 I4B). As noted in Karska et al. (2013), where a subsample of the sources was analyzed, the OH emission does not resemble the emission in other molecular species. Here, only a few source concurrently show compact [O I] and OH emission and extended H$_2$O and CO (e.g., NGC1333 I4A and B1 c).

Extended emission in at least one species (atomic or molecular) is detected in 19 Class 0, 19 Class I, and 2 Class II sources (see Tables 1 and 2). Thus, there is no clear indication that the evolutionary stage strongly influences the extent of the observed emission in general. However, among the sources that show extended emission in both H$_2$O and CO, 11 out of 17 are Class 0 objects (65%). At the same time, only 5 out of 13 sources with the extended emission seen only in [O I] are Class 0s (38%).
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Spatial extent of line emission in an example source, Elias 29. The panels show (from top to bottom) the line emission in the CO 24–23 line at 108.7 µm, the H₂O 2₁₂–1₀₁ line at 179.5 µm, the OH 84.6 µm line, and the [O I] line at 63 µm. The left column shows the observed line emission in 3σ contours, the central column shows the point-source model using the simulated PSF of Herschel, and the right column shows the residual between the observations and the models. The dashed contours represent negative values. The arrows indicate the directions of the red and blue outflow lobes in CO 3–2 from Yıldız et al. (2015).</figcaption></figure>

In conclusion, extended emission is detected in 40 out of 90 sources (44%). A similar fraction of the sources with extended and compact emission (50%) was seen in the WISH survey alone (Karska et al. 2013). However, only 28% of sources show extended emission in molecular species i.e., excluding

[O I]. The line emission is more often extended in molecular species for the less evolved sources, and in atomic species for the more evolved ones. This is consistent with the idea put forth by Nisini et al. (2015), that the jet becomes more atomic over time.
<table><caption>**Table 2**
Sources with Extended Line and Continuum Emission</caption><thead><tr><th rowspan="2">ID</th><th rowspan="2">Source</th><th colspan="3">H<sub>2</sub>O 179 µm</th><th colspan="3">CO 186 µm</th><th colspan="3">OH 84 µm</th><th colspan="3">[O I] 63 µm</th><th rowspan="2">Remarks</th></tr><tr><th>Line</th><th>Cont</th><th>Align</th><th>Line</th><th>Cont</th><th>Align</th><th>Line</th><th>Cont</th><th>Align</th><th>Line</th><th>Cont</th><th>Align</th></tr></thead><tbody><tr><td>1</td><td>L1448 IRS2<sup>a</sup></td><td>...</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>X</td><td>...</td><td>n</td><td>...</td></tr><tr><td>3</td><td>L1448 C(N)</td><td>?</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td><td>...</td><td>n</td><td>X</td><td>...</td><td>n</td><td>multiple sources</td></tr><tr><td>4</td><td>L1448 C(S)</td><td>?</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>...</td><td>...</td><td>n</td><td>X</td><td>...</td><td>n</td><td>Lee et al. (2013)</td></tr><tr><td>6</td><td>L1455 IRS1</td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td><td>...</td><td>n</td><td>X</td><td>...</td><td>n</td><td>...</td></tr><tr><td>12</td><td>HH12<sup>a</sup></td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td></tr><tr><td>14</td><td>NGC1333 I4A</td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td><td>X</td><td>y</td><td>...</td><td>...</td><td>y</td><td>mispointing</td></tr><tr><td>16</td><td>NGC1333 I4B</td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td><td>?</td><td>n</td><td>Herczeg et al. (2012)</td></tr><tr><td>25</td><td>B1 a</td><td>...</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td><td>...</td><td>...</td><td>X</td><td>...</td><td>n</td><td>...</td></tr><tr><td>26</td><td>B1 c</td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>27</td><td>B1 SMM11<sup>a</sup></td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>X</td><td>...</td><td>n</td><td>...</td></tr><tr><td>28</td><td>HH211 MMS<sup>a</sup></td><td>X</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>...</td><td>...</td><td>...</td><td>X</td><td>...</td><td>n</td><td>...</td></tr><tr><td>29</td><td>IC348 MMS<sup>a</sup></td><td>X</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>...</td><td>...</td><td>...</td><td>X</td><td>...</td><td>n</td><td>...</td></tr><tr><td>30</td><td>IC348 a<sup>a</sup></td><td>...</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>...</td><td>...</td><td>...</td><td>X</td><td>...</td><td>n</td><td>...</td></tr><tr><td>31</td><td>L1489</td><td>...</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>X</td><td>...</td><td>n</td><td>mispointing</td></tr><tr><td>32</td><td>I04169<sup>a</sup></td><td>...</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>...</td><td>...</td><td>y</td><td>X</td><td>...</td><td>n</td><td>...</td></tr><tr><td>33</td><td>I04181<sup>a</sup></td><td>...</td><td>...</td><td>y</td><td>...</td><td>...</td><td>y</td><td>...</td><td>...</td><td>y</td><td>X</td><td>...</td><td>n</td><td>...</td></tr><tr><td>34</td><td>IRAM04191</td><td>...</td><td>...</td><td>y</td><td>...</td><td>...</td><td>y</td><td>...</td><td>...</td><td>y</td><td>X</td><td>...</td><td>n</td><td>...</td></tr><tr><td>36</td><td>DG Tau B<sup>a</sup></td><td>...</td><td>...</td><td>y</td><td>...</td><td>...</td><td>y</td><td>...</td><td>...</td><td>y</td><td>X</td><td>...</td><td>n</td><td>...</td></tr><tr><td>37</td><td>I04248<sup>a</sup></td><td>?</td><td>X</td><td>n</td><td>?</td><td>X</td><td>n</td><td>...</td><td>...</td><td>?</td><td>X</td><td>...</td><td>n</td><td>...</td></tr><tr><td>38</td><td>I04264<sup>a</sup></td><td>...</td><td>...</td><td>y</td><td>...</td><td>...</td><td>y</td><td>...</td><td>...</td><td>y</td><td>X</td><td>...</td><td>n</td><td>...</td></tr><tr><td>39</td><td>L1551 IRS5</td><td>?</td><td>X</td><td>?</td><td>X</td><td>X</td><td>y</td><td>...</td><td>...</td><td>...</td><td>X</td><td>X</td><td>y</td><td>mispointing</td></tr><tr><td>41</td><td>L1527</td><td>X</td><td>X</td><td>y</td><td>X</td><td>X</td><td>y</td><td>...</td><td>X</td><td>n</td><td>X</td><td>X</td><td>y</td><td>mispointing</td></tr><tr><td>42</td><td>TMR1</td><td>X</td><td>X</td><td>y</td><td>X</td><td>X</td><td>y</td><td>X</td><td>X</td><td>y</td><td>X</td><td>X</td><td>y</td><td>mispointing</td></tr><tr><td>43</td><td>TMC1A</td><td>...</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>mispointing</td></tr><tr><td>44</td><td>TMC1</td><td>...</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td><td>...</td><td>...</td><td>X</td><td>...</td><td>n</td><td>weak CO</td></tr><tr><td>45</td><td>HH 46</td><td>...</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>X</td><td>...</td><td>n</td><td>van Kempen et al. (2010b)</td></tr><tr><td>49</td><td>DK Cha</td><td>X</td><td>X</td><td>y</td><td>X</td><td>X</td><td>y</td><td>X</td><td>X</td><td>y</td><td>X</td><td>X</td><td>y</td><td>mispointing</td></tr><tr><td>51</td><td>I15398</td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td><td>X</td><td>y</td><td>X</td><td>X</td><td>n</td><td>mispointing</td></tr><tr><td>52</td><td>GSS30 IRS1</td><td>X</td><td>X</td><td>y</td><td>X</td><td>X</td><td>y</td><td>X</td><td>X</td><td>y</td><td>X</td><td>X</td><td>y</td><td>multiple sources</td></tr><tr><td>53</td><td>VLA1623</td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>multiple sources</td></tr><tr><td>56</td><td>Elias29</td><td>...</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td><td>...</td><td>...</td><td>X</td><td>X</td><td>n</td><td>small CO resid.</td></tr><tr><td>61</td><td>RNO 91</td><td>?</td><td>X</td><td>?</td><td>...</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>X</td><td>X</td><td>y</td><td>cont/line overlap</td></tr><tr><td>63</td><td>L483</td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>v</td><td>...</td><td>X</td><td>n</td><td>X</td><td>X</td><td>y</td><td>cont/line overlap</td></tr><tr><td>64</td><td>Aqu-MM2<sup>a</sup></td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>?</td><td>?</td><td>?</td><td>X</td><td>?</td><td>n</td><td>...</td></tr><tr><td>66</td><td>Ser SMM1</td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>Dionatos et al. (2014)</td></tr><tr><td>67</td><td>Ser SMM3</td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>X</td><td>...</td><td>n</td><td>X</td><td>...</td><td>n</td><td>contamin. by SerSMM6</td></tr><tr><td>68</td><td>Ser SMM4</td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>X</td><td>...</td><td>n</td><td>X</td><td>...</td><td>n</td><td>Dionatos et al. (2013)</td></tr><tr><td>86</td><td>CrA-44<sup>a</sup></td><td>...</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td></tr><tr><td>88</td><td>B335</td><td>...</td><td>X</td><td>n</td><td>...</td><td>X</td><td>n</td><td>...</td><td>...</td><td>...</td><td>X</td><td>...</td><td>n</td><td>...</td></tr><tr><td>89</td><td>L1157</td><td>X</td><td>X</td><td>n</td><td>X</td><td>X</td><td>n</td><td>...</td><td>...</td><td>...</td><td>X</td><td>...</td><td>n</td><td>weak CO</td></tr></tbody></table>

Note. X notes the cases where emission is extended, whereas y/n refers to whether the emission in line and in continuum is aligned (y) or not (n). Non-detection of extended emission is marked with “-.” Question mark (?) is used when the emission is not detected on the map. Sources with detected extended emission in both CO 14–13 and [O I] 63 µm are in boldface.

### 3.3. High-velocity Emission in [O I]

The [O I] 63 µm line often includes emission from a fast jet, which is detectable if the velocity exceeds ~90 km s⁻¹, i.e., the approximate spectral resolution of PACS at this wavelength. The high-velocity emission is produced by an atomic jet that is embedded in the molecular emission (van Kempen et al. 2010b; Nisini et al. 2015; Dionatos & Güdel 2017).

Figure 4 shows the [O I] profiles for the sources where the high-velocity line wings are detected. The spectra are extracted from the single spaxel where the continuum peaks, to avoid the effects of instrumental line shifts between spaxels that can be introduced by the instrument. The residuals are calculated by subtracting the Gaussian profile fitted with the instrumental line width and the line center left as a free parameter. The line wing

emission is reported for the sources where the integrated emission in the wing exceeds the 3σ flux uncertainty.

The most remarkable [O I] line wings are detected at the position of Serpens SMM6—a source that was not specifically targeted by the surveys, but is located at the edge of the PACS map of Serpens SMM3. The strong, blueshifted wing in HH 46 reported in van Kempen et al. (2010b) and Karska et al. (2013) traces the well-known outflow extending beyond the dense core. L1551-IRS5 shows extended [O I] emission in the PACS maps (see Lee et al. 2014a), consistent with the detected line wings. Similar results are obtained for the fully sampled [O I] maps in Nisini et al. (2015) and Dionatos & Güdel (2017).

In comparison to HIFI line profiles, only BHR71 and HH46 show the high-velocity wings in both [O I] and H₂O l₁₀–l₁₀

<footnote><sup>a</sup> For these WILL sources, the CO 24–23 or CO 21–20 lines are used instead of the CO 14–13 line at 186 µm.</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Line profiles of the [O I] 63 µm for the sources where the high-velocity emission is detected. The spectra are taken at the central position of the continuum peak, except for the sources marked with a star; in those instances, a few spaxels were summed due to mispointing. The sampling of the spectra is different for the line scans and full scans. Blue and red areas show the line wing emission, typically beyond ±90 km s⁻¹, resulting from the subtraction of the Gaussian profile (in green) from the line profile.</figcaption></figure>

(Kristensen et al. 2012; Green et al. 2013; Mottram et al. 2017). The remaining sources show narrow emission in the H₂O l₁₀–l₀₁ transitions, suggesting that the [O I] line does not trace the same kinematic or physical structures as H₂O (see also Nisini et al. 2015; Mottram et al. 2017). However, further observations with the German REceiver for Astronomy at Terahertz Frequencies (GREAT Heyminck et al. 2012) heterodyne instrument on the Stratospheric Observatory for Infrared Astronomy are needed to fully resolve the [O I] line profile.

In summary, 12 sources show high-velocity wings in the [O I] 63 µm line—including Ser SMM6, which was additionally detected on the map of Ser SMM3. All of those protostars also show extended [O I] emission on the PACS maps (see Section 3.2), suggesting that they drive fast, atomic jets. The presence of high-velocity emission does not correlate with the evolutionary stage because the detections are equally split between the Class 0 and Class I sources. The lack of high-velocity emission in the majority of sources indicates that most of the [O I] emission is emitted at velocities below ~90 km s⁻¹.

# 4. Analysis

## 4.1. Molecular Excitation

The detection of multiple transitions of a given molecule enables the excitation conditions—and ultimately, the physical conditions—of the gas to be determined (see Section 3.1, Karska et al. 2013). Here, we present rotational diagrams of H₂O, CO, and OH and determine the statistics of rotational temperatures (*T*<sub>rot</sub>) and numbers of emitting molecules (N) for the entire sample. The diagrams are used in Section 4.2 to calculate the total line emission in each species.

Figure 5 shows example rotational diagrams obtained for the central region of L1157, a well-known low-mass protostar driving a large-scale outflow (Bachiller et al. 2001; Benedettini

et al. 2012; Lefloch et al. 2012). The observations of CO are well-described by two independent linear fits, which correspond to rotational temperatures of ~320 and ~710 K, referred to as the “warm” and “hot” components (Karska et al. 2013). The break in the diagram is located at CO *J*<sub>up</sub> ~ 25, with upper level energies of ~1800 K at *λ* ~ 100 µm, where the spectrum is not properly calibrated, and thus the fluxes of CO 25–24 and 26–25 lines at 104 and 100 µm are not readily available. The two temperature components are associated with different velocity components of the line profile of CO 16–15 in velocity-resolved observations (Kristensen et al. 2017b). The H₂O and OH lines, on the other hand, both show large scatter in rotational diagrams and each has only a single temperature component fitted to their data (Figure 5), corresponding to temperatures of ~110 K and ~80 K, respectively. The scatter is due to high critical densities of H₂O and OH lines, which are subthermally excited and often optically thick (Herczeg et al. 2012; Manoj et al. 2013; Wampfler et al. 2013; Mottram et al. 2014).

The rotational temperatures obtained for L1157 are representative of the low-mass protostars in general (see diagrams for the remaining sources in the Appendix in Figures 18–23 for sources with line scans and Figure 24 for sources with the full spectra). Figure 6 shows histograms of rotational temperatures of the CO warm and hot components calculated for sources where the full PACS spectrum was obtained (see also Table 3). The distribution shows a clear peak for the CO warm (*J* ~ 14–24) with a median at 324 K (mean of 325 ± 62 K). The hot component (*J* ≳ 24) is less commonly detected and shows a much broader range of values, from about 600 to 1100 K, with the median at 719 K (mean of 764 ± 174 K). The median rotational temperatures of H₂O and OH are 141 K and 84 K, respectively, and are typical for the majority of the sources (see Figure 7). The high-temperature tail of the H₂O
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Rotational diagrams of CO, H₂O, and OH for our example protostar, L157. The base 10 logarithm of the number of emitting molecules from a level *u*, $N_u$, divided by the degeneracy of the level, *g*<sub>*u*</sub>, is shown as a function of energy of the upper level in kelvins, *E*<sub>up</sub>. Blue and red solid lines show linear fits to the data and the corresponding rotational temperatures.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 6.** Histograms of the CO rotational temperatures for the sources with full spectra from ~60 to 190 µm. The pink color shows the distributions of temperatures calculated using the CO $J_{up} = 14–25$ lines ($E_{up} = 580–1800$ K), and the light-blue color indicates the CO $J_{up} \ge 26$ ($E_{up} \ge 1800$ K) lines. Median values for those two components are drawn with the dashed lines.</figcaption></figure>

temperature distribution indicates sources with additional hot emission in the H₂O rotational diagrams, similar to CO. Decomposition of the H₂O diagrams for the nine sources with the largest number of detected hot water lines ($E_{up} \gtrsim 600$ K) yields a median value of hot H₂O rotational temperature of 410 K. The residual temperature of the warm H₂O is 300 K. However, because H₂O and OH are subthermally excited (Mottram et al. 2014), rotational temperatures do not reflect the true temperatures of the gas.

The above results are consistent with similar measurements from smaller surveys of low-mass protostars, where the prevalence of a 300 K component in CO rotational diagrams was identified (Green et al. 2013; Karska et al. 2013; Manoj et al. 2013; Lee et al. 2014a; Lindberg et al. 2014). The extended sample presented here allows us also to derive typical rotational temperatures of H₂O (130 K) and OH (84 K), and to isolate additional hot components in the H₂O and CO diagrams. The rotational temperatures of the hot components show a broad range of values and trace the most energetic processes in young stellar objects. The diagrams for all sources will be used in Section 4.2.1 to calculate the total line emission in each molecular species, and thus to determine the cooling rate of hot and warm gas in low-mass protostars.

## 4.2. Molecular and Atomic Cooling

The fractions of gas cooling emitted in different molecular and atomic species can help to constrain the physical processes

that heat the gas. For example, a high ratio of molecular to atomic line emission is predicted by continuous C-type shock models (Kaufman & Neufeld 1996; Flower & Pineau des Forêts 2010), whereas the increase of atomic emission as the protostar evolves is explained by increasing UV fields (Nisini et al. 2002; Visser et al. 2012) or increased shock velocity (Neufeld & Dalgarno 1989). Below, we calculate the cooling budget of the gas for the full sample of sources, which is larger than any previous study, by a factor of three, and evenly distributed over the Class 0 and I stages.

### 4.2.1. Calculations

The procedure to calculate line luminosities in each species depends on whether the full spectrum in the 55–210 µm was observed (i.e., full spectroscopy mode) or only the selected lines were targeted (i.e., line scan mode).

The procedure for the full scan mode is as follows. The total luminosity in the atomic lines is calculated by summing the fluxes of the two [O I] lines in the PACS spectra, at 63 and 145 µm, and using the distances listed in Table 1. The [C II] line flux is not included because only 10 sources show reliable detections (see Section 3.1). The line luminosity of CO is obtained by the addition of fluxes of the detected lines and extrapolated fluxes of lines located around 100 µm or blended with other species (e.g., CO 23–22 at 113 µm and CO 31–30 at 84 µm). The latter are obtained using the linear fits to CO diagrams if available (see Section 4.1). When reliable fits to the rotational diagrams are not possible, typically in the hot component, the line fluxes of the detected lines are summed and the fluxes of the lower-J lines are determined using the fit to the warm component. The only lines included in the interpolation are those with upper energies lower than the energy of the highest detected level. The line luminosities of H₂O and OH lines are calculated by the addition of detected lines. Fluxes of lines blended with CO transitions are determined by subtracting the CO fluxes obtained from the fit to the CO diagrams. No further extrapolation is implemented.

In order to calculate the line luminosities for the sources observed in line spectroscopy mode, we take advantage of the results obtained for the sources with full PACS spectra. The mean value of the ratio of [O I] 63 µm to [O I] 145 µm is 11.6 ± 4.6 for the sources observed in the WISH and DIGIT surveys where both lines were targeted. The value is consistent with the ratio of 10.5 obtained for the WISH survey alone
<table><caption>**Table 3**
Rotational Temperatures and Numbers of Emitting Molecules</caption><thead><tr><th rowspan="2">ID</th><th rowspan="2">Source</th><th colspan="2">CO J<sub>up</sub> = 14-26</th><th colspan="2">CO J<sub>up</sub> &ge; 27</th><th colspan="2">H<sub>2</sub>O</th><th colspan="2">OH</th><th rowspan="2">Mode</th></tr><tr><th>T<sub>rot</sub> (K)</th><th>log<sub>10</sub>N</th><th>T<sub>rot</sub> (K)</th><th>log<sub>10</sub>N</th><th>T<sub>rot</sub> (K)</th><th>log<sub>10</sub>N</th><th>T<sub>rot</sub> (K)</th><th>log<sub>10</sub>N</th><th>F/L</th></tr></thead><tbody><tr><td>1</td><td>L1448 IRS2</td><td>319(23)</td><td>49.1(0.1)</td><td>492(10)</td><td>48.5(0.1)</td><td>143(18)</td><td>45.8(0.2)</td><td>33(6)</td><td>54.2(0.6)</td><td>L</td></tr><tr><td>2</td><td>L1448 IRS3</td><td>281(16)</td><td>49.7(0.1)</td><td>678(66)</td><td>48.3(0.2)</td><td>141(19)</td><td>46.0(0.2)</td><td>39(12)</td><td>53.9(0.9)</td><td>L</td></tr><tr><td>3</td><td>L1448 C(N)</td><td>351(14)</td><td>49.1(0.1)</td><td>894(75)</td><td>48.2(0.1)</td><td>152(18)</td><td>46.3(0.2)</td><td>123(17)</td><td>52.2(0.2)</td><td>F</td></tr><tr><td>4</td><td>L1448 C(S)</td><td>294(16)</td><td>49.0(0.1)</td><td>—</td><td>—</td><td>84(11)</td><td>46.3(0.3)</td><td>94(18)</td><td>51.7(0.3)</td><td>F</td></tr><tr><td>5</td><td>I03235</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>6</td><td>L1455 IRS1</td><td>334(31)</td><td>48.3(0.1)</td><td>—</td><td>—</td><td>124(30)</td><td>45.6(0.3)</td><td>37(15)</td><td>53.2(1.2)</td><td>F</td></tr><tr><td>7</td><td>L1455 IRS3</td><td>177(38)</td><td>48.4(0.4)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>F</td></tr><tr><td>8</td><td>NGC1333 I1</td><td>387(24)</td><td>48.4(0.1)</td><td>—</td><td>—</td><td>140(27)</td><td>45.6(0.3)</td><td>—</td><td>—</td><td>L</td></tr><tr><td>9</td><td>NGC1333 I2A</td><td>334(93)</td><td>48.9(0.3)</td><td>—</td><td>—</td><td>127(62)</td><td>46.5(0.4)</td><td>—</td><td>—</td><td>F</td></tr><tr><td>10</td><td>NGC1333 I2B</td><td>357(11)</td><td>48.5(0.0)</td><td>—</td><td>—</td><td>154(20)</td><td>45.1(0.2)</td><td>38(6)</td><td>53.5(0.4)</td><td>L</td></tr><tr><td>11</td><td>HRF 65</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>12</td><td>PER08</td><td>303(31)</td><td>48.9(0.2)</td><td>—</td><td>—</td><td>210(28)</td><td>45.5(0.2)</td><td>36(6)</td><td>53.8(0.5)</td><td>L</td></tr><tr><td>13</td><td>PER09</td><td>313(30)</td><td>49.1(0.2)</td><td>699(212)</td><td>48.3(0.5)</td><td>175(12)</td><td>45.9(0.1)</td><td>35(5)</td><td>54.2(0.5)</td><td>L</td></tr><tr><td>14</td><td>NGC1333 I4A</td><td>260(9)</td><td>49.5(0.1)</td><td>633(130)</td><td>48.1(0.4)</td><td>105(18)</td><td>46.4(0.3)</td><td>150(214)</td><td>51.6(0.9)</td><td>FL</td></tr><tr><td>15</td><td>PER10</td><td>342(51)</td><td>48.8(0.2)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>40(14)</td><td>53.6(1.0)</td><td>L</td></tr><tr><td>16</td><td>NGC1333 I4B</td><td>343(9)</td><td>49.6(0.1)</td><td>896(42)</td><td>48.6(0.1)</td><td>183(15)</td><td>46.5(0.1)</td><td>84(14)</td><td>52.8(0.3)</td><td>F</td></tr><tr><td>17</td><td>NGC1333 I4C</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>18</td><td>I03267</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>19</td><td>I03271</td><td>379(51)</td><td>48.5(0.2)</td><td>572(85)</td><td>48.1(0.3)</td><td>166(19)</td><td>45.5(0.2)</td><td>35(6)</td><td>53.8(0.5)</td><td>L</td></tr><tr><td>20</td><td>I03282</td><td>318(10)</td><td>48.4(0.1)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>21</td><td>I03292</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>22</td><td>IRAS03301</td><td>355(25)</td><td>48.4(0.1)</td><td>1089(370)</td><td>47.3(0.4)</td><td>176(22)</td><td>45.4(0.2)</td><td>109(20)</td><td>52.1(0.3)</td><td>F</td></tr><tr><td>23</td><td>B1 SMM3</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>24</td><td>B1 d</td><td>390(78)</td><td>48.6(0.3)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>25</td><td>B1 a</td><td>293(10)</td><td>48.8(0.1)</td><td>—</td><td>—</td><td>211(54)</td><td>45.3(0.3)</td><td>103(20)</td><td>51.8(0.3)</td><td>F</td></tr><tr><td>26</td><td>B1 c</td><td>228(15)</td><td>48.8(0.1)</td><td>—</td><td>—</td><td>51(21)</td><td>46.3(0.7)</td><td>—</td><td>—</td><td>F</td></tr><tr><td>27</td><td>B1 SMM11</td><td>322(14)</td><td>48.6(0.1)</td><td>—</td><td>—</td><td>127(29)</td><td>45.3(0.3)</td><td>35(8)</td><td>53.9(0.7)</td><td>L</td></tr><tr><td>28</td><td>HH 211 MMS</td><td>273(25)</td><td>49.4(0.2)</td><td>—</td><td>—</td><td>71(15)</td><td>46.5(0.4)</td><td>41(10)</td><td>53.3(0.6)</td><td>L</td></tr><tr><td>29</td><td>IC348 MMS</td><td>411(146)</td><td>48.3(0.5)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>35(10)</td><td>53.5(0.9)</td><td>L</td></tr><tr><td>30</td><td>IC348 a</td><td>259(19)</td><td>49.0(0.2)</td><td>—</td><td>—</td><td>96(18)</td><td>45.4(0.3)</td><td>34(4)</td><td>53.7(0.4)</td><td>L</td></tr><tr><td>31</td><td>L1489</td><td>347(13)</td><td>48.3(0.1)</td><td>867(108)</td><td>47.2(0.2)</td><td>191(22)</td><td>45.1(0.2)</td><td>102(18)</td><td>51.5(0.3)</td><td>F</td></tr><tr><td>32</td><td>I04169</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>33</td><td>I04181</td><td>446(86)</td><td>47.4(0.2)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>38(6)</td><td>52.7(0.4)</td><td>L</td></tr><tr><td>34</td><td>IRAM04191</td><td>242(16)</td><td>47.9(0.1)</td><td>—</td><td>—</td><td>130(32)</td><td>44.8(0.2)</td><td>83(31)</td><td>50.4(0.4)</td><td>F</td></tr><tr><td>35</td><td>FS Tau B</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>36</td><td>DG Tau B</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>37</td><td>I04248</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>38</td><td>I04264</td><td>434(74)</td><td>47.7(0.2)</td><td>—</td><td>—</td><td>182(22)</td><td>44.6(0.2)</td><td>34(3)</td><td>53.2(0.3)</td><td>L</td></tr><tr><td>39</td><td>L1551 IRS5</td><td>562(95)</td><td>48.4(0.1)</td><td>751(171)</td><td>47.7(0.4)</td><td>—</td><td>—</td><td>39(11)</td><td>53.3(0.8)</td><td>F</td></tr><tr><td>40</td><td>I04325</td><td>290(43)</td><td>47.9(0.3)</td><td>—</td><td>—</td><td>310(202)</td><td>44.4(0.4)</td><td>—</td><td>—</td><td>L</td></tr><tr><td>41</td><td>L1527</td><td>380(55)</td><td>47.9(0.2)</td><td>—</td><td>—</td><td>185(40)</td><td>45.2(0.2)</td><td>84(51)</td><td>51.7(0.7)</td><td>F</td></tr><tr><td>42</td><td>TMR1</td><td>314(11)</td><td>48.5(0.1)</td><td>—</td><td>—</td><td>193(31)</td><td>45.4(0.2)</td><td>108(24)</td><td>51.8(0.3)</td><td>F</td></tr><tr><td>43</td><td>TMC1A</td><td>269(53)</td><td>48.3(0.3)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>F</td></tr><tr><td>44</td><td>TMC1</td><td>338(8)</td><td>48.3(0.1)</td><td>856(174)</td><td>47.2(0.3)</td><td>148(24)</td><td>44.9(0.2)</td><td>103(19)</td><td>51.5(0.3)</td><td>F</td></tr><tr><td>45</td><td>HH 46</td><td>372(60)</td><td>49.1(0.2)</td><td>—</td><td>—</td><td>68(9)</td><td>46.4(0.2)</td><td>100(60)</td><td>52.4(0.6)</td><td>L</td></tr><tr><td>46</td><td>Ced110 IRS4</td><td>484(88)</td><td>47.4(0.2)</td><td>—</td><td>—</td><td>106(44)</td><td>44.9(0.5)</td><td>128(139)</td><td>51.1(0.8)</td><td>L</td></tr><tr><td>47</td><td>CHA01</td><td>278(30)</td><td>48.3(0.2)</td><td>—</td><td>—</td><td>155(82)</td><td>44.7(0.4)</td><td>34(7)</td><td>53.3(0.7)</td><td>L</td></tr><tr><td>48</td><td>BHR71</td><td>353(13)</td><td>49.3(0.1)</td><td>1072(85)</td><td>47.9(0.1)</td><td>125(23)</td><td>45.8(0.3)</td><td>87(17)</td><td>52.1(0.4)</td><td>F</td></tr><tr><td>49</td><td>DK Cha</td><td>393(21)</td><td>49.0(0.1)</td><td>866(338)</td><td>48.2(0.5)</td><td>—</td><td>—</td><td>67(12)</td><td>52.7(0.4)</td><td>F</td></tr><tr><td>50</td><td>CHA02</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>51</td><td>I15398</td><td>291(8)</td><td>48.9(0.1)</td><td>—</td><td>—</td><td>78(82)</td><td>45.6(1.1)</td><td>79(45)</td><td>51.7(0.7)</td><td>L</td></tr><tr><td>52</td><td>GSS30 IRS1</td><td>342(16)</td><td>49.2(0.1)</td><td>865(84)</td><td>48.0(0.2)</td><td>245(22)</td><td>46.0(0.1)</td><td>99(18)</td><td>52.2(0.3)</td><td>F</td></tr><tr><td>53</td><td>VLA 1623</td><td>286(14)</td><td>48.9(0.1)</td><td>1074(406)</td><td>47.1(0.4)</td><td>165(40)</td><td>45.3(0.3)</td><td>71(16)</td><td>51.9(0.4)</td><td>F</td></tr><tr><td>54</td><td>WL12</td><td>328(9)</td><td>48.5(0.1)</td><td>690(58)</td><td>47.4(0.2)</td><td>202(25)</td><td>45.0(0.2)</td><td>94(17)</td><td>51.5(0.3)</td><td>F</td></tr><tr><td>55</td><td>WL22</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>56</td><td>Elias29</td><td>347(10)</td><td>49.2(0.1)</td><td>638(10)</td><td>48.4(0.1)</td><td>288(33)</td><td>46.0(0.1)</td><td>112(27)</td><td>52.1(0.3)</td><td>F</td></tr><tr><td>57</td><td>IRS44</td><td>385(32)</td><td>47.0(0.1)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>F</td></tr><tr><td>58</td><td>IRS46</td><td>310(35)</td><td>47.8(0.2)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>F</td></tr><tr><td>59</td><td>IRS63</td><td>364(45)</td><td>47.2(0.2)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>F</td></tr><tr><td>60</td><td>OPH02</td><td>358(10)</td><td>48.4(0.1)</td><td>488(143)</td><td>48.1(0.7)</td><td>165(19)</td><td>45.2(0.2)</td><td>37(8)</td><td>53.5(0.6)</td><td>L</td></tr><tr><td>61</td><td>RNO91</td><td>231(30)</td><td>47.9(0.2)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>107(104)</td><td>51.0(0.9)</td><td>L</td></tr><tr><td>62</td><td>L260 SMM1</td><td>423(63)</td><td>47.6(0.2)</td><td>—</td><td>—</td><td>185(22)</td><td>44.5(0.2)</td><td>36(3)</td><td>53.0(0.3)</td><td>L</td></tr><tr><td>63</td><td>L483</td><td>371(32)</td><td>48.6(0.1)</td><td>606(96)</td><td>48.0(0.3)</td><td>146(17)</td><td>45.7(0.2)</td><td>109(84)</td><td>51.9(0.7)</td><td>L</td></tr></tbody></table>
<table><caption>**Table 3**
(Continued)</caption><thead><tr><th rowspan="2">ID</th><th rowspan="2">Source</th><th colspan="2">CO J<sub>up</sub> = 14–26</th><th colspan="2">CO J<sub>up</sub> &ge; 27</th><th colspan="2">H<sub>2</sub>O</th><th colspan="2">OH</th><th rowspan="2">Mode</th></tr><tr><th>T<sub>rot</sub> (K)</th><th>log<sub>10</sub>N</th><th>T<sub>rot</sub> (K)</th><th>log<sub>10</sub>N</th><th>T<sub>rot</sub> (K)</th><th>log<sub>10</sub>N</th><th>T<sub>rot</sub> (K)</th><th>log<sub>10</sub>N</th></tr></thead><tbody><tr><td>64</td><td>Aqu-MM2</td><td>284(40)</td><td>49.1(0.3)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>65</td><td>Aqu-MM4</td><td>278(46)</td><td>49.2(0.3)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>66</td><td>Ser SMM1</td><td>349(20)</td><td>50.6(0.1)</td><td>606(32)</td><td>49.7(0.1)</td><td>103(12)</td><td>47.3(0.2)</td><td>83(13)</td><td>53.6(0.3)</td><td>F</td></tr><tr><td>67</td><td>Ser SMM4</td><td>269(13)</td><td>50.2(0.1)</td><td>—</td><td>—</td><td>76(28)</td><td>47.0(0.5)</td><td>67(49)</td><td>53.0(1.0)</td><td>F</td></tr><tr><td>68</td><td>Ser SMM3</td><td>298(13)</td><td>50.0(0.1)</td><td>—</td><td>—</td><td>123(27)</td><td>46.8(0.2)</td><td>—</td><td>—</td><td>F</td></tr><tr><td>69</td><td>SerpS-MM1</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>70</td><td>SerpS-MM18</td><td>204(34)</td><td>50.1(0.5)</td><td>—</td><td>—</td><td>123(19)</td><td>46.0(0.3)</td><td>—</td><td>—</td><td>L</td></tr><tr><td>71</td><td>Aqu-MM6</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>72</td><td>Aqu-MM7</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>73</td><td>Aqu-MM10</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>74</td><td>Aqu-MM14</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>75</td><td>W40-MM3</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>76</td><td>W40-MM5</td><td>339(54)</td><td>48.4(0.3)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>77</td><td>W40-MM26</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>78</td><td>W40-MM27</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>79</td><td>W40-MM28</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>80</td><td>W40-MM34</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>81</td><td>W40-MM36</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>L</td></tr><tr><td>82</td><td>RCrA IRS5A</td><td>298(9)</td><td>48.5(0.1)</td><td>—</td><td>—</td><td>219(30)</td><td>45.1(0.2)</td><td>113(17)</td><td>51.9(0.3)</td><td>F</td></tr><tr><td>83</td><td>RCrA IRS5N</td><td>299(75)</td><td>47.8(0.4)</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>F</td></tr><tr><td>84</td><td>RCrA IRS7A</td><td>307(10)</td><td>49.5(0.1)</td><td>719(55)</td><td>48.4(0.2)</td><td>218(24)</td><td>46.0(0.2)</td><td>114(17)</td><td>52.9(0.3)</td><td>F</td></tr><tr><td>85</td><td>RCrA IRS7B</td><td>281(8)</td><td>49.1(0.1)</td><td>837(141)</td><td>47.5(0.3)</td><td>208(28)</td><td>45.3(0.2)</td><td>119(17)</td><td>52.0(0.3)</td><td>F</td></tr><tr><td>86</td><td>CrA-44</td><td>343(15)</td><td>48.2(0.1)</td><td>—</td><td>—</td><td>117(49)</td><td>44.6(0.5)</td><td>37(5)</td><td>53.1(0.4)</td><td>L</td></tr><tr><td>87</td><td>L723</td><td>354(31)</td><td>48.7(0.1)</td><td>—</td><td>—</td><td>105(49)</td><td>45.3(0.5)</td><td>50(17)</td><td>52.6(0.8)</td><td>L</td></tr><tr><td>88</td><td>B335</td><td>283(11)</td><td>48.4(0.1)</td><td>840(411)</td><td>47.0(0.6)</td><td>140(40)</td><td>44.7(0.4)</td><td>101(63)</td><td>51.1(0.6)</td><td>F</td></tr><tr><td>89</td><td>L1157</td><td>324(13)</td><td>49.2(0.1)</td><td>711(106)</td><td>48.2(0.3)</td><td>114(20)</td><td>46.3(0.3)</td><td>77(40)</td><td>52.5(0.7)</td><td>F</td></tr><tr><td>90</td><td>L1014</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>F</td></tr></tbody></table>

Note. Mode refers to the line (L) and full (F) spectroscopy with PACS. Non-detection of the components on a rotational diagram is marked with “–.” Uncertainties are shown in parentheses.

<figure><img src="image_10.png" /><figcaption>**Figure 7.** Histograms of the H₂O (left) and OH (right) rotational temperatures for the sources with full spectra from ~60–190 µm. Median values for those two temperatures are drawn with the dashed lines.</figcaption></figure>

(Karska et al. 2013). We therefore multiply the fluxes of the [O I] 63 µm by a factor of ~1.086 (±0.034) to calculate the total line luminosities of [O I] for the sources from the WILL survey.

The line luminosities of CO are obtained using linear fits to the rotational diagrams, in the same manner as for the full scan observations. In order to determine the H₂O and OH line luminosities, we first used the full PACS spectra to calculate the respective line luminosities, if the objects were observed in the line scan mode. The ratio of the observed-to-calculated luminosities using limited number of lines is 3.0 ± 1.4 for H₂O and 2.1 ± 0.6 for OH in the WILL settings, and 2.1 ± 0.7 for H₂O and 1.4 ± 0.4 for OH in the WISH line scan settings. We

adopt those values to calculate the total line luminosities only for the sources where the number of detected lines allows us to fit the linear component of the rotational diagrams (see Table 3). For the remaining sources, we refrain from using this correction and list only the lower limits for the H₂O and OH luminosities.

The full list of derived total line luminosities is presented in Table 4. We refrain from listing the CO line luminosities with $J_u < 14$, which are inaccessible to PACS. The APEX/CHAMP⁺ and HIFI survey of Yıldız et al. (2013) shows that those lower-$J$ CO lines trace a physical component that is intrinsically different from the one seen in the PACS CO lines, namely the entrained outflow gas with temperatures of $T \lesssim 100$ K. Recent analysis of full CO ladders with PACS and SPIRE confirm that the temperatures and distribution of line emission vary significantly for CO lines above and below $J_u \sim 14$ (Yang et al. 2017; Y.-L. Yang et al. 2018, in preparation). The inclusion of those $J_u < 14$ CO line fluxes could therefore add some confusion to the interpretation of the far-infrared lines.

### 4.2.2. Absolute Line Luminosities

The distributions of the line to bolometric luminosity ratios for various species across the sample of Class 0 and I sources are illustrated in Figure 8 (see also Figure 25 for absolute fluxes). The largest median line luminosity divided by $L_{bol}$ is that of CO (3.3 · 10⁻⁴), followed by H₂O (3.0 · 10⁻⁴), [O I]
<table><caption>**Table 4**
Total Line Luminosities of H₂O, CO, OH, and [O I]</caption><thead><tr><th>ID</th><th>H<sub>2</sub>O</th><th>CO warm</th><th>CO hot<br>(10<sup>-3</sup> L<sub>☉</sub>)</th><th>OH</th><th>[O I] 63</th><th>[O I] tot</th><th>Rem.</th></tr></thead><tbody><tr><td>1</td><td>3.29</td><td>4.17</td><td>0.79</td><td>1.83</td><td>2.61</td><td>2.84</td><td>c</td></tr><tr><td>2</td><td>5.05</td><td>11.03</td><td>1.25</td><td>2.33</td><td>6.86</td><td>7.45</td><td>c</td></tr><tr><td>3</td><td>12.62</td><td>5.37</td><td>3.00</td><td>3.21</td><td>0.66</td><td>0.69</td><td></td></tr><tr><td>4</td><td>4.04</td><td>2.70</td><td>–</td><td>0.59</td><td>0.40</td><td>0.44</td><td>h</td></tr><tr><td>5</td><td>–</td><td>–</td><td>–</td><td>–</td><td>0.39</td><td>0.43</td><td>c</td></tr><tr><td>6</td><td>1.10</td><td>1.34</td><td>–</td><td>0.30</td><td>0.19</td><td>0.22</td><td>h</td></tr><tr><td>7</td><td>–</td><td>0.10</td><td>–</td><td>0.05</td><td>0.15</td><td>0.16</td><td></td></tr><tr><td>8</td><td>1.83</td><td>1.20</td><td>0.11</td><td>0.34</td><td>0.28</td><td>0.31</td><td>c, lh</td></tr><tr><td>9</td><td>2.50</td><td>2.10</td><td>–</td><td>0.21</td><td>–</td><td>–</td><td></td></tr><tr><td>10</td><td>0.75</td><td>1.39</td><td>–</td><td>1.04</td><td>1.31</td><td>1.42</td><td>c</td></tr><tr><td>11</td><td>–</td><td>–</td><td>–</td><td>–</td><td>0.19</td><td>0.20</td><td>c</td></tr><tr><td>12</td><td>2.38</td><td>2.41</td><td>0.10</td><td>1.36</td><td>10.82</td><td>11.75</td><td>c, lh</td></tr><tr><td>13</td><td>5.87</td><td>4.18</td><td>1.25</td><td>2.59</td><td>–</td><td>–</td><td>c, oc</td></tr><tr><td>14</td><td>5.95</td><td>6.07</td><td>0.68</td><td>0.47</td><td>0.43</td><td>0.43</td><td>no</td></tr><tr><td>15</td><td>–</td><td>2.14</td><td>0.08</td><td>1.40</td><td>–</td><td>–</td><td>c, lh, oc</td></tr><tr><td>16</td><td>25.57</td><td>14.92</td><td>7.72</td><td>4.72</td><td>0.32</td><td>0.30</td><td></td></tr><tr><td>17</td><td>–</td><td>–</td><td>–</td><td>–</td><td>0.12</td><td>0.13</td><td>c</td></tr><tr><td>18</td><td>0.02</td><td>0.01</td><td>–</td><td>–</td><td>–</td><td>–</td><td>lw,lh</td></tr><tr><td>19</td><td>2.06</td><td>1.32</td><td>0.52</td><td>1.07</td><td>0.37</td><td>0.40</td><td>c</td></tr><tr><td>20</td><td>–</td><td>0.77</td><td>–</td><td>0.09</td><td>0.21</td><td>0.23</td><td>c</td></tr><tr><td>21</td><td>–</td><td>0.05</td><td>–</td><td>–</td><td>0.23</td><td>0.25</td><td>c</td></tr><tr><td>22</td><td>2.03</td><td>0.94</td><td>0.31</td><td>1.82</td><td>0.64</td><td>0.75</td><td></td></tr><tr><td>23</td><td>0.00</td><td>0.01</td><td>–</td><td>–</td><td>0.14</td><td>0.15</td><td>c, lc</td></tr><tr><td>24</td><td>0.24</td><td>2.09</td><td>–</td><td>0.03</td><td>1.83</td><td>1.99</td><td>c, lh, loh</td></tr><tr><td>25</td><td>1.31</td><td>1.65</td><td>–</td><td>0.92</td><td>0.62</td><td>0.75</td><td></td></tr><tr><td>26</td><td>1.12</td><td>0.91</td><td>–</td><td>–</td><td>–</td><td>–</td><td></td></tr><tr><td>27</td><td>0.52</td><td>1.32</td><td>–</td><td>1.15</td><td>1.78</td><td>1.93</td><td>c</td></tr><tr><td>28</td><td>6.44</td><td>4.99</td><td>–</td><td>0.99</td><td>1.94</td><td>2.11</td><td>c</td></tr><tr><td>29</td><td>0.00</td><td>1.01</td><td>0.03</td><td>0.49</td><td>0.88</td><td>0.95</td><td>c, lh</td></tr><tr><td>30</td><td>0.74</td><td>1.75</td><td>–</td><td>0.76</td><td>1.19</td><td>1.29</td><td>c</td></tr><tr><td>31</td><td>0.88</td><td>0.79</td><td>0.20</td><td>0.39</td><td>0.28</td><td>0.30</td><td></td></tr><tr><td>32</td><td>0.02</td><td>0.05</td><td>–</td><td>0.08</td><td>0.66</td><td>0.72</td><td>c, lm</td></tr><tr><td>33</td><td>0.05</td><td>0.16</td><td>–</td><td>0.18</td><td>0.12</td><td>0.13</td><td>c, lw</td></tr><tr><td>34</td><td>0.07</td><td>0.12</td><td>–</td><td>0.04</td><td>0.09</td><td>0.10</td><td></td></tr><tr><td>35</td><td>0.03</td><td>0.02</td><td>–</td><td>0.03</td><td>0.06</td><td>0.06</td><td>c, lm</td></tr><tr><td>36</td><td>–</td><td>0.03</td><td>0.01</td><td>0.05</td><td>0.47</td><td>0.51</td><td>c, lm</td></tr><tr><td>37</td><td>–</td><td>–</td><td>–</td><td>–</td><td>0.10</td><td>0.11</td><td>c</td></tr><tr><td>38</td><td>0.21</td><td>0.28</td><td>0.01</td><td>0.30</td><td>0.02</td><td>0.02</td><td>c, lh</td></tr><tr><td>39</td><td>0.14</td><td>2.06</td><td>0.48</td><td>0.28</td><td>3.49</td><td>3.67</td><td></td></tr><tr><td>40</td><td>0.11</td><td>0.20</td><td>0.01</td><td>0.04</td><td>0.49</td><td>0.53</td><td>c, lh, loh</td></tr><tr><td>41</td><td>0.28</td><td>0.44</td><td>–</td><td>0.36</td><td>0.40</td><td>0.43</td><td>lh</td></tr><tr><td>42</td><td>1.39</td><td>0.97</td><td>–</td><td>0.91</td><td>0.38</td><td>0.43</td><td></td></tr><tr><td>43</td><td>0.00</td><td>0.41</td><td>–</td><td>0.06</td><td>1.18</td><td>1.18</td><td>no</td></tr><tr><td>44</td><td>0.31</td><td>0.65</td><td>0.17</td><td>0.40</td><td>0.53</td><td>0.57</td><td></td></tr><tr><td>45</td><td>2.11</td><td>4.90</td><td>0.23</td><td>3.69</td><td>19.12</td><td>20.30</td><td></td></tr><tr><td>46</td><td>0.19</td><td>0.17</td><td>–</td><td>0.26</td><td>0.75</td><td>0.77</td><td></td></tr><tr><td>47</td><td>0.26</td><td>0.50</td><td>0.02</td><td>0.24</td><td>0.52</td><td>0.57</td><td>c, lh</td></tr><tr><td>48</td><td>2.43</td><td>9.01</td><td>3.11</td><td>1.35</td><td>2.47</td><td>2.61</td><td></td></tr><tr><td>49</td><td>0.76</td><td>4.93</td><td>1.61</td><td>1.10</td><td>3.46</td><td>3.59</td><td></td></tr><tr><td>50</td><td>0.06</td><td>0.04</td><td>–</td><td>0.09</td><td>0.13</td><td>0.14</td><td>c, lm</td></tr><tr><td>51</td><td>0.73</td><td>1.82</td><td>–</td><td>0.50</td><td>0.94</td><td>0.99</td><td></td></tr><tr><td>52</td><td>9.08</td><td>5.51</td><td>2.01</td><td>1.92</td><td>1.46</td><td>1.55</td><td></td></tr><tr><td>53</td><td>1.00</td><td>2.10</td><td>0.21</td><td>1.00</td><td>0.38</td><td>0.44</td><td></td></tr><tr><td>54</td><td>0.64</td><td>1.13</td><td>0.20</td><td>0.35</td><td>0.23</td><td>0.29</td><td></td></tr><tr><td>55</td><td>0.02</td><td>0.02</td><td>–</td><td>–</td><td>2.95</td><td>3.20</td><td>c, lm</td></tr><tr><td>56</td><td>8.57</td><td>6.06</td><td>1.56</td><td>2.30</td><td>1.16</td><td>1.27</td><td></td></tr><tr><td>57</td><td>–</td><td>0.02</td><td>–</td><td>–</td><td>0.14</td><td>0.15</td><td></td></tr><tr><td>58</td><td>0.08</td><td>0.16</td><td>–</td><td>–</td><td>0.04</td><td>0.04</td><td>no</td></tr><tr><td>59</td><td>0.02</td><td>0.05</td><td>–</td><td>0.03</td><td>0.09</td><td>0.10</td><td></td></tr><tr><td>60</td><td>0.81</td><td>0.92</td><td>0.26</td><td>0.77</td><td>0.53</td><td>0.57</td><td>c</td></tr><tr><td>61</td><td>0.02</td><td>0.11</td><td>–</td><td>0.10</td><td>0.38</td><td>0.40</td><td></td></tr><tr><td>62</td><td>0.17</td><td>0.22</td><td>0.01</td><td>0.23</td><td>0.28</td><td>0.31</td><td>c, lh</td></tr><tr><td>63</td><td>2.05</td><td>1.63</td><td>0.47</td><td>1.14</td><td>0.45</td><td>0.49</td><td></td></tr></tbody></table>
<table><caption>**Table 4**
(Continued)</caption><thead><tr><th>ID</th><th>H<sub>2</sub>O</th><th>CO warm</th><th>CO hot<br>(10<sup>-3</sup> L<sub>☉</sub>)</th><th>OH</th><th>[O I] 63</th><th>[O I] tot</th><th>Rem.</th></tr></thead><tbody><tr><td>64</td><td>1.13</td><td>3.31</td><td>—</td><td>0.00</td><td>0.30</td><td>0.33</td><td>c, lw</td></tr><tr><td>65</td><td>0.52</td><td>3.52</td><td>0.06</td><td>0.11</td><td>0.27</td><td>0.30</td><td>c, lm</td></tr><tr><td>66</td><td>66.07</td><td>142.98</td><td>29.26</td><td>31.69</td><td>22.86</td><td>25.71</td><td></td></tr><tr><td>67</td><td>10.82</td><td>35.62</td><td>8.31</td><td>4.82</td><td>17.24</td><td>18.52</td><td></td></tr><tr><td>68</td><td>8.63</td><td>24.25</td><td>1.24</td><td>1.94</td><td>7.32</td><td>7.84</td><td></td></tr><tr><td>69</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>2.814</td><td>3.056</td></tr><tr><td>70</td><td>3.78</td><td>11.39</td><td>0.10</td><td>0.12</td><td>—</td><td>—</td><td>oc</td></tr><tr><td>71</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td></td></tr><tr><td>72</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td></td></tr><tr><td>73</td><td>0.10</td><td>0.12</td><td>—</td><td>—</td><td>—</td><td>—</td><td></td></tr><tr><td>74</td><td>—</td><td>0.04</td><td>—</td><td>0.05</td><td>—</td><td>—</td><td>c, lc, loh</td></tr><tr><td>75</td><td>0.05</td><td>0.10</td><td>—</td><td>—</td><td>—</td><td>—</td><td>lm,oc</td></tr><tr><td>76</td><td>0.06</td><td>1.01</td><td>—</td><td>0.10</td><td>55.02</td><td>59.75</td><td>c, lm</td></tr><tr><td>77</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>oc</td></tr><tr><td>78</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>oc</td></tr><tr><td>79</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>oc</td></tr><tr><td>80</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>oc</td></tr><tr><td>81</td><td>—</td><td>—</td><td>—</td><td>—</td><td>0.55</td><td>0.60</td><td>c</td></tr><tr><td>82</td><td>0.82</td><td>0.82</td><td>0.13</td><td>0.69</td><td>19.61</td><td>20.86</td><td></td></tr><tr><td>83</td><td>0.08</td><td>0.16</td><td>—</td><td>0.04</td><td>8.09</td><td>8.82</td><td></td></tr><tr><td>84</td><td>8.23</td><td>8.83</td><td>2.39</td><td>5.84</td><td>147.35</td><td>157.64</td><td></td></tr><tr><td>85</td><td>1.43</td><td>2.72</td><td>0.44</td><td>0.97</td><td>39.14</td><td>43.39</td><td></td></tr><tr><td>86</td><td>0.16</td><td>0.57</td><td>0.02</td><td>0.35</td><td>0.95</td><td>1.03</td><td>c, lh</td></tr><tr><td>87</td><td>0.29</td><td>1.85</td><td>0.15</td><td>0.27</td><td>0.63</td><td>0.69</td><td></td></tr><tr><td>88</td><td>0.18</td><td>0.57</td><td>0.09</td><td>0.12</td><td>0.15</td><td>0.16</td><td></td></tr><tr><td>89</td><td>3.92</td><td>5.65</td><td>1.53</td><td>1.73</td><td>1.79</td><td>1.92</td><td></td></tr><tr><td>90</td><td>—</td><td>—</td><td>—</td><td>0.04</td><td>0.09</td><td>0.09</td><td>no</td></tr></tbody></table>

Note. “CO warm” (w) and “CO hot” (h) in the header refer to the CO lines with $J_{up} = 14–26$ and $J_{up} \ge 27$, respectively. The “[O I] tot” is the sum of the line luminosities of the [O I] lines at 63 and 145 µm. Remarks mean: c—values derived from line scans and corrected for the missing lines; no—non-detection of the [O I] line at 145 µm; oc—contamination of the [O I] emission on the map; lw, lc, lh, loh, lm—lower limits of the H<sub>2</sub>O, CO w, CO h, OH, and all molecules, respectively; h—line luminosities of CO h are added to the CO w. Non-detections are shown as “—.”

(2.4 · 10<sup>-4</sup>), and OH (1.5 · 10<sup>-4</sup>). The distributions vary depending on the considered species.

For CO, the total line luminosities divided by $L_{bol}$ are significantly larger for Class 0 than for Class I sources (see Figure 8); the median for the former is 6.2 · 10<sup>-4</sup>, versus 2.7 · 10<sup>-4</sup> for Class I. Similar trends are not immediately seen in the rest of the molecular species. Both H<sub>2</sub>O and OH show almost identical distributions for Class 0 and I sources, with median line luminosities over $L_{bol}$ that are almost equal (3.1 · 10<sup>-4</sup> versus 2.7 · 10<sup>-4</sup> for H<sub>2</sub>O, and 1.4 · 10<sup>-4</sup> versus 1.5 · 10<sup>-4</sup> for OH). The [O I] line luminosities over $L_{bol}$ are also similar between the two classes, and show a clear peak concentrated in the 10<sup>-4</sup>–10<sup>-3</sup> bins.

These results are qualitatively consistent with the far-IR line luminosities from the WISH survey alone (Karska et al. 2013). The cooling by CO was found to be dominant, with a median value of ~5.7 · 10<sup>-3</sup> L<sub>☉</sub> for Class 0 and ~0.6 · 10<sup>-3</sup> L<sub>☉</sub> for Class I. Similarly, H<sub>2</sub>O was the second most important coolant at ~5.3 · 10<sup>-3</sup> L<sub>☉</sub> for Class 0 and ~0.5 · 10<sup>-3</sup> L<sub>☉</sub> for Class I. The median line luminosities for the entire sample were ~2.0 · 10<sup>-3</sup> for both CO and H<sub>2</sub>O, and the median bolometric luminosity was 3.8 L<sub>☉</sub>.

It is noteworthy that the CO and H<sub>2</sub>O absolute luminosities obtained in the WISH survey for the Class 0 sources are a factor of 3–5 higher than the median values for the entire sample probed here. This illustrates the bias toward the brightest outflow sources targeted in WISH, which is reduced

by the addition of the DIGIT and WILL samples. In contrast, the CO and H<sub>2</sub>O luminosities analyzed here for Class I are a factor of 2 higher than for the Class I sources in the WISH sample, reducing the differences due to the evolutionary stage.

The cooling in [O I] and OH is consistent, to within a factor of 2, between the combined and WISH-only samples. The ratios of the [O I] luminosities for Class 0 and I sources are about 1.4 in the extended sample and 2.2 in the WISH survey, illustrating that the differences in the [O I] cooling with evolutionary stage are less significant than previously observed (also with respect to the ISO results, see Nisini et al. 2002; Mottram et al. 2017). The trends in the line luminosities from Class 0 to Class I are further discussed in Section 6.1.

### 4.2.3. Contributions of Various Species to the Total Far-infrared Gas Cooling

Low-mass protostars show a wide range of relative contributions from H<sub>2</sub>O, CO, OH, and [O I] to the total far-infrared line luminosities, as illustrated by eight example sources in Figure 9. The highest fraction of cooling due to CO (~65%) is seen in BHR 71, where prominent emission from high-J CO lines is detected and accompanied by much lower cooling in H<sub>2</sub>O and [O I] (~15% each), and to smaller extent OH (~7%). A considerable fraction of gas cooling in CO is also detected in NGC1333 IRAS4B (~40%), but in this source the emission from a large number of H<sub>2</sub>O lines dominates the cooling budget (~50%) when in the presence of weak [O I]
<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 8.** Histograms of the CO (top left), H₂O (top right), OH (bottom left), and [O I] (bottom right) cooling over bolometric luminosities for all sources with at least one detection in a given species, except for Class II sources and sources possibly contaminated by PDR emission (see Table 1 for details). The red color shows the distributions for Class 0 sources, and blue indicates Class I sources.</figcaption></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

emission (Herczeg et al. 2012). This source most resembles the results found for PACS Bright Red Sources (Tobin et al. 2016a). The highest relative line emission of OH is seen in IRAS 03301 (~30%), with a comparable fraction contributed by H₂O and to a smaller extent CO and [O I]. Protostars in the Corona Australis region, e.g., R CrA IRS 5N, show the dominant far-IR cooling via [O I] (~97%), likely due to the presence of increased UV fields from a nearby Herbig Be star (Lindberg et al. 2014).

The fractions of cooling contributed by various species do not depend on the source parameters, i.e., its bolometric temperature and luminosity (see Figures 26 and 27 in the Appendix). The spread in the line luminosities divided by the total far-infrared line luminosities (FIRL) is substantial for all species, but clearly the largest for [O I]. We find, however, that the highest ratios of LCO/FIRL are found for Class 0 sources, whereas the highest ratios of LOH/FIRL are seen in Class I sources (see also Section 6.3).

A better quantity to describe the far-infrared budget is the ratio of line luminosities of various species. As illustrated by Figure 2, the correlations between molecular species are very

strong (~6σ), and only somewhat weaker between the molecules and [O I] (~4–5σ). As expected, the line ratios of those species cover a narrow range of values for the majority of the protostars (see Figure 28 in the Appendix). Similar characteristics have been seen in the sample of protostars in Perseus. This uniformity implies that the entire sample can be treated as one, a consequence that will be utilized below.

**5. Comparisons to Models of Shocks and Photodissociation Regions**

Far-infrared line emission can be compared to shock models in order to derive the physical conditions of the medium and the properties of shock waves. A critical part of such comparisons is ensuring that the relevant species are emitted from the same location(s) in young stellar objects.

Karska et al. (2013) analyzed the patterns of spatially resolved far-IR line emission toward 18 protostars from the WISH survey and concluded that (i) the emission follows the outflow directions as defined from CO 6–5 (Yıldız et al. 2012, 2015); (ii) high-J CO emission ($J_u \ge 14$) seen in
<figure><img src="image_15.png" /><figcaption>**Figure 9.** Fractions of gas cooling contributed by CO (orange), H₂O (blue), OH (green), and [O I] (red), to the total far-infrared line cooling in eight example sources.</figcaption></figure>

PACS is well-aligned with the emission in H₂O, but differs with respect to [O I]. For the same protostars, Santangelo et al. (2012) and Kristensen et al. (2017b) show that the velocity-resolved profiles of CO 16–15 and H₂O *I*₁₀–*I*₁₀ are almost identical, which strengthens the conclusion that the two species are connected.

Assuming the same origin of high-*J* CO and H₂O, Karska et al. (2014b) compared the observed line ratios of molecular species obtained for 22 protostars in Perseus (WILL survey) to the available stationary *C*-* and *J*-type shock models in dark clouds fully shielded from UV. In this way, the uncertainty in the distance and any large-scale environmental effects were minimized. The observed line ratios of various same-molecule pairs of H₂O, CO, and OH lines cover a narrow range and agree with the models of *C*-type stationary shocks propagating at (pre-shock) densities of 10⁴–10⁵ cm⁻³ (but not with the *J*-type models; see top panel of Figure 8 in Karska et al. 2014b). However, the line ratios of H₂O/CO, H₂O/OH, and CO/OH lines are overestimated by stationary *C*-* and *J*-shock models by 1–2 orders of magnitude with respect to observations. In order to reconcile these models and observations, Karska et al. (2014b) proposed that some H₂O is photo-dissociated by FUV photons, and thus its abundance is lowered with respect to OH and CO.

A number of low-mass sources show velocity-resolved emission from light (ionized) hydrides, e.g., CH, CH⁺, OH⁺ (Kristensen et al. 2013; Benz et al. 2016). The velocity structure is such that this emission originates in shocks. The observations were compared to models of fully dissociative shocks (Neufeld & Dalgarno 1989): the molecular emission is consistent with the molecules reforming in the post-shock zone. The velocities required to dissociate the gas (>>50 km s⁻¹) are inconsistent with the observed velocities (~10 km s⁻¹); instead, dissociation must come from elsewhere. Kristensen et al. (2013) proposed that the gas is dissociated by UV photons from the nearby accreting protostar, and that the observed signatures present direct evidence of UV irradiated shocks.

Further evidence comes from observations of H₂O and high-*J* CO. When the H₂O abundance is inferred from comparison to high-*J* CO 16–15 emission (Kristensen et al. 2017b), the total abundance is ~10⁻⁶. In warm shocked gas where *T* > 300 K, all oxygen is expected to be driven into H₂O (e.g., Bergin et al. 1998), and the total H₂O abundance reaches ~10⁻⁴. The observed decrease of two orders of magnitude implies that not all oxygen is driven into H₂O. From a simple chemistry calculation, Kristensen et al. (2017b) showed that the abundance is consistent with a moderate UV field dissociating the H₂O (G₀ ~ 10⁻¹ – 1), thus again demonstrating that UV irradiation likely dominates the chemistry, whereas the shocks dominate the excitation.

While other solutions cannot be excluded, these would have to explain the multi-species line ratios, light (ionized) hydrides, and low absolute water abundance. One specific example of such a potential solution is non-stationary *C*-type shocks (Flower & Pineau des Forêts 1999; Lesaffre et al. 2004b, 2004a). Flower & Pineau des Forêts (2013) found satisfying non-stationary fits to PACS observations of CO, H₂O, and OH in one protostar, NGC1333 IRAS 4B. However, the predictions of these models for the emission from ionized hydrides have not yet been investigated.

In the following sections, we measure the line ratios of H₂O/CO, H₂O/OH, and CO/OH lines for the entire sample presented here, and compare them to state-of-the-art models of stationary *C*-type shocks illuminated by UV irradiation (Section 5.1). These models predict that a significant fraction of molecules are photodissociated, which increases the abundances of atomic and ionic species, particularly O and C⁺ and light ionized hydrides observed with HIFI (Kristensen et al. 2013). This in turn changes the emission spectrum of these atomic species. To test this hypothesis, we first update the observed molecular line ratios for the full sample, introducing the UV-irradiated shocks (Section 5.1) and comparing the atomic/ionic emission first to stationary shock models (Section 5.2), then to PDR models (Section 5.3), and finally to irradiated shock models (Section 5.4). The reason for this
<figure><img src="image_16.png" /></figure>

**Figure 10.** Ratios of line fluxes in units of erg cm⁻² s⁻¹, comparing different species as a function of logarithm of density of the pre-shock gas, $n_H$. Filled symbols show models of fully shielded C-shocks from Kaufman & Neufeld (1996) (circles), and C-shocks irradiated by UV fields of $G_0 = 0.1$ (squares) and $G_0 = 10$ (stars) from Melnick & Kaufman (2015) and M. Kaufman (2018, in preparation). Models are calculated for pre-shock densities of $v = 15$ km s⁻¹ (green), $v = 20$ km s⁻¹ (red), $v = 30$ km s⁻¹ (orange), and $v = 40$ km s⁻¹ (navy blue). Not shown on the central and right figures are the model ratios for pre-shock density $log_{10}n = 4$ and $G_0 = 10$, which have values ~2 × 10⁻². The observations are shown as light blue boxes. The horizontal blue line indicates the median values of ratios for all sources, and the vertical line demarcates the standard deviation.

approach is to isolate the effects of shocks and UV irradiation (PDR) before combining them.

## 5.1. Molecular Line Ratios versus Models of UV-irradiated Shocks

UV photons have an important impact on the chemical and thermal structure of a shock (Lesaffre et al. 2013; Melnick & Kaufman 2015). The increase in the ionization fraction results in a tighter coupling between the ionized and neutral fluids, and thus decreases the coupling length. The decreased coupling length effectively means that the mechanical energy is deposited more rapidly into the gas, leading to higher peak temperatures for a given shock velocity than in fully shielded shocks. In addition, the molecular and atomic abundances depend strongly on the strength of the radiation field and the gas density. As illustrated in Figure 1 of Melnick & Kaufman (2015), the pre-shock abundance of gas-phase atomic oxygen decreases as the density increases, because more oxygen is frozen-out onto the dust grains when shielded from UV photons. At the same time, the oxygen abundance scales directly with the strength of the UV field, which photodissociates H₂O. At pre-shock densities of 10⁵ cm⁻³, the atomic oxygen abundance is 10⁻⁶–10⁻⁴ for UV fields $G_0$ of 0.1 to 10. H₂O photodissociation also takes place in the post-shock gas, thus efficiently lowering its column-averaged abundance.

The physical conditions in these irradiated shocks depend very strongly on the charge balance, and as such it is crucial to keep accurate track of the charge balance through the shock. This is done in the shock models of Melnick & Kaufman (2015), where both the gas and grain charge balances are calculated at each step of the models, and the model results show that the shocks are stable.

Figure 10 shows the observed line ratios of selected CO, H₂O, and OH lines for the full sample of protostars and the results from stationary C-type shock models (Kaufman & Neufeld 1996). There is a general trend for these shock models to overestimate the observed emission ratios, most clearly seen for the H₂O 404–313/OH 84 µm line ratio. The results obtained for the extended sample of sources presented here are consistent with the narrow ranges obtained for the sample of 22 protostars from Perseus (Karska et al. 2014b). Fully shielded C-type shock models from Kaufman & Neufeld (1996) still

overestimate the ratios when compared to the new observations. The same ratios, calculated using shock models illuminated by UV radiation, show a better agreement with the observations for a range of shock parameters (Melnick & Kaufman 2015; M. Kaufman 2018, in preparation).

The largest difference between the UV and non-UV C-shocks is seen in the ratio of the H₂O 404–313 and OH 84.6 µm lines, which is reduced in the new models by two orders of magnitude at pre-shock densities of 10⁴ and 10⁵ cm⁻³. The ratio of the H₂O 404–313 and CO 16–15 lines is best reproduced by UV-irradiated C-shocks at pre-shock densities of 10⁴–10⁵ cm⁻³, but the differences with respect to the models without UV are small. Similar conclusions hold also for other pairs of H₂O/CO, H₂O/OH, and CO/OH transitions (see Figure 29), as well as for the ratios of total line luminosities in H₂O/OH, etc. (see Section 6.1). Based on these line ratios and the observed chemical signatures (Kristensen et al. 2013), a scenario where emission arises in UV-irradiated stationary shocks seems very likely.

## 5.2. Atomic Line Fluxes versus Stationary Shock Models

Before comparing the observed atomic/ionic emission from O and C⁺ to irradiated shock models, it is instructive to first compare to stationary shock models without external UV radiation. To do so, we use the line fluxes from C- and J-type shock models as presented in Flower & Pineau des Forêts (2015).

The model intensities in units of erg cm⁻² s⁻¹ sr⁻¹ are translated to W cm⁻², assuming that the emission entirely fills one spaxel in the PACS maps (1 sr ~ 2.1 10⁻⁹ π). A size of one spaxel is chosen despite the fact that PACS maps in the [O I] and [C II] lines often show emission extending to more than one spaxel (in this work and Karska et al. 2013), because the actual emitting region observed by each spaxel is likely only a fraction of the spaxel size (i.e., the “filling factor” is below unity). A possible underestimation by a factor of a few of the emitting region size does not affect the conclusions below given the orders of magnitude variations probed by the models and observations.

Comparison of absolute observed and model line fluxes of the [O I] 63 µm and [C II] 158 µm lines are shown in Figure 11 (top panel). The median observed [O I] flux, calculated for
<figure><img src="image_17.png" /><figcaption>**Figure 11.** Absolute fluxes of the [O I] line at 63 µm (top) and the [C II] line at 158 µm (bottom), as predicted by the C- and J-shock models (full lines) of Flower & Pineau des Forêts (2015), and compared to observations (horizontal lines). Median observed fluxes of [O I] shown in the top panel are calculated only for those sources where the emission is associated with the source and not large-scale cloud emission. The minimum detected flux of [O I] is also shown, for reference. With regard to [C II], in the rare cases that the line is actually detected and spatially associated with the source, the fluxes are on the order of magnitude shown on the figure.</figcaption></figure>

sources with emission spatially associated with YSOs, equals ~4 · 10⁻²⁰ W cm⁻² and falls between the predictions for the C- and J-type shock models for a wide range of shock velocities. The C-type shock model fluxes are insensitive to the shock velocities; they equal ~10⁻²¹ W cm⁻² for a pre-shock density of 10⁵ cm⁻³, and ~10⁻²² W cm⁻² for a pre-shock density of 10⁴ cm⁻³. These values are clearly inconsistent with the data.

The J-type shock model fluxes, on the other hand, fit even the brightest observed [O I] lines. A sharp increase from about 10⁻²² W cm⁻² to 10⁻¹⁸ W cm⁻² occurs when the shock becomes dissociative, at velocities of about 20 km s⁻¹. Depending on the size of the emitting region, which is likely to be lower than the full spaxel area, the observations of all absolute line fluxes of [O I] can be reproduced with J-type shocks.

The observed fluxes and limits of the [C II] line at 158 µm greatly exceed the model predictions for both C- and J-type shock models (Figure 11, bottom panel). Whenever the line is detected and associated with a YSO, the fluxes exceed 10⁻²¹ W cm⁻², four orders of magnitude above the model C-shock fluxes and a factor of a few above the peak [C II] flux from the J-shocks, at velocities of about 30 km s⁻¹. In the majority of the sources, however, the [C II] line is not detected and only an upper limit can be used for comparisons with the

<figure><img src="image_18.png" /><figcaption>**Figure 12.** Observed line ratio of the [C II] line at 158 µm and the [O I] line at 63 µm, as functions of the [C II] line intensity (blue circles). Models of PDRs from Kaufman et al. (1999) are shown for densities from 10³ to 10⁷ cm⁻³ (in dashed lines) and for incident UV from 10¹ to 10⁶.⁵ G₀ (in solid lines). Small magenta dots and crosses indicate line ratios, assuming that 90% and 75% of [O I] flux comes from the jet, respectively. Two cloud-related PDR regions in the W40 cloud are shown with blue diamonds.</figcaption></figure>

models. For those sources, the observed limit is consistent with both J- and C-type shocks.

### 5.3. Atomic Line Fluxes versus Models of Photodissociation Regions

As shown in the previous section, stationary C-type shock models produce [O I] and [C II] emission (when detected) at levels that are insufficient by several orders of magnitude. Because [C II] is a well-known PDR tracer, it is instructive to check whether PDR models could explain the observed fluxes.

Producing [C II] emission in sufficient quantities requires hard UV photons with $\lambda < 1100$ Å, likely originating in the vicinity of the protostar, in accretion flows at the accretion shock boundary layer and/or fast bow-shock (e.g., Spaans et al. 1995; van Kempen et al. 2009a). Models of PDRs (Tielens & Hollenbach 1985) can be used to constrain the UV field and densities by using the absolute intensities of atomic and ionic lines, as well as molecules.

In our case, where most of the molecular emission and some of the [O I] emission likely originate in shocks, comparisons to the absolute line intensities of [C II] are the most reliable measure of FUV alone. To better constrain the range of possible parameters, the ratio of [C II] and [O I] can be used, taking into account that a fraction of the [O I] emission may arise in from dissociative shocks associated with the jets. This ratio rapidly decreases with density, controlled mainly by [O I] due to its high critical density of about ~5 · 10⁵ cm⁻³, which is two orders of magnitude higher than for [C II] (Kaufman et al. 1999).

Figure 12 compares the observed [C II]/[O I] versus [C II] intensities for the subset of sources detected in [CII] to the PDR model predictions from Kaufman et al. (1999). The [C II] intensities are calculated assuming a size of one spaxel, and shown only for sources where the [C II] emission is spatially associated with YSOs. The range of observed [C II] intensities is 10⁻⁵–10⁻⁴ erg cm⁻² s⁻¹ sr⁻¹, whereas [C II]/[O I] ranges from 10⁻² to 10⁰. The corresponding model densities range from 10⁵ to 10⁶ cm⁻³. The majority of the sources show a very similar incident UV field, about 10² G₀ on scales of ~1000 au,
with the exception of a more massive source, Serpens SMM1 (#66), which is in the $10^3 G_0$ regime. Independent, high angular resolution observations of free-free emission on scales of <1000 au illustrate the presence of a strong UV field toward this source (Hull et al. 2016).

Possible contributions from shocks to the [O I] intensity would decrease both the densities and the UV field matching the observations (see Figure 12). For example, if 90% of [O I] flux comes from the shock, corresponding to an increase in the observed [C II]/[O I] by a factor of 10, the best-fit densities are in the range $10^4-10^5 \text{ cm}^{-3}$ and UV field of ~$10^1-10^2 G_0$. In fact, the spectrally resolved line profile of [O I] in a single outflow position in NGC1333 I4A, observed with SOFIA-GREAT by Kristensen et al. (2017a), resembles the high-velocity H$_2$O and CO 16–15 profiles associated with the shocks observed with Herschel by Santangelo et al. (2014a). Similarly, [C II] profiles from HIFI, obtained for a subsample of WISH sources, reveal that the origin of emission may be shocks rather than a PDR (Kristensen et al. 2013; Benz et al. 2016). These factors suggest that the actual position of the PDR-only emission in these sources lies above and to the left of the observed fluxes, so the densities and $G_0$ values should be considered as upper limits.

Finally, we note that the diagnostic diagram from Figure 12 can be used to distinguish between PDRs associated with YSOs and clouds. For comparison with the local PDRs, two sources observed within a strong PDR in the W40 cloud (W40-MM26 and W40-MM27) are shown. Both of them are located in the low-density and high-UV regime that is very distinct from the other observed YSOs.

## 5.4. Atomic Line Fluxes versus Models of UV-irradiated Shocks

Velocity-resolved spectra clearly suggest that [O I] and [C II] emission is associated with shocks (e.g., Benz et al. 2016; Kristensen et al. 2017a). The two previous Sections (5.2 and 5.3) suggest that the same place stationary shocks fail is where PDR models succeed, i.e., in reproducing the atomic/ionic emission. This, in turn, suggests that for these species, shocks set the dynamics and PDRs set the chemistry and excitation.

The presence of UV photons increases the ionization fraction in the pre-shock gas, leading to gas that is hotter and more compressed for a given shock velocity than without FUV photons (Melnick & Kaufman 2015). In addition, the pre-shock gas-phase abundances are altered and depend strongly on the strength of the radiation field and the gas density. For low values of the field, more O-bearing species are locked in ices, while for high fields they are desorbed into the gas phase. FUV radiation can also photodissociate H$_2$O in the post-shock gas, and thus lower the column-averaged abundance of H$_2$O and increase the O abundance (see Kristensen et al. 2017b, for an example calculation).

The abundances of atomic species are therefore expected to be significantly higher in UV illuminated shocks, with respect to models of shielded shocks. Figure 13 shows that the fluxes of the [O I] and [C II] scale directly with the assumed UV fields; indeed, they are a few orders of magnitude above fully shielded C-shock models (Flower & Pineau des Forêts 2015). The critical density of [O I] at 63 µm is ~5 × $10^5 \text{ cm}^{-3}$, and so, in the models assuming pre-shock densities of $n = 10^5 \text{ cm}^{-3}$, the absolute line flux quickly increases even at low pre-shock velocities ($v \sim 5–10 \text{ km s}^{-1}$). At higher shock velocities, the

<figure><img src="image_19.png" /><figcaption>**Figure 13.** Absolute fluxes of the [O I] line at 63 µm (top) and the [C II] line at 158 µm (bottom) predicted by C- (full, red) and J-shock (dashed) models of Flower & Pineau des Forêts (2015) and UV-illuminated C-shock models (Melnick & Kaufman 2015: M. Kaufman 2018, in preparation) for $G_0 = 0.1, 1,$ and 10 (full lines, green to blue). All models assume a pre-shock density of $10^5 \text{ cm}^{-3}$. The observed fluxes shown as horizontal lines are the same as in Figure 11.</figcaption></figure>

line flux changes are small, up to a factor of 2, between 10 and $20 \text{ km s}^{-1}$. The maximum shock velocities, above which the shock becomes dissociative, are lower than in the fully shielded C-shocks, equal to about $30 \text{ km s}^{-1}$ for $G_0 = 0.1$ and $20 \text{ km s}^{-1}$ for $G_0 = 10$ (all values for pre-shock densities of $10^5 \text{ cm}^{-3}$). Similar trends are seen for the [C II] line, except that the initial rise is shallower due to the lower critical density of the line (~$3 \times 10^3 \text{ cm}^{-3}$).

The model line fluxes predicted by UV illuminated C-shocks agree well with the detected [O I] line luminosities and non-detections of [C II] emission for the majority of the sources (Figure 11). The maximum value of the [O I] 63 µm flux observed with PACS is ~$1.5 \cdot 10^{-18} \text{ W cm}^{-2}$, setting the upper limit on UV fields of $G_0 = 1$. The median [O I] flux is about two orders of magnitude lower, suggesting that the “filling factor” of the UV illuminated shocks is below unity, similar to the conclusions drawn from the HIFI H$_2$O line energetics (Mottram et al. 2014).

# 6. Discussion

## 6.1. Origin of Far-IR Emission in FUV-irradiated C-shocks

Far-IR line emission observed with Herschel toward low-mass protostars is characterized by: (i) a spatially extended pattern along the outflow direction, in cases where emission is resolved, but not spatially coincident with the low-J CO
entrained gas (see Section 3.2, Karska et al. 2013; Nisini et al. 2015); (ii) broad molecular line profiles with velocities up to ~50 km s⁻¹ (Kristensen et al. 2012, 2017b; San José-García et al. 2013; Mottram et al. 2014, 2017); (iii) a universal CO rotational temperature of ~300 K, independent of protostellar luminosity (see Section 4.1, Manoj et al. 2013, Karska et al. 2013, Green et al. 2013; Matuszak et al. 2015; Jiménez-Donaire et al. 2017); (iv) an overall cooling budget in far-IR lines similar to predictions of stationary C-type shocks (see Section 4.2, Karska et al. 2013; Lee et al. 2014a). Altogether, these characteristics suggest that the bulk of emission arises either in outflow cavity shocks (e.g., Mottram et al. 2014) or in the molecular disk wind (Panoglou et al. 2012; Yvart et al. 2016).

Comparisons of specific line fluxes with shock models offer an opportunity to further determine the pre- and post-shock density of the gas, as well as the shock parameters themselves (its velocity and type, dependent on the ionization fraction and the presence of a magnetic field). However, many different shock models reproduce the observed line fluxes of certain far-IR species for individual targets, resulting in a broad range of the derived shock parameters (e.g., Benedettini et al. 2012; Dionatos et al. 2013; Santangelo et al. 2013; Busquet et al. 2014; Lee et al. 2014a). A more homogeneous comparison of ~20 protostars in Perseus with stationary C- and J-type shock models from Kaufman & Neufeld (1996) and Flower & Pineau des Forêts (2010) illustrated that, in fact, none of those models can reproduce line ratios of different species (e.g., H₂O/CO, H₂O/OH, and CO/OH, Karska et al. 2014b). Additionally, stationary shock models alone cannot reproduce the observed CO ladders of Class 0/I protostars (van Kempen et al. 2010b; Visser et al. 2012).

In Section 5, we showed the model predictions of far-IR spectra for shocks propagating at pre-shock densities of 10³–10⁵ cm⁻³ and irradiated by UV fields of G₀ equal 0.1, 1, and 10 (Melnick & Kaufman 2015; M. Kaufman 2018, in preparation). Line ratios such as H₂O 4₀₄ – 3₁₃/OH 84 µm generally decrease in the presence of UV photons that photodissociate H₂O into OH and O. Stationary C-type shocks also clearly cannot account for the emission in O and C⁺ (Figure 11), but separating the emission from the shock and the possible PDR is non-trivial with unresolved line profiles. The order of magnitude estimates of UV fields with PDR models require assumptions about the contribution of the jet in the [O I] emission (Figure 12).

The C-shock models illuminated by FUV are in agreement with *selected* line ratios presented in Karska et al. (2014b). A comparison involving all observed transitions is shown in Figure 14. The total far-infrared line luminosities in H₂O, CO, and OH were calculated in Section 4.2, and their sum is indicated as L<sub>FIRL</sub>. The total line luminosities from the models are calculated using the transitions accessible with PACS: the H₂O lines located in the 56–94.7 µm and 108.0–180.5 µm ranges, the CO lines with J<sub>up</sub> = 14–25 and 26–49, and 8 OH doublets (at 65, 71, 79, 84, 119, and 163 µm). The observed ratios of H₂O/CO, H₂O/OH, CO/OH, and H₂O/[O I] show a Gaussian distribution, and therefore are representative for the entire sample (Figure 25).

The trends in the model line ratios result from the amount of oxygen available in the gas phase and the length scale over which the temperature and abundances are elevated behind the shock. The abundance of oxygen scales almost linearly with the

<figure><img src="image_20.png" /><figcaption>**Figure 14.** Ratios of total line luminosities in various far-infrared species, as predicted by UV illuminated C-type shock models (solid lines) and calculated from the observations (light blue boxes), as a function of pre-shock densities. All models corresponding to shock velocities *v* equal 20 km s⁻¹ and UV fields parameterized by G₀ equal 10 (in blue) and 0.1 (in orange). Observed minimum and maximum values of line ratios are calculated excluding lower limits. The median values from observations are shown as horizontal lines.</figcaption></figure>

logarithm of G₀/n (Melnick & Kaufman 2015; M. Kaufman 2018, in preparation), and thus, for stronger UV fields and for a given pre-shock density, the abundance of H₂O is larger (see the trends in the H₂O/CO ratio). Additionally, the length scale is inversely proportional to the square root of pre-shock density (L ~ 1/√n) at the assumed A<sub>V</sub> = 10, so for larger pre-shock densities, the shock-averaged column of H₂O decreases (see Figure 2 in Melnick & Kaufman 2015).

Because H₂O is efficiently formed by hydrogenation of OH at *T* > 230 K (Bergin et al. 1998), the peak abundance of H₂O behind the shock corresponds to the drop in the OH abundance. Further out from the shock, H₂O is photodissociated by the UV photons, and a higher G₀ means a lower H₂O/OH ratio (see Figure 14). The increase in OH abundances with increasing UV field also explains the decrease of the CO/OH ratio for G₀ = 10. The trend in H₂O/[O I] resembles that of H₂O/OH, except that at densities as low as 10³ cm⁻³, both H₂O and OH are efficiently photodissociated, and the ratio of the H₂O/[O I] for high G₀ drops to ~10⁻². The balance between O, OH, and H₂O also depends on the H/H₂ ratio and temperature, which have to be considered.

The ratios of total line luminosities calculated from the models and from the observations show a good agreement with the observed range of pre-shock densities, 10⁴–10⁵ cm⁻³. The H₂O/OH and H₂O/[O I] ratios are also explained by the pre-shock densities of 10³ cm⁻³, but CO is not well-reproduced at these lower densities. The UV fields considered here (G₀ of 0.1 and 10) and illuminating C-shocks produce model line ratios in the same range as the observed ratios.
## 6.2. Impact of UV Irradiation on the CO Ladder

The shape of the CO ladder in the far-IR is universal across Class 0 and I protostars (Section 4.1, e.g., Green et al. 2013; Karska et al. 2013; Manoj et al. 2013; Lindberg et al. 2014) as well as across several orders of magnitudes in luminosity (Karska et al. 2014a; Mashian et al. 2015; Matuszak et al. 2015). In the energy range covered by $J_{up} = 14–24$, the CO rotational diagram typically consists of a single linear component, corresponding to the temperature of 320 K with a standard deviation <20% (the so-called “warm” component). Out of 90 sources from our sample, 59 protostars show the warm component. Out of those protostars, 21 sources (more than 1/3) show an additional linear component corresponding to the temperature of ~720 K with a standard deviation <20% (the so-called “hot” component).

Several interpretations have been proposed to explain the shape of the CO ladder in low-mass protostars. Visser et al. (2012) modeled the shape of the PACS CO ladder in three objects with a combination of passively heated envelope, UV-heated cavity walls, and small-scale C-type shocks. The bulk of emission was attributed to a PDR and shocks, with a tentative trend of UV photons having an increased role for more evolved sources. Indeed, more recent models confirm that the 300 K component in CO ladders can be well-reproduced even by pure UV heating of the outflow cavities (Lee et al. 2014b, 2015). Observationally, the presence of UV photons is supported by extended emission in $^{13}$CO $J = 6–5$, which delineates the outflow cavity walls in nearby protostars (Yıldız et al. 2012, 2015). However, the CO transitions in a broad range of $J$ levels cannot be explained by UV heating alone.

Neufeld (2012) reproduced the curved shape of the rotational diagram using a single component fit, assuming a subthermal excitation of CO (densities of ~$10^3$ cm$^{-3}$ and temperatures above 1000 K). Apart from the the sources with the highest-$J$ CO transitions, successful fits of this kind were obtained for most of the protostars observed in the HOPS and DIGIT key programs (Green et al. 2013; Manoj et al. 2013). An alternative approach considers the ladder as the combination of two distinct physical components, with densities above ~$10^4–10^5$ cm$^{-3}$ (e.g., Karska et al. 2013). Flower & Pineau des Forêts (2013) associate those two components with C- (warm component) and $J$- (hot component) shocks, while Neufeld et al. (2014) explain them as a combination of shocks with different velocities. A comprehensive analysis of the high-$J$ CO line profiles from HIFI associates two distinct velocity components with two excitation components, corresponding to the warm and hot PACS components (Kristensen et al. 2017b).

As shown in previous section, the observed far-IR line fluxes are mostly produced in C-type shocks, which are likely ubiquitous in the regions of outflow-envelope interactions. At the same time, there is a strong spatial and kinematic association of high-$J$ CO emission with H$_2$O (Kristensen et al. 2012, 2017b; Yıldız et al. 2013; Mottram et al. 2014, 2017). The required pre-shock densities are on the order of $10^5–10^6$ cm$^{-3}$, translating to densities >$10^6$ cm$^{-3}$, adopting a compression factor of ≥10 in these C-type shocks (see Section 5.3 in Karska et al. 2013).

The only feasible alternative to C-type shocks are molecular disk winds, where excitation of H$_2$O and high-$J$ CO is caused by processes to those in molecular shocks (Panoglou et al. 2012; Yvart et al. 2016). The wind models match the velocity-resolved H$_2$O 557 GHz and more highly excited line

<figure><img src="image_21.png" /><figcaption>**Figure 15.** Synthetic CO ladders calculated using C-shock models irradiated by UV photons (Melnick & Kaufman 2015; M. Kaufman 2018, in preparation). The models are calculated for a pre-shock density of ~$10^5$ cm$^{-3}$, a shock velocity of $v = 20$ km s$^{-1}$, and two values of UV fields: $G_0 = 0.1$ (yellow) and 10 (blue).</figcaption></figure>

profiles very well, but predictions for high-$J$ CO lines like those presented here are not yet available.

Fully shielded, stationary C-shock models cannot reproduce the entire CO ladder at once (van Kempen et al. 2010b; Visser et al. 2012). It is therefore interesting to explore the effect of UV irradiation of shocks on the shape of those CO ladders. Figure 15 compares two C-shock models calculated for UV fields $G_0$ equal of 0.1 and 10 (Melnick & Kaufman 2015; M. Kaufman 2018, in preparation), for a single pre-shock density of ~$10^5$ cm$^{-3}$ and a shock velocity of $v = 20$ km s$^{-1}$. The data points correspond to the transitions located in the PACS range, up to $J_{up} = 36$ (at 72.8 µm).

Two linear fits to the diagrams give rotational temperatures of ~340 K and ~530 K for the $G_0$ of 0.1, and temperatures of ~470 K and ~710 K for the $G_0$ of 10. Clearly, in the presence of very low UV fields ($G_0 = 0.1$), the CO rotational temperature of the warm component is in good agreement with observations (see Figure 6). The temperature of the hot component is within the observed ranges as well. Similarly, the model with $G_0$ of 10 shows the hot component characterized by a temperature of about ~710 K, which is higher but still consistent with observations. The warm component temperature here is at the higher end of the observations (Figure 6). A full grid of models is required to assess whether a single model can account for the entire CO ladder.

Observationally, the high-temperature component at CO ladders is detected in 21 sources (Section 4.1) and can be associated with a specific Gaussian component in the velocity-resolved line profiles from HIFI (Kristensen et al. 2017b). The fraction of emission in this particular profile component, compared to the rest of the emission associated with the bulk outflow, is ~20% (hot component) and ~80% (warm component) of the total line emission. This is in agreement with the fractions contributed by the warm and hot components seen on CO rotational diagrams. The absence of the hot component in the majority of the sources is due to low S/N rather than the presence or lack of UV radiation.

In summary, preliminary models of C-shocks irradiated by FUV qualitatively explain the decrease in the amount of H$_2$O
<table><caption>**Table 5**
Evolution of far-IR Line Luminosities</caption><thead><tr><th rowspan="2"></th><th colspan="2">Class 0</th><th colspan="2">Class I</th></tr><tr><th>Mean</th><th>Median</th><th>Mean</th><th>Median</th></tr></thead><tbody><tr><td>log<sub>10</sub>(L<sub>CO</sub>/L<sub>bol</sub>)</td><td>-3.37</td><td>-3.21</td><td>-3.66</td><td>-3.56</td></tr><tr><td>log<sub>10</sub>(L<sub>CO</sub>/L<sub>FIRL</sub>)</td><td>-0.47</td><td>-0.35</td><td>-0.66</td><td>-0.53</td></tr><tr><td>log<sub>10</sub>(L<sub>H<sub>2</sub>O</sub>/L<sub>bol</sub>)</td><td>-3.60</td><td>-3.50</td><td>-3.73</td><td>-3.57</td></tr><tr><td>log<sub>10</sub>(L<sub>H<sub>2</sub>O</sub>/L<sub>FIRL</sub>)</td><td>-0.83</td><td>-0.71</td><td>-0.85</td><td>-0.75</td></tr><tr><td>log<sub>10</sub>(L<sub>OH</sub>/L<sub>bol</sub>)</td><td>-3.97</td><td>-3.86</td><td>-3.85</td><td>-3.82</td></tr><tr><td>log<sub>10</sub>(L<sub>OH</sub>/L<sub>FIRL</sub>)</td><td>-1.18</td><td>-0.98</td><td>-0.90</td><td>-0.81</td></tr><tr><td>log<sub>10</sub>(L<sub>[OII]</sub>/L<sub>bol</sub>)</td><td>-3.53</td><td>-3.55</td><td>-3.52</td><td>-3.65</td></tr><tr><td>log<sub>10</sub>(L<sub>[OII]</sub>/L<sub>FIRL</sub>)</td><td>-0.81</td><td>-0.75</td><td>-0.60</td><td>-0.55</td></tr><tr><td>log<sub>10</sub>(L<sub>H<sub>2</sub>O</sub>/L<sub>CO</sub>)</td><td>-0.30</td><td>-0.33</td><td>-0.19</td><td>-0.13</td></tr><tr><td>log<sub>10</sub>(L<sub>H<sub>2</sub>O</sub>/L<sub>OH</sub>)</td><td>0.42</td><td>0.32</td><td>0.07</td><td>0.07</td></tr><tr><td>log<sub>10</sub>(L<sub>CO</sub>/L<sub>OH</sub>)</td><td>0.68</td><td>0.68</td><td>0.26</td><td>0.23</td></tr><tr><td>log<sub>10</sub>(L<sub>H<sub>2</sub>O</sub>/L<sub>[OII]</sub>)</td><td>-0.003</td><td>0.04</td><td>-0.23</td><td>-0.24</td></tr></tbody></table>

relative to, e.g., CO and OH, and perhaps the excitation of the highest-*J* CO lines. The average values of UV fields that match our observations are on the order of 0.1–10 times the interstellar radiation field. The order-of-magnitude estimates of UV fields presented here are in agreement with a recent survey of ionized hydrides, where UV fields determined in low-mass protostars are 2–400 times the interstellar value (Benz et al. 2016).

The next step is to calculate a full grid of shock models in order to verify that the conclusions reached here, based on just a few model calculations, are robust. This will further assist in demonstrating that the warm component is reproduced by a large range of shock conditions.

### 6.3. Evolution of the Far-infrared Line Emission

The changes in physical processes and conditions as the protostar evolves from Class 0 to Class I should be reflected in the cooling by various atomic and molecular species and the total far-IR gas cooling budget.

As demonstrated in Figure 8 (Section 4.2.2), the distributions of line luminosities over $L_{bol}$ for each far-IR species are similar between Class 0 and Class I protostars, except for CO. The overall line cooling is dominated by CO and H$_2$O, followed by [O I] and OH, consistent with previous surveys (Karska et al. 2013). The spread in line luminosities—both absolute and divided by $L_{bol}$—is significant for both Class 0 and I protostars (see Table 5). In order to track the evolutionary changes, we therefore normalize the line cooling in each species with the total line luminosity in the far-IR, defined by Nisini et al. (2002) as $L_{FIRL} = L_{CO} + L_{[O I]} + L_{H2O} + L_{OH}$. As a result, the spread of values within each class of objects decreases (see Table 5).

Figure 16 illustrates how line luminosities of CO, H$_2$O, [O I], and OH change between the Class 0 and I stages. The dominant cooling in the CO lines in Class 0 protostars decreases by a factor of ~2.3. On the other hand, the line cooling in H$_2$O, [O I], and OH do not change significantly. This is confirmed by two-sample Kolmogorov–Smirnov (K–S) tests comparing the ratios of line luminosities over $L_{bol}$ for Class 0 and I sources. Only the $L(CO)/L_{bol}$ ratio shows a statistically significant

<figure><img src="image_22.png" /><figcaption>**Figure 16.** Median line cooling in CO, H$_2$O, [O I], and OH over bolometric luminosities (top) and total far-IR line cooling (bottom) for Class 0 and Class I sources.</figcaption></figure>

difference between these evolutionary stages (6% chance of being drawn from the same distribution). Thus, the less-evolved sources emit more copiously in CO, which—unlike H$_2$O—is not easily destroyed by photodissociation (Kristensen et al. 2017b).

The redistribution of cooling in molecular and atomic channels does not strongly affect the total far-IR line cooling ($L_{FIRL}$), which decreases only by a factor of 1.2, from $4.5 \times 10^{-3} L_{\odot}$ in Class 0 to $3.7 \times 10^{-3} L_{\odot}$ in Class I. We find that $L_{FIRL}$ shows no significant correlation with $T_{bol}$, but clearly correlates with $L_{bol}$ (Figure 17), consistent with previous studies (Nisini et al. 2002; Karska et al. 2013). The difference between Class 0 and I objects is confirmed by K–S tests, with a probability of less than 1% that the $L_{FIRL}$ are drawn from the same distribution. Removal of the $L_{FIRL}-L_{bol}$ dependence, i.e., the quantity $L_{FIRL}/L_{bol}$, would allow us to isolate a very weak relation with the bolometric temperature, but the K–S test fails due to the large spread of values. This large spread of $L_{FIRL}/L_{bol}$ values, on top of the decrease in total far-IR cooling with time, shows that the processes responsible for the line cooling likely depend on object-to-object characteristics, e.g., local environment and the amount of UV radiation illuminating the shocked gas.

An almost linear relation between the total far-IR cooling and bolometric luminosity ($L_{FIRL} \sim 10^{-2} L_{bol}$) was first reported based on *ISO* data and interpreted as a consequence of a wind/jet interactions with the surroundings, driven by protostellar accretion and subsequent ejection (Giannini et al. 2001; Nisini et al. 2002). In fact, $L_{FIRL}$ can be used as a direct measure of mechanical luminosity deposited by the jet/outflow (Maret et al. 2009). For $v = 15$ km s$^{-1}$ shocks propagating into the ambient density of $10^5$ cm$^{-3}$ and illuminated by UV fields $G_0 = 1$ (Section 5), the mass-loss rates corresponding to the observed line cooling can be calculated following Equation (2) from Maret et al. (2009):

$$ \frac{1}{2} \dot{M} v^2 = (1 - f_m) \frac{1}{f_x} L_{FIRL}. \quad (1) $$

Adopting $(1 - f_m) \sim 0.75$ and $f_x \sim 0.25$, where $f_m$ is the fraction of shock mechanical energy translated into excitation, and $f_x$ is the fraction of cooling due to far-IR transitions of CO, H$_2$O, [O I], and OH for the best-fitting shock model (the remaining cooling contributed by H$_2$), we find mass-loss rates of, $\dot{M} \sim 5 \times$
<figure><img src="image_23.png" /><figcaption>**Figure 17.** Top panel shows total far-infrared line luminosity ($L_{FIRL}$) vs. bolometric luminosity for Class 0 (red symbols) and Class I sources (blue symbols), respectively. Triangles show the sources where lower limits of $L_{FIRL}$ are calculated. Pink dots denote sources where the line cooling in at least one species is 0. The black solid line shows a fit to the entire sample, and the red dashed line shows a fit to the Class 0 sources with at least one detection in each species and with lower limits excluded. The bottom pane is the same as above, but $L_{FIRL}/L_{bol}$ is plotted vs. the bolometric temperature.</figcaption></figure>

$10^{-7} M_{\odot} \text{yr}^{-1}$ for Class 0 protostars and $\dot{M} \sim 4 \times 10^{-7} M_{\odot} \text{yr}^{-1}$ for Class I protostars.

Mass-loss rates on the order of $10^{-7} M_{\odot} \text{yr}^{-1}$ are consistent with the rates calculated using the fully sampled maps of outflows from Class 0 protostars obtained in the [O I] line at 63 µm (Nisini et al. 2015; Mottram et al. 2017). Using such maps, the [O I] jet tangential velocity and its length projected onto the plane of the sky can be determined, but similar observations are not available for a statistical sample of protostars. In fact, the sources mapped as part of this project are well-known for their bright outflows, and the derived mass-loss rates from the [O I] line are probably at the higher end of the expected values. Thus, examining the total far-IR line cooling coupled with shock models seems to be a valid method of determining the mass-loss rates for protostars, and more reliable than the [O I] alone.

Mottram et al. (2017) found that the ratio of mass in the entrained outflow to the envelope mass varies between ~0.1% and 10%, peaking at about 1% for both Class 0 and I protostars

in the WILL sample. In this context, similar values of the mass-loss rates found here are generally in agreement with their argument in favor of an approximately constant entrainment efficiency per unit length during Class 0/I. The relatively low values of the mass-loss rate of $10^{-7} M_{\odot} \text{yr}^{-1}$ suggest that the core-to-star formation efficiency is likely higher than 50%.

## 7. Summary and Conclusions

Herschel/PACS observations in the surroundings of low-mass protostars characterize the cooling of the gas at the earliest stages of star formation. A combination of atomic and molecular tracers provides hints about the underlying heating processes that produce the hot gas observed here. The bulk of molecular emission traces non-dissociative shocks occurring in the outflows. UV photons influence the chemistry in those shocks, altering the abundances of key cooling species. Our main conclusions, addressing each of the questions raised in the introduction, are:

1. Rich far-IR line emission of H$_2$O, CO, OH, and [O I] is detected in ~70% of the targeted sources, allowing the statistical and unbiased analysis of such emission in the largest sample of protostars so far.

2. Lines of H$_2$O and CO $J_{up} \ge 14$ are strongly correlated, and a weaker relation is found between the molecular species and [O I].

3. Fifty-six percent of sources show compact atomic and molecular emission on $10^3$ au scales. The remaining sources show extended emission on at least $10^4$ au scales covered within our survey, mostly in [O I]. Twenty-five sources (28%) show clear extended emission in molecular tracers. Among 17 sources that show extended emission in both CO and H$_2$O lines, 11 are Class 0 objects. At the same time, only 5 out of 13 sources with extended emission in [O I] are Class 0 objects. The emission is extended along the direction of the outflow seen in the CO 3–2 maps of the regions, but not emitting from the same gas (Mottram et al. 2017).

4. In 10 sources for which the [O I] shows extended emission on $10^4$ au scales, a high-velocity ($v \ge 90 \text{ km s}^{-1}$) component emerges in the line profiles. Thus, [O I] is closely related to the atomic jet, as suggested by previous studies (e.g., Nisini et al. 2015). However, the bulk of the [O I] emission is spectrally unresolved.

5. Analysis of the molecular excitation using rotational diagrams gives a median $T_{\text{rot}} \sim 320 \text{ K}$ for CO ($E_{\text{up}} \le 1800 \text{ K}$), $T_{\text{rot}} \sim 130 \text{ K}$ for H$_2$O ($E_{\text{up}} \le 700 \text{ K}$), and $T_{\text{rot}} \sim 85 \text{ K}$ for OH. Additionally, emission from hot CO and H$_2$O is detected for 24% and 10% of sources, respectively, covering a broad range of rotational temperatures with a median at ~720 K for CO and at ~410 K for H$_2$O. Densities $\gtrsim 10^4 \text{ cm}^{-3}$ and kinetic temperatures $\gtrsim 300 \text{ K}$ are required to explain the excitation.

6. The far-IR line cooling budget in Class 0 sources is dominated by CO (~40%), followed by H$_2$O and [O I] ($\gtrsim 20\%$). In Class I sources, the cooling is dominated by [O I] (~40%), and CO and H$_2$O ($\gtrsim 20\%$). The fractions of cooling contributed by various species do not depend strongly on bolometric luminosity.

7. Line flux ratios of different molecules (e.g., H$_2$O/OH, H$_2$O/CO) suggest that the bulk of emission does not arise in standard C-type shocks. These ratios, along with observations of light hydrides (Kristensen et al. 2013; Benz et al. 2016) and low H$_2$O absolute abundances
(Kristensen et al. 2017b) instead point to emission originating in UV-irradiated shocks.

8. Models of UV-irradiated shocks successfully reproduce molecular line ratios for pre-shock densities of ~$10^5$ cm$^{-3}$ and $G_0$ of ~0.1–10. More detailed modeling is required to match emission from individual sources to specific shock models.

9. Comparisons of the atomic line fluxes with stationary shock models show that the observations cannot be reproduced with non-dissociative C-shocks. While the [O I] fluxes could be mitigated with an additional J-shock component, the [C II] line detected in 10 sources requires UV irradiation. Comparisons to models of PDRs allow us to estimate the strength of the UV fields $G_0$ ~ 10, assuming that 90% of the [O I] emission arises in the dissociative jet shocks.

10. New models of C-shocks illuminated by UV can reproduce the absolute line fluxes of [O I] and non-detections of [C II].

11. Far-IR line cooling does not change significantly from the Class 0 to Class I stage. As a proxy of the mechanical energy deposited by the jet/outflow, this allows the calculation of mass-loss rates of $10^{-7} M_{\odot} yr^{-1}$. These relatively low values suggest that the core-to-star formation efficiency is likely higher than 50%. The nearly constant value obtained for Class 0 and I sources implies that the accretion/ejection and associated feedback mechanisms are comparable across the protostellar evolution.

We wish to thank the entire WISH, DIGIT, and WILL teams for stimulating discussions and the common effort in analyzing and interpreting the Herschel observations. A.K. acknowledges support from the Foundation for Polish Science (FNP) and the Polish National Science Center grants 2013/11/N/ST9/00400 and 2016/21/D/ST9/01098. Sub-millimeter astronomy in Copenhagen is supported by the European Research Council (ERC), under the European Unions Horizon 2020 research and innovation programme (grant agreement No 646908) through ERC Consolidator Grant “S4F.” Herschel was an ESA space

observatory with science instruments provided by the European-led Principal Investigator consortia, and with important participation from NASA. Astrochemistry in Leiden is supported by the Netherlands Research School for Astronomy (NOVA), by a Royal Netherlands Academy of Arts and Sciences (KNAW) professor prize, by a Spinoza grant, and by grant 614.001.008 from the Netherlands Organisation for Scientific Research (NWO). J.C.M. acknowledges support from the European Research Council under the European Community’s Horizon 2020 framework program (2014–2020) via the ERC Consolidator grant “From Cloud to Star Formation” (CSF) (project number 648505). Support for this work, part of the Herschel Open Time Key Project Program, was provided by NASA through an award issued by the Jet Propulsion Laboratory, California Institute of Technology. N.S. acknowledges support from the Polish National Science Center grant 2014/15/B/ST9/02111. Research conducted within the scope of the HECOLS International Associated Laboratory was supported in part by the Polish NCN grant DEC-2013/08/M/ST9/00664.

## Appendix A: Rotational Diagrams

Figures 18 and 19 show CO rotational diagrams for the WILL sources. Separate linear fits are done to the transitions located in the warm and hot components, the same as used in Karska et al. (2013) and Green et al. (2013). Figures 20 and 21 show H$_2$O rotational diagrams with only one linear fit to all observed lines. Table 3 summarizes the results for all sources.

Figures 24(a)–(j) show CO, H$_2$O, and OH rotational diagrams for the DIGIT sources. Separate linear fits are done at CO diagrams to the transitions located in the warm and hot components and single component fits to the H$_2$O and OH diagrams. Tables 6 and 7 show H$_2$O and OH rotational temperatures and numbers of emitting molecules calculated using all available lines (full scans) and the subsets of lines, corresponding to those targeted by the WISH and WILL surveys (line scans).

<table><caption>**Table 6**
Comparison of H$_2$O Rotational Temperatures and Numbers of Emitting Molecules</caption><thead><tr><th rowspan="2">ID</th><th rowspan="2">Source</th><th colspan="2">Full Spectra</th><th colspan="2">WISH Line Scan</th><th colspan="2">WILL Line Scan</th></tr><tr><th>T<sub>rot</sub>(K)</th><th>log<sub>10</sub>N</th><th>T<sub>rot</sub>(K)</th><th>log<sub>10</sub>N</th><th>T<sub>rot</sub>(K)</th><th>log<sub>10</sub>N</th></tr></thead><tbody><tr><td>3</td><td>L1448 C(N)</td><td>152(18)</td><td>46.3(0.2)</td><td>151(19)</td><td>46.4(0.2)</td><td>176(24)</td><td>46.2(0.2)</td></tr><tr><td>4</td><td>L1448 C(S)</td><td>84(11)</td><td>46.3(0.3)</td><td>89(14)</td><td>46.3(0.3)</td><td>83(16)</td><td>46.1(0.4)</td></tr><tr><td>6</td><td>L1455 IRS1</td><td>124(30)</td><td>45.6(0.3)</td><td>97(24)</td><td>45.6(0.3)</td><td>132(18)</td><td>45.4(0.2)</td></tr><tr><td>14</td><td>NGC1333 I4A</td><td>105(18)</td><td>46.4(0.3)</td><td>97(14)</td><td>46.0(0.2)</td><td>97(21)</td><td>45.7(0.4)</td></tr><tr><td>16</td><td>NGC1333 I4B</td><td>183(15)</td><td>46.5(0.1)</td><td>145(16)</td><td>46.7(0.2)</td><td>153(13)</td><td>46.5(0.2)</td></tr><tr><td>22</td><td>IRAS03301</td><td>176(22)</td><td>45.4(0.2)</td><td>162(18)</td><td>45.4(0.2)</td><td>179(25)</td><td>45.4(0.2)</td></tr><tr><td>25</td><td>B1 a</td><td>211(54)</td><td>45.3(0.3)</td><td>169(47)</td><td>45.6(0.4)</td><td>186(49)</td><td>45.3(0.3)</td></tr><tr><td>31</td><td>L1489</td><td>191(22)</td><td>45.1(0.2)</td><td>172(22)</td><td>45.2(0.2)</td><td>193(29)</td><td>45.1(0.2)</td></tr><tr><td>42</td><td>TMR1</td><td>193(31)</td><td>45.4(0.2)</td><td>211(41)</td><td>45.4(0.2)</td><td>239(66)</td><td>45.4(0.3)</td></tr><tr><td>44</td><td>TMC1</td><td>148(24)</td><td>44.9(0.2)</td><td>143(28)</td><td>44.9(0.3)</td><td>174(46)</td><td>44.8(0.3)</td></tr><tr><td>48</td><td>BHR71</td><td>125(23)</td><td>45.8(0.3)</td><td>138(33)</td><td>45.9(0.4)</td><td>146(38)</td><td>45.6(0.4)</td></tr><tr><td>52</td><td>GSS30 IRS1</td><td>245(22)</td><td>46.0(0.1)</td><td>217(32)</td><td>46.1(0.2)</td><td>201(23)</td><td>46.0(0.2)</td></tr><tr><td>53</td><td>VLA 1623</td><td>165(40)</td><td>45.3(0.3)</td><td>96(15)</td><td>45.5(0.3)</td><td>106(28)</td><td>45.4(0.4)</td></tr><tr><td>54</td><td>WL12</td><td>202(25)</td><td>45.0(0.2)</td><td>149(20)</td><td>45.2(0.2)</td><td>187(22)</td><td>45.0(0.2)</td></tr><tr><td>56</td><td>Elias29</td><td>288(33)</td><td>46.0(0.1)</td><td>236(35)</td><td>46.0(0.2)</td><td>231(33)</td><td>45.9(0.2)</td></tr><tr><td>66</td><td>Ser SMM1</td><td>103(12)</td><td>47.3(0.2)</td><td>107(9)</td><td>47.4(0.2)</td><td>116(12)</td><td>47.2(0.2)</td></tr><tr><td>82</td><td>RCrA IRS5A</td><td>219(30)</td><td>45.1(0.2)</td><td>202(33)</td><td>45.2(0.2)</td><td>222(48)</td><td>45.1(0.3)</td></tr><tr><td>84</td><td>RCrA IRS7A</td><td>218(24)</td><td>46.0(0.2)</td><td>183(18)</td><td>46.1(0.2)</td><td>209(27)</td><td>45.9(0.2)</td></tr><tr><td>85</td><td>RCrA IRS7B</td><td>208(28)</td><td>45.3(0.2)</td><td>177(23)</td><td>45.5(0.2)</td><td>198(36)</td><td>45.3(0.3)</td></tr><tr><td>88</td><td>B335</td><td>140(40)</td><td>44.7(0.4)</td><td>159(51)</td><td>44.8(0.3)</td><td>111(36)</td><td>44.7(0.5)</td></tr><tr><td>89</td><td>L1157</td><td>114(20)</td><td>46.3(0.3)</td><td>101(15)</td><td>46.2(0.2)</td><td>99(23)</td><td>46.1(0.4)</td></tr></tbody></table>
<figure><img src="image_24.png" /><figcaption>**Figure 18.** Rotational diagrams of CO for Perseus sources observed as part of the WILL program. Blue and red solid lines show linear fits to the data and the corresponding rotational temperatures, when at least three lines are detected in a given component. The numbers in brackets correspond to the object identification numbers (see Table 1). L1448 MM and NGC1333 I4B are shown here, but they are not listed separately in Table 3 because existing full scans from DIGIT and WISH programs for those sources provide better estimates of rotational temperatures.</figcaption></figure>
<figure><img src="image_25.png" /><figcaption>Figure 19. Same as Figure 18, but for the remaining sources from the WILL program.</figcaption></figure>
<figure><img src="image_26.png" /><figcaption>**Figure 20.** Rotational diagrams of H₂O for Perseus sources observed as part of the WILL program. Blue solid lines show linear fits to the data and the corresponding rotational temperatures, when at least four lines are detected.</figcaption></figure>
<figure><img src="image_27.png" /><figcaption>Figure 21. Same as Figure 20, but for the remaining sources from the WILL program.</figcaption></figure>
<figure><img src="image_28.png" /><figcaption>**Figure 22.** Rotational diagrams of OH for Perseus sources observed as part of the WILL program. Blue solid lines show linear fits to the data and the corresponding rotational temperatures, when at least three doublets are detected.</figcaption></figure>
<figure><img src="image_29.png" /><figcaption>Figure 23. Same as Figure 22, but for the remaining sources from the WILL program.</figcaption></figure>

<table><caption>Table 7
Comparison of OH Rotational Temperatures and Numbers of Emitting Molecules</caption><thead><tr><th rowspan="2">ID</th><th rowspan="2">Source</th><th colspan="2">Full spectra</th><th colspan="2">WISH line scan</th><th colspan="2">WILL line scan</th></tr><tr><th>T<sub>rot</sub>(K)</th><th>log<sub>10</sub>N</th><th>T<sub>rot</sub>(K)</th><th>log<sub>10</sub>N</th><th>T<sub>rot</sub>(K)</th><th>log<sub>10</sub>N</th></tr></thead><tbody><tr><td>3</td><td>L1448 C(N)</td><td>123(17)</td><td>52.2(0.2)</td><td>113(91)</td><td>52.3(0.7)</td><td>33(6)</td><td>54.4(0.6)</td></tr><tr><td>4</td><td>L1448 C(S)</td><td>94(18)</td><td>51.7(0.3)</td><td>54(16)</td><td>52.3(0.6)</td><td>29(4)</td><td>54.1(0.6)</td></tr><tr><td>6</td><td>L1455 IRS1</td><td>37(15)</td><td>53.2(1.2)</td><td>37(15)</td><td>53.4(1.2)</td><td>37(15)</td><td>53.4(1.2)</td></tr><tr><td>14</td><td>NGC1333 I4A</td><td>150(214)</td><td>51.6(0.9)</td><td>150(214)</td><td>51.6(0.9)</td><td>35(17)</td><td>53.8(1.5)</td></tr><tr><td>16</td><td>NGC1333 I4B</td><td>84(14)</td><td>52.8(0.3)</td><td>109(84)</td><td>52.5(0.7)</td><td>35(9)</td><td>54.5(0.8)</td></tr><tr><td>22</td><td>IRAS03301</td><td>109(20)</td><td>52.1(0.3)</td><td>181(208)</td><td>51.9(0.6)</td><td>43(13)</td><td>53.5(0.8)</td></tr><tr><td>25</td><td>B1 a</td><td>103(20)</td><td>51.8(0.3)</td><td>163(196)</td><td>51.7(0.7)</td><td>44(21)</td><td>53.3(1.2)</td></tr><tr><td>31</td><td>L1489</td><td>102(18)</td><td>51.5(0.3)</td><td>102(70)</td><td>51.5(0.7)</td><td>37(12)</td><td>53.3(0.9)</td></tr><tr><td>42</td><td>TMR1</td><td>108(24)</td><td>51.8(0.3)</td><td>132(141)</td><td>51.7(0.8)</td><td>32(8)</td><td>54.1(0.9)</td></tr><tr><td>44</td><td>TMC1</td><td>103(19)</td><td>51.5(0.3)</td><td>103(73)</td><td>51.5(0.7)</td><td>35(10)</td><td>53.4(0.9)</td></tr><tr><td>48</td><td>BHR71</td><td>87(17)</td><td>52.1(0.4)</td><td>72(41)</td><td>52.2(0.8)</td><td>29(9)</td><td>54.5(1.1)</td></tr><tr><td>52</td><td>GSS30 IRS1</td><td>99(18)</td><td>52.2(0.3)</td><td>110(84)</td><td>52.2(0.7)</td><td>34(8)</td><td>54.2(0.7)</td></tr><tr><td>53</td><td>VLA 1623</td><td>71(16)</td><td>51.9(0.4)</td><td>126(117)</td><td>51.6(0.7)</td><td>48(30)</td><td>52.8(1.4)</td></tr><tr><td>54</td><td>WL12</td><td>94(17)</td><td>51.5(0.3)</td><td>112(94)</td><td>51.4(0.7)</td><td>34(9)</td><td>53.5(0.9)</td></tr><tr><td>56</td><td>Elias29</td><td>112(27)</td><td>52.1(0.3)</td><td>149(167)</td><td>52.1(0.7)</td><td>36(10)</td><td>54.2(0.8)</td></tr><tr><td>66</td><td>Ser SMM1</td><td>83(13)</td><td>53.6(0.3)</td><td>109(79)</td><td>53.4(0.7)</td><td>42(17)</td><td>54.9(1.1)</td></tr><tr><td>82</td><td>RCrA IRS5A</td><td>113(17)</td><td>51.9(0.3)</td><td>86(70)</td><td>52.0(1.0)</td><td>30(5)</td><td>54.4(0.6)</td></tr><tr><td>84</td><td>RCrA IRS7A</td><td>114(17)</td><td>52.9(0.3)</td><td>90(80)</td><td>52.9(1.0)</td><td>31(11)</td><td>55.1(1.2)</td></tr><tr><td>85</td><td>RCrA IRS7B</td><td>119(17)</td><td>52.0(0.3)</td><td>104(100)</td><td>52.0(0.9)</td><td>33(8)</td><td>54.1(0.8)</td></tr><tr><td>88</td><td>B335</td><td>101(63)</td><td>51.1(0.6)</td><td>101(63)</td><td>51.1(0.6)</td><td>60(42)</td><td>51.7(1.3)</td></tr><tr><td>89</td><td>L1157</td><td>77(40)</td><td>52.5(0.7)</td><td>77(40)</td><td>52.5(0.7)</td><td>32(9)</td><td>54.4(0.9)</td></tr></tbody></table>
<figure><img src="image_30.png" /><figcaption>**Figure 24.** (a) Similar to Figure 5, but for L1448 C(N) and L1448 C(S)—based on measurements from Lee et al. (2013)—and for L1455 IRS1 (IRAS03245), L1455 IRS3 (see also Green et al. 2013), and NGC1333 I2A (see also Karska et al. 2013). (b) Similar to Figure 5, but for NGC1333 IRAS4A, NGC1333 IRAS4B (based on Herczeg et al. 2012), IRAS 03301, B1-a, and B1-c. (c) Similar to Figure 5, but for L1489, IRAM04191, L1551 IRS5, L1527, and TMR1. (d) Similar to Figure 5, but for TMC1 A, TMC1, BHR 71, DK Cha, and GSS30 IRS1. (e) Similar to Figure 5, but for VLA 1623, WL 12, Elias 29, Oph IRS44, and Oph IRS 46. (f) Similar to Figure 5, but for Oph IRS 63, Ser SMM1 (see also Goicoechea et al. 2012), Ser SMM4 and 3 (see also Dionatos et al. 2013), and CrA IRS 5A (based on measurements from Lindberg et al. 2014). (g) Similar to Figure 5, but for CrA IRS 5N, 7A, 7B (based on measurements from Lindberg et al. 2014), B335, and L1014. (h) Similar to Figure 5, but for CrA IRS 5N, 7A, 7B (based on measurements from Lindberg et al. 2014), B335, and L1014. (i) Similar to Figure 5, but for line scan observations of the WISH sources: HH46, Ced110 IRS4, and L723 (see also Karska et al. 2013). (j) Similar to Figure 5, but for line scan observations of the WISH sources: RNO 91, L483, and L723 (see also Karska et al. 2013).</figcaption></figure>
<figure><img src="image_31.png" /><figcaption>Figure 24. (Continued.)</figcaption></figure>
<figure><img src="image_32.png" /><figcaption>Figure 24. (Continued.)</figcaption></figure>
<figure><img src="image_33.png" /><figcaption>Figure 24. (Continued.)</figcaption></figure>
<figure><img src="image_34.png" /><figcaption>Figure 24. (Continued.)</figcaption></figure>
<figure><img src="image_35.png" /><figcaption>Figure 24. (Continued.)</figcaption></figure>
<figure><img src="image_36.png" /><figcaption>Figure 24. (Continued.)</figcaption></figure>
<figure><img src="image_37.png" /><figcaption>Figure 24. (Continued.)</figcaption></figure>
<figure><img src="image_38.png" /><figcaption>Figure 24. (Continued.)</figcaption></figure>
<figure><img src="image_39.png" /><figcaption>Figure 24. (Continued.)</figcaption></figure>

## Appendix B
Line Cooling

The distribution of line luminosities for various species across the entire sample is illustrated in Figure 25 (see also Table 5).

Correlations of the far-IR cooling with $L_{bol}$ and $T_{bol}$ are shown in Figures 26 and 27.

Luminosity ratios of selected species as a function of bolometric temperature are shown in Figure 28.
<figure><img src="image_40.png" /><figcaption>**Figure 25.** Histograms of the CO (top left), H₂O (top right), OH (bottom left), and [O I] (bottom right) cooling for all sources with at least one detection in a given species. The red color shows the distributions for Class 0 sources and blue for Class I sources.</figcaption></figure>
<figure><img src="image_41.png" /><figcaption>**Figure 26.** Ratio of line luminosities of selected species and the total far-infrared line emission as a function of bolometric temperature. Objects observed in the full spectroscopy mode are marked with orange dots. The dashed blue vertical line corresponds to $T_{bol} = 70$ K, with the Class 0 sources located to the left and the Class I sources to the right side of the line.</figcaption></figure>

<figure><img src="image_42.png" /><figcaption>**Figure 28.** Luminosity ratios of selected species as a function of bolometric temperature. Objects observed in the full spectroscopy mode are marked with orange dots.</figcaption></figure>

<figure><img src="image_43.png" /><figcaption>**Figure 27.** Similar to Figure 26, but the ratios of the line luminosities of selected species and the total far-infrared line emission are shown as a function of bolometric luminosity.</figcaption></figure>
<figure><img src="image_44.png" /><figcaption>Figure 29. Similar to Figure 10, but for other sets of lines (including H₂O 2₁₂–I₀₁ at 179 µm and CO 21–20 at 124 µm).</figcaption></figure>

## ORCID iDs

Agata Karska https://orcid.org/0000-0001-8913-925X

Michael J. Kaufman https://orcid.org/0000-0002-2521-1985

Lars E. Kristensen https://orcid.org/0000-0003-1159-3721

Ewine F. van Dishoeck https://orcid.org/0000-0001-7591-1907

Gregory J. Herczeg https://orcid.org/0000-0002-7154-6065

Łukasz Tychoniec https://orcid.org/0000-0002-9470-2358

Johan E. Lindberg https://orcid.org/0000-0003-3811-4591

Joel D. Green https://orcid.org/0000-0003-1665-5709

Yao-Lun Yang https://orcid.org/0000-0001-8227-2816

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