11institutetext: Departamento de Astronomía, Universidad de Chile, Santiago,
Chile
11email<EMAIL_ADDRESS>22institutetext: Dipartimento di Fisica,
Università di Roma ”Tor Vergata”, Via della Ricerca Scientifica 1, I-00133,
Roma, Italy 33institutetext: Department of Astronomy, University of Belgrade -
Faculty of Mathematics, Studentski trg 16, 11000 Belgrade, Serbia
44institutetext: Instituto de Astrofísica de La Plata (UNLP-CONICET), La
Plata, Argentina 55institutetext: Faculdad de Ciencias Astronómicas y
Geofísicas, Universidad Nacional de La Plata, Paseo del Bosque s/n, 1900, La
Plata, Argentina 66institutetext: INAF - IAPS, via Fosso del Cavaliere, 100,
I-00133 Roma, Italy 77institutetext: Dept. Ciencias Integradas, Facultad de
Ciencias Experimentales, Centro de Estudios Avanzados en Física, Matemática y
Computación, Unidad Asociada GIFMAN, CSIC-UHU, Universidad de Huelva, Spain

# SiO Outflows in the Most Luminous and Massive Protostellar Sources of the
Southern Sky

N. Guerra-Varas , , 112233 M. Merello 11 L. Bronfman 11 N. Duronea , 4455 D.
Elia 66 R. Finger 11 E. Mendoza 77

(July, 2023; Accepted to A&A)

###### Abstract

Context. High-mass star formation remains far less understood than low-mass
star formation. It entails the ejection of matter through molecular outflows,
which disturb the protostellar clump. Studying these outflows and the shocked
gas caused by them is key for a better understanding of this process.

Aims. The present study aims to characterise the behaviour of molecular
outflows in the most massive protostellar sources in the Southern Galaxy by
looking for evolutionary trends and associating the presence of shocked gas
with outflow activity.

Methods. We present APEX SEPIA180 (Band 5) observations (beamwidth $\sim$36”)
of SiO(4-3) molecular outflow candidates towards a well-selected sample of 32
luminous and dense clumps, which are candidates to harbouring Hot Molecular
Cores. We study the emission of the SiO(4-3) line, which is an unambiguous
tracer of shocked gas, and recent and active outflow activity, as well as the
HCO+(2-1) and H13CO+(2-1) lines.

Results. Results show that 78% of our sample (25 sources) present SiO
emission, revealing the presence of shocked gas. Nine of these sources are
also found to have wings in the HCO+(2-1) line, indicating outflow activity.
The SiO emission of these 9 sources is generally more intense ($T_{a}>1$ K)
and wider ($\sim 61$ km s-1 FWZP) than the rest of the clumps with SiO
detection ($\sim 42$ km s-1 FWZP), suggesting that the outflows in this group
are faster and more energetic. Three positive linear correlations are found: a
weak one between the bolometric luminosity and outflow power, and two strong
ones: between the outflow power and the rate of matter expulsion, and between
the kinetic energy and outflow mass. These correlations suggest that more
energetic outflows bear to mobilise more material. No correlation was found
between the evolutionary stage indicator $L/M$ and SiO outflow properties,
supporting that molecular outflows happen throughout the whole high-mass star
formation process.

Conclusions. We conclude that sources with both SiO emission and HCO+ wings
and sources with only SiO emission are in an advanced stage of evolution in
the high-mass star formation process, and there is no clear evolutionary
difference between them. The former present more massive and more powerful SiO
outflows than the latter. Therefore, looking for more outflow signatures such
as HCO+ wings could help identify more massive and active massive star-forming
regions in samples of similarly evolved sources, and could also help identify
sources with older outflow activity.

###### Key Words.:

stars: formation – stars: massive – ISM: clouds – ISM: jets and outflows –
ISM: molecules

##  1 Introduction

Massive stars are crucial to the evolution of the interstellar medium (ISM)
and galaxies. However, they are difficult to observe and study because they
are very scarce (about 1% of stellar populations), have short timescales,
large heliocentric distances, and are embedded in very complex environments,
with high extinction and turbulence (e.g. Motte et al., 2018). Thus, high-mass
star formation remains much less understood than low-mass star formation.

The current picture for high-mass star formation takes place in massive dense
cores (MDCs) embedded in massive clouds, called Massive Star-Forming (MSF)
regions, and can be described by four main phases (van der Tak, 2004; Motte et
al., 2018; Elia et al., 2021; Urquhart et al., 2022; Jiao et al., 2023).
Initially, in the quiescent or starless phase, the clump has no embedded
objects and is not visible at 70 $\mu$m. Later, in the Young Stellar Object
Phase (YSO), the clump has warmed up enough to be detected at 70 $\mu$m. In
this stage, ($\sim 10^{4}$ yrs), there is an embedded cold and collapsing
prestellar core. When a protostar appears (protostellar phase, $\sim 3\times
10^{5}$ yrs), it feeds on inflow material and its mass increases until
becoming a high-mass protostar. Within this phase, the Hot Molecular Core
(HMC) stage can be identified. Then, as the protostar evolves and its
temperature increases, it starts emitting ultraviolet (UV) radiation, which is
quickly ionising the surrounding gas. This starts the Ultra-Compact (UC) HII
region phase ($\sim 10^{5}$ \- $10^{6}$ yrs).

Massive star formation entails a greatly relevant feedback process: molecular
outflows and jets, i.e., matter expulsion at high velocities due to angular
momentum conservation during matter accretion (Arce et al., 2007; Bally, 2016;
Motte et al., 2018). This feedback process occurs throughout the whole of the
high-mass formation process (Li et al., 2020; Yang et al., 2022; Urquhart et
al., 2022), and outflow features have been used as an indication of massive
star formation activity (Li et al., 2019; Liu et al., 2020). In order to
understand how massive stars form, the study of molecular outflows in MSF
regions is imperative.

The study of outflows heavily depends on the tracer used. There is no such
thing as a perfect outflow tracer (Bally, 2016). However, the SiO molecule has
been found to be a very good tracer of outflow activity and shocked material
and has been broadly used for that purpose (e.g. Beuther et al., 2002; López-
Sepulcre, A. et al., 2011; Bally, 2016; Li et al., 2019b; Liu et al., 2021;
Liu, D.J. et al., 2021; Liu et al., 2022; De Simone et al., 2022). Si falls
onto the icy mantles of dust grains of the ISM. When hit by shocks of gas, the
dust grains can sublimate to the gaseous state, releasing the Si. Thus, the Si
in the gas phase can react with O to form SiO, making it observable in the
millimetre (mm), sub-mm, and centimetre (cm) regimes via its rotational
transitions (Schilke et al., 1997; Klaassen & Wilson, 2007; Gusdorf, A. et
al., 2008). Unlike other molecules, SiO has a key advantage. Its emission is
not easily contaminated by excited ambient material, making it an unambiguous
tracer of shocked material and thus outflow activity. Studying SiO emission
can shed light on the kinematics of outflows, as well as relevant chemical
processes that occur in shock environments such as the formation of complex
organic molecules (COMs) (Bally, 2016; Li et al., 2020; Rojas-García et al.,
2022). Both broad (Full Width Zero Power (FWZP) $\geq 20$ km s-1) and narrow
(FWZP $\leq 10$ km s-1) spectral width SiO emission have been observed (Garay
et al., 2010; Leurini et al., 2014; Bally, 2016; Csengeri et al., 2016; Li et
al., 2019b; Zhu et al., 2020). It is thought that broad-width emission is due
to high-velocity collimated shocks, while narrow-width emission is associated
with less collimated low-velocity shocks, such as cloud-cloud collisions. It
is possible to identify wings in the SiO spectral profile when it has a broad
width, which are manifestations of SiO outflows. These have been extensively
studied (Beuther et al., 2002; Liu et al., 2021; Liu, D.J. et al., 2021).
Moreover, SiO outflow activity has been found to decrease and get less
collimated over time (Arce et al., 2007; Sakai et al., 2010; López-Sepulcre,
A. et al., 2011). However, there is currently no consensus on whether SiO
abundance decreases over time (Csengeri et al., 2016; Li et al., 2019b; Liu et
al., 2022), and some works even conclude that SiO emission is much harder to
interpret than just a shock tracer (Widmann et al., 2016).

Another very helpful outflow tracer is HCO+ emission (Myers et al., 1996;
Rawlings et al., 2004; Klaassen & Wilson, 2007; Bally, 2016; Li et al., 2019a;
Liu et al., 2020; He et al., 2021). This species traces the surrounding
material of protostar regions (Rawlings et al., 2004) and traces the disk
material in low-mass star formation (Dutrey et al., 1997). This species can
trace both inflow and outflow motions (Klaassen & Wilson, 2007). When outflows
are strong enough, they can be observed in broad high-velocity wings in the
spectral profile (Wu et al., 2005; He et al., 2021). When HCO+, and other
species such as CO, are dragged outwards due to the outflow, their spectral
profiles present wings. This is caused by the greater velocity gradient of the
dragged material. However, the spectral profile of this species experiences
significant absorption, which often complicates its analysis. Moreover,
studying the emission of an HCO+ isotopologue, H13CO+, can help distinguish
between outflows and ambient dense gas, as it traces dense gas only (see
Section 3.1).

SiO line emissions are associated with recent and active outflow of matter, as
shock chemistry processes happen in $10^{2}$ to $10^{4}$ yrs, whilst the HCO+
wing observations are associated with old ‘fossil’ outflows (Arce et al.,
2007; Klaassen & Wilson, 2007; López-Sepulcre et al., 2016; Li et al., 2019a).
The detection of only one of these phenomena is enough to indicate the
presence of a molecular outflow. If both are detected, then one can confirm
without ambiguity that there is ongoing matter expulsion (Klaassen & Wilson,
2007). Outflows are associated with an advanced stage of evolution. If a
molecular core does not have an outflow, it may be because it has not reached
this point yet. However, it is also possible that it has already experienced a
significant loss of material, and/or accretion and outflow activity has
ceased.

In this work, we present SiO(2-1), HCO+(2-1) and H13CO+(2-1) APEX Band 5
observations toward a well-selected sample of 32 very massive and luminous
protostellar sources, which are amongst the brightest clumps in the Southern
Milky Way. This study aims to answer the following research questions: How do
SiO outflows behave in the most massive protostellar sources? Do any SiO
outflow properties exhibit an evolutionary trend? Is the presence of shocked
gas associated with outflow activity? What can different outflow signatures
tell us about similarly evolved sources?

This paper is organised as follows: in Sect. 2 we describe the studied sample,
selection criteria and the observations. In Sect. 3, we analyse the data and
describe how outflow and SiO detections were analysed. In Sect. 4, we
calculate the outflows properties of the clumps and the SiO emission. In Sect.
5, we present relevant correlations, carry out a cross-check between SiO and
outflow detections, and discuss possible evolutionary trends. Finally, in
Sect. 6, we provide a summary of our main results and present our conclusions.

##  2 Observations

###  2.1 Source Selection

The studied sample consists of 32 protostellar clumps (HMC candidates) from
the Hi-GAL catalogue of compact sources (Elia et al., 2021), associated with
CS(2-1) line emission from IRAS PSC sources with far infrared colours of Ultra
Compact HII regions by Bronfman et al. (1996). Their characteristics are
presented in Table 1 (sources marked with a black diamond $\blacklozenge$ have
saturated Hi-GAL observations; see Appendix A). They have been named with ‘HC’
(Hot Core) and a number in increasing order for convenience.The sources were
selected as follows:

  1. 1.

Kinematic distances ¡ 6 kpc (these were obtained from Reid et al. (2009), Hi-
GAL distances were not used; see Appendix B).

  2. 2.

Strong CS emission (Bronfman et al., 1996): Main-beam temperature in CS
$T_{MB}(\text{CS})\geq 1.5$ K.

  3. 3.

Surface densities above the threshold for the formation of massive stars:
$\Sigma>0.2$ g cm-2 (e.g. Butler & Tan, 2012; Merello et al., 2018).

  4. 4.

Masses $>100$ $M_{\odot}$ (Elia et al., 2021).

  5. 5.

High values of the evolutionary stage indicator luminosity-to-mass ratio
$L/M$. Values larger than $1$ are associated with internal protostellar
heating and the appearance of new stars in massive clumps (López-Sepulcre, A.
et al., 2011; Molinari et al., 2016).

Although low-mass star-forming clumps may also have a large value of $L/M$,
the lower limit set on the mass of the clump together with a large $L/M$
ensures our sample will only consist of massive protostellar clumps.

The sources in our sample are in an advanced stage of evolution, either in the
protostellar or compact HII region phase. A histogram of the luminosity-to-
mass ratio $L/M$, which acts as an evolutionary stage indicator, is presented
in Fig. 1 (see Table 1). This parameter $L/M$ has a minimum value of $3$
$L_{\odot}/M_{\odot}$, a maximum of $154$ $L_{\odot}/M_{\odot}$, a mean of 45
$L_{\odot}/M_{\odot}$ and a median of 30 $L_{\odot}/M_{\odot}$.

The sources are very energetic, with bolometric luminosities up to $\sim
2.3\times 10^{5}L_{\odot}$. The selection criteria of the sources allowed us
to work with luminous, strong and relatively near clumps only. They are among
the most luminous sources in the southern sky, and some of them have been
extensively studied (see Appendix C). The continuum dust properties of the
sources are shown in Table 2 (sources marked with a black diamond
$\blacklozenge$ have saturated Hi-GAL observations; see Appendix A) and were
obtained from a SED fit (Elia et al., 2021). Compared with the general
population of Hi-GAL protostellar sources (Elia et al., 2017, 2021), we see
that our sample is much more massive and luminous. The median value for H2
mass derived from dust $M_{dust}$ and bolometric luminosity $L_{Bol}$ for our
sample is 828 $M_{\odot}$ and 19839 $L_{\odot}$ respectively, whilst for Hi-
GAL protostellar sources, these values are equal to 464 $M_{\odot}$ and 1071
$L_{\odot}$ respectively. When comparing with the rest of the Hi-GAL sources
within 6 kpc, the contrast is even bigger, since the mean bolometric
luminosity is 206 $L_{\odot}$ and the mean dust mass is 88 $M_{\odot}$ in this
region of the Galaxy. Finally, Fig. 2 shows the distribution in the Galactic
plane of the sources presented in this work.

Source | Hi-GAL Name | IRAS Name | $\alpha$ | $\delta$ | $D$ |  $V_{LSR}$(CS)
---|---|---|---|---|---|---
|  |  | (J2000.0) | (J2000.0) | (kpc) | (km s-1)
HC01 | HIGALBM5.6373+0.2352 | 17545-2357 | 17:57:35.0328 | -23:58:08.472 | 2.95 | 9.1
HC02 $\blacklozenge$ | HIGALBM5.8856-0.3920 | 17574-2403 | 18:00:30.4080 | -24:03:59.663 | 2.94 | 9.3
HC03 | HIGALBM6.7951-0.2571 | 17589-2312 | 18:01:57.7152 | -23:12:34.844 | 3.56 | 21.1
HC04 $\blacklozenge$ | HIGALBM10.4631+0.0298 | 18056-1952 | 18:08:36.5496 | -19:52:14.534 | 5.29 | 68.9
HC05 | HIGALBM12.8892+0.4895 | 18089-1732 | 18:11:51.4224 | -17:31:27.620 | 2.88 | 33.8
HC06 | HIGALBM12.9083-0.2603 | 18117-1753 | 18:14:39.5184 | -17:52:00.710 | 2.96 | 36.6
HC07 | HIGALBM16.5849-0.0505 | 18182-1433 | 18:21:09.0672 | -14:31:49.184 | 3.84 | 59.1
HC08 | HIGALBM301.1365-0.2259 | 12326-6245 | 12:35:35.1552 | -63:02:32.633 | 4.31 | -39.4
HC09 | HIGALBM309.9212+0.4781 | 13471-6120 | 13:50:42.2184 | -61:35:12.466 | 5.35 | -58.4
HC10 | HIGALBM311.6269+0.2898 | 14013-6105 | 14:04:55.0536 | -61:20:07.120 | 4.57 | -56.2
HC11 | HIGALBM312.1074+0.3094 | 14050-6056 | 14:08:41.9400 | -61:10:42.391 | 3.60 | -48.4
HC12 | HIGALBM317.4080+0.1102 | 14453-5912 | 14:49:07.8000 | -59:24:45.623 | 2.69 | -39.9
HC13 | HIGALBM323.4594-0.0789 | 15254-5621 | 15:29:19.5696 | -56:31:21.918 | 4.09 | -67.5
HC14 | HIGALBM326.7806-0.2411 | 15450-5431 | 15:48:55.2096 | -54:40:38.525 | 3.87 | -64.7
HC15 | HIGALBM327.3918+0.1996 | 15464-5348 | 15:50:18.4992 | -53:57:05.612 | 5.05 | -88.6
HC16 $\blacklozenge$ | HIGALBM330.8814-0.3656 | 16065-5158 | 16:10:20.4504 | -52:05:56.908 | 3.77 | -62.2
HC17 | HIGALBM331.2786-0.1883 | 16076-5134 | 16:11:26.7480 | -51:41:56.044 | 4.88 | -87.7
HC18 | HIGALBM332.2951-0.0938 | 16119-5048 | 16:15:45.4104 | -50:55:54.512 | 3.17 | -48.4
HC19 | HIGALBM332.5443-0.1226 | 16132-5039 | 16:17:01.2000 | -50:46:46.643 | 3.10 | -46.7
HC20 $\blacklozenge$ | HIGALBM333.1246-0.4244 | 16172-5028 | 16:20:58.1904 | -50:35:19.190 | 3.33 | -51.2
HC21 | HIGALBM335.5848-0.2894 | 16272-4837 | 16:30:58.5120 | -48:43:52.183 | 3.22 | -46.6
HC22 | HIGALBM339.6221-0.1209 | 16424-4531 | 16:46:06.1080 | -45:36:44.003 | 2.60 | -33.2
HC23 | HIGALBM340.2740-0.2098 | 16452-4504 | 16:48:53.3160 | -45:10:20.420 | 2.78 | -45.5
HC24 | HIGALBM341.1268-0.3456 | 16489-4431 | 16:52:33.2568 | -44:36:10.613 | 2.72 | -40.6
HC25 | HIGALBM342.0590+0.4212 | 16489-4318 | 16:52:32.8656 | -43:23:45.553 | 4.63 | -71.0
HC26 | HIGALBM342.7076+0.1257 | 16524-4300 | 16:56:03.1296 | -43:04:43.489 | 2.74 | -41.9
HC27 | HIGALBM345.0035-0.2239 | 17016-4124 | 17:05:11.1168 | -41:29:05.665 | 2.82 | -26.6
HC28 | HIGALBM350.0154+0.4332 | 17143-3700 | 17:17:45.4032 | -37:03:11.642 | 3.87 | -31.5
HC29 | HIGALBM350.1024+0.0805 | 17160-3707 | 17:19:27.3216 | -37:11:05.788 | 5.54 | -69.5
HC30 | HIGALBM351.0412-0.3354 | 17204-3636 | 17:23:50.2800 | -36:38:57.138 | 2.70 | -18.0
HC31 | HIGALBM352.3155-0.4422 | 17244-3536 | 17:27:48.6096 | -35:39:11.207 | 1.33 | -10.8
HC32 | HIGALBM354.6619+0.4800 | 17271-3309 | 17:30:22.6008 | -33:11:17.668 | 3.73 | -20.9
Table 1: List of the studied sample sources. Source | $L_{bol}$ | $M_{dust}$ | $T_{dust}$ | ${L/M}$
---|---|---|---|---
| ($10^{3}L_{\odot}$) | ($M_{\odot}$) | (K) | ($L_{\odot}/M_{\odot}$)
HC01 | 11.14 | 394.0 | 25.8 | 28.0
HC02 $\blacklozenge$ | 16.75 | 2017.0 | 25.0 | 72.0
HC03 | 20.57 | 1141.0 | 23.1 | 18.0
HC04 $\blacklozenge$ | 0.77 | 8675.0 | 25.0 | 25.0
HC05 | 22.04 | 540.0 | 33.4 | 41.0
HC06 | 42.28 | 1328.0 | 22.6 | 32.0
HC07 | 17.47 | 535.0 | 31.5 | 33.0
HC08 | 227.44 | 2803.0 | 33.5 | 81.0
HC09 | 222.95 | 1477.0 | 34.4 | 151.0
HC10 | 121.44 | 1458.0 | 30.4 | 83.0
HC11 | 68.39 | 701.0 | 25.6 | 98.0
HC12 | 2.70 | 785.0 | 18.3 | 3.0
HC13 | 142.72 | 929.0 | 31.5 | 154.0
HC14 | 8.67 | 799.0 | 19.4 | 11.0
HC15 | 13.55 | 1074.0 | 22.9 | 13.0
HC16 $\blacklozenge$ | 56.05 | 1962.0 | 25.0 | 3.0
HC17 | 100.00 | 1400.0 | 32.0 | 71.0
HC18 | 14.98 | 949.0 | 22.4 | 16.0
HC19 | 2.22 | 756.0 | 18.8 | 3.0
HC20 $\blacklozenge$ | 114.35 | 4980.0 | 25.0 | 3.0
HC21 | 19.10 | 1608.0 | 23.3 | 12.0
HC22 | 13.86 | 321.0 | 24.1 | 43.0
HC23 | 4.19 | 341.0 | 33.4 | 12.0
HC24 | 6.12 | 390.0 | 20.0 | 16.0
HC25 | 23.05 | 1001.0 | 23.2 | 23.0
HC26 | 24.66 | 585.0 | 28.8 | 42.0
HC27 | 67.66 | 1030.0 | 34.0 | 66.0
HC28 | 33.62 | 230.0 | 40.0 | 146.0
HC29 | 162.23 | 2083.0 | 27.5 | 78.0
HC30 | 11.50 | 456.0 | 27.0 | 25.0
HC31 | 4.56 | 105.0 | 25.9 | 43.0
HC32 | 6.34 | 859.0 | 20.6 | 7.0
Table 2: Clump properties. Figure 1: Histogram for the luminosity to mass
ratio $L/M$ in logarithmic scale. The red and purple vertical lines denote the
median ($30$ $L_{\odot}/M_{\odot}$) and the mean ($45$ $L_{\odot}/M_{\odot}$)
respectively. Groups A, B and C are defined in Table 6. Figure 2: Galactic
distribution of the sources. The orange point corresponds to the Sun and the
green point to the Galactic centre. The red crosses are the sources studied in
this paper. The blue circles are centred in the Sun and the black ones in the
Galactic centre. They mark the 1 kpc, 5 kpc and 10 kpc distances.

###  2.2 APEX Observations

Observations were made using the SEPIA180 instrument at the Atacama Pathfinder
Experiment (APEX)111https://www.apex-
telescope.org/ns/instruments/sepia/sepia180/ in the Atacama Desert in Chile
(Belitsky et al., 2018), for 10 nights between November 2018 and October 2019.
The observations were made in single-pointing mode. For each source, a region
free from emission was taken as reference from the dust maps at 250 $\mu$m by
Herschel, typically at $300-500^{\prime\prime}$ from the source. The system
temperature was 174.30 K on average.

The band was tuned at 172 GHz in the LSB to observe the H13CO+(2-1) (173.507
GHz) and SiO(4-3) (173.688 GHz) lines, and centred at the HCO+(2-1) line
(178.375 GHz). The spectral resolution used was of $\Delta V=0.2$ km s-1,
which gives a typical RMS noise temperature of $25$ mK, and the main beam
efficiency $\eta_{MB}$ was equal to $0.83$. APEX observations have an antenna
temperature uncertainty of about 20 % (APEX staff, private communication). The
frequency of the transitions used was obtained from the
SPLATALOGUE222https://splatalogue.online//advanced1.php database. This
frequency range corresponds to the Band 5 of the Atacama Large Millimetre/Sub-
millimetre Array.

The beam angular size can be calculated with the frequency $f$ of a spectral
line with $\theta^{\prime\prime}=7.8^{\prime\prime}\times 800/f$. For these
observations, this results in a beam angular size of approximately
$36^{\prime\prime}$.

The CLASS software from the GILDAS333https://www.iram.fr/IRAMFR/GILDAS/
software package was used to reduce the spectra. It is used to process
single–dish spectra and is oriented towards the processing of a large number
of spectra. For every spectral line, the baseline was subtracted at first
order and then centred to the $V_{LSR}$ of the corresponding source.

##  3 Analysis

The SiO(4-3), H13CO+(2-1) and HCO+(2-1) spectral profiles of the HC02 source
are presented in Fig. 3 as an example, where the red dotted line is at FWZP,
and the blue line in the H13CO+ panel shows the Gaussian fit (see Appendix D
for the rest, in Figs. 7 to 37).

Results for the HCO+(2-1), H13CO+(2-1) and SiO(4-3) spectral lines are
displayed in Table 3, 4 and 5 respectively. We have calculated the spatial
beam size $R$ with the angular beam size $\theta$ and distance to the source
$D$:

$R\text{ (pc) }=\theta\left(\text{${}^{\prime\prime}$}\right)\cdot D\text{
(pc)}\cdot\frac{\pi}{180}\frac{1}{3600}$ (1)

Figure 3: Spectral Profiles for the source HC02, Group A. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.

Note that since our observations do not resolve the singular clump, the
spatial beam size is diluted and introduces uncertainties. We compared the
beam size of the sources at the H13CO+(2-1) line with their beam-deconvolved
sizes measured at 250 $\mu$m continuum emission obtained from the Hi-GAL
catalogue of compact sources (Elia et al., 2021). The H13CO+ line traces cold
surrounding material, and, on the other hand, cold dust is expected to emit at
around 250 $\mu$m, i.e. they trace mostly the same dense gas (e.g. Elia et
al., 2017). Thus, we computed the ratio between the clump sizes in 250 $\mu$m
and in the H13CO+(2-1) line. This indicates how beam dilution affects our
results. We found that the beam size in our APEX observations is on average
$2.35$ times larger than the size of the clump at 250 $\mu$m. On the other
hand, the SiO(4-3) line has an angular resolution of 36”, which corresponds to
0.087 pc at a distance of 1 kpc. The distances to our sources range from 1.33
kpc to 5.54 kpc. These uncertainties will propagate linearly to the column
densities to be calculated in Sect. 4.1.2.

###  3.1 Clump Tracer Emission

The HCO+ and H13CO+ species are commonly used as dense gas tracers. They are
treated as linear rigid rotors (Mladenović, 2017) and are expected to present
a Gaussian profile. In spite of being isotopologues, these lines present
different behaviours. At a kinetic temperature of 20 K, the HCO+(2-1) and
H13CO+(2-1) lines have optically thin critical densities of $4.2\times 10^{5}$
cm-3 and $3.8\times 10^{5}$ cm-3 respectively, and effective excitation
densities of $1.7\times 10^{3}$ cm-3 and $7.1\times 10^{4}$ cm-3 respectively
(Shirley, 2015). The HCO+ has a much lower effective density than its
isotopologue, which indicates that HCO+ traces regions with lower density,
such as outflows and jets, which are usually less dense than the surrounding
material. This is why HCO+ traces both outflows and the surrounding material,
whilst H13CO+ only traces the latter. The differences between these two lines
are visually clear in their spectral profiles (see Fig. 3 and Appendix D).
HCO+ emission experiences significant absorption and self-absorption (Klaassen
& Wilson, 2007), thus it is not possible to quantify properties of the clump
using this spectral profile only. In addition, H13CO+ emission is optically
thin and does not present absorption. Therefore, the Gaussian parameters
fitted to the H13CO+(2-1) spectral profiles were used to calculate the
properties of the cores for all the sources, and the velocity of the
H13CO+(2-1) Gaussian peak was used to centre the standard of rest velocity
VLSR of the sources. The parameters of the HCO+(2-1) spectral lines are
displayed in Table 3, and the results from the Gaussian fit to the H13CO+(2-1)
spectral profile are displayed in Table 4.

We note that if the outflow is strong enough, it is possible that the H13CO+
line presents wings as well, like is the case for the source e.g. HC20 (see
Fig. 25). Since the sources in our sample are extreme, it is reasonable to see
this feature. The wings in the H13CO+ line are much smaller than the ones in
the HCO+ line, and it is still possible to properly fit a Gaussian curve.

Source | RMS | Area | FWZP | Peak $T_{MB}$ | Wings
---|---|---|---|---|---
| (K) | (K km s-1) | (km s-1) | (K) |
HC01 | 0.04 | 11.9 | 23.97 | 2.73 |
HC02 | 0.10 | 124.7 | 92.12 | 13.00 | ✓
HC03 | 0.09 | 11.7 | 19.86 | 2.35 |
HC04 | 0.10 | 50.8 | 29.45 | 4.74 |
HC05 | 0.11 | 7.3 | 19.86 | 2.15 |
HC06 | 0.11 | 25.5 | 46.58 | 2.37 | ✓
HC07 | 0.12 | 16.1 | 16.10 | 4.52 |
HC08 | 0.03 | 61.4 | 53.43 | 6.83 | ✓
HC09 | 0.03 | 13.9 | 26.37 | 3.29 |
HC10 | 0.03 | 6.4 | 27.06 | 2.17 |
HC11 | 0.03 | 5.1 | 18.84 | 1.24 |
HC12 | 0.04 | 9.0 | 19.86 | 2.49 |
HC13 | 0.05 | 28.7 | 27.06 | 5.74 |
HC14 | 0.03 | 17.3 | 28.13 | 4.12 |
HC15 | 0.02 | 24.8 | 31.17 | 3.46 |
HC16 | 0.02 | 44.2 | 55.82 | 4.58 | ✓
HC17 | 0.03 | 23.7 | 53.77 | 2.20 | ✓
HC18 | 0.04 | 11.4 | 40.75 | 2.02 | ✓
HC19 | 0.05 | 8.3 | 10.96 | 2.55 |
HC20 | 0.05 | 104.3 | 45.89 | 11.14 | ✓
HC21 | 0.05 | 45.2 | 35.27 | 9.37 | ✓
HC22 | 0.09 | 17.8 | 23.29 | 3.32 |
HC23 | 0.03 | 17.0 | 27.06 | 3.25 |
HC24 | 0.04 | 9.8 | 19.18 | 2.67 |
HC25 | 0.05 | 4.6 | 19.52 | 1.21 |
HC26 | 0.03 | 21.5 | 20.21 | 5.43 |
HC27 | 0.04 | 20.1 | 52.40 | 2.44 | ✓
HC28 | 0.02 | 15.5 | 24.66 | 2.28 |
HC29 | 0.02 | 33.3 | 29.45 | 4.51 |
HC30 | 0.03 | 19.3 | 28.08 | 4.11 |
HC31 | 0.03 | 14.4 | 14.73 | 2.88 |
HC32 | 0.03 | 12.4 | 20.20 | 3.45 |
Table 3: HCO+ spectral line data. Source | $R$ | RMS | Area | Width | Position | Peak $T_{MB}$
---|---|---|---|---|---|---
| (pc) | (K) | (K km s-1) | (km s-1) | (km s-1) | (K)
HC01 | 0.26 | 0.02 | 2.4 | 2.29 | 8.4 | 1.00
HC02 | 0.26 | 0.03 | 18.7 | 4.68 | 9.3 | 3.75
HC03 | 0.31 | 0.02 | 3.9 | 2.83 | 21.0 | 1.29
HC04 | 0.46 | 0.03 | 7.5 | 7.09 | 66.8 | 0.99
HC05 | 0.25 | 0.02 | 4.0 | 3.80 | 33.1 | 0.99
HC06 | 0.26 | 0.02 | 7.0 | 3.91 | 37.3 | 1.67
HC07 | 0.33 | 0.02 | 2.9 | 3.23 | 59.5 | 0.84
HC08 | 0.38 | 0.01 | 6.8 | 4.58 | -39.5 | 1.40
HC09 | 0.47 | 0.02 | 3.8 | 3.09 | -57.9 | 1.16
HC10 | 0.40 | 0.02 | 4.4 | 3.19 | -54.9 | 1.30
HC11 | 0.31 | 0.01 | 1.3 | 2.96 | -48.1 | 0.43
HC12 | 0.23 | 0.02 | 1.8 | 1.99 | -40.2 | 0.86
HC13 | 0.36 | 0.03 | 4.2 | 2.94 | -68.0 | 1.34
HC14 | 0.34 | 0.03 | 1.6 | 2.52 | -64.9 | 0.59
HC15 | 0.44 | 0.03 | 3.1 | 3.80 | -88.7 | 0.77
HC16 | 0.33 | 0.03 | 5.8 | 4.40 | -62.7 | 1.24
HC17 | 0.425 | 0.03 | 4.0 | 4.60 | -87.8 | 3.84
HC18 | 0.28 | 0.03 | 2.8 | 2.99 | -48.5 | 0.88
HC19 | 0.27 | 0.03 | 1.1 | 1.67 | -47.0 | 0.60
HC20 | 0.29 | 0.03 | 22.4 | 5.48 | -53.2 | 3.84
HC21 | 0.28 | 0.02 | 7.8 | 3.54 | -46.6 | 2.07
HC22 | 0.23 | 0.02 | 2.7 | 2.44 | -34.3 | 1.04
HC23 | 0.24 | 0.01 | 2.8 | 2.85 | -46.2 | 0.92
HC24 | 0.24 | 0.02 | 1.9 | 2.23 | -40.8 | 0.78
HC25 | 0.40 | 0.01 | 2.2 | 4.19 | -71.0 | 0.48
HC26 | 0.24 | 0.02 | 4.1 | 3.04 | -40.8 | 1.27
HC27 | 0.25 | 0.02 | 7.4 | 6.30 | -27.0 | 1.10
HC28 | 0.34 | 0.01 | 2.6 | 3.74 | -31.5 | 0.65
HC29 | 0.48 | 0.01 | 5.1 | 3.72 | -69.4 | 1.28
HC30 | 0.24 | 0.01 | 3.8 | 3.09 | -18.0 | 1.16
HC31 | 0.12 | 0.01 | 4.1 | 3.05 | -10.6 | 1.27
HC32 | 0.325 | 0.01 | 1.1 | 2.30 | -20.5 | 0.44
Table 4: H13CO+ Spectral Line Data. Source | $R$ | RMS | Area | Width | Position | Peak
---|---|---|---|---|---|---
| (pc) | (mK) | (K km s-1) | (km s-1) | (km s-1) | (K)
|  |  | Full | Red Wing | Blue Wing | FWZP | Red Wing | Blue Wing |  |
HC01 | 0.26 | 0.02 | 0.4 | - | - | 33.90 | - | - | 10.1 | 0.05
HC02 | 0.26 | 0.028 | 26.8 | 7.5 | 14.6 | 92.12 | 40.11 | 47.33 | 10.0 | 1.11
HC03 | 0.31 | 0.02 | 1.0 | 0.4 | 0.5 | 27.05 | 13.59 | 10.64 | 21.1 | 0.17
HC04 | 0.46 | 0.03 | 8.4 | 1.1 | 3.8 | 45.55 | 11.51 | 26.95 | 67.2 | 0.59
HC05 | 0.25 | 0.02 | 2.3 | 0.5 | 1.2 | 43.15 | 16.95 | 22.41 | 33.1 | 0.22
HC06 | 0.26 | 0.02 | 5.0 | 2.1 | 1.7 | 49.32 | 24.06 | 21.35 | 36.9 | 0.39
HC07 | 0.33 | 0.02 | 2.5 | 0.6 | 1.2 | 47.26 | 16.56 | 27.47 | 59.4 | 0.26
HC08 | 0.38 | 0.01 | 13.5 | 5.5 | 6.1 | 74.66 | 35.58 | 34.50 | -39.1 | 1.57
HC09 | 0.47 | 0.01 | 1.0 | 0.4 | 0.3 | 36.64 | 19.13 | 14.42 | -58.1 | 0.12
HC10 | 0.40 | 0.01 | 0.8 | 0.1 | 0.3 | 19.18 | 4.88 | 11.11 | -53.5 | 0.15
HC11 | 0.31 | 0.014 | 0.1 | - | - | 14.73 | - | - | -50.1 | 0.06
HC12 | 0.23 | 0.02 | 1.3 | 0.4 | 0.6 | 30.82 | 11.74 | 17.09 | -39.2 | 0.25
HC13 | 0.36 | 0.03 | 0.0 | - | - | 0.00 | - | - | -67.5 | 0.08
HC14 | 0.34 | 0.03 | 0.0 | - | - | 0.00 | - | - | -64.7 | 0.08
HC15 | 0.44 | 0.03 | 2.4 | 0.6 | 0.8 | 29.80 | 11.34 | 14.66 | -87.9 | 0.34
HC16 | 0.33 | 0.03 | 6.5 | 2.4 | 2.2 | 42.81 | 20.25 | 18.17 | -62.9 | 0.48
HC17 | 0.425 | 0.03 | 12.3 | 3.3 | 5.9 | 56.85 | 26.33 | 25.93 | -86.7 | 0.78
HC18 | 0.28 | 0.03 | 15.6 | 1.3 | 0.5 | 36.99 | 19.59 | 14.40 | -49.4 | 0.21
HC19 | 0.27 | 0.03 | 0.0 | - | - | 0.00 | - | - | 0.0 | 0.07
HC20 | 0.29 | 0.02 | 11.8 | 1.3 | 6.4 | 50.34 | 18.90 | 25.97 | -53.3 | 0.94
HC21 | 0.28 | 0.02 | 2.3 | 2.9 | 4.5 | 60.96 | 23.95 | 33.46 | -46.3 | 0.97
HC22 | 0.23 | 0.02 | 19.1 | 0.8 | 2.0 | 87.67 | 27.45 | 57.78 | -34.6 | 0.15
HC23 | 0.24 | 0.01 | 1.6 | 0.6 | 0.7 | 44.86 | 19.48 | 22.53 | -45.8 | 0.15
HC24 | 0.24 | 0.01 | 1.5 | 0.6 | 0.6 | 46.92 | 21.63 | 23.06 | -40.3 | 0.15
HC25 | 0.40 | 0.02 | 0.9 | 0.3 | 0.3 | 31.51 | 13.29 | 14.02 | -70.3 | 0.09
HC26 | 0.24 | 0.02 | 1.5 | 0.4 | 0.6 | 30.14 | 9.84 | 17.25 | -40.5 | 0.22
HC27 | 0.25 | 0.02 | 17.6 | 6.1 | 6.9 | 74.66 | 34.50 | 33.86 | -25.3 | 1.02
HC28 | 0.34 | 0.01 | 0.8 | 0.3 | 0.2 | 31.85 | 15.56 | 12.55 | -30.8 | 0.10
HC29 | 0.48 | 0.01 | 2.1 | 0.8 | 0.6 | 42.47 | 22.89 | 15.86 | -68.5 | 0.16
HC30 | 0.24 | 0.01 | 0.0 | 0.9 | 0.2 | 45.21 | 29.28 | 12.83 | 18.7 | 0.15
HC31 | 0.12 | 0.013 | 0.3 | - | - | 17.81 | - | - | -12.5 | 0.05
HC32 | 0.325 | 0.01 | 0.3 | - | - | 33.56 | - | - | -19.2 | 0.04
Table 5: SiO Spectral Line Data.

Since wings in the HCO+ spectral profile are a very good indicator of
outflows, its (2-1) spectral line was used to determine the presence of
molecular outflows through the detection of wings. In the literature, spectral
lines with wings are usually modelled by a Lorentz distribution. However, this
line presents significant absorption in our data, which makes any curve fit
far too inaccurate. Thus, HCO+ wings were checked for as follows: the sum of
the widths of the red and blue wings was obtained by subtracting the baseline
width of the Gaussian fit of the H13CO+ line from the HCO+ FWZP; if the sum of
the widths is larger than 25 km s-1, then the given source is deemed to have
HCO+ wings. As modelled by Gusdorf, A. et al. (2008) (see also Leurini et al.
(2014)), shocks trigger erosion of grains and SiO can be efficiently produced
only if shock speeds are above 25 km s-1. Results show (see Table 3) that 28%
of our sample (9 sources) present wings in the HCO+ spectral profile (e.g. see
Fig. 13). However, we note that, due to the lack of spatial information, there
is significant uncertainty in these results.

###  3.2 SiO Detection

We checked whether the sources present SiO emission, which directly traces
outflows and shocked gas. Emission at $5\sigma$ or more was considered. SiO
emission was found in 78% of our sample (25 sources). Results are displayed in
Table 5.

The material ejected by bipolar outflows conforms two lobes, as modelled in
Rawlings et al. (2004). Depending on the inclination angle, this produces
mainly two features: the red and blue wings. While centred at the velocity of
each source, the width from the Gaussian fit to the H13CO+(2-1) line was
subtracted from the SiO(4-3) spectral profile width to obtain the width of the
red and blue wings. With these measurements (see Table 5) the velocity
integrated intensity of the SiO wings were obtained and further used to
calculate the physical properties of the outflows.

There are a few sources that have particularly intense SiO emission, such as
the source HC02 (associated to IRAS 17574-2403). The peak of the emission of
these sources is $\geq 20$ times the RMS and they have $T_{peak}>0.7$ K. For a
more detailed description and summary of previous works done on these sources,
see Appendix C.

According to these results, we have divided the sample into three groups, as
seen in Table 6: 9 sources present both SiO detection and HCO+ wings, 16
sources present SiO emission and no HCO+ wings, and the remaining 7 present
neither.

Group | SiO Detection | HCO+ Wings | No. of Sources
---|---|---|---
A | ✓ | ✓ | 9
B | ✓ | - | 16
C | - | - | 7
Table 6: Grouping of the sources.

##  4 Results

We calculated the following properties of the clumps and their outflows.

###  4.1 Properties of the Clump

####  4.1.1 Virial Masses

The Gaussian width of the H13CO+(2-1) spectral line was used to calculate the
virial mass of the clump. Assuming that it is gravitationally bound, so that
the virial theorem applies, the virial mass can be calculated as follows (e.g.
Merello et al., 2013):

$\displaystyle\left(\frac{M_{\text{virial}}}{M_{\odot}}\right)=210\left(\frac{\Delta
V}{\text{km s}^{-1}}\right)^{2}\left(\frac{R}{\text{pc}}\right)$ (2)

where $\Delta V$ is the line’s Gaussian width, and $R$ is the spatial beam
size of the source.

Results show (see Table 7) that these sources have very high virial masses,
reaching up to $4.9\times 10^{3}M_{\odot}$. However, the beam of the
observation instrument APEX is larger than the clump, thus the observations
include more material.

####  4.1.2 LTE Mass

The Local Thermodynamic Equilibrium (LTE) mass of the clump was calculated
using the LTE formalism, assuming the emission is optically thin. The H13CO+
is a linear and rigid rotor molecule. Thus, the column density $N_{J}$ was
calculated as follows (e.g. Garden et al., 1991; Sanhueza et al., 2012):

$\displaystyle\begin{aligned}
N_{J}&=\frac{3h}{8\pi^{3}\mu^{2}}\frac{U(T_{ex})}{(J+1)}\frac{\exp{\left(\frac{E_{J}}{kT_{ex}}\right)}}{\left[1-\exp{\left(\frac{-h\nu}{kT_{ex}}\right)}\right]}\\\
&\times\frac{1}{\left(J(T_{ex})-J(T_{bg})\right)}\int T_{MB}d\nu\end{aligned}$
(3)

Here, $k$ is the Boltzmann constant, $h$ is the Planck constant,
$\mu=3.89\times 10^{-18}$ (D) is the electric dipole momenta and
$E_{J}=hBJ(J+1)$ is the energy in the level $J$ (in this case, $J=1$), where
$B=43377.165$ (MHz) is the rotational constant. The intensity $J(T)$ is
defined for a given frequency $\nu$ as:

$J(T)=\frac{h\nu}{k}\frac{1}{\exp{\left(\frac{h\nu}{kT}-1\right)}}$ (4)

Finally, $U(T)$ is the partition function:

$\displaystyle
U(T)=\sum_{J=0}^{\infty}g_{J}\exp{\left[\frac{-hBJ(J+1)}{kT_{ex}}\right]}\approx\frac{k}{hB}\left(T_{ex}+\frac{hB}{3k}\right),$
(5)

where $g_{J}=2J+1$ is the rotational degeneracy. A cosmic background
temperature $T_{bg}$ of $2.75$ K was considered. The excitation temperature
$T_{ex}$ was set to a standard value of $30$ K, which is close to the median
of the dust temperatures (e.g. Elia et al., 2017) (26.4 $\pm$ 6.0 K). The
total column density in units of cm-2 can be obtained by multiplying $N_{J}$
by the abundance of H13CO+:
$\left[\text{H}_{2}/\text{H}^{13}\text{CO}^{+}\right]=3.0\times 10^{10}$
(Blake et al., 1987). Finally, the LTE mass is obtained by multiplying the
total column density by the area of the source:

$\displaystyle M_{\text{LTE}}=N_{\text{tot}}\pi R^{2}$ (6)

where $R$ is the radius of the beam. These results are also shown in Table 7.

We compared our LTE mass estimates to the clump mass derived from dust
emission obtained by Hi-GAL (Elia et al., 2017, 2021). The ratio between the
dust and LTE masses has a mean of 2.11, a median of 1.64 and a standard
deviation of 1.34. The origin of this uncertainty can come from the assumed
temperature as well as the H13CO+ abundance. Furthermore, the dust masses from
Hi-GAL used here were calculated by fitting a SED which was scaled to the
angular size at 250 $\mu$m (Elia et al., 2013; Motte, F. et al., 2010) (we
note that for the four saturated sources of the sample, the mass used here was
obtained using the flux at 500 $\mu$m instead; see Appendix A for the
treatment of saturated sources). The H13CO+ line and emission at 250 $\mu$m
trace mostly the same dense gas and their angular sizes are within a factor of
2.35 on average (see Section 3), which is consistent with the difference seen
between the masses. This indicates our estimates are sound.

The uncertainty of the molecular observations is $\sim$ 20 %, which affects
the Gaussian fit parameters, and propagates to the rest of the clump’s
properties. Because of the propagating error, the column density can be
considered to have $10-20$ % of uncertainty, whilst the mass uncertainty is
$<30$ %. The distances are also a source of uncertainty, which affects the
beam radius and masses (see Appendix B).

Source | $M_{vir}$ | $N_{tot}$ | $M_{LTE}$ | $M_{vir}/M_{LTE}$ | Group
---|---|---|---|---|---
| ($M_{\odot}$) | ($10^{22}$ cm-2) | ($M_{\odot}$) |  |
HC01 | 284 | 5.36 | 242 | 1.17 | C
HC02 | 1181 | 40.99 | 1839 | 0.64 | A
HC03 | 521 | 8.50 | 559 | 0.93 | B
HC04 | 4867 | 16.39 | 2381 | 2.04 | B
HC05 | 760 | 8.73 | 376 | 2.02 | B
HC06 | 828 | 15.24 | 693 | 1.19 | A
HC07 | 735 | 6.34 | 485 | 1.51 | B
HC08 | 1656 | 14.91 | 1438 | 1.15 | A
HC09 | 936 | 8.37 | 1245 | 0.75 | B
HC10 | 849 | 9.66 | 1047 | 0.81 | B
HC11 | 579 | 2.95 | 199 | 2.91 | C
HC12 | 195 | 4.00 | 150 | 1.30 | B
HC13 | 645 | 9.17 | 796 | 0.81 | C
HC14 | 450 | 3.49 | 271 | 1.66 | C
HC15 | 1332 | 6.81 | 901 | 1.48 | B
HC16 | 1334 | 12.69 | 937 | 1.42 | A
HC17 | 1887 | 8.78 | 1086 | 1.74 | A
HC18 | 519 | 6.16 | 322 | 1.61 | A
HC19 | 158 | 2.35 | 117 | 1.35 | C
HC20 | 1829 | 49.04 | 2823 | 0.65 | A
HC21 | 741 | 178 | 920 | 0.81 | A
HC22 | 284 | 5.92 | 208 | 1.37 | B
HC23 | 414 | 6.14 | 247 | 1.68 | B
HC24 | 247 | 4.07 | 156 | 1.58 | B
HC25 | 1488 | 4.73 | 526 | 2.83 | B
HC26 | 465 | 9.02 | 352 | 1.32 | B
HC27 | 2050 | 16.19 | 669 | 3.07 | A
HC28 | 993 | 5.67 | 441 | 2.25 | B
HC29 | 1400 | 11.12 | 1772 | 0.79 | B
HC30 | 473 | 8.39 | 318 | 1.49 | B
HC31 | 227 | 9.06 | 83 | 2.73 | C
HC32 | 360 | 2.38 | 172 | 2.09 | C
Table 7: Properties obtained from H13CO$+$ emission.

####  4.1.3 Virial and LTE Mass Comparison

The ratio between the virial and LTE mass can provide information about the
gravitational stability of the source. High values of this ratio indicate that
the internal kinetic energy of the source is too high and that it is not
massive enough to be gravitationally stable. Since the material traced by
H13CO+ emission should be both gravitationally bound and in local
thermodynamic equilibrium, the virial and LTE mass should match within a
factor of $\sim 2$ when magnetic effects are not considered. Results are
presented in Table 7. The ratio between the virial and LTE mass has a mean
value of 1.54, a median of 1.45, a minimum of 0.64 and a maximum of 3.07. Only
8 sources have a ratio of 2.00 or higher. Thus, the virial and LTE masses are
in good agreement.

###  4.2 Properties of the SiO Outflows

####  4.2.1 Outflow Mass

We calculated the LTE mass for the SiO outflows in the red and blue wings.
With an assumption of optically thin thermal SiO(4-3) emission in LTE (e.g.
Liu et al., 2021), the column densities $N_{J}$, $N_{tot}$ and the LTE mass
were calculated as described in Sect. 4.1.2 using a rotational constant $B$ of
$21711.96$ (MHz), an electric dipole moment $\mu$ of $3.10\times 10^{-18}$
(D), an excitation temperature $T_{ex}$ of $18$ K and an SiO abundance
$\left[\text{H}_{2}/\text{SiO}\right]$ of $10^{9}$ (Liu et al., 2021; Sanhueza
et al., 2012), standard values for this type of sources. If a higher $T_{ex}$
of 25 K or 30 K was used, the values of the outflow masses would increase by
16.32% and 29.42% respectively. Since SiO abundances can drastically vary in
different MSF regions (in up to six orders of magnitude, Ziurys et al. (1989);
Martin-Pintado et al. (1992); Li et al. (2019b)), using an inadequate choice
for this parameter could artificially modify the results. Here, we use a
standard value for $\left[\text{H}_{2}/\text{SiO}\right]$, accepted for
protostellar objects. Results are displayed in Table 8.

####  4.2.2 Dynamical Properties

Further characteristics of the outflow were computed as follows (Beuther et
al., 2002): momentum $P_{out}$, kinetic energy $E_{kin}$, characteristic
timescale $t$, mechanical force or flow of momentum $F$, rate of matter
expulsion $\dot{M}$ and mechanical luminosity or power $L_{m}$.

$\displaystyle P_{out}=M_{r}V_{r}+M_{b}V_{b}$ (7)

$\displaystyle E_{kin}=\frac{1}{2}M_{r}V_{r}^{2}+\frac{1}{2}M_{b}V_{b}^{2}$
(8)

$\displaystyle t=\frac{2R}{\left(V_{r}+V_{b}\right)}$ (9)

$\displaystyle F_{m}=\frac{P_{\text{out}}}{t}$ (10)

$\displaystyle\dot{M}_{out}=\frac{M_{\text{out}}}{t}$ (11)

$\displaystyle L_{m}=\frac{E_{\text{kin}}}{t}$ (12)

Here, $R$ is the radius of the source, $M_{\text{out}}=M_{r}+M_{b}$ is the
total outflow mass, and $V_{b}$ and $V_{r}$ are the maximum velocities of the
outflows, which corresponds to $|V_{LSR}-V_{i}|$ (Beuther et al., 2002; Liu,
D.J. et al., 2021), where $V_{i}$ is the velocity at each the extreme of the
SiO emission baseline. Results are displayed in Table 8.

Source | $N_{R}$ | $N_{B}$ | $M_{R}$ | $M_{B}$ | $M_{out}$ | $P_{out}$ | $E_{kin}$ | $t$ | $\dot{M}$ | $F$ | $L_{m}$ | Group
---|---|---|---|---|---|---|---|---|---|---|---|---
| ($10^{20}$ cm-2) | ($M_{\odot}$) | ($M_{\odot}$ km s-1) | ($10^{46}$ erg) | ($10^{4}$ yr) | ($10^{-4}M_{\odot}$ yr-1) | ($10^{-3}M_{\odot}$ km s-1 yr-1) | ($L_{\odot}$) |
HC02 | 77.02 | 150.54 | 34.5 | 67.4 | 101.9 | 4813 | 183 | 0.5 | 187 | 884.91 | 2784 | A
HC03 | 4.34 | 4.64 | 2.9 | 3.0 | 5.9 | 79 | 1 | 2.2 | 3 | 3.54 | 5 | B
HC04 | 11.78 | 38.75 | 17.1 | 56.2 | 73.3 | 1971 | 17 | 2.0 | 37 | 99.56 | 69 | B
HC05 | 4.87 | 11.93 | 2.1 | 5.1 | 7.2 | 164 | 3 | 1.1 | 6 | 14.42 | 19 | B
HC06 | 21.79 | 17.54 | 9.9 | 8.0 | 17.9 | 443 | 12 | 1.0 | 17 | 43.30 | 97 | A
HC07 | 6.47 | 12.68 | 4.9 | 9.7 | 14.6 | 372 | 5 | 1.4 | 11 | 26.83 | 29 | B
HC08 | 57.04 | 63.19 | 54.9 | 60.8 | 115.7 | 4316 | 165 | 1.0 | 118 | 438.71 | 1390 | A
HC09 | 3.83 | 3.25 | 5.7 | 4.8 | 10.5 | 194 | 4 | 2.5 | 4 | 7.81 | 15 | B
HC10 | 1.36 | 2.81 | 1.5 | 3.0 | 4.5 | 48 | 0.2 | 4.1 | 1 | 1.19 | 0.4 | B
HC12 | 3.96 | 6.05 | 1.5 | 2.3 | 3.8 | 60 | 1 | 1.5 | 3 | 4.03 | 3 | B
HC15 | 5.73 | 7.82 | 7.6 | 10.3 | 17.9 | 271 | 3 | 2.9 | 6 | 9.39 | 9 | B
HC16 | 24.69 | 22.75 | 18.2 | 16.7 | 34.9 | 749 | 17 | 1.5 | 23 | 49.91 | 97 | A
HC17 | 33.47 | 60.78 | 41.3 | 75.0 | 116.3 | 3299 | 95 | 1.5 | 80 | 225.54 | 537 | A
HC18 | 13.31 | 5.63 | 6.9 | 2.9 | 9.9 | 193 | 4 | 1.5 | 7 | 13.19 | 25 | A
HC20 | 13.77 | 65.74 | 7.9 | 37.8 | 45.7 | 1255 | 21 | 1.1 | 41 | 111.37 | 156 | A
HC21 | 29.53 | 46.83 | 15.9 | 25.2 | 41.0 | 1294 | 27 | 0.9 | 46 | 143.79 | 249 | A
HC22 | 8.19 | 20.50 | 2.9 | 7.2 | 10.0 | 506 | 8 | 0.5 | 20 | 100.10 | 135 | B
HC23 | 5.70 | 7.14 | 2.3 | 2.9 | 5.1 | 116 | 2 | 1.1 | 5 | 11.00 | 18 | B
HC24 | 6.02 | 6.47 | 2.3 | 2.5 | 4.8 | 112 | 2 | 1.0 | 5 | 11.38 | 21 | B
HC25 | 2.93 | 3.15 | 3.3 | 3.5 | 6.8 | 107 | 2 | 2.5 | 3 | 4.25 | 5 | B
HC26 | 3.94 | 5.99 | 1.5 | 2.3 | 3.9 | 61 | 0.5 | 1.5 | 2 | 3.95 | 3 | B
HC27 | 63.10 | 71.16 | 26.0 | 29.3 | 55.3 | 2064 | 78 | 0.6 | 86 | 320.61 | 1004 | A
HC28 | 2.73 | 1.71 | 2.1 | 1.3 | 3.4 | 56 | 1 | 2.1 | 2 | 2.70 | 4 | B
HC29 | 8.74 | 6.45 | 13.9 | 10.2 | 24.1 | 526 | 15 | 2.2 | 11 | 23.64 | 55 | B
HC30 | 9.51 | 2.36 | 3.6 | 0.9 | 4.5 | 124 | 4 | 1.0 | 4 | 12.14 | 35 | B
Table 8: Properties of the SiO outflows.

The uncertainty of the observations (20%; see Section 2.2) propagates to these
calculated properties. The outflow column density and mass have about 10 - 20%
and $<30$% of uncertainty, respectively. The momentum and kinetic energy have
the same uncertainty as the mass, whilst the force, rate of matter expulsion
and mechanical luminosity have an additional source of uncertainty due to the
dynamical timescales, which comes from the distances and the instrumental
error ($\sim$20%).

A statistical description of these results is shown in Table 9. The typical
rate of matter expulsion for mid and early massive protostars ranges from
$10^{-5}$ to a few times $10^{-3}M_{\odot}$ yr-1, and the typical momentum
from $10^{-4}$ to $10^{-2}$ $M_{\odot}$ km s-1 (Arce et al., 2007). Our
results for the rate of matter expulsion are well within this typical range.
The momentum is generally higher, with a mean of $922$ $M_{\odot}$ km s-1,
indicating that the outflows in our sample are generally very fast and/or
massive. Furthermore, the SiO outflows studied here present properties that
are within the range of results presented in other works but are more massive
and powerful. This is the case for the sample of protostellar candidates
studied by Beuther et al. (2002), which were traced with CO(2-1), as well as
the sample of massive young stellar objects (MYSOs) and compact HII regions
traced with 12CO(2-1) and 13CO(2-1) by Maud et al. (2015). Similarly, our
sample has more massive and powerful SiO outflows than other studies that have
traced them with the SiO(5-4) spectral line, such as the sample of infrared
dark clouds (IRDCs) studied by Liu et al. (2021), for which our results are
larger by up to three orders of magnitude. Thus, not only our results are in
good accordance with other works in the literature, but our sources stand out
because of their powerful outflows.

| $M_{out}$ | $P_{out}$ | $E_{kin}$ | $t$ | $\dot{M}$ | $F$ | $L_{m}$
---|---|---|---|---|---|---|---
| ($M_{\odot}$) | ($M_{\odot}$ km s-1) | ($10^{46}$ erg) | ($10^{4}$ yr) | ($10^{-4}M_{\odot}$ yr-1) | ($10^{-3}M_{\odot}$ km s-1 yr-1) | ($L_{\odot}$)
Mean | 30 | 928 | 27 | 1.6 | 29 | 102.69 | 271
STD. | 36 | 1358 | 50 | 0.8 | 45 | 196.34 | 622
Min. | 3 | 48 | 0.2 | 0.5 | 1 | 1.19 | 0.4
25% | 5 | 112 | 2 | 1.0 | 4 | 7.81 | 9
Median | 11 | 271 | 4 | 1.5 | 7 | 14.42 | 29
75% | 41 | 1255 | 17 | 2.1 | 37 | 100.10 | 135
Max. | 116 | 4813 | 183 | 4.1 | 187 | 884.91 | 2784
Table 9: Statistics of the properties of the outflow.

##  5 Discussions

###  5.1 Correlations

We looked for correlations between the properties of the outflows and the
properties of their hosting clump. We found three relevant correlations:
between the bolometric luminosity and outflow power, between the outflow power
and the rate of matter expulsion, and between the kinetic energy of the
outflow and outflow mass. Their rank correlation coefficients were calculated
and the Python package sklearn.linear_model (Pedregosa et al., 2012) was used
to perform a linear regression in order to find the slope of these
correlations. Our results show that, for these three correlations, the rank
correlation coefficients are positive, as well as the slopes.

A weak linear trend between the bolometric luminosity and the outflow power
shown in Fig. 4 was found. This correlation tells us that, given that a source
has a molecular outflow, the more luminous the source, the more energetic its
outflow will be. Therefore, it is possible that it will power more massive and
energetic outflows. However, this correlation has a large amount of
dispersion, it is not possible to make definitive conclusions. Other studies
have also found this correlation: Wu, Y. et al. (2004), Liu, D.J. et al.
(2021) and Maud et al. (2015) found it in the 12CO and 13CO lines, and Liu,
D.J. et al. (2021) also found it on the HCO+ and CS lines. It has also been
found in other SiO transitions by Csengeri et al. (2016); Li et al. (2019b);
Liu et al. (2021). All of these species are outflow tracers and the linear
regressions done have always given a positive slope. Thus, in spite of being a
weak correlation in our sample, it is still positive and is in agreement with
the trends found by these other works. Thus, the idea that more luminous
sources are able to produce more powerful shocks (Codella et al., 1999) cannot
be discarded. Since this has been found in various SiO transitions and outflow
tracers, and now in the SiO(4-3) one as well, it is a possibly universal trend
to molecular outflows in MSF regions.

Figure 4: Bolometric luminosity ($L_{\odot}$) vs. outflow power $L_{m}$
($L_{\odot}$) in logarithmic scale.

As shown in Fig. 5, there is a close linear relationship between the kinetic
energy and the outflow mass. This correlation has a Spearman $\rho$
coefficient of 0.93 and a slope of 0.69. It is strong and suggests that the
more massive an outflow is, the faster it will be.

Figure 5: Kinetic energy ($10^{46}$ erg) vs. outflow mass ($M_{\odot}$) in
logarithmic scale. The Spearman $\rho$ rank correlation coefficient is equal
to 0.93 and the slope is equal to 0.69.  Figure 6: Outflow power $L_{m}$
($L_{\odot}$) vs. rate of matter expulsion $\dot{M}$ ($10^{-4}M_{\odot}$ yr-1)
in logarithmic scale. The Spearman $\rho$ rank correlation coefficient is
equal to 0.97 and the slope is equal to 0.70.

Note that this correlation is physically equivalent to one between the outflow
power and the rate of mass expulsion, as these parameters are proportional to
the inverse of the characteristic timescale (see Equations 11 and 12):

$t=\frac{M_{out}}{\dot{M}_{out}}=\frac{E_{kin}}{L_{m}}$ (13)

Thus, this correlation carries the uncertainties of the dynamical timescale
previously discussed. However, it is still useful to analyse this trend as it
provides intuitive physical significance and a direct comparison with other
works is possible. In our sample, this is a strong relation: its Spearman
$\rho$ rank correlation coefficient is equal to 0.97 and its slope is equal to
0.70 (see Fig. 6). This relationship tells us that the more powerful the
outflow is, the faster it ejects matter. Therefore, in addition to expelling
more material, energetic outflows expel this material faster. This trend has
also been found by other studies, such as Beuther et al. (2002) and Liu, D.J.
et al. (2021) in the CO line and its isotopologues. Liu, D.J. et al. (2021)
found this trend in other outflow tracers too, such as HCO+ and CS, indicating
that this trend is common to outflows independent of the tracer used. Finding
this trend in SiO here further supports this idea.

The correlations found here suggest that, since sources with a larger
bolometric luminosity are more energetic, their outflows also are. These
energetic outflows bear to mobilise more material. Thus, their rate of mass
loss is high, which translates into large outflow masses. These correlations
agree with the dependency suggested by Liu, D.J. et al. (2021) (see also Wu,
Y. et al., 2004): bolometric luminosity $\rightarrow$ outflow energy
$\rightarrow$ rate of mass loss $\rightarrow$ outflow mass.

###  5.2 Evolutionary Stage Indicator L/M

The luminosity to mass ratio $L/M$ can be used as an evolutionary stage
indicator (e.g. Molinari et al., 2016; Elia et al., 2021; Urquhart et al.,
2022). In the first stages of star formation, the core is cold and actively
accreting matter, so $L/M\leq 1$. Eventually, the temperature and luminosity
increase, while the mass remains virtually unchanged. This results in a value
of $L/M\geq 1$. It has been found that the more luminous sources in the Galaxy
usually have $L/M\geq 10$ (López-Sepulcre, A. et al., 2011; Molinari et al.,
2016). The sources in the sample studied here are in an advanced stage of the
star-forming process, as $L/M$ has values ranging from $3$
$L_{\odot}/M_{\odot}$ up to $177$ $L_{\odot}/M_{\odot}$, with a mean of 58
$L_{\odot}/M_{\odot}$ and a median of 41 $L_{\odot}/M_{\odot}$ (see Table 2).
Furthermore, we looked for correlations between $L/M$ and the SiO outflow
properties and found that they are not correlated. Other works have also
failed to find such correlations (Liu et al., 2022; Maud et al., 2015; Liu,
D.J. et al., 2021). This strongly suggests that molecular outflows are present
throughout the whole of the high-mass star formation process (Csengeri et al.,
2016; Urquhart et al., 2022).

###  5.3 Cross-Check between SiO and HCO+ Wings Detections

All of the sources that present wings in the HCO+ line, also present SiO
emission above $5\sigma$. We compared these sources (Group A) with the rest of
the clumps with SiO detections (Group B) (see Table 6). Table 10 shows a
statistical comparison of the spectral parameters, outflow properties and the
evolutionary stage indicator $L/M$ between these groups.

SiO spectral profiles with FWZP $>20$ km s-1 are considered broad line widths
due to high-velocity shocks (Duarte-Cabral, A. et al., 2014; Zhu et al.,
2020). We note that all the sources in both Groups A and B exhibit broad line
widths, with a minimum FWZP of 19.18 km s-1, a mean value of 47.15 km s-1, a
median value of 44.86 km s-1 and a maximum of 92.12 km s-1. This means that
all of the sources where SiO was detected have experienced recent outflow
activity, which has manifested in high-velocity shocks, typically associated
with collimated jets, and it is strong enough to produce SiO outflows
(Csengeri et al., 2016; Li et al., 2019b; Liu et al., 2022). This confirms the
sources in both Groups A and B are protostellar (Zhu et al., 2020).

Furthermore, the SiO spectral profile of the sources in Group A is wider and
more intense, indicating that the outflows in this group are more massive,
faster and more energetic than those in Group B (Schilke et al., 1997; Duarte-
Cabral, A. et al., 2014; Liu et al., 2022) (see Table 10). Their mean outflow
mass is larger than those in Group B by a factor of 4.8, their mean momentum
by a factor of 7, their mean kinetic energy by a factor of 14.7, their dynamic
timescale by a factor of 0.58, their rate of matter expulsion by a factor of
8.7, their outflow force by a factor of 12, and their outflow power by a
factor of 25.1. Sources in Group A are possibly more collimated too, as broad-
width SiO detection is associated with them. Further studies of the spatial
morphology of these outflows could confirm this trend.

Even though SiO outflow activity has been found to decrease and get less
collimated over time (Arce et al., 2007; Sakai et al., 2010; López-Sepulcre,
A. et al., 2011), results show that sources in Group A and B are virtually in
the same stage of evolution because their evolutionary stage indicator $L/M$
have similar values. Table 10 shows that the evolutionary stage indicator
$L/M$ has a mean value of 40 ($L_{\odot}/M_{\odot}$) and 47
($L_{\odot}/M_{\odot}$), and a median of 32 ($L_{\odot}/M_{\odot}$) and 29
($L_{\odot}/M_{\odot}$) for Groups A and B, respectively. Thus, sources in
Group A and B are most likely equally evolved, even within the protostellar
phase (Motte et al., 2018). The fact that sources in Group A have more intense
and massive SiO outflows, but both groups are in the same evolutionary stage,
suggests that the presence of wings in the HCO+ spectral profile could help
identify sources with stronger SiO outflows. Therefore, checking for wings in
the HCO+ line could help identify more massive and active MSF regions in
samples of similarly evolved sources. Alternatively, since HCO+ emission is
associated with old outflow activity (Li et al., 2019a), sources in Group B
might have just recently started exhibiting strong outflow activity, allowing
for SiO outflows to be detected, and are too new to produce wings in the HCO+
spectral profile. Meanwhile, sources in Group A might have started exhibiting
outflow activity long enough time ago for wings in the HCO+ spectral profile,
a signal of old outflows, to form. In this scenario, SiO outflows detected
from the sources in Group A have been active for a longer time, which might be
a consequence of their large mass, power and luminosity. Thus, checking for
wings in the HCO+ line might also help identify sources whose outflows have
been active for longer. Further research with larger samples and better
resolution could provide insight into which of these two scenarios is more
likely and significant.

| FWZP | Peak | Full Area | $M_{out}$ | $P_{out}$ | $E_{kin}$ | $t$ | $\dot{M}$ | $F$ | $L_{m}$ | $L/M$
---|---|---|---|---|---|---|---|---|---|---|---
| (km s-1) | (K) | (K km s-1) | ($M_{\odot}$) | ($M_{\odot}$ km s-1) | ($10^{46}$ erg) | ($10^{4}$ yr) | ($10^{-4}M_{\odot}$ yr-1) | ($10^{-3}M_{\odot}$ km s-1 yr-1) | ($L_{\odot}$) | ($L_{\odot}/M_{\odot}$)
Group | A | B | A | B | A | B | A | B | A | B | A | B | A | B | A | B | A | B | A | B | A | B
Mean | 59.86 | 40.01 | 0.8 | 0.2 | 12.4 | 3.0 | 60 | 13 | 2047 | 298 | 67 | 4 | 1.1 | 1.9 | 67 | 8 | 247.93 | 21.00 | 704 | 27 | 40 | 47
STD | 17.69 | 15.29 | 0.4 | 0.1 | 7.4 | 4.7 | 41 | 17 | 1705 | 472 | 68 | 5 | 0.4 | 0.9 | 58 | 9 | 276.95 | 31.61 | 910 | 35 | 33 | 45
Min. | 36.99 | 19.18 | 0.2 | 0.1 | 2.3 | 0.04 | 10 | 3 | 193 | 48 | 4 | 0.2 | 0.5 | 0.5 | 7 | 1 | 13.19 | 1.19 | 25 | 0.4 | 3 | 3
25% | 49.32 | 30.65 | 0.5 | 0.2 | 6.5 | 1.0 | 35 | 5 | 749 | 75 | 17 | 1 | 0.9 | 1.1 | 23 | 3 | 49.91 | 4.01 | 97 | 5 | 12 | 17
Median | 56.85 | 39.56 | 0.9 | 0.2 | 12.3 | 1.5 | 46 | 6 | 1294 | 120 | 27 | 3 | 1.0 | 1.8 | 46 | 5 | 143.79 | 10.20 | 249 | 17 | 32 | 29
75% | 74.66 | 45.30 | 1.0 | 0.2 | 15.6 | 2.3 | 102 | 12 | 3299 | 296 | 95 | 4 | 1.5 | 2.3 | 86 | 7 | 320.61 | 16.73 | 1004 | 31 | 71 | 52
Max. | 92.12 | 87.67 | 1.6 | 0.6 | 26.8 | 19.1 | 116 | 73 | 4813 | 1971 | 183 | 17 | 1.5 | 4.1 | 187 | 37 | 884.91 | 100.10 | 2784 | 135 | 81 | 151
Table 10: Statistics of the spectral parameters and outflow properties of
sources from Groups A and B.

##  6 Summary and Conclusions

The aim of this work was to study shocked matter and SiO outflows in very
massive, luminous and powerful protostellar sources. We characterised them,
searched for any evolutionary trends they might exhibit, associated the
presence of shocked gas with outflow activity, and cross-checked SiO emission
with other outflow signatures. We used single-dish APEX/SEPIA Band 5
observations of 32 of the brightest massive protostellar sources in the
Southern Galaxy. We studied their outflow activity using the SiO and HCO+
tracers, as well as their general clump properties with H13CO+ emission. The
following is a summary of our main results and conclusions:

  1. 1.

The SiO emission detection rate above $5\sigma$ is 78% (25 sources). All SiO
detections have a broad line width due to high-velocity shocks, which confirms
these sources are well-evolved into the protostellar phase. Furthermore, 28%
of our sample (9 sources) shows wings in the HCO+ spectral profile.

  2. 2.

We calculated the dynamical properties of the SiO outflows. Results show they
are very massive, fast and energetic. Outflow mass has a minimum value of $3$
$M_{\odot}$, a median of $10$ $M_{\odot}$, a mean of $30$ $M_{\odot}$, and a
maximum value of $116$ $M_{\odot}$. Outflow momentum has a minimum value of
$50$ $M_{\odot}$ km s-1, a median of $271$ $M_{\odot}$ km s-1, a mean of $922$
$M_{\odot}$ km s-1, and a maximum value of $4812$ $M_{\odot}$ km s-1. The
kinetic energy of the outflow has a minimum value of $0.1\times 10^{46}$ erg,
a median of $4\times 10^{46}$ erg, a mean of $27\times 10^{46}$ erg, and a
maximum value of $183\times 10^{46}$ erg. Outflow power has a minimum value of
$1.24\times 10^{-3}M_{\odot}$ km s-1 yr-1, a median of $14.24\times
10^{-3}M_{\odot}$ km s-1 yr-1, a mean of $102.25\times 10^{-3}M_{\odot}$ km
s-1 yr-1, and a maximum value of $884.85\times 10^{-3}M_{\odot}$ km s-1 yr-1.

  3. 3.

We found three positive linear correlations involving SiO outflows properties:
a weak one between the bolometric luminosity and outflow power (Fig. 4), a
strong one between the outflow power and the rate of matter expulsion (Fig.
6), and between the kinetic energy and outflow mass (Fig. 5). They are both
positive correlations. The second and third have very low dispersion, but the
former has high dispersion. These correlations suggest that the more energetic
the outflow, the more material it bears to mobilise.

  4. 4.

We did not find any correlations between the evolutionary stage indicator
$L/M$ and SiO outflow properties. This agrees with the idea that molecular
outflows are a ubiquitous phenomenon throughout the process of high-mass star
formation.

  5. 5.

We performed a cross-check between SiO detection and the presence of wings in
the HCO+ line. Sources in Group A (sources that present both features; see
Table 6) have more massive, faster, more energetic and more collimated SiO
outflows than sources in Group B (sources that only exhibit SiO emission).
Sources in both groups are in an advanced stage of evolution in the high-mass
star formation process, and there is no clear evolutionary difference between
them. Thus, since SiO emission is such a good tracer of outflow activity,
checking for wings in the HCO+ line could help identify more massive and
active MSF regions in samples of similarly evolved sources. Alternatively,
checking for wings in the HCO+ line might help identify sources whose outflows
have been active for longer, since HCO+ traces old outflow activity, whilst
SiO traces recent and active outflows.

Our findings show potential for further studies of sources in an advanced
stage of evolution ($L/M>10$) and their molecular outflows.

###### Acknowledgements.

We thank the anonymous referee for their helpful and insightful comments. This
publication is based on data acquired with the Atacama Pathfinder Experiment
(APEX) under programme ID [TP.C-NNNN(R)]. APEX is a collaboration between the
Max-Planck-Institut fur Radioastronomie, the European Southern Observatory,
and the Onsala Space Observatory. M.M. acknowledges support from ANID,
Programa de Astronomía - Fondo ALMA-CONICYT, project 3119AS0001. L.B. and R.F.
gratefully acknowledge support by the ANID BASAL projects ACE210002 and
FB210003, FONDEF ID21I10359 and FONDECYT 1221662. E.M. acknowledges support
under the grant ”Maria Zambrano” from the UHU funded by the Spanish Ministry
of Universities and the ”European Union NextGenerationEU”.

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##  Appendix A Treatment of Saturated Sources

There are four sources in our sample with saturated observations (with a
$\blacklozenge$ in Table 1 and 2): HC02, HC04, HC16 and HC20. Their dust mass
$M_{d}$ was estimated at $500$ $\mu$m (e.g. Merello et al. 2013; Motte et al.
2007):

$\displaystyle M_{d}=\frac{F_{\nu}D^{2}}{\kappa_{\nu}B_{\nu}(T_{d})},$ (14)

where $D$ is the distance to the source, $F_{\nu}$ is the flux density,
$\kappa_{\nu}$ is the opacity and $B_{\nu}(T_{d})$ is Planck’s function, at
frequency $\nu=599.585$ GHz. The dust temperature $T_{d}$ was set to $25$ K.
The opacity $\kappa_{500}$ for dense clumps with typical conditions has a
value of $5.04$ cm2 g-1 at $500$ $\mu$m (Ossenkopf & Henning 1994).

The bolometric luminosity $L_{bol}$ was calculated using the flux density at
$70$ $\mu$m, which has been found to be a good estimator for the total
luminosity of protostellar objects when using the following empirical relation
(Elia et al. 2017):

$\displaystyle L_{bol}(L_{\odot})=2.56\cdot{F_{70}}^{1.00}(Jy)$ (15)

The flux densities at $500$ $\mu$m and $70$ $\mu$m were obtained from the Hi-
GAL catalogue Elia et al. (2021).

##  Appendix B Distances

The distances used for the selection of the sources $D_{sel}$ are the
kinematic distances from Reid et al. (2009) using the local standard of rest
velocity VLSR taken from Bronfman et al. (1996). Once the selection was made,
the distances to the sources were corrected as seen in Table 11. The distance
measured through trigonometric parallax from Reid et al. (2019) was used for
the sources that have it. For the sources that do not have a distance
calculated with parallax, the kinematic distances from Reid et al. (2014) were
used instead. This left us with distances with the least possible uncertainty.
These corrected distances were the ones used in the calculation of the
properties of the sources.

Source | $D_{sel}$ | $D_{new}$ | Type
---|---|---|---
| (kpc) | (kpc) |
HC01 | 2.33 | 2.95 | Parallax
HC02 | 2.25 | 2.94 | Parallax
HC03 | 3.64 | 3.56 | Parallax
HC04 | 5.49 | 5.29 | Parallax
HC05 | 3.42 | 2.88 | Parallax
HC06 | 3.61 | 2.96 | Parallax
HC07 | 4.27 | 3.84 | Parallax
HC08 | 4.31 | 4.31 | Kinematic
HC09 | 5.35 | 5.35 | Kinematic
HC10 | 4.30 | 4.57 | Kinematic
HC11 | 3.37 | 3.60 | Kinematic
HC12 | 2.53 | 2.69 | Kinematic
HC13 | 4.04 | 4.09 | Kinematic
HC14 | 3.81 | 3.87 | Kinematic
HC15 | 5.08 | 5.05 | Kinematic
HC16 | 3.68 | 3.77 | Kinematic
HC17 | 4.90 | 4.88 | Kinematic
HC18 | 3.05 | 3.17 | Kinematic
HC19 | 3.00 | 3.10 | Kinematic
HC20 | 3.22 | 3.33 | Kinematic
HC21 | 3.13 | 3.22 | Kinematic
HC22 | 2.60 | 2.60 | Parallax
HC23 | 3.37 | 2.78 | Parallax
HC24 | 3.17 | 2.72 | Parallax
HC25 | 3.26 | 4.63 | Kinematic
HC26 | 3.37 | 2.74 | Parallax
HC27 | 2.29 | 2.82 | Kinematic
HC28 | 3.78 | 3.87 | Kinematic
HC29 | 5.61 | 5.54 | Kinematic
HC30 | 2.78 | 2.70 | Parallax
HC31 | 2.16 | 1.33 | Parallax
HC32 | 4.15 | 3.73 | Parallax
Table 11: Distances to the sources in the studied sample.

##  Appendix C Notes on Particular Sources

Some of the sources in our sample were found to be of particular interest
because the intensity of their SiO outflows stands out from the rest (peak
$>0.7$ K). They are all of potential interest for future work. A brief
description of the studies that have been carried out about these sources is
shown here.

###  C.1 HC02: HIGALBM5.8856-0.3920, IRAS 17574-2403

This source (see Fig. 3) presents a particularly intense outflow. Despite not
being the most massive, it has the maximum rate of matter expulsion calculated
here. In addition, its spectral profiles shown in Fig. 3 suggest that there is
a second cloud at $15.7$ km s-1, and absorption at $\sim 20$ km s-1. It has
been extensively studied since its discovery (Acord et al. 1997). Zahorecz et
al. (2017) observed this source with APEX in the Band 5 and found that it does
not present D2CO emission, suggesting that it is past the early stages of
evolution. It was mapped at 12 mm and 7 mm by Nicholas et al. (2011a) and
Nicholas et al. (2011b) respectively, and its [OI] spectra were resolved by
Leurini, S. et al. (2015). Its magnetic fields were studied by Tang et al.
(2009) and Fernández-López et al. (2021). Su et al. (2009) reported a dense
and hot-molecular cocoon in the environment of the source. Furthermore, its
outflow has been extensively studied. The outflow of this source was mapped in
the SiO(5-4) line by Sollins et al. (2004), traced in the SiO(8-7) line by
Klaassen & Wilson (2007), and Zapata et al. (2019) found indications that it
is an explosive multi-polar outflow. This was confirmed in Zapata et al.
(2020), where a graph and animation modelling the source are presented,
clearly showing the multiple lobes.

###  C.2 HC08: HIGALBM301.1365-0.2259, IRAS 12326-6245

This source (see Fig. 13) presents the most intense ($T_{peak}=1.57$ K) SiO
emission of our sample and the most massive outflow ($M_{out}=116M_{\odot}$).
There are multiple infrared and radio sources deeply embedded in this clump
(Henning et al. 2000; Murphy et al. 2010), and it presents one of the
strongest molecular outflows in the southern sky (Araya et al. 2005). This
suggests it is already in an advanced stage of evolution (Dedes, C. et al.
(2011)). Finally, Duronea, N. U. et al. (2021) present a study of the IR
bubble S169 associated with this source, and conclude that star formation is
actively taking place.

###  C.3 HC17: HIGALBM331.2786-0.1883, IRAS 16076-5134

This source presents one of the strongest outflows in our sample, which is
clearly seen in both its HCO+ and SiO lines (see Fig. 22). Its HCO+ line
presents significant absorption and the SiO profile is one of the widest in
our sample (FWZP = 52.26 km s-1). It has been an object of interest in
numerous studies. Zinchenko et al. (2000) present C18O and HNCO observations
and find that HNCO emission is most likely related to shocks of matter,
similar to SiO emission. They detected HNCO emission in this source. Lee et
al. (2001, 2002) reported shock-excited H2 emission, in addition to an outflow
powered by a deeply embedded object in the former. Furthermore, De Buizer, J.
M. et al. (2009) present single-dish SiO(6–5) observations and evidence of
outflow, and Baug et al. (2020) present images of the CO outflow observed with
ALMA.

###  C.4 HC20: HIGALBM333.1246-0.4244, IRAS 16172-5028

The SiO intensity and the clear asymmetry of the spectral lines of this source
make it particularly interesting. As is clear in Fig. 25, its HCO+ line
experiences more absorption on the blue side than on the red side. The H13CO+
even shows a wing on the red side, indicating that the outflow is particularly
intense. The SiO line has a particular profile: its intensity decreases at the
same velocity as the HCO+ absorption and the H13CO+ wing. This suggests that
there might be a second colder cloud at around 50 km s-1. Rojas-García et al.
(2022) map this source at 216.968 GHz and also report the possibility of a
second source nearby. They also present a chemical profile of this source,
where several COMs and SiO are detected. This source was also studied by Lo et
al. (2007), where strong SiO and water maser emissions were detected. Lo et
al. (2014) present a [CI] mapping of the source. Moreover, Figuerêdo et al.
(2005) show this source contains an embedded OB star cluster in very early
evolutionary stages, and the presence of infall was confirmed by Wiles et al.
(2016).

###  C.5 HC21: HIGALBM335.5848-0.2894, IRAS 16272-4837

This source presents one of the most intense ($97.0$ km s-1) and wide ($57.41$
km s-1) SiO profiles in the sample, as clearly seen in Fig. 26. The studies
done on this source include the discovery of water emission toward this source
(van der Tak, F. F. S. et al. 2019), which has also been used as an
evolutionary indicator because it can only be detected when the inner hot gas
has reached a temperature of at least 300 K (van der Tak 2004). Emission of
HNCO, another shock tracer, was found by Yu et al. (2018). Moreover, Garay et
al. (2002) suggest that there is a young massive protostar embedded in this
clump and it is still undergoing an intense accretion phase. This corresponds
well with our findings and further suggests this is a HMC. Finally, ALMA
observations of this source are presented by Olguin et al. (2021), where
evidence of infall and rotation motions was found.

###  C.6 HC27: HIGALBM345.0035-0.2239, IRAS 17016-4124

This source presents a very wide (68.36 km s-1) and intense (1.02 K) SiO
emission (see Fig. 32). In addition, its HCO+ profile presents significant
self-absorption and absorption. These characteristics make it a particularly
interesting source. Several studies have conducted observations towards this
source. Zinchenko et al. (2000) present C18O and HNCO emission observations,
where it was found that high-velocity gas enhances the abundance of HNCO.
Furthermore, mid-infrared observations are presented by Morales et al. (2009),
and Testi et al. (1998) present H2O maser emission detection. Krishnan et al.
(2013) and Voronkov et al. (2014) have found methanol maser emission as well.
This source has been mapped with Large APEX BOlometer CAmera (LABOCA) at APEX
by Gómez et al. (2014). Finally, Yu & Wang (2015) present MALT90 (Millimetre
Astronomy Legacy Team 90 GHz) observations of the N2H+, H13CO+, HCO+, HNC,
C2H, HC3N and SiO spectral lines, and conclude that the sources in their
sample are associated with dense clumps and recent outflow activity.

##  Appendix D Spectral Profiles at the SiO(4-3), H13CO+(2-1) and HCO+(2-1)
Lines

Figure 7: Spectral profiles for the source HC01, Group C. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 8: Spectral Profiles for the source HC03, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 9: Spectral Profiles for the source HC04, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 10: Spectral Profiles for the source HC05, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 11: Spectral Profiles for the source HC06, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 12: Spectral Profiles for the source HC07, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 13: Spectral Profiles for the source HC08, Group A. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 14: Spectral Profiles for the source HC09, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 15: Spectral Profiles for the source HC10, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 16: Spectral Profiles for the source HC11, Group C. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 17: Spectral Profiles for the source HC12, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 18: Spectral Profiles for the source HC13, Group C. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 19: Spectral Profiles for the source HC14, Group C. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 20: Spectral Profiles for the source HC15, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 21: Spectral Profiles for the source HC16, Group A. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 22: Spectral Profiles for the source HC17, Group A. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 23: Spectral Profiles for the source HC18, Group A. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 24: Spectral Profiles for the source HC19, Group C. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 25: Spectral Profiles for the source HC20, Group A. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 26: Spectral Profiles for the source HC21, Group A. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 27: Spectral Profiles for the source HC22, Group A. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 28: Spectral Profiles for the source HC23, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 29: Spectral Profiles for the source HC24, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 30: Spectral Profiles for the source HC25, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 31: Spectral Profiles for the source HC26, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 32: Spectral Profiles for the source HC27, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 33: Spectral Profiles for the source HC28, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 34: Spectral Profiles for the source HC29, Group A. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 35: Spectral Profiles for the source HC30, Group B. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 36: Spectral Profiles for the source HC31, Group C. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.
Figure 37: Spectral Profiles for the source HC32, Group C. The red dotted line
is at FWZP, and the blue line in the H13CO+ panel shows the Gaussian fit.