11institutetext: Department of Physical Science, Graduate School of Science,
Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531,
Japan
11email<EMAIL_ADDRESS>22institutetext: Chile Observatory,
National Astronomical Observatory of Japan, National Institutes of Natural
Science, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan 33institutetext: Centro
de Astrobiología (CSIC/INTA), Ctra de Torrejón a Ajalvir, km 4, E-28850
Torrejón de Ardoz, Spain 44institutetext: European Southern Observatory, Karl-
Schwarzschild-Str. 2, 85748, Garching bei München, Germany 55institutetext:
Joint Institute for VLBI ERIC (JIVE), Postbus 2, NL-7990 AA Dwingeloo, the
Netherlands 66institutetext: INAF-Osservatorio Astrofisico di Arcetri, L.go E.
Fermi 5, 50125 Firenze, Italy 77institutetext: Max-Planck-Institut für
Extraterrestrische Physik, Giessenbachstrasse 1, 85748 Garching bei München,
Germany 88institutetext: Kavli Institute for Astronomy and Astrophysics,
Peking University, 5 Yiheyuan Road, Haidian District, Beijing 100871, China

# Singly- and doubly-deuterated formaldehyde in massive star-forming regions

S. Zahorecz 1122 I. Jimenez-Serra 33 L. Testi 44 K. Immer 55 F. Fontani 66 P.
Caselli 77 K. Wang 88 T. Onishi 11

(Received ; accepted )

###### Abstract

Context. Deuterated molecules are good tracers of the evolutionary stage of
star-forming cores. During the star formation process, deuterated molecules
are expected to be enhanced in cold, dense pre-stellar cores and to deplete
after protostellar birth.

Aims. In this paper we study the deuteration fraction of formaldehyde in high-
mass star-forming cores at different evolutionary stages to investigate
whether the deuteration fraction of formaldehyde can be used as an
evolutionary tracer.

Methods. Using the APEX SEPIA Band 5 receiver, we extended our pilot study of
the $J$=3$\rightarrow$2 rotational lines of HDCO and D2CO to eleven high-mass
star-forming regions that host objects at different evolutionary stages. High-
resolution follow-up observations of eight objects in ALMA Band 6 were
performed to reveal the size of the H2CO emission and to give an estimate of
the deuteration fractions HDCO/H2CO and D2CO/HDCO at scales of $\sim$6”
(0.04-0.15 pc at the distance of our targets).

Results. Our observations show that singly- and doubly deuterated H2CO are
detected toward high-mass protostellar objects (HMPOs) and ultracompact H II
regions (UC H II regions), the deuteration fraction of H2CO is also found to
decrease by an order of magnitude from the earlier HMPO phases to the latest
evolutionary stage (UC H II), from $\sim$0.13 to $\sim$0.01. We have not
detected HDCO and D2CO emission from the youngest sources (high-mass starless
cores, HMSCs).

Conclusions. Our extended study supports the results of the previous pilot
study: the deuteration fraction of formaldehyde decreases with evolutionary
stage, but higher sensitivity observations are needed to provide more
stringent constraints on the D/H ratio during the HMSC phase. The calculated
upper limits for the HMSC sources are high, so the trend between HMSC and HMPO
phases cannot be constrained.

###### Key Words.:

ISM: molecules; stars:formation; Astrochemistry

##  1 Introduction

Deuterium fractionation, and how it changes as star-formation proceeds, is a
powerful tool to establish the evolutionary stage and age of star-forming
cores. The formation of deuterated molecules is favoured at low temperatures
(T $\leq$ 20 K) and at high densities (n $\geq 10^{4}$ cm-3) in molecular
cloud cores, at the ideal conditions for CO freeze out (Caselli et al., 1999,
2002). However, deuterated molecules are also observed with relatively high
abundances in warmer environments, e.g. in circumstellar disks and in hot
cores (e.g. Salinas et al., 2017; Sakai et al., 2018). Different chemical
processes contribute to the deuteration enrichment at different temperatures.
At low (T=10-20 K) temperatures the dominant gas-phase process is
H${}_{3}^{+}$+HD$\rightleftharpoons$H2D++H2. At high temperatures (T=30-50 K),
however, the CH${}_{3}^{+}$+HD$\rightleftharpoons$CH2D++H2 and
C2H${}_{2}^{+}$+HD$\rightleftharpoons$C2HD++H2 reactions become important (see
detailed gas-phase deuteration models by e.g. Roueff et al., 2007; Roueff &
Lique, 2013). Reactions on the grain surfaces can also influence the D/H ratio
via low-temperature surface reactions during the pre-stellar/starless phase
that enrich the D/H ratio of molecules in the solid phase. These molecules can
then be desorbed into the gas phase during the warm protostellar phase (e.g.
Brown & Millar, 1989a, b; Tielens, 1983).

We can characterize the deuteration fraction, $D_{\mathrm{frac}}$, as the
relative abundance between a species containing a deuterium atom as compared
to the same species containing a hydrogen atom. It is thus expected that
$D_{\mathrm{frac}}$ is enhanced in cold and dense pre-stellar cores, and it
should then decrease after protostellar birth, when the young stellar object
heats up the central region of the core (Caselli, 2002). Several studies (see
eg. Crapsi et al., 2005; Caselli et al., 2008; Emprechtinger et al., 2009)
have confirmed this theoretical scenario for low-mass star forming cores, with
the observations of deuterated species produced by gas-phase reactions (e.g.
H2D+ and N2D+). Recent studies have shown that high $D_{\mathrm{frac}}$ values
are also typical for high-mass star-forming cores and that the
$D_{\mathrm{frac}}$ of some species could be an evolutionary tracer also in
the intermediate and high-mass regime (e.g. Busquet et al., 2010; Fontani et
al., 2011, 2015; Sakai et al., 2012; Zahorecz et al., 2017).

Recent theoretical studies (e.g. Bovino et al., 2017; Körtgen et al., 2018;
Hsu et al., 2021) have shown that the evolution of the deuterium enrichment
depends on several factors, such as the initial physical conditions, grain
size distribution, depletion fraction and cosmic ray ionization rate.
Observational studies (e.g. Crapsi et al., 2005; Emprechtinger et al., 2009;
Fontani et al., 2011, 2015; Treviño-Morales et al., 2014) have confirmed that
the deuterium chemistry is a good chemical clock for both low-mass and high-
mass star-forming cores. However, in order to have an accurate estimate of the
evolutionary stage of the source, it is necessary to use as many different
molecular tracers as possible since the derived Dfrac may differ due to
variations in the chemical evolution of the different species (see e.g.,
Treviño-Morales et al., 2014).

We can distinguish the following evolutionary stages in high-mass star-forming
regions: HMSCs - high-mass starless cores, HMPOs - high-mass protostellar
objects and UC H II regions - ultracompact H II regions (e.g. Beuther et al.,
2007; Tan et al., 2014). Gerner et al. (2014) derived chemical age of
$\sim$6$\times$104, $\sim$4$\times$104 and $\sim$104 yrs for the HMSC, HMPO
and UC H II stage, respectively. Their derived total timescale for the high-
mass star-formation is consistent with theoretical estimates of $\sim$105 yrs.
Based on the study of several deuterated species in 27 massive cores in
different evolutionary stages from HMSCs to UC H II regions, Fontani et al.
(2011, 2015) found that species formed exclusively in the gas (N2H+) showed
different evolutionary trends from those formed partially (NH3) or totally
(CH3OH) on grain mantles. The $D_{\mathrm{frac}}$(N2H+) is higher in the HMSC
phase and it drops by about an order of magnitude during the HMPO and UC H II
stages, while deuterated methanol is detected only towards HMPOs and
externally heated HMSCs. Therefore, high $D_{\mathrm{frac}}$(N2H+) is a good
indicator of the initial conditions in starless/pre-stellar cores, while high
$D_{\mathrm{frac}}$(CH3OH) values are a good probe of the earliest
protostellar phases (Fontani et al., 2015). $D_{\mathrm{frac}}$(NH3) does not
show significant difference across the different evolutionary stages, and
thus, there is no dominant formation pathways (gas-phase vs. grains) for NH3
and its deuterated forms.

Like NH3, formaldehyde (H2CO) can also be produced both in the gas phase and
on grain surfaces. The two main pathways for the production of H2CO involve
CH${}_{3}^{+}$ in the gas phase (see Yamamoto, 2017) and multiple
hydrogenation of CO on the ices (see e.g. Roberts & Millar, 2007). Its gas
phase pathway is similar to the one of N2H+, but it can also occur at warmer
temperatures (30-50 K, see Parise et al., 2009). The ice phase formation route
of H2CO is similar to that of CH3OH and their deuterated forms. Laboratory
work and observational studies of low-mass protostars suggest an important
contribution from grain surface chemistry to the production of H2CO (Watanabe,
2005; Roberts & Millar, 2007; Bergman et al., 2011). However the relative
importance of the grain surface versus gas-phase formation routes remains
unclear. Furthermore, only a handful D2CO detections in high-mass star-forming
regions are available (D2CO has been firmly detected toward the Orion Compact
Ridge, NGC 7129-FIRS 2, AFGL5142, IRAS05358+3543 and tentatively toward the
MonR2 ultra-compact H II region; Fuente et al., 2005; Treviño-Morales et al.,
2014; Turner, 1990; Zahorecz et al., 2017).

All these initial results suggest that H2CO and its deuterated species form
mostly on grain surfaces, but more observations carried out with
interferometers (i.e. at high-angular resolution) are needed to separate the
HDCO and D2CO emission originating from the small and dense cores and to get a
more detailed view of the formaldehyde deuteration in high-mass star-forming
regions.

In this paper, we report our findings of a search for HDCO and D2CO emission
toward an extended sample of high-mass star-forming regions at different
evolutionary stages, using APEX and ALMA telescopes. The source sample and the
observations are described in Section 2, while our results are presented in
Section 3. In Section 4, we discuss our results and put them in context with
respect to previous findings in low-mass and high-mass star-forming regions.
In Section 5, we summarize our conclusions.

##  2 Observations and target selection

In this section, we describe our selected sources and the single-dish and
interferometric observations we have carried out for our study.

###  2.1 Selected targets

The selected sources are extracted from the sample of Fontani et al. (2011),
for which the deuteration fraction of other molecules (e.g. N2H+, CH3OH and
NH3) has been measured (Fontani et al., 2015). We have selected the brightest
sources from each evolutionary class, which are observable with the Atacama
Pathfinder EXperiment (APEX111This publication is based on data acquired with
the Atacama Pathfinder Experiment (APEX). APEX is a collaboration between the
Max-Planck-Institut für Radioastronomie, the European Southern Observatory,
and the Onsala Space Observatory.) telescope from the southern hemisphere.
Table 1 reports the observed central coordinates, velocities, distances,
kinetic temperatures and source evolutionary classification for our targets.
The sample is divided into three high-mass starless cores (HMSCs), three high-
mass protostellar objects (HMPOs), two sources containing HMSC and HMPO (which
would represent an intermediate stage between HMSC and HMPO) and three
ultracompact H II regions, see details below. The source coordinates have been
centred at interferometric mm/cm continuum peaks or high-density gas tracer
peaks (e.g. NH3 with VLA) that are separated by at least $\sim$10$\arcsec$
from other cores. The APEX beam is $\sim$34” at 190 GHz. Therefore, for
AFGL5142 and IRAS05358+3543, multiple cores at different evolutionary stages
are covered within the same pointing. We categorize these two sources as a
transitional stage between HMSCs and HMPOs in our work.

Name | RA | DEC | vLSR | d | Tkin |  12C/13C
---|---|---|---|---|---|---
| [hh:mm:ss.s] | [dd:mm:ss] | [km/s] | [kpc] | [K] |
HMSC |
G028-C1 | 18:42:46.9 | -04:04:08 | $78.3$ | $5.0$ | 17 | 37.3
G034-F2 | 18:53:16.5 | +01:26:10 | $57.7$ | $3.7$ | - | 45.4
G034-G2 | 18:56:50.0 | +01:23:08 | $43.6$ | $2.9$ | - | 50.4
HMSC/HMPO |
AFGL5142 | 05:30:48.0 | +33:47:54 | $-3.9$ | $1.8$ | 25∗ | 57.2
IRAS05358+3543 | 05:39:13.0 | +35:45:51 | $-17.6$ | $1.8$ | 35∗ | 57.2
HMPO |
18089-1732 | 18:11:51.4 | -17:31:28 | $32.7$ | $3.6$ | 38 | 46.0
18517+0437 | 18:54:14.2 | +04:41:41 | $43.7$ | $2.9$ | - | 50.4
G75-core | 20:21:44.0 | +37:26:38 | $0.2$ | $3.8$ | 96 | 44.8
UC H II |
G5.89-0.39 | 18:00:30.5 | -24:04:01 | $9.0$ | $1.3$ | - | 60.4
I19035-VLA1 | 19:06:01.5 | +06:46:35 | $32.4$ | $2.2$ | 39 | 54.7
19410+2336 | 19:43:11.4 | +23:44:06 | $22.4$ | $2.1$ | 21 | 55.3
Table 1: List of the observed sources and their coordinates, LSR velocities,
distances, kinetic temperatures, and 12C/13C ratio at the corresponding
distance. The distances and kinetic temperatures were adopted from Fontani et
al. (2011). The ∗ symbols indicate that we use the average Tkin values of the
HMSCs and HMPOs within our APEX beam.

###  2.2 IRAM-30m H2CO observations

Previous observations of these objects were performed using the IRAM-30m
telescope (details can be found in Fontani et al., 2011, 2015). The frequency
setups included the 3${}_{0,3}-2_{0,2}$, 3${}_{2,2}-2_{2,1}$ and
3${}_{2,1}-2_{2,0}$ transitions of H2CO. The spectroscopic information of
these transitions is shown in Table 2 (Müller et al., 2005). The spectra were
obtained and calibrated in antenna temperature units, T${}_{A}^{*}$ and then
converted to main beam brightness temperature, TMB, with the following
equation: T${}_{A}^{*}$ = T${}_{\mathrm{MB}}\eta_{\mathrm{MB}}$, where a main
beam efficiency, $\eta_{\mathrm{MB}}$ of 0.66 was used. The H2CO line emission
was detected in all sources and the measured intensities show a wide range
between 0.24 K$<T_{\mathrm{MB}}<$13 K (see Fig. 1).

###  2.3 APEX SEPIA observations

The sources were observed with the APEX SEPIA receiver (Swedish-ESO PI
receiver for APEX; Billade et al., 2012; Belitsky et al., 2018), as part of
the ESO E-095.F-9808A, E-096.C-0484A and E097.C-0897A projects between July
2015 and June 2016. The first results based on the science verification
dataset for AFGL5142, IRAS05358+3543 and G5.89-0.39 were presented in Zahorecz
et al. (2017). We carried out single-pointing observations of HDCO and D2CO
emission using the position switching observing mode. The J2000 central
coordinates used in our observations are shown in Table 1. The observed
transitions of HDCO (at 185 GHz and 193 GHz) and D2CO (at 174.4 GHz) are shown
in Table 2. The pointing was checked every 60-90 mins, and the typical system
temperatures were 150 K. The beam size at 183 GHz was $\sim$34$\arcsec$. The
spectra were obtained and calibrated in antenna temperature units and then
converted to main beam brightness temperature using $\eta_{\mathrm{MB}}$ of
0.68. The XFFTS spectrometer provided a velocity resolution of 0.112 km s-1,
0.059 km s-1 and 0.066 km s-1 for the H${}_{2}^{13}$CO (at 206 GHz), HDCO (at
185-193 GHz) and D2CO (at 174 GHz) transitions, respectively. However, for the
data analysis, we smoothed the spectra to a uniform velocity resolution of 0.5
km/s. At this velocity resolution, we reached an rms of $\sim$ 0.01 K with
typical integration times between 32 and 48 minutes. The PWV was 0.3-1.5 mm.
The data were reduced and analysed with the Gildas software222See
http://www.iram.fr/IRAMFR/GILDAS. (Pety, 2005).

###  2.4 ALMA Cycle 5 observations

We performed high-resolution single pointing observations with ALMA in Cycle 5
as part of the 2017.1.01157.S project (PI: S. Zahorecz). We used the Atacama
Compact Array (ACA, Morita Array; Iguchi et al., 2009). Band 6 observations
were executed for G028-C1, G34-F2, G34-G2, 18089-1732, 18517+0437, G5.89-0.39,
I1935-VLA1 and 1941+2336. We used two setups to observe selected molecular
lines, including H${}_{2}^{13}$CO, and to observe the continuum emission.
Table 2 contains the basic information of the observed H${}_{2}^{13}$CO
transition. In this paper, we use the continuum and H${}_{2}^{13}$CO emission
information at 213 GHz to derive the source sizes. A detailed analysis of all
the detected lines will be presented in a following paper. A continuum
sensitivity of at least $\sim$20 mJy/beam was achieved for the targets. For
the three HMSC cores, a higher sensitivity of $\sim$3 mJy/beam was achieved.
For the molecular line observations, a sensitivity of 0.1 Jy/beam was achieved
at a velocity resolution of 0.086 km/s.

Transition | Frequency | Eu | Telescope | Beff |  $\Delta$v | FWHM
---|---|---|---|---|---|---
| [MHz] | [K] |  |  | [km s-1] | [”]
H2CO |  |
3${}_{0,3}-2_{0,2}$ | 218222.192 | 10.5 | IRAM | 0.62 | 0.26 | 11
3${}_{2,1}-2_{2,0}$ | 218760.066 | 57.6 | IRAM | 0.62 | 0.26 | 11
3${}_{2,2}-2_{2,1}$ | 218475.632 | 57.6 | IRAM | 0.62 | 0.26 | 11
H${}_{2}^{13}$CO |  |
3${}_{0,3}-2_{0,2}$ | 212811.184 | 10.2 | ALMA | 0.75 | 0.09 | 5 - 8
3${}_{1,2}-2_{1,1}$ | 219908.525 | 22.4 | IRAM | 0.62 | 0.26 | 11
3${}_{1,3}-2_{1,2}$ | 206131.626 | 21.7 | APEX | 0.72 | 0.06 | 30
HDCO |  |
3${}_{0,3}-2_{0,2}$ | 192893.256 | 9.3 | APEX | 0.72 | 0.06 | 32
3${}_{1,3}-2_{1,2}$ | 185307.113 | 16.9 | APEX | 0.72 | 0.06 | 34
3${}_{2,1}-2_{2,0}$ | 193907.460 | 41.1 | APEX | 0.72 | 0.06 | 32
3${}_{2,2}-2_{2,1}$ | 193391.605 | 41.1 | APEX | 0.72 | 0.06 | 32
D2CO |  |
3${}_{0,3}-2_{0,2}$ | 174413.115 | 8.4 | APEX | 0.72 | 0.07 | 36

Table 2: Targeted transitions and beam sizes, beam coupling efficiencies and
spectral resolution

of our IRAM 30m, APEX SEPIA and ALMA Band 6 observations.

##  3 Results

In this section, we present the line and continuum emission detected toward
our targets. We use the ALMA Band 6 data to estimate the source sizes. Our
calculations of the excitation temperature and column density of formaldehyde
and its deuterated species are based on the single-dish APEX and IRAM spectra.
We also present the column density ratios of the detected molecules.

###  3.1 Line spectra of deuterated H2CO species

In Fig. 1, we present the H2CO, HDCO and D2CO 3${}_{0,3}-2_{0,2}$ lines and
the H${}_{2}^{13}$CO 3${}_{1,2}-2_{1,1}$ line toward our sources observed with
the IRAM-30m and APEX telescopes. Six sources show multi-velocity components;
we performed the calculations separately for them. Neither HDCO nor D2CO
emission were detected toward the HMSC sources. The HDCO lines (upper energy
levels of 18.5-50.4 K) are clearly detected in seven sources (all sources
except the HMSC sources and I19035-VLA1). The D2CO 3${}_{0,3}-2_{0,2}$
transition is only detected clearly toward four sources: the two HMSC/HMPO
sources (AFGL5142 and IRAS05358+3543), one HMPO object (18517+0437) and one UC
H II region (19410+2336). We tentatively detected the same line toward one
more HMPO object, G75-core and one more UC H II regions, I19035-VLA1, but
further observations are needed to confirm these detections. We use only the
clear detections in our calculations, and consider the rest as upper limits.

Figure 1: Spectra of the H2CO 3${}_{0,3}-2_{0,2}$ and H${}_{2}^{13}$CO
3${}_{1,2}-2_{1,1}$ lines (top two panels) observed with the IRAM 30m
telescope (Fontani et al., 2011, 2015) and HDCO 3${}_{0,3}-2_{0,2}$ and D2CO
3${}_{0,3}-2_{0,2}$ lines (bottom two panels) observed with APEX SEPIA Band 5
receiver (Zahorecz et al., 2017, and this work). Red lines indicate the fitted
spectra. Horizontal lines indicate the TMB=0 K and the 3 $\sigma$ level.
Vertical line indicates the VLSR for each source. The sources are sorted by
evolutionary state, the order is the same as their order in Table 1.

Figure 2: cont

We have checked the H${}_{2}^{13}$CO 3${}_{0,3}-2_{0,2}$ and continuum
emission of our sources in our Band 6 ALMA data. The continuum emission was
detected for 6 objects out of the 8 sources covered in our observations. We
observed, but not detected compact continuum sources above 3$\sigma$ toward
two sources in the youngest, HMSC evolutionary stage (G034-F2 and G034-G2) at
our sensitivity and resolution. We note that Kong et al. (2017) observed these
objects and detected 1.3 mm continuum emission of $\sim$1-3 mJy beam-1 with a
beam size of 1.5”$\times$1.0”. The H${}_{2}^{13}$CO emission was not detected
toward any of the HMSC sources. For the objects with detection, the
H${}_{2}^{13}$CO emission is associated with the same region as the continuum
emission. Figure 3 shows the continuum maps at 213 GHz and the
H${}_{2}^{13}$CO contours overplotted. We derived the effective radius of the
sources based on the 2D Gaussians fitted to the continuum maps. The derived
source sizes are between 3” and 5.8”. We note that in Zahorecz et al. (2017)
we used 6” as the source size for AFGL5142, IRAS05358+3543 and G5.89-0.39. In
our actual calculations, we updated the size of G5.89-0.39 based on its ALMA
continuum emission. AFGL5142 and IRAS05358+3543 have no ALMA data and G028-C1,
G034-F2 and G034-G2 have no H${}_{2}^{13}$CO detection and / or continuum
detection. We kept the assumption of 6” source size for these five objects in
our calculations.

Figure 3: 211 GHz continuum maps toward G028-C1, G034-F2, G034-G2, 18089-1732,
18517+0437, G5.89-0.39, I19035-VLA1 and 19410+2336 (sorted by evolutionary
stage). The black contours indicate the 3, 5, 10 and 15 $\sigma$ levels of
H${}_{2}^{13}$CO 3${}_{0,3}-2_{0,2}$ integrated intensity, where $\sigma$ is
0.1 Jy/beam. No H${}_{2}^{13}$CO 3${}_{0,3}-2_{0,2}$ emission was detected
toward G028-C1. Neither continuum nor H${}_{2}^{13}$CO 3${}_{0,3}-2_{0,2}$
emission was detected toward the cores in the G034 region.

###  3.2 Molecular column densities and column density ratios

To estimate the molecular column densities from the APEX and IRAM spectra of
H2CO, H${}_{2}^{13}$CO, HDCO and D2CO, we used the MADCUBA software that
assumes LTE conditions (Martín et al., 2019). We have used the SLIM (Spectral
Line Identification and Modeling) tool to produce synthetic spectra of the
observed molecules. When generating the synthetic spectra the beam size is
taken into account by the software to return the appropriate line intensities.
The MADCUBA-AUTOFIT tool was used to derive the physical conditions of the gas
by comparing the observed spectra with the LTE synthetic spectra taking into
account all transitions considered. The autofit tool uses the Levenberg-
Marquardt algorithm to provide the best nonlinear least-squared fit (see
details in Martín et al., 2019). We adopted a source size of
$3.\\!^{\prime\prime}0$ \- $6.\\!^{\prime\prime}0$ according to the continuum
sizes measured with ALMA and following Zahorecz et al. (2017) and Fontani et
al. (2015) for sources without continuum detection. We derived the excitation
temperature of the gas, Tex, using the four APEX HDCO transitions (Table 2).
The derived average temperature is $\sim$32 K with a standard deviation of 17
K. We used these temperatures to fit the H${}_{2}^{13}$CO, HDCO and D2CO
transitions. For the brightest sources, we could not fit all the detected H2CO
transitions using these low Tex temperature. In this case, we used the H2CO
lines independently to derive their excitation temperature. For the youngest
sources, the HMSCs, no HDCO emission was detected, therefore we derived the
excitation temperature based on the H2CO lines. We used the 3$\sigma$ noise
levels to provide the upper limits to the intensity of the non-detected lines.

We have estimated the H2CO column densities from the H${}_{2}^{13}$CO column
density using the 12C/13C ratio (see in Table 1) derived by Milam et al.
(2005) as a function of Galactocentric distance to minimize the optical
depth’s effect. In Table 4, we report the derived excitation temperatures and
column densities of H2CO, H${}_{2}^{13}$CO, HDCO and D2CO.

In Table 3, we report the calculated column density ratios of HDCO/H2CO,
D2CO/H2CO and D2CO/HDCO. The column density ratio HDCO/H2CO corresponds to the
Dfrac(H2CO) value. The presented column density ratios are source-averaged
values. We note that the different source distance can in principle introduce
biases in the comparison, because the linear scale observed is not the same.
However, in our study we see from the interferometric images that the emission
of the lines is more compact than the beam, and hence the emission arising
from the (different) envelope region should not influence the derived source-
averaged ratios in a significant way. The D2CO/HDCO column density ratios show
no clear trend since they have a large scatter around the median value of 0.21
(standard deviation of 2.16). The N(HDCO)/N(H2CO) and N(D2CO)/N(H2CO) ratios
show a similar trend. The deuteration fraction of singly deuterated
formaldehyde shows higher values, around 0.1 at the HMSC-HMPO stage and it
decreases to 0.01 at the UC H II phase. The deuteration fraction of the doubly
deuterated formaldehyde reaches 0.03 at the earliest stages and drops down to
0.003 at the most evolved phase.

Source | Stage | N(HDCO) | N(D2CO) | N(D2CO) | F
---|---|---|---|---|---
|  | N(H2CO) | N(HDCO) | N(H2CO) |
G028-C1 | HMSC |  $<$0.297 |  $<$1.223 |  $<$0.364 | -
G034-F2 | HMSC |  $<$0.513 |  $<$0.794 |  $<$0.408 | -
G034-F2 | HMSC |  $<$0.520 |  $<$0.794 |  $<$0.413 | -
G034-G2 | HMSC |  $<$0.339 |  $<$0.794 |  $<$0.269 | -
G034-G2 | HMSC |  $<$0.688 |  $<$0.794 |  $<$0.546 | -
AFGL5142 | HMSC/HMPO | 0.162$\pm$0.035∗ | 0.153$\pm$0.035 | 0.025$\pm$0.003∗ | 1.05$\pm$0.34
AFGL5142 | HMSC/HMPO | 0.105$\pm$0.017∗ | 0.268$\pm$0.051 | 0.028$\pm$0.004∗ | 0.39$\pm$0.11
IRAS05358+3543 | HMSC/HMPO | 0.122$\pm$0.018∗ | 0.180$\pm$0.031 | 0.022$\pm$0.003∗ | 0.68$\pm$0.17
18089-1732 | HMPO | 0.018$\pm$0.004∗ |  $<$0.055 |  $<$0.001∗ |  $>$0.32
18089-1732 | HMPO | 0.030$\pm$0.013∗ |  $<$0.066 |  $<$0.002∗ |  $>$0.45
18517+0437 | HMPO | 0.304$\pm$0.144∗ | 0.097$\pm$0.031 | 0.029$\pm$0.016∗ | 3.19$\pm$2.77
18517+0437 | HMPO | 0.001$\pm$0.001∗ | 5.397$\pm$2.540 | 0.005$\pm$0.003∗ | 0.0002$\pm$0.0003
G75-core | HMPO | 0.053$\pm$0.013∗ |  $<$0.103 |  $<$0.005∗ |  $>$0.56
G5.89-0.39 | UC H II | 0.004$\pm$0.001∗ |  $<$0.080 |  $<$0.001∗ |  $>$0.02
G5.89-0.39 | UC H II | 0.008$\pm$0.001∗ |  $<$0.0282 |  $<$0.001∗ |  $>$0.06
I19035-VLA1 | UC H II |  $<$0.021∗ |  $<$0.759 |  $<$0.016∗ | -
19410+2336 | UC H II | 0.021$\pm$0.006∗ | 0.206$\pm$0.072 | 0.004$\pm$0.001∗ | 0.11$\pm$0.05
Table 3: Calculated column density ratios for the observed species. We note
that ∗ sign at the numbers indicate that the values calculated based on the
H${}_{2}^{13}$CO line assuming a 12C/13C ratio according to Milam et al.
(2005). Each velocity component is shown as a separate row.

##  4 Discussion

In this section we compare our results with those inferred from previous
observational studies (Section 4.1). We also put our results in context with
theoretical studies of formaldehyde deuteration via grain-surface and gas-
phase processes (Section 4.2).

###  4.1 Comparison with previous observational studies

Fontani et al. (2011) presented the kinetic temperatures based on ammonia
data. Nine sources from our sample have available ammonia temperatures with
values lying between $\sim$20-40 K, except for the G75-core, which has a
higher kinetic temperature of 96 K. The HDCO-based temperature estimates are
in good agreement with the ammonia temperatures for most of the sources: they
are in the 15-40 K range. G5.89-0.39 and I19035-VLA1 show higher HDCO
excitation temperatures, $\sim$60-70 K. For the youngest HMSC sources, we only
detected H2CO. The excitation temperatures fall into the 20-30 K range. For
some of the sources, the HDCO derived temperatures were too low to fit the
line intensity ratios of the observed H2CO transitions. Also in these cases,
we derived the H2CO excitation temperature, finding values a factor of 2-3
higher than the HDCO values, in the range of $\sim$70-130 K.

Fontani et al. (2015) have proposed that in high-mass star-forming regions the
different trend for the deuteration pattern of different molecules such as
N2H+, HNC, NH3 and CH3OH as a function of evolutionary stage, is likely due to
the way deuteration occurs for the different species: for N2H+, detuteration
occurs in the gas phase, while for CH3OH it occurs on grain surfaces; for NH3,
deuteration likely occurs via a mixture of these two processes. In the
following, we discuss the likelihood of each of these two chemical routes to
drive the formation of the deuterated forms of H2CO during the massive star
formation process.

###  4.2 Grain-surface deuteration of H2CO

Traditionally, it has been assumed that the deuterated forms of H2CO are a
product of grain-surface chemistry. Indeed, Taquet et al. (2012) showed that
the gas-phase formation time-scales of D2CO are longer than the depletion
time-scales in the pre-stellar phase and, therefore, one would expect D2CO to
be a product of material processed on solid ices. Consequently, the
N(D2CO)/N(H2CO) ratio should show an evolutionary trend similar to that
derived for $D_{\mathrm{frac}}$(CH3OH), which peaks at the HMPO phase (Fontani
et al., 2015). If HDCO showed a similar behaviour to D2CO, we could conclude
that HDCO also forms mostly on dust grains. This hypothesis would be supported
by the fact that HDCO is detected in hot cores and hot corinos while N2D+ is
not (see e.g. Fuente et al., 2005).

Fig. 4 shows that the column density ratios of N(HDCO)/N(H2CO) and
N(D2CO)/N(H2CO) decrease from the HMSC-HMPO phase to the UC H II phase by
factors of $\geq$10\. We note that for the two sources in the HMSC/HMPO
transitional category (AFGL5142 and IRAS05358+3543), we cannot disentangle the
contribution of the HMSC cores from the HMPO ones. However, from our
observations it is clear that they show higher column density ratios than
those found for the UC H II regions, confirming the decrease of the
N(HDCO)/N(H2CO) and N(D2CO)/N(H2CO) trend. Based on the available upper limits
for the HMSC cores, we cannot exclude the possibility that the D2CO/H2CO
column density ratio peaks in the early phases. However, the upper limits
obtained for the HMSC cores suggest a lower or, at most, equal HDCO/H2CO
column density ratios than those of the HMPO objects. This behaviour is
similar to the trend observed for $D_{\mathrm{frac}}$(CH3OH) but with a larger
scatter. This suggests that grain surface chemistry may be the main formation
mechanism for HDCO and D2CO.

Figure 4: Comparison of observed column density ratios of H2CO, HDCO and D2CO.
Upper limits are shown with red symbols. The arrow in the top panel indicates
the increasing time from the HMSC phase towards the UC H II phase.

Rodgers & Charnley (2002) proposed a grain surface formation scenario for
these molecules in which H2CO and its deuterated forms represent intermediate
steps in the formation of CH3OH and deuterated-CH3OH via hydrogenation and
D-addition reactions. They defined the F parameter (see Equation 1 below) to
investigate the extent by which surface chemistry is responsible for the
production of HDCO and D2CO. Rodgers & Charnley (2002) found that gas-phase
chemistry should produces F values between 1.6 and 2.3, and grain surface
chemistry should result in F values $\geq$ 1\. Previous observations, however,
have reported F values lower than 1, which are not consistent with the cases
presented above. Alternatively, low F values could be obtained through a grain
surface chemistry over a long time period (Rodgers & Charnley, 2002), because
longer time-scales allow the conversion of HDCO into D2CO on the surface of
dust grains. We derived the F parameter based on our calculated HDCO/H2CO and
D2CO/H2CO ratios using the definition of Rodgers & Charnley (2002):

$F=\frac{[\mathrm{HDCO}/\mathrm{H}_{2}\mathrm{CO}]^{2}}{[\mathrm{D}_{2}\mathrm{CO}/\mathrm{H_{2}CO}]}.$
(1)

In our sample sources with D2CO detections, F lies between 0.1 and 1.1 (except
18517+0437, where the two fitted components show F values $\sim$3 and
$\sim$0.001). For the sources with only upper limits for the detection of
D2CO, the lower limits for the F values are within 0.1 and 0.6. These values
cannot be explained by gas phase chemistry, but are more consistent with grain
surface chemistry models.

Table 3 also shows that the D2CO/HDCO ratio remains constant at $\sim$0.2,
within the uncertainties, regardless of the source or evolutionary stage
(except for 18517+0437). As for the low-mass regime, the ratio HDCO/D2CO lies
well below the statistical value given as
D-species/D2-species=4$\times$(D-species/H-species)-1, consistent with the
grain surface formation scenario (see Ceccarelli et al., 2014).

Ceccarelli et al. (2014) calculate the column density ratios for HDCO/H2CO and
D2CO/H2CO for a sample of low-mass star-forming cores (see their Figure 5).
The derived ratios lie close to 1 for those objects. The average derived
$\frac{\mathrm{HDCO}/\mathrm{H_{2}CO}}{\mathrm{D_{2}CO}/\mathrm{H_{2}CO}}$
ratio is $\sim$5.3 with a standard deviation of 3.4 (1.1 if we exclude the two
velocity components of the 18517+0437 region, showing a large difference from
the other sources) for our high-mass star-forming regions. If we compare these
findings with the results of Ceccarelli et al. (2014), it is possible that the
higher values measured toward our sample is the result of the shorter time-
scales available in the high-mass regime for the formation of D2CO in the ices
(Taquet et al., 2012; Rodgers & Charnley, 2002). In fact, the HDCO/H2CO ratios
are factors $\sim$10 or more larger than $D_{\mathrm{frac}}$(CH3OH) in high-
mass star-forming regions, which is also consistent with the shorter time-
scales available for deuteration in high-mass star formation with respect to
the low-mass case, and with the formation of these species via hydrogenation
and D-addition reactions on grain surfaces (Turner, 1990; Rodgers & Charnley,
2002).

Turner (1990) reported the first interstellar detection of a multiply
deuterated molecule, D2CO in the Orion KL ridge component with a D2CO/H2CO
column density ratio of 0.021. The calculated HDCO/H2CO column density ratio
was 0.14. These ratios could not be reproduced by ion-molecule gas phase
reactions, but they can be fitted by the model of grain surface reactions of
Tielens (1983). Additional studies toward dark clouds TMC-1 and L183 were
performed by Turner (2001) and they reported HDCO / H2CO column density ratios
of 0.059 and 0.068, respectively.

In addition, Fontani et al. (2014) successfully detected HDCO towards the
protostellar bow-shock L1157-B1 where material from icy mantles is thought to
be freshly released due to mantle evaporation. They have found a column
density ratio of HDCO/H2CO value of 0.1, similar to the values found in our
study. Bianchi et al. (2017) studied the deuteration in Sun-like protostars.
Their Figure 9 shows measured column density ratios of HDCO/H2CO as a function
of the bolometric luminosity for both low-mass and high-mass star-forming
regions from the protostellar phase to the Class I phase. They have also found
that the average column density ratio measured in Class 0 sources for HDCO is
$\sim$0.12. However, D2CO shows an increase going from pre-stellar cores, with
an average value of N(D2CO/H2CO)$\sim$0.045, to Class 0 sources ($\sim$0.15)
and then a strong decrease in the Class I protostar phase (see the case of
SVS13-A; Bianchi et al., 2017). Our results indicate a similar, but not
identical, evolutionary behaviour since no clear detection of deuterated
formaldehyde is available for the HMSC sources.

As part of the ALMA-PILS survey, Persson et al. (2018) and Manigand et al.
(2020) have reported the deuterium fraction of formaldehyde for IRAS
16293-2422 A and B. Their relative evolutionary stages are under debate,
although recent studies suggest that the B component is at an early
evolutionary stage (van der Wiel et al., 2019). Formaldehyde abundance is
lower towards the A component with a HDCO/H2CO column density ratio of around
0.049 and 0.065 for the A and B components, respectively. They agree well with
our results for the HMPO sources. Persson et al. (2018) and Manigand et al.
(2020) have also found that the doubly-deuterated isotopologue D2CO is
significantly enhanced compared to the singly-deuterated isotopologue toward
the B component. The calculated D2CO/H2CO column density ratios are 0.041 and
0.006, similar to the values obtained for our HMPO sources. For the B source,
the column density ratio of D2CO/HDCO is slightly larger than the column
density ratio HDCO/H2CO, which is consistent with formaldehyde forming in the
ice as soon as CO is frozen onto grains.

Figure 5 shows the comparison of the observed H2CO, HDCO and D2CO column
density ratios in different environments based on the works mentioned in this
section.

Figure 5: Comparison of the observed N(D2CO)/N(H2CO) (top panel) and
N(D2CO)/N(H2CO) (bottom panel) column density ratios for our sources and for
prestellar cores (Turner, 2001; Bacmann et al., 2003; Chacón-Tanarro et al.,
2019), low-mass protostars (Parise et al., 2006; Ceccarelli et al., 2014;
Bianchi et al., 2017; Fontani et al., 2014; Manigand et al., 2020), and
sources in the Orion region (Turner, 1990; Parise et al., 2009) region.

###  4.3 Gas-phase deuteration of H2CO

Alternatively to the grain-surface formation of HDCO and D2CO, the deuterated
forms of H2CO could be produced by gas-phase chemistry. Roberts & Millar
(2007) and Roueff et al. (2007) proposed that deuterium fractionation of H2CO
may occur via the fractionation of CH${}_{3}^{+}$ (CH2D+ $\rightarrow$ CH4D+
$\rightarrow$ CH2D $\rightarrow$ HDCO) or of H2CO directly via the reaction
with H2D+. In particular, in Bergman et al. (2011)’s gas-phase steady-state
models based on the reaction network of Roueff et al. (2007), these authors
also predict a decrease of the deuteration of H2CO from the HMSC/HMPO stage to
the UC H II region phase as the temperature exceeds 40 K. The predicted values
for the D/H ratio inferred from HDCO/H2CO and D2CO/HDCO ratios are indeed
consistent with our observations (see their Figure 12). Indeed, while the
HDCO/H2CO ratio gives $\sim$0.1 for T$\sim$10-30 K and $\leq$0.04 for
T$\geq$40 K, the D2CO/H2CO ratio remains relatively flat at $\sim$0.2 for
T$\sim$10-40 K, as observed in our sample. The only difference between our
observations and the predictions by Bergman et al. (2011) is that, while in
our observations the HDCO/H2CO ratio drops by more than one order of magnitude
from the HMPO to the UC H II region stage, the chemical modelling predicts a
smaller drop by only factors 3-4. Parise et al. (2009) found high deuterium
fractionation toward the Orion Bar PDR region. The calculated deuterium
fractions are consistent with predictions of pure gas-phase chemistry models
at warm temperatures. They have found an N(HDCO)/N(H2CO) ratio of 0.0057. This
value is in the range found for the UC H II regions in our sample.

In any case, to distinguish between the grain-surface from the gas-phase
scenarios we would need to obtain stringent upper limits to the HDCO/H2CO
ratios at the HMSC stage. From our observations, these limits can get as low
as $\leq$0.1 when considering the rms measured over the whole linewidth of the
lines, which is still consistent with the gas-phase results from Bergman et
al. (2011)’s models (grain-surface deuteration is expected to give much lower
upper limits as a consequence of freeze-out in the cold conditions of HMSC).
Therefore, although our results suggest that grain surface deuteration is the
most likely mechanism for the formation of HDCO and D2CO in star-forming
regions, higher sensitivity observations are needed to provide more stringent
constraints to the column density ratio of HDCO/D2CO during the HMSC phase.

##  5 Summary

We have observed 213 GHz continuum, H${}_{2}^{13}$CO, HDCO and D2CO emission
with APEX and ALMA toward a sample of high-mass star-forming regions at
different evolutionary stages. HDCO transitions were detected for all of them
except the three youngest sources in the HMSC stage, while the D2CO line was
detected only for four sources from the HMSC-HMPO stage to the UC H II stage.
The H${}_{2}^{13}$CO emitting regions are similar to the continuum source
sizes, they are in the range of 3” - 5.8” corresponding to 0.02-0.07 pc at the
distance of the investigated regions. The column density ratio of HDCO / H2CO
shows the highest values of $\sim$0.13 in the earlier evolutionary stages
(HMSC-HMPO) and then decreases by an order of magnitude toward the UC H II
phase to $\sim$0.01. This study confirms the idea that H2CO, and its
deuterated species, form mostly on grain surfaces although some gas-phase
contribution is expected at the warm HMPO stage. The calculated upper limits
for the HMSC sources are high, around 0.5, so we cannot constrain the trend
between HMSC and HMPO phases. More sensitive follow-up observations are needed
for the HMSC sources to better constrain the upper limits. The observed column
density ratios are in good agreement with the values previously reported in
the literature for low-mass prestellar cores, protostellar objects and PDR
regions.

###### Acknowledgements.

This paper makes use of the following ALMA data: ADS/JAO.ALMA#2017.1.01157.S.
ALMA is a partnership of ESO (representing its member states), NSF (USA) and
NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI
(Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA
Observatory is operated by ESO, AUI/NRAO and NAOJ. This research was partially
supported by the NAOJ ALMA Scientific Research Grant Number 2016-03B, the
Italian Ministry of Education, Universities and Research through the grant
Progetti Premiali 2012 iALMA (CUP C52I13000140001), the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) - Ref no. FOR 2634/1
TE 1024/1-1, the DFG cluster of excellence ORIGINS (www.origins-cluster.de),
the EU Horizon2020 research and innovation programme, Marie Sklodowska-Curie
grant agreement 823823 (Dustbusters RISE project), and the European Research
Council (ERC) via the ERC Synergy Grant ECOGAL (grant 855130). Ke Wang
acknowledges support by the National Key Research and Development Program of
China (2017YFA0402702), the National Science Foundation of China (11721303),
and the starting grant at the Kavli Institute for Astronomy and Astrophysics,
Peking University (7101502016). I.J.-S. has received partial support from the
Spanish FEDER (project number ESP2017-86582-C4-1-R) and the State Research
Agency (AEI; project number PID2019-105552RB-C41).

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##  Appendix A Observed H2CO, HDCO, and D2CO lines

In Table 4 and we report the parameters derived fitting single or multiple
velocity components to the detected lines with MADCUBA.

Source | Size | Species | N | Tex | vLSR | T${}_{\mathrm{NH_{3}}}$
---|---|---|---|---|---|---
| [”] ([pc]) |  | [1013 cm-2] | [K] | [km/s] | [K]
HMSC
G028-C1 | 6.0 (0.15) | H2CO | 2.72$\pm$0.34 | 30.2$\pm$4.9 | 80.1$\pm$0.1 | 17
| 6.0 (0.15) | HDCO |  $<$0.81 | 30.2$\pm$4.9 |  | 17
| 6.0 (0.15) | D2CO |  $<$0.99 | 30.2$\pm$4.9 |  | 17
G034-F2 | 6.0 (0.11) | H2CO | 1.23$\pm$0.30 | 25.2$\pm$8.2 | 58.9$\pm$0.5 |
| 6.0 (0.11) |  | 1.21$\pm$0.31 | 31.2$\pm$10.8 | 56.8$\pm$0.5 |
| 6.0 (0.11) | HDCO |  $<$0.63 | 30.5 |  |
| 6.0 (0.11) | D2CO |  $<$0.50 | 30.5 |  |
G034-G2 | 6.0 (0.08) | H2CO | 1.48$\pm$0.12 | 19.0$\pm$4.8 | 42.0$\pm$0.2 |
| 6.0 (0.08) |  | 0.73$\pm$0.01 | 29.6$\pm$12.8 | 43.8$\pm$0.2 |
| 6.0 (0.08) | HDCO |  $<$0.50 | 24 |  |
| 6.0 (0.08) | D2CO |  $<$0.40 | 24 |  |
HMSC/HMPO
AFGL5142 | 6.0 (0.05) | H2CO | 876.51$\pm$57.11 | 13.6$\pm$0.9 | -1.7$\pm$0.1 | 25
| 6.0 (0.05) |  | 401.61$\pm$14.18 | 22.4$\pm$6.4 | -3.8$\pm$0.1 | 25
| 6.0 (0.05) | H${}_{2}^{13}$CO | 2.03$\pm$0.14 | 13.6$\pm$0.9 | -2.2$\pm$0.2 | 25
| 6.0 (0.05) |  | 1.17$\pm$0.10 | 22.4$\pm$6.4 | -3.8$\pm$0.2 | 25
| 6.0 (0.05) | HDCO | 18.79$\pm$3.82 | 13.6$\pm$0.9 | -2.2$\pm$0.2 | 25
| 6.0 (0.05) |  | 7.03$\pm$0.99 | 22.4$\pm$6.4 | -3.8$\pm$0.2 | 25
| 6.0 (0.05) | D2CO | 2.88$\pm$0.32 | 13.6$\pm$0.9 | -2.2$\pm$0.2 | 25
| 6.0 (0.05) |  | 1.89$\pm$2.42 | 22.4$\pm$6.4 | -3.8$\pm$0.2 | 25
IRAS05358+3543 | 6.0 (0.05) | H2CO | 100.51$\pm$3.68 | 71.9$\pm$3.3 | -16.2$\pm$0.1 | 35
| 6.0 (0.05) | H${}_{2}^{13}$CO | 1.96$\pm$0.14 | 27.2$\pm$6.0 | -16.2$\pm$0.1 | 35
| 6.0 (0.05) | HDCO | 13.69$\pm$1.75 | 27.2$\pm$6.0 | -16.1$\pm$0.1 | 35
| 6.0 (0.05) | D2CO | 2.46$\pm$0.28 | 27.2$\pm$6.0 | -16.4$\pm$0.2 | 35
HMPO
18089-1732 | 3.6 (0.06) | H2CO | 360.46$\pm$7.49 | 84.7$\pm$1.5 | 35.0$\pm$0.5 | 38
| 3.6 (0.06) |  | 184.09$\pm$5.28 | 80.8$\pm$2.4 | 32.3$\pm$0.5 | 38
| 3.6 (0.06) | H${}_{2}^{13}$CO | 8.91$\pm$0.65 | 18.7$\pm$11.8 | 34.2$\pm$0.2 | 38
| 3.6 (0.06) |  | 4.42$\pm$0.49 | 22.5$\pm$17.4 | 31.9$\pm$0.2 | 38
| 3.6 (0.06) | HDCO | 7.28$\pm$1.76 | 18.7$\pm$11.8 | 34.2$\pm$0.2 | 38
| 3.6 (0.06) |  | 6.04$\pm$2.63 | 22.5$\pm$17.4 | 31.9$\pm$0.2 | 38
| 3.6 (0.06) | D2CO |  $<$0.39 | 20 |  | 38
18517+0437 | 5.3 (0.07) | H2CO | 137.19$\pm$16.22 | 22.6$\pm$6.5 | 44.2$\pm$0.5 |
| 5.3 (0.07) |  | 20.59$\pm$3.03 | 23.8$\pm$9.2 | 45.1$\pm$0.5 |
| 5.3 (0.07) | H${}_{2}^{13}$CO | 1.03$\pm$0.48 | 22.6$\pm$6.5 | 44.0$\pm$0.1 |
| 5.3 (0.07) |  | 2.66$\pm$0.48 | 23.8$\pm$9.2 | 44.6$\pm$0.2 |
| 5.3 (0.07) | HDCO | 15.73$\pm$2.00 | 22.6$\pm$6.5 | 43.9$\pm$0.1 |
| 5.3 (0.07) |  | 0.13$\pm$0.02 | 23.8$\pm$9.2 | 45.7$\pm$0.5 |
| 5.3 (0.07) | D2CO | 1.53$\pm$0.47 | 22.6$\pm$6.5 | 43.8$\pm$0.5 |
| 5.3 (0.07) |  | 0.72$\pm$0.33 | 23.8$\pm$9.2 | 44.9$\pm 0.5$ |
G75-core | 6.0 (0.11) | H2CO | 152.4$\pm$4.79 | 34.9$\pm$12.3 | 0.5$\pm$0.1 | 96
| 6.0 (0.11) |  | 16.79$\pm$2.18 | 34.9$\pm$12.3 | -4.0$\pm$0.2 | 96
| 6.0 (0.11) | H${}_{2}^{13}$CO | 5.12$\pm$0.11 | 34.9$\pm$12.3 | -0.1$\pm$0.1 | 96
| 6.0 (0.11) | HDCO | 12.18$\pm$2.89 | 34.9$\pm$12.3 | -0.1$\pm$0.2 | 96
| 6.0 (0.11) | D2CO |  $<$1.26 | 34.9$\pm$12.3 |  | 96
UC H II
G5.89-0.39 | 3.0 (0.02) | H2CO | 8062$\pm$732 | 132.6$\pm$10.5 | 11.5$\pm$0.2 |
| 3.0 (0.02) |  | 2667$\pm$567 | 86.0$\pm$7.6 | 8.4$\pm$0.2 |
| 3.0 (0.02) | H${}_{2}^{13}$CO | 130.30$\pm$12.32 | 70.0$\pm$7.5 | 11.6$\pm$0.2 |
| 3.0 (0.02) | HDCO | 31.32$\pm$3.00 | 70.0$\pm$7.5 | 11.7$\pm$0.2 |
| 3.0 (0.02) |  | 182.26$\pm$29.73 | 37.1$\pm$3.4 | 8.4$\pm$0.2 |
| 3.0 (0.02) |  | 89.08$\pm$9.00 | 37.1$\pm$3.4 | 8.4$\pm$0.2 |
| 3.0 (0.02) | D2CO |  $<$2.51 | 53 |  |
I19035–VLA1 | 4.8 (0.05) | H2CO | 92.65$\pm$2.92 | 60.3$\pm$2.0 | 33.1$\pm$0.1 | 39
| 4.8 (0.05) | H${}_{2}^{13}$CO | 4.10$\pm$0.52 | 60.3$\pm$2.0 | 32.9$\pm$0.2 | 39
| 4.8 (0.05) | HDCO |  $<$4.79 | 60.3$\pm$2.0 |  | 39
| 4.8 (0.05) | D2CO |  $<$3.63 | 60.3$\pm$2.0 |  | 39
19410+2336 | 5.8 (0.06) | H2CO | 16.27$\pm$1.34 | 60.1$\pm$4.8 | 22.7$\pm$0.1 | 21
| 5.8 (0.06) | H${}_{2}^{13}$CO | 5.59$\pm$0.19 | 25.4$\pm$11.1 | 22.5$\pm$0.1 | 21
| 5.8 (0.06) | HDCO | 6.43$\pm$1.82 | 25.4$\pm$11.1 | 22.4$\pm$0.2 | 21
| 5.8 (0.06) | D2CO | 1.32$\pm$0.28 | 25.4$\pm$11.1 | 22.6$\pm$0.2 | 21
Table 4: Fitted H2CO, H${}_{2}^{13}$CO, HDCO and D2CO excitation temperatures
and column densities. We note that to estimate the upper limits of the HDCO
and / or D2CO column densities for G034-F2, G034-G2, 18089-1732, and
G5.89-0.39, we used one component only and we used an average excitation
temperature based on the successful fits of H2CO / HDCO. No error bar is
provided for Tex in these cases. Source velocities and sizes are also
indicated. The last column shows the kinetic temperatures adopted from Fontani
et al. (2011).