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Astronomy &Astrophysics A&A 658, A135 (2022)
https://doi.org/10.1051/0004-6361/202141662
© J. M. Winters et al. 2022
Molecules, shocks, and disk in the axi-symmetric wind of the
MS-type AGB star RS Cancri?
J. M. Winters1
, D. T. Hoai2
, K. T. Wong1
, W.-J. Kim3,4
, P. T. Nhung2
, P. Tuan-Anh2
, P. Lesaffre5
,
P. Darriulat2, and T. Le Bertre6
1Institut de Radioastronomie Millimétrique (IRAM), 300 rue de la Piscine, Domaine Universitaire, 38406 St. Martin d’Hères, France
e-mail: winters@iram.fr
2Department of Astrophysics, Vietnam National Space Center (VNSC), Vietnam Academy of Science and Technology (VAST),
18 Hoang Quoc Viet, Cau Giay, Ha Noi, Vietnam
3Instituto de Radioastronomía Milimétrica (IRAM), Av. Divina Pastora 7, Núcleo Central, 18012, Granada, Spain
4I. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, 50937 Köln, Germany
5Laboratoire de Physique de l’École Normale Supérieure, 24 rue Lhomond, 75231 Paris, France
6LERMA, UMR 8112, CNRS and Observatoire de Paris, PSL Research University, 61 av. de l’Observatoire, 75014 Paris, France
Received 29 June 2021 / Accepted 29 November 2021
ABSTRACT
Context. The latest evolutionary phases of low- and intermediate-mass stars are characterized by complex physical processes like
turbulence, convection, stellar pulsations, magnetic fields, condensation of solid particles, and the formation of massive outflows that
inject freshly produced heavy elements and dust particles into the interstellar medium.
Aims. By investigating individual objects in detail, we wish to analyze and disentangle the effects of the interrelated physical processes
on the structure of the wind-forming regions around them.
Methods. We use the Northern Extended Millimeter Array to obtain spatially and spectrally resolved observations of the semi-
regular asymptotic giant branch (AGB) star RS Cancri and apply detailed 3D reconstruction modeling and local thermodynamic
equilibrium radiative transfer calculations in order to shed light on the morpho-kinematic structure of its inner, wind-forming
environment.
Results. We detect 32 lines of 13 molecules and isotopologs (CO, SiO, SO, SO 2, H2O, HCN, PN), including several transitions from
vibrationally excited states. HCN, H13CN, and millimeter vibrationally excited H 2O, SO,34SO, SO 2, and PN are detected for the first
time in RS Cnc. Evidence for rotation is seen in HCN, SO, SO 2, and SiO(v=1). From CO and SiO channel maps, we find an inner,
equatorial density enhancement, and a bipolar outflow structure with a mass-loss rate of 110 7M yr 1for the equatorial region and
of210 7M yr 1for the polar outflows. The12CO/13CO ratio is measured to be 20on average, 242in the polar outflows and
193in the equatorial region. We do not find direct evidence of a companion that might explain this kind of kinematic structure, and
explore the possibility that a magnetic field might be the cause of it. The innermost molecular gas is influenced by stellar pulsation and
possibly by convective cells that leave their imprint on broad wings of certain molecular lines, such as SiO and SO.
Conclusions. RS Cnc is one of the few nearby, low-mass-loss-rate, oxygen-rich AGB stars with a wind displaying both an equatorial
disk and bipolar outflows. Its orientation with respect to the line of sight is particularly favorable for a reliable study of its morpho-
kinematics. Nevertheless, the mechanism causing early spherical symmetry breaking remains uncertain, calling for additional high
spatial- and spectral-resolution observations of the emission of different molecules in different transitions, along with more thorough
investigation of the coupling among the different physical processes at play.
Key words. stars: AGB and post-AGB – circumstellar matter – stars: mass-loss – stars: winds, outflows –
stars: individual: RS Cnc – radio lines: stars
1. Introduction
Mass-loss in red giants is due to a combination of stellar
pulsations and radiation pressure on dust forming in dense
shocked regions in the outer stellar atmosphere (e.g., Höfner &
Olofsson 2018). Even if the basic principles are understood, a
fully consistent picture – including the role of convection, the
time-dependent chemistry, and a consistent description of dust
formation – still needs to be developed. In particular, the contri-
bution of transparent grains to the acceleration of matter close
?NOEMA data (FITS format) are only available at the CDS via anony-
mous ftp to cdsarc.u-strasbg.fr (130.79.128.5 ) or via http:
//cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/658/A135to the stellar photosphere (Norris et al. 2012) still needs to be
assessed.
The mechanisms shaping circumstellar environments around
asymptotic giant branch (AGB) stars are vividly debated. Among
them, magnetic fields (Matt et al. 2000; Duthu et al. 2017), bina-
rity (Theuns & Jorissen 1993; Mastrodemos & Morris 1999;
Decin et al. 2020), stellar rotation (Dorfi & Höfner 1996), and
common-envelope evolution (Olofsson et al. 2015; Glanz &
Perets 2018) have been considered.
A major difficulty is to explain the observed velocity field
in axi-symmetrical sources, with larger velocities at high lati-
tudes than at low latitudes (Hoai et al. 2014; Nhung et al. 2015b).
Also, recent observations of rotating structures and streams bring
additional conundrums (Tuan-Anh et al. 2019; Hoai et al. 2019).
A135, page 1 of 27
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License ( https://creativecommons.org/licenses/by/4.0 ),
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. | 10.1051_0004-6361_202141662 | page_0000 |
A&A 658, A135 (2022)
We have concentrated our efforts on two relatively close
(d150pc) sources that show composite profiles in CO rota-
tional lines (Winters et al. 2003): EP Aqr (Winters et al. 2007,
hereafter referred to as W2007), and RS Cnc (Libert et al. 2010).
Data obtained at IRAM show that these two sources have an
axi-symmetrical structure with a low-velocity ( 2 km s 1) wind
close to the equatorial plane, and faster ( 8 km s 1) outflows
around the polar axes (Hoai et al. 2014; Nhung et al. 2015b). For
EP Aqr, W2007 find a radial dependence of the density show-
ing intermediate maxima. Additional data obtained with ALMA
(Nhung et al. 2019b; Homan et al. 2018b) reveal a spiral structure
explaining the earlier W2007 results.
RS Cnc is one of the best examples of the interaction between
the stellar wind from an AGB star and the surrounding interstel-
lar medium (Hoai et al. 2014). Its high declination makes RS
Cnc an ideal target for the Northern Extended Millimeter Array
(NOEMA). Previous studies based on IRAM data show that it is
a twin of EP Aqr, but observed at a different angle, with a polar
axis inclined at about 30with respect to the line of sight (Libert
et al. 2010; Hoai et al. 2014; Nhung et al. 2015b). This is favor-
able for studying polar and equatorial structures simultaneously,
whereas the different viewing angle between EP Aqr and RS Cnc
can be exploited to discriminate between different models in
explaining the observed composite CO line profiles (Le Bertre
et al. 2016). In contrast to EP Aqr, technetium is detected in the
atmosphere of RS Cnc (Lebzelter & Hron 1999), proving that it
is evolving along the thermal pulsing asymptotic giant branch
(TP-AGB) in the Hertzsprung-Russell (HR) diagram. From a
chemical point of view, RS Cnc is in a slightly more advanced
evolutionary stage on the AGB, as indicated by its spectral clas-
sification as an MS star (see below) and by a higher photospheric
ratio of12C/13C (35; Smith & Lambert (1986), but see Sect. 4.1
for an improved evaluation based on CO rotational lines from the
circumstellar environment).
RS Cnc is a semi-regular variable star with periods of 122 d
and248 days (Adelman & Dennis 2005), located at a distance
of150pc (Gaia Collaboration 2021; Bailer-Jones et al. 2021).
It is listed as S-star CSS 589 in Stephenson (1984) based on
its spectral classification M6S given in Keenan (1954). With
its weak ZrO bands, its chemical type is intermediate between
M and S (Keenan 1954). The stellar temperature is estimated
toT3200 K and its luminosity is L4950 L (Dumm &
Schild 1998). From CO rotational line observations, two circum-
stellar wind components were identified: an equatorial structure
expanding at about 2 km s 1and a bipolar outflow reaching a
terminal velocity of vexp8km s 1(Libert et al. 2010; Hoai
et al. 2014), carrying mass-loss rates of 410 8M yr 1and
810 8M yr 1, respectively (see Sect. 4.1 for an improved
value of the mass-loss rate derived here). Lines of12CO,
13CO, SiO, and HI were detected from previous observations
at millimeter (mm) and radio wavelengths (Nyman et al. 1992;
Danilovich et al. 2015; de Vicente et al. 2016; Gérard & Le Bertre
2003; Matthews & Reid 2007).
NOEMA was recently equipped with the wide band cor-
relator PolyFiX, covering a total bandwidth of 15.6 GHz and
therefore offering the potential to observe several lines from
different species simultaneously. In this paper we present new
data obtained with NOEMA in D- and A-configuration, com-
plemented by short spacing observations obtained at the IRAM
30m telescope. Observational details are summarized in Sect. 2
and our results are presented in Sect. 3. Section 4 contains a
discussion of the morphological structures and compares them
to similar structures found in EP Aqr. Our conclusions are
summarized in Sect. 5.2. Observations
New observations of RS Cnc have been obtained in CO(2–1)
with NOEMA/WideX in the (extended) nine-antenna A-
configuration in December 2016 (Nhung et al. 2018) and
with NOEMA/PolyFiX in the (compact) nine-antenna D-
configuration during the science verification phase of PolyFiX
in December 2017 and in the ten-antenna A-configuration in
February 2020. The WideX correlator covered an instanta-
neous bandwidth of 3.8 GHz in two orthogonal polarizations
with a channel spacing of 2 MHz. Additionally, up to eight
high-spectral resolution units could be placed on spectral lines,
providing channel spacings down to 39 kHz. WideX was decom-
missioned in September 2017 and replaced in December 2017 by
the new correlator PolyFiX. This new correlator simultaneously
covers 7.8 GHz in two sidebands and for both polarizations, and
provides a channel spacing of 2 MHz throughout the 15.6 GHz
total bandwidth. In addition, up to 128 high-spectral-resolution
“chunks” can be placed in the 15.6 GHz-wide frequency range
covered by PolyFiX for both polarizations, each providing a fixed
channel spacing of 62.5 kHz over their 64 MHz bandwidth.
RS Cnc was observed with two individual frequency setups
covering a total frequency range of 32 GHz in the 1.3 mm atmo-
spheric window (see Fig. 1). We used the two quasars J0923+282
and 0923+392 as phase and amplitude calibrators; these were
observed every20 min. Pointing and focus of the telescopes
was checked about every hour, and corrected when necessary.
The bandpass was calibrated on the strong quasars 3C84 and
3C273, and the absolute flux scale was fixed on MWC349
and LkHa101, respectively. The accuracy of the absolute flux
calibration at 1.3 mm is estimated to be better than 20%.
In order to add the short spacing information filtered out by
the interferometer, in May and July 2020 we observed at the
IRAM 30m telescope maps of 10by 10using the On-The-Fly
(OTF) mode. This turned out to be necessary for the12CO(2–
1) and13CO(2–1) lines but was not needed for the SiO lines,
whose emitting region was found to be smaller than 300. In the
case of the12CO(2–1) and13CO(2–1) lines, the interferometer
filters out large-scale structures that account for about two-thirds
and three-quarters, respectively, of the total line flux, informa-
tion that is recovered by adding the short spacing data from the
OTF map. A comparison of the respective line profiles is shown
in Fig. A.1.
The data were calibrated and imaged within the GILDAS1
suite of software packages using CLIC for the NOEMA data
calibration and the uvtable creation, CLASS for calibrating the
OTF maps, and the MAPPING package for merging and subse-
quent uvfitting, imaging, and self-calibration of the combined
data sets. Continuum data were extracted for each sideband of
the two frequency setups individually by filtering out spectral
lines, and then averaging over 400 MHz bins to properly rescale
theuvcoordinates to the mean frequency of each bin. Phase
self-calibration was performed on the corresponding continuum
data. The gain table containing the self-calibration solutions was
then applied to the spectral line uvtables using the SELFCAL
procedures provided in MAPPING.
The resulting data sets were imaged applying either natu-
ral weighting, or, on the high-signal-to-noise (S/N) cubes, by
applying robust weighting with a threshold of 0.1 to increase
the spatial resolution by typically a factor 2. The resulting
dirty maps were then CLEANed using the Hogbom algorithm
(Högbom 1974).
1https://www.iram.fr/IRAMFR/GILDAS
A135, page 2 of 27 | 10.1051_0004-6361_202141662 | page_0001 |
J. M. Winters et al.: Molecules, shocks, and disk in the axi-symmetric wind of the MS-type AGB star RS Cancri
Table 1. Properties of the combined data sets for all detected lines.
Line Frequency Eu=k Peak flux FWHP beam size PA 1 noise vel.res Comments(a)
(GHz) (K) (Jy) (arcsec) (arcsec2) (deg) (mJy beam 1) ( km s 1)
12CO(2–1) 230.538000 16.6 53.971 10.841 6.160.01 0.480.30 36 2.88 0.5 A+D+30m, rw
13CO(2–1) 220.398684 15.9 4.693 0.948 7.200.01 0.500.31 35 2.79 0.5 A+D+30m, rw
SiO(v=0,5–4) 217.104919 31.3 17.464 3.523 1.710.01 0.510.32 36 3.38 0.5 A+D, rw, sc
SiO(v=1,5–4) 215.596018 1800.2 0.105 0.025 0.190.02 0.580.43 38 1.71 1.0 A, nw, sc, Feb 2020: no maser
SiO(v=1,5–4) 215.596018 1800.2 0.105 0.025 0.190.02 2.101.80 0 2.71 0.5 D, nw, sc, Dec 2017: maser
SiO(v=2,5–4) 214.088575 3552.1 0.013 0.005 0.350.09 1.000.74 35 1.03 3.0 A+D, nw, double peak profile (?)
SiO(v=0,6–5) 260.518009 43.8 23.906 4.817 1.620.01 0.430.26 32 3.39 0.5 A+D, rw, sc
SiO(v=1,6–5) 258.707324 1812.7 0.168 0.038 0.110.01 0.600.42 26 1.96 1.0 A+D, nw, sc
29SiO(v=0,5–4) 214.385752 30.9 5.372 1.083 1.190.01 0.520.32 37 1.12 3.0 A+D, rw, sc
Si17O(v=0,6–5) 250.744695 42.1 0.340 0.076 0.880.04 1.901.50 36 4.15(b)3.0 D, nw, sc tentative identification
29Si17O(v=0,6–5) 247.481525 41.6 0.020 0.008 0.730.44 1.901.50 26 2.10 3.0 D, nw, sc, tentative detection
SO(5(5)–4(4)) 215.220653 44.1 0.455 0.093 0.790.01 0.510.32 36 1.16 3.0 A+D, rw, sc
SO(6(5)–5(4)) 219.949442 35.0 0.634 0.130 0.800.01 0.500.31 36 1.17 3.0 A+D, rw, sc
SO(6(6)–5(5)) 258.255826 56.5 0.870 0.178 0.740.01 0.430.27 32 1.59 3.0 A+D, rw, sc
SO(7(6)–6(5)) 261.843721 47.6 1.168 0.238 0.780.01 0.430.26 32 1.38 3.0 A+D, rw, sc
34SO(6(5)–5(4)) 215.839920 34.4 0.030 0.009 0.920.11 0.910.80 69 0.86 3.0 A+D, nw
34SO(5(6)–4(5)) 246.663470 49.9 0.026 0.009 0.930.14 0.690.48 26 0.99 3.0 A+D, nw
SO2(16(3,13)–16(2,14)) 214.689394 147.8 0.021 0.006 0.500.06 0.900.68 37 1.06 3.0 A+D, nw, sc
SO2(22(2,20)–22(1,21)) 216.643304 248.4 0.023 0.007 0.380.05 0.890.67 36 1.11 3.0 A+D, nw, sc
SO2(28(3,25)–28(2,26)) 234.187057 403.0 0.022 0.006 0.190.05 0.710.56 46 1.28 3.0 A+D, nw, sc
SO2(14(0,14)–13(1,13)) 244.254218 93.9 0.043 0.011 0.430.03 0.690.49 27 1.00 3.0 A+D, nw, sc
SO2(10(3, 7)–10(2, 8)) 245.563422 72.7 0.025 0.007 0.360.04 0.690.49 28 1.00 3.0 A+D, nw, sc
SO2(15(2,14)–15(1,15)) 248.057402 119.3 0.015 0.005 0.260.06 0.690.48 27 1.07 3.0 A+D, nw, sc
SO2(32(4,28)–32(3,29)) 258.388716 531.1 0.020 0.006 0.210.04 0.630.45 25 1.10 3.0 A+D, nw, sc
SO2( 9(3, 7)– 9(2, 8)) 258.942199 63.5 0.026 0.008 0.490.05 0.640.45 26 1.08 3.0 A+D, nw, sc
SO2(30(4,26)–30(3,27)) 259.599448 471.5 0.022 0.005 0.120.03 0.630.45 25 1.03 3.0 A+D, nw, sc
SO2(30(3,27)–30(2,28)) 263.543953 459.0 0.019 0.006 0.160.04 0.610.42 26 1.25 3.0 A+D, nw, sc
SO2(34(4,30)–34(3,31)) 265.481972 594.7 0.020 0.006 0.190.04 0.610.42 26 1.27 3.0 A+D, nw, sc
H2O(v2=1,5(5,0)–6(4,3)) 232.686700(c)3462.0 0.0290.007 unresolved 0.71 0.57 47 1.17 3.0 A+D, nw, sc, JPL
H2O(v2=1,7(7,0)–8(6,3)) 263.451357(d)4474.7 0.0210.005 unresolved 0.61 0.42 26 1.17 3.0 A+D, nw, sc, JPL
HCN(3–2) 265.886434 25.5 1.116 0.234 0.760.01 0.420.26 32 4.80 0.5 A+D, rw, sc
H13CN(3–2) 259.011798 24.9 0.041 0.011 0.710.05 0.640.45 26 0.95 3.0 A+D, nw, sc
PN(N=5–4,J=6–5) 234.935694 33.8 0.028 0.009 0.800.10 0.700.56 47 1.00 3.0 A+D, nw, sc
Notes. Line frequencies and upper level energies are from the CDMS (Müller et al. 2005), unless otherwise stated. The quoted flux uncertainties
include the rms of the fits and the absolute flux calibration accuracy of 20%, the uncertainties quoted for the source sizes refer to the rms errors
of the Gaussian fits (see text).(a)A: NOEMA A-configuration, D: NOEMA D-configuration, 30 m: short spacing data, rw: robust weighting, nw:
natural weighting, sc: self-calibrated, JPL: Spectral line catalog by NASA/JPL (Pickett et al. 1998).(b)Increased noise at band edge.(c)Belov et al.
(1987).(d)Pearson et al. (1991).
The beam characteristics and sensitivities of the individual
combined data sets from A- and D-configuration (and including
the pseudo-visibilities from the OTF maps, where appropriate)
are listed in Table 1 for all detected lines.
3. Results
The PolyFiX data, covering the frequency ranges 213–221 GHz
(setup1, LSB), 228-236 GHz (setup1, USB), 243–251 GHz
(setup2, LSB), and 258–266 GHz (setup2, USB) with two setups
(see Fig. 1), showed different lines of CO and SiO, and, for the
first time, many lines of species like SO, SO 2, HCN, and PN and
some of their isotopologs. Furthermore, the data confirmed the
H2O line at 232.687 GHz already detected serendipitously withWideX in 2016, with a second H 2O line at 263.451 GHz seen for
the first time in RS Cnc.
All lines covered by the same setup (1 or 2, see Fig. 1) share
the same phase-, amplitude-, and flux calibration. All 32 detected
lines are listed in Table 1.
3.1. Continuum
Figure 2 shows the continuum map from A-configuration only,
using robust weighting to increase the spatial resolution to
0:39000:2200at PA 28. After self-calibration, S/N = 492 is
obtained. The continuum source is unresolved, a point source
fit results in a flux at 247 GHz of 23.65 4.7 mJy (where the
quoted error accounts for the accuracy of the absolute flux cali-
bration of 20%) and a source position at RA = 09:10:38.780 and
A135, page 3 of 27 | 10.1051_0004-6361_202141662 | page_0002 |
A&A 658, A135 (2022)
Fig. 1. Overview of the frequency ranges observed with PolyFiX using two spectral setups (setup1: red and setup2: blue, respectively). Lower
diagrams : zoom onto the individual spectra covering 7.8 GHz each. Upper row : setup1, lower row : setup2. The central 20 MHz at the border
between inner and outer baseband are blanked out, i.e., set to zero, as this region is contaminated by the LO2 separation of the 8 GHz-wide IF in
the IF processor (“LO2 zone”).
Dec = 30:57:46.62 in February 2020. All line data cubes dis-
cussed in the remainder of this paper are re-centered on this
continuum position.
The source position is offset from the J2000 coordinates by
0.2600in RA and by 0.6800in Dec, consistent with the proper
motion of RS Cnc ( 10.72 mas yr 1in RA and 33.82 mas yr 1
in Dec, Gaia Collaboration 2021; Bailer-Jones et al. 2021). From
the PolyFiX data, spanning a total frequency range of about
53 GHz, we determine a spectral index of 1.99 0.09 for RS Cnc
in the 1 mm range, which is fully consistent with a black body
spectrum of the continuum (see also Libert et al. 2010).
3.2. Detected molecules and lines
Within the total frequency coverage of about 32 GHz, we detect
32 lines of 13 molecules and isotopologs, including several tran-
sitions from vibrationally excited states. All these lines are listed
in Table 1 and are presented in the following sections. The peak
flux and FWHP of the line-emitting regions, as listed in Table 1,are determined by circular Gaussian fits in the uv-plane to the
central channel (if the source is (partially) spatially resolved) or
by point-source fits to the central channel (if the source is unre-
solved). All line profiles shown in the following sections in Fig. 3
and Figs. 5 through 14 are integrated over square apertures whose
sizes are given in each figure caption. Two-component profiles
are seen in CO and13CO only, and not in any other of the lines
detected here.
We looked for but did not detect the vibrationally excited
12CO(v=1, 2–1) line, nor do we detect C18O(2–1), result-
ing in 3upper limits for the line peaks of 6 mJy beam 1and
3 mJy beam 1, respectively (the12CO(v=1, 2–1) line was not
covered in our A-configuration data).
3.2.1. CO
The profiles of12CO(2–1),13CO(2–1) (see Fig. 3), and12CO(1–
0) (see Libert et al. 2010) show a very distinct shape composed
of a broad component that extends out to vlsr;8 km s 1and
A135, page 4 of 27 | 10.1051_0004-6361_202141662 | page_0003 |
J. M. Winters et al.: Molecules, shocks, and disk in the axi-symmetric wind of the MS-type AGB star RS Cancri
Fig. 2. Continuum map around 247 GHz from A-configuration. Con-
tours are plotted in 100 steps, where 1 is 47.6 Jy beam 1. The
synthesized beam is indicated in the lower left corner.
Fig. 3. CO line profiles, showing a two-component structure. Left:
12CO(2–1). Right :13CO(2–1). A-configuration and D-configuration are
merged, OTF data are added, and the spectral resolution is 0.5 km s 1.
The CO emission is integrated over the central 22002200, i.e., over the
full field of view of the NOEMA antennas at 230 GHz.
Fig. 4. Sketch of the geometrical structure of the wind components as
inferred from the current data (see Sect. 4.1). The sketch is not to scale:
there is a smooth transition between the equatorial enhancement and the
polar outflows.
a narrow component indicating velocities of 2 km s 1with
respect tovlsr;=7km s 1. Velocity-integrated intensity maps of
CO are shown in Fig. 18, indicating a clear kinematic structure
in the north–south direction. In Fig. 4, we present a schematic
representation of the geometrical structure of RS Cnc as implied
by the data; see Sect. 4.1. The CO emitting region is spatially
extended, consisting of a dense equatorial structure that corre-
sponds to the low-velocity expansion and an inclined, bipolar
Fig. 5. Profiles of SiO ground-state and first vibrationally excited state
lines. Left: SiO(6–5): upper :v=1,lower :v=0. A-configuration and D-
configuration merged. Right : SiO(5–4): upper :v=1, D-configuration
(black) and A-configuration (red), lower :v=0, A-configuration and D-
configuration merged. The spectral resolution is 1 km s 1for (v=1) and
0.5 km s 1for the (v=0) lines, respectively. The emission is integrated
over the central 500500aperture.
structure corresponding to an outflow at a projected velocity
of 8 km s 1. These structures were discussed in Hoai et al.
(2014) based on Plateau de Bure data obtained on12CO(2–1)
and12CO(1–0) that had a spatial resolution of about 100. The
model built by these latter authors was later refined by Nhung
et al. (2018) based on12CO(2–1) data obtained with the WideX
correlator in NOEMA’s A-configuration, providing a spatial res-
olution of 0:44000:2800. Nhung et al. (2018) find a position
angle of the projected bipolar outflow axis of !=7(measured
counter-clockwise from north) and an inclination angle of the
outflow axis with respect to the line of sight of i=30. The CO
distribution is further investigated in Sect. 4.1 below.
Such a structure had already been found in the S-type star 1
Gru (Sahai 1992), which was later confirmed by higher spatial
resolution observations using ALMA (Doan et al. 2017). This
object has a G0V companion (Feast 1953) and possibly a sec-
ond, much closer companion (Homan et al. 2020). In Hoai et al.
(2014), we reported for RS Cnc the possible presence of a com-
panion seen in the12CO(1–0) channel maps at velocities around
6.6 km s 1and located about 100west-northwest of the contin-
uum source. The new data allow for a more detailed study of this
feature, which is presented in Sect. 4.1.
3.2.2. SiO
We detect a suite of28Si16O (henceforth SiO) transitions, includ-
ing the vibrational ground-state lines of SiO(5–4) and SiO(6–5),
the first and second vibrationally excited state of SiO(5–4), and
the first vibrationally excited state of SiO(6–5). All SiO pro-
files are shown in Figs. 5 and 6. The spatial region emitting the
vibrational ground-state lines extends out to about 200from the
continuum peak (see Table 1, Fig. 18, and Sect. 4.2). Interest-
ingly, we detect a strong maser component on the SiO( v=1,
J=5–4) line at vlsr14km s 1in the data obtained in
December 2017, which had completely disappeared when we
re-observed RS Cnc in February 2020 (see Fig. 5). Such behav-
ior is well known for pulsating AGB stars, and lends support to
A135, page 5 of 27 | 10.1051_0004-6361_202141662 | page_0004 |
A&A 658, A135 (2022)
Fig. 6. Profile around the SiO( v=2,J=5–4) line frequency. A-
configuration and D-configuration merged. The spectral resolution is
1 km s 1and the emission is integrated over the central 100100aperture.
the idea that the SiO masers are excited by infrared pumping as
opposed to collisional pumping (see, e.g., Pardo et al. 2004).
The SiO(v=2,J=5–4) line is detected above the 3 level
of 3 mJy beam 1over a broad range of Doppler velocities from
at least 5 to 18 km s 1(Fig. 6). Given its high excitation energy
(3500 K), we expect this line to trace exclusively the inner-
most region around RS Cnc, as was the case in oCet, where
SiO(v=2) absorption and emission was spatially resolved by
ALMA (Wong et al. 2016). Its broad line width suggests that
it may trace the same high-velocity wings seen in other detected
SiO lines (Sect. 3.3). However, our detection is too weak to allow
for a detailed study of the morpho-kinematics of the emission.
At the upper edge of the LSB of setup 2 at 250.744 GHz,
we serendipitously detect a strong line that we identify as
ground-state Si17O(6–5) at 250.7446954 GHz (Müller et al.
2013) from the Cologne Database of Molecular Spectroscopy
(CDMS2, Müller et al. 2005); the profile is shown in Fig. 7. This
line and other transitions of Si17O have already been detected
in a number of well-studied objects, such as the S-type star
W Aql (De Beck & Olofsson 2020), the M-type star R Dor
(De Beck & Olofsson 2018), and the evolved, high-mass-loss-
rate oxygen-rich star IK Tau (Velilla Prieto et al. 2017). No
other Si17O transitions are covered in our setups, but there is a
highly excited H 2O line at 250.7517934 GHz ( v2=2,J(Ka;Kc)=
9(2,8)–8(3,5); Eu=k=6141 K) listed in the JPL catalog3and pre-
dicted by Yu et al. (2012) from the Bending-Rotation approach
analysis. If the detected line was H 2O emission, it would be
redshifted from the systemic velocity by about 9 km s 1. As indi-
cated by the modeling of Gray et al. (2016), the 250.752 GHz
line may exhibit strong maser action in regions of hot gas
(Tkin=1500 K) with cool dust ( Td1000 K). While we can-
not unequivocally exclude some contamination from a potential
new, redshifted H 2O maser, we consider Si17O a more likely
identification of the 250.744 GHz emission. From the respective
integrated line intensities of Si16O(6–5) and Si17O(6–5), which
are163 Jy km s 1and3 Jy km s 1, and taking the difference
of the Einstein coefficients of the transitions into account, we
estimate the isotopolog ratio16O/17O50, assuming equal exci-
tation conditions for both transitions and optically thin emission
of both lines. This value is much lower than the solar isotopic
ratio of2700 (Lodders et al. 2009) due to dredge-up events
(Karakas & Lattanzio 2014; Hinkle et al. 2016) and is broadly
consistent with those obtained in the M-type star R Dor and the
S-type star W Aql (61–74; De Beck & Olofsson 2018, 2020).
The initial mass of RS Cnc is about 1:5M (Libert et al. 2010)4,
2https://cdms.astro.uni-koeln.de
3https://spec.jpl.nasa.gov/ftp/pub/catalog/catform.
html
4As quoted in Libert et al. (2010), the value of 1:5M was esti-
mated by Busso & Palmerini (their priv. comm.) using the FRANEC
).Fig. 7. Line profiles of SiO isotopologs. Upper left : profile of the
247.482 GHz line, possibly29Si17O(6–5); D-configuration, only. Lower
left: Si17O(6–5): D-configuration, only (line was not covered in A-
configuration). Right :29SiO(5–4); A-configuration and D-configuration
merged. The spectral resolution in all cases is 3 km s 1and the emission
is integrated over the central 500500aperture.
which is in the same range as R Dor ( 1:4M ; De Beck &
Olofsson 2018) and W Aql ( 1:6M ; De Nutte et al. 2017) that
gives a16O/17O ratio of<1000 (Hinkle et al. 2016). However,
we note that the oxygen isotopic ratio (16O/17O) derived from
the line intensity ratio is likely underestimated if the Si16O line
is not optically thin, as has been shown in De Beck & Olofsson
(2018), who obtained a value of 400in R Dor with radiative
transfer modeling. Indeed, we demonstrate in Sect. 4.2 that the
Si16O emission in RS Cnc is optically thick, especially within a
projected radius of 100. A photospheric16O/17O ratio of 710 in
RS Cnc (=HR 3639) was estimated by Smith & Lambert (1990)
from the spectra of near-infrared overtone band transitions of
C16O and C17O, which is probably a more realistic ratio. We
do not cover C17O(2–1) in our setups and therefore cannot give
an independent estimate of the16O/17O ratio. As Si18O(6–5) and
C18O(2–1) are either not covered or not detected, there is not
enough information from our data to obtain a meaningful con-
straint on the initial stellar mass from oxygen isotopic ratios (e.g.
from the17O/18O ratio; De Nutte et al. 2017).
We detect a line at 247.482 GHz at low S/N that might be
identified as29Si17O(v=0,J=6–5) at 247.4815250 GHz based
on the line list by Müller et al. (2013) and used in the CDMS
(see Fig. 7). However, in contrast to Si17O(6–5),29Si17O(6–5)
has never been detected; only higher-J lines of29Si17O have
been tentatively detected in R Dor ( J=7–6 and J=8–7, De
Beck & Olofsson 2018). More specifically, the 247.482 GHz line
is seen with an integrated line intensity of 0:08Jy km s 1in
our D-configuration data only, observed in December 2017, but it
does not show up in the A-configuration data, taken in February
2020. This may largely be due to the much reduced brightness
stellar evolution code (Cristallo et al. 2011) and the molecular abun-
dances determined by Smith & Lambert. Smith & Lambert (1990)
reported oxygen isotopic ratios of16O/17O=710 and16O/18O=440 in RS
Cnc (their Table 9). The17O/18O ratio of 0.62 corresponds to an initial
mass of 1.4–1.5 M in the comparative study of De Nutte et al. (2017),
who investigated the17O/18O isotopic ratio as a sensitive function of
initial mass of low-mass stars based on the models of Stancliffe et al.
(2004), Karakas & Lattanzio (2014), and the FRANEC model.
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).
Fig. 8. HCN line profiles. Left: HCN(3–2); A-configuration and D-
configuration merged with a spectral resolution of 0.5 km s 1.Right :
H13CN(3–2); A-configuration and D-configuration merged with a spec-
tral resolution of 3 km s 1. The emission of both lines is integrated over
the central 200200.
sensitivity in the A-configuration, which is a factor of approxi-
mately 15 smaller because of the smaller synthesized beam area
rather than some variable maser action in this line. Based on
the D-configuration data, the source position of the 247.482 GHz
emission appears slightly offset toward the northwest direction
from the Si17O(6–5) emission. Further data on29Si17O, possibly
covering the J=6–5,J=7–6, and J=8–7 transitions, would
be needed to draw any firm conclusion.
3.2.3. HCN
We clearly detect the HCN(3–2) and H13CN(3–2) lines; the
profiles are displayed in Fig. 8, and velocity-integrated inten-
sity maps of both species are shown in Fig. B.1. Both lines
are slightly spatially resolved and a circular Gaussian fit to
HCN(3–2) gives a peak flux of 1.12 Jy and a FWHP size of 0.7600
on the merged data. To our knowledge, this is the first detection
of HCN and H13CN in RS Cnc (see Sect. 4.4). From the first-
moment map (shown in Fig. 17, left), a clear velocity pattern
is evident that indicates possible rotation in the HCN-emitting
region (see Sect. 3.4). Also, the velocity-integrated intensity
maps presented in Fig. B.1 show a clear kinematic structure in
the east–west direction.
Formation of the HCN molecule in oxygen-rich environ-
ments is further discussed in Sect. 4.4. A modeling using the 1D
local thermodynamic equilibrium (LTE) radiative transfer code
XCLASS (Möller et al. 2017, see Appendix D) gives a column
density for HCN in RS Cnc of N HCN=1:61015cm 2, cor-
responding to an abundance of X(HCN/H 2)=6:610 7. This
value is well within the range found for other M- and S-type
stars as modeled by Schöier et al. (2013), who find X(HCN/H 2)
equal to a few times 10 7(for more details see Sect. 4.4 and
Appendix D).
3.2.4. H 2O
The WideX spectrum obtained in A-configuration in Decem-
ber 2016 serendipitously revealed a line at 232.687 GHz that we
ascribe to the J(Ka,Kc)=5(5,0)–6(4,3) transition of o-H 2O in
thev2=1vibrational state. The H 2O source is weak and seems
still unresolved within the synthesized beam of 0:5000:3400
obtained in the A-configuration in February 2020, consistent
with its high upper-state energy of 3462 K. The line profile is
shown in Fig. 9. With the follow-up observations employing
PolyFiX in D-configuration and A-configuration we also cov-
ered and detected the 263.451 GHz o-H 2Ov2=1,J(Ka,Kc)=
7(7,0)–8(6,3) line (Fig. 9, right; Eu=k=4475 K). Both lines
are resampled to a resolution of 3 km s 1, data are merged
from A-configuration and D-configuration, and the emission is
Fig. 9. H2O line profiles. Left: H 2O line at 232.687 GHz. Right : H 2O
line at 263.451 GHz. Data are merged from A-configuration and D-
configuration, the spectral resolution is 3 km s 1, and the emission of
both lines is integrated over the central 100100aperture.
integrated over an aperture of 100100. Intensity maps of both
lines are shown in Fig. B.2, testifying to the compactness of the
H2O-emitting region.
These are the first detections of millimeter vibrationally
excited H 2O emission in RS Cnc. We note that the 22 GHz
H2O maser in the ground state was tentatively detected by
Szymczak & Engels (1995) in one of the two epochs they cov-
ered, but the 22 GHz line is not detected in other observations
(Dickinson et al. 1973; Lewis 1997; Han et al. 1995; Yoon et al.
2014). RS Cnc also shows clear photospheric H 2O absorption at
2:7m (Merrill & Stein 1976; Noguchi & Kobayashi 1993), and
at1:3m (7500 cm 1; Joyce et al. 1998), although the H 2O band
near 900 nm is not detected (Spinrad et al. 1966).
Both the 232 and 263 GHz water lines have upper levels
belonging to the so-called transposed backbone in the v2=1
vibrationally excited state of H 2O, that is Ka=JandKc=0or
1 (see Fig. 1 of Alcolea & Menten 1993). The 232 GHz line was
first detected in evolved stars together with the 96 GHz line from
another transposed backbone upper level by Menten & Melnick
(1989) toward the red supergiant VY CMa and the AGB star
W Hya. The latter is an M-type star with a similar mass-loss
rate to RS Cnc. The authors find that the 232 GHz line emission
in both stars may be of (quasi-)thermal nature while the 96 GHz
line clearly showed maser action. The (unpublished) detection of
the 263 GHz line was mentioned in Alcolea & Menten (1993),
who also described a mechanism that may lead to a system-
atic overpopulation of the transposed backbone upper levels in
thev2=1state of H 2O in the inner region of circumstellar
envelopes. If the vibrational decay routes (to the ground state)
of the transposed backbone upper levels become more optically
thick than the lower levels in the v2=1state, then differential
radiative trapping may cause population inversion of these lines.
Additional vibrationally excited H 2O emission lines from trans-
posed backbone upper levels were predicted and later detected in
VY CMa by Menten et al. (2006) and Kami ´nski et al. (2013). We
observed the 232 GHz line in RS Cnc at three epochs (December
2016, December 2017, and February 2020) and the 263 GHz line
at the latter two epochs, and the emission appears to be stable in
time for both lines. The profiles appear to be very similar, both
are broad, even broader than the (ground-state) lines of other
species reported here, and there is no sign for any narrow com-
ponent in either of the two profiles at any of the epochs. As the
lines should arise from a region very close to the star – compat-
ible with their broad widths; see Sect. 3.3 – one might expect
to see time variations due to the varying density and radiation
field caused by the stellar pulsation, in particular if the emission
were caused by maser action, as seen on the SiO( v=1;5–4)
line observed in December 2017 (see Fig. 5). Also, the model-
ing of Gray et al. (2016) shows only very little inversion of the
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A&A 658, A135 (2022)
Fig. 10. Profiles of the four detected SO lines, with A-configuration
and D-configuration merged. The spectral resolution is 3 km s 1and the
emission is integrated over the central 200200aperture.
Fig. 11. Profiles of the two34SO lines detected here, with A-
configuration and D-configuration merged. The spectral resolution is
3 km s 1and the emission is integrated over the central 200200aperture.
involved level populations for the 263 GHz H 2O transition. We
therefore think that both lines could be thermally excited. A def-
inite assessment of the nature of the vibrationally excited H 2O
emission would however require some detailed modeling of the
emission, together with high-sensitivity monitoring of the line
profiles with high spectral resolution, possibly including other
H2O lines from transposed backbone upper levels and/or known
maser lines for comparison, which is beyond the scope of the
present paper.
3.2.5. SO
Four lines of SO are detected (see Fig. 10) along with two lines of
the isotopolog34SO (Fig. 11). These represent the first detections
of SO and34SO in RS Cnc. SO has been observed in several M-
type stars, including R Dor and W Hya, (Danilovich et al. 2016)),
but remains undetected in S-type stars (e.g., W Aql, Decin et al.
2008; De Beck & Olofsson 2020). All SO lines detected here
are slightly spatially resolved with a FWHP around 0:800and
therefore seem to be emitted from the same region as HCN.
Velocity-integrated intensity maps of SO are shown in Fig. B.3.
The SO lines show the same velocity pattern (indicating rota-
tion) as HCN, although the velocity resolution of the SO lines is
only 3 km s 1; see Fig. B.3 and the first-moment map in the right
panel of Fig. 17.
Using the integrated line strengths of SO(6(5)–5(4))
and34SO(6(5)–5(4)) found here ( 4.69 Jy km s 1and
0.20 Jy km s 1, respectively) and taking the difference of
the Einstein coefficients of the transitions into account, weestimate the isotopolog ratio32SO/34SO23, assuming equal
excitation conditions for both transitions and optically thin
emission of both lines. This value is in good agreement with
the values of 21.68:5and 18.55:8derived from the radiative
transfer models for M-type stars by Danilovich et al. (2016,
2020), respectively. We note that, for the S-type star W Aql,
an Si32S/Si34S isotopolog ratio of 10.6 2:6was derived by
De Beck & Olofsson (2020). As32S is mainly produced by
oxygen burning in massive stars and, to a lesser extent, in type
Ia supernovae, and as34S is formed by subsequent neutron
capture (e.g., Nomoto et al. 1984; Wilson & Matteucci 1992;
Timmes et al. 1995; Hughes et al. 2008), the32S/34S isotopic
ratio remains virtually unaltered during AGB evolution (see, e.g.
tables in the FRUITY5database, Cristallo et al. 2011) and there-
fore should reflect the chemical initial conditions of the natal
cloud from which the star has formed. The spread in the isotopic
ratio seen among the different AGB stars mentioned above
would then rather be indicative of the Galactic environment in
which the star has formed (see, e.g., Chin et al. 1996; Humire
et al. 2020) instead of reflecting any evolutionary effect. For the
low-mass-loss-rate M-type stars R Dor and W Hya, Danilovich
et al. (2016) reproduce their observed line profiles best with
centrally peaked SO (and SO 2) distributions, consistent with the
maps presented in Fig. B.3.
3.2.6. SO 2
In SO 2, 11 lines are detected; their parameters are summarized
in Table 2, and all profiles are shown in Fig. C.1. These are the
first detections of SO 2in RS Cnc. A previous survey with the
IRAM 30 m telescope by Omont et al. (1993) did not detect
SO2in RS Cnc with an rms noise of 0.052 K (or 0:25Jy
at 160.8 GHz). As an example, we show the SO 2(14(0,14)–
13(1,13)) line at 244.3 GHz, only in Fig. 12. A first-moment
map of the SO 2(14(0,14)–13(1,13)) line is shown in Fig. 17
in the middle left panel. Although the source remains barely
resolved (source size 0:4300) by the beam ( 0:69000:4900), there
is a signature of a rotating structure in SO 2, as was also seen
in EP Aqr (Homan et al. 2018b; Tuan-Anh et al. 2019). Inte-
grated intensity maps of three SO 2lines (SO 2(9(3, 7)–9(2, 8)),
which has the lowest upper level energy of the SO 2lines detected
here ( Eu=64K); SO 2(14(0,14)–13(1,13)), the strongest line,
and SO 2(34(4,30)–34(3,31)), which has the highest upper level
energy of the detected lines, Eu=595K) are shown in Fig. B.4.
All lines show kinematic structure in the E–W direction, approx-
imately orthogonal to the outflow structure seen in CO and SiO,
cf. Fig. 18.
We derive the rotational temperature and column density
of the SO 2-emitting region with a population diagram analysis
(Sect. 3.6) and by an XCLASS modeling (Appendix D). Both
methods give a similar rotational temperature of 320 350K
and a column density of 3:51015cm 2.
3.2.7. PN
We detect a line at 234.936 GHz that we ascribe to the PN
molecule, which would be the first detection of PN in RS Cnc.
PN has been detected in several M-type stars (e.g., De Beck
et al. 2013; Ziurys et al. 2018), and in the C-rich envelopes of
IRC +10216 and CRL 2688 (Guélin et al. 2000; Cernicharo et al.
2000; Milam et al. 2008). The presence of PN in an MS-type star
therefore does not seem to come as a surprise. However, RS Cnc
5http://fruity.oa-teramo.inaf.it/
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Table 2. Parameters of the detected SO 2lines used for the population diagram analysis.
Frequency WI=R
S(v)dv g ulog10(Aul) Eu=kab
(GHz) (Jy km s 1) (s 1) (K) (arcsec2)
214.6894 0.1410.0385 33 –4.0043 147.843 0.90 0.68
216.6433 0.166 0.0434 45 –4.0329 248.442 0.89 0.67
234.1871 0.1600.0439 57 –3.8401 403.033 0.71 0.56
244.2542 0.293 0.0698 29 –3.7855 93.901 0.69 0.49
245.5634 0.170 0.0451 21 –3.9240 72.713 0.69 0.49
248.0574 0.119 0.0333 31 –4.0939 119.328 0.69 0.48
258.3887 0.153 0.0396 65 –3.6773 531.100 0.63 0.45
258.9422 0.192 0.0524 19 –3.8800 63.472 0.64 0.45
259.5994 0.182 0.0448 61 –3.6835 471.496 0.63 0.45
263.5440 0.152 0.0448 61 –3.7227 459.038 0.61 0.42
265.4820 0.168 0.0448 69 –3.6426 594.661 0.61 0.42
Notes. Data are merged from A-configuration and D-configuration. Quoted errors include the rms errors of the Gaussian fits in the uvplane and
the absolute flux calibration accuracy of 20%. The SO 2line parameters are retrieved from the CDMS and are based on the calculations by Lovas
(1985) and Müller & Brünken (2005).
Fig. 12. Profile of SO 2(14(0,14)–13(1,13)) with A-configuration and D-
configuration merged, a spectral resolution of 3 km s 1, and emission
integrated over the central 200200aperture.
Fig. 13. Profile of PN( N=5–4,J=6–5) with A-configuration and D-
configuration merged, a spectral resolution of 3 km s 1, and emission
integrated over the central 200200aperture.
appears to be the source with lowest mass-loss rate in which this
molecule has been reported so far. The PN line profile is shown
in Fig. 13. The line is spatially resolved at 0:800, which places it
in about the same region as HCN and SO. The first-moment map
of this line also shows signatures of rotation but due to the weak-
ness of the line, the evidence is low. An integrated intensity map
of PN is presented in Fig. B.5, showing that the line-emitting
region is slightly spatially resolved. The 3feature seen about
1:500south of the phase center should not be considered as a
detection but rather as a noise peak, as long as this structure is
not confirmed by higher sensitivity observations.
Fig. 14. Line wings in SiO(5–4) and SiO(6–5) compared to CO(2–1).
The emission is integrated over the central 500500aperture.
Fig. 15. High velocities close to the line of sight as seen in SiO. PV
maps are shown in the Vzvs.Rplane for SiO(5–4) ( left) and SiO(6–5)
(right ). The horizontal black line indicates the wind terminal velocity
as traced in CO and the white scale bar indicates the spatial resolution.
R=p
(Dec)2+(RA)2,jVzj=jvlsr vlsr;j:
3.3. High-velocity wings in SiO, and in other molecules
In SiO, five lines in three different vibrational states ( v=0,1,2)
are detected (see Figs. 5 and 6). The vibrational ground-state
lines clearly indicate the presence of material at velocities much
higher than the wind terminal velocity of 8 km s 1as traced by
CO lines at this stellar latitude (see Sect. 4.1). This is illustrated
in Fig. 14, and in Fig. 15 where we define vz=vlsr vlsr;, the
Doppler velocity relative to the star. The high-velocity region
is centered on the line of sight and is confined to the inner
0:300; see Fig. 15. A similar feature was seen in high-spatial-
resolution observations of other oxygen-rich, low-mass-loss-rate
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A&A 658, A135 (2022)
AGB stars, such as W Hya (Vlemmings et al. 2017), EP Aqr
(Tuan-Anh et al. 2019), oCet (Hoai et al. 2020), R Dor (Decin
et al. 2018; Nhung et al. 2019a, 2021), and in 15 out of 17 sources
observed in the ALMA Large Program ATOMIUM (Decin et al.
2020; Gottlieb et al. 2022), calling for a common mechanism
causing high-velocity wings in this type of object. In the case
of EP Aqr, where the bipolar outflow axis almost coincides with
the line of sight (with an inclination angle of i10), the high-
velocity wings were interpreted in terms of narrow polar jets.
For R Dor and oCet, which do not show obvious signs of axial
symmetry in their winds, such an interpretation could not be
retained and it was argued instead that the high-velocity wings
were caused by (a mixture of) turbulence, thermal broadening,
and some effect of shocks, acting at distances below some 10 to
15 AU from the central star. The presence of broad wings in the
SiO lines emitted from RS Cnc, whose symmetry axis is inclined
by30with respect to the line of sight (see Sect. 4.1), lends sup-
port to the latter type of interpretation and casts serious doubts
on the polar jet interpretation proposed earlier for EP Aqr, which
shows a morpho-kinematics similar to that of RS Cnc (Nhung
et al. 2015b). Indeed, if the broad line widths are present regard-
less of the orientation of a possible symmetry axis with the line
of sight, they must be caused by a mechanism of nondirectional
(accounting for the resolving beam) nature. A possible candi-
date, whose action is limited to the close vicinity of the star,
is pulsation-driven shocks that dissipate their energy relatively
close to the star and imply positive and negative velocities in the
shocked region that can be much higher than the terminal out-
flow velocity of the wind. Such structures could be explained
by the B-type models discussed in Winters et al. (2000b) as
presented in Winters et al. (2002); see their Fig. 3. Recent 3D
model calculations that self-consistently describe convection and
fundamental-mode radial pulsations in the stellar mantle would
provide the physical mechanism that leads to the development of
such shocks close to the star surface (e.g., Freytag et al. 2017)
and could therefore replace the simplified inner boundary condi-
tion (the so-called “piston approximation”) that was used in the
earlier 1D models mentioned above.
In the data presented here, wings at high Doppler velocity
are seen in nearly all lines detected with sufficient sensitivity
to probe the profile over at least vlsr;10km s 1. This is illus-
trated in Fig. 16, where vzprofiles are integrated over a circle
of radius 0:200centered on the star. Gaussian profiles centered
at the origin are shown as visual references (not fits), showing
how absorption produces asymmetric profiles. A major differ-
ence is seen between vibrational ground-state lines, which have
a Gaussian FWHM of 10km s 1, and vibrationally excited-
state lines, which have a Gaussian FWHM of 14km s 1.
Such a difference is not surprising, assuming that the high-
velocity wings are formed in the inner layer of the circumstellar
envelope (CSE), which is preferentially probed by the ( v=1)
lines. In this context, we note that Rizzo et al. (2021) recently
reported the detection of a narrow SiO( v=1, 1–0) maser line
in RS Cnc at a velocity of +14 km s 1with respect to the
star’s lsr velocity. The effect of shocks on line profiles was first
observed in the near-infrared range on CO ro-vibrational lines,
probing the stellar photosphere and the innermost circumstellar
region within10R(e.g., Cyg, an S-type star, Hinkle et al.
1982). Very-high-angular-resolution observations obtained over
the past decade using VLT, VLTI, and ALMA show that the
effect of shocks from pulsations and convection cell ejections
is confined within some 10 AU from the star (see, e.g., Khouri
et al. 2018; Höfner & Olofsson 2018; Ohnaka et al. 2019, and
references therein). Rotation, when observed, is instead found
Fig. 16. Line profiles of different molecules on a logarithmic intensity
scale. Gaussian profiles are shown for comparison, FWHM =10km s 1
for the ground-state lines of all molecules, and FWHM =14km s 1
for the (v=1) lines of SiO. All observed profiles are integrated over
R<0:200.
to extend beyond this distance, typically up to 20 AU (e.g.,
Vlemmings et al. 2018; Homan et al. 2018a; Nhung et al. 2021).
The angular resolution of the present data is insufficient to detect
such differences directly; however, the effect of rotation and
shocks on lines of sight contained within a beam centered on the
star depends on the region probed by each specific line: lines that
probe the inner layers exclusively, such as the ( v=1) lines, are
mostly affected by shocks, and somewhat by rotation; CO lines,
for which the probed region extends very far out, see little effects
of rotation and even less effects of shocks because the emission
from the inner envelope provides too small a fraction of the total
emission. Between these two extremes, the relative importance
of the contributions of shocks and rotation depends on the radial
extent of the region probed by the line. Such an interpretation is
consistent with the data displayed in Fig. 16.
3.4. Rotation
In Fig. 17, we present first-moment maps of HCN(3–2) (left),
SO2(14(0,14)–13(1,13)) (middle left), SiO( v=1, 6–5) (middle
right), and SO(7(6)–6(5)) (right). At projected distances from
the star not exceeding 0:500, all four tracers display approximate
anti-symmetry with respect to a line at PA10. This is sugges-
tive of the presence of rotation in the inner CSE layer around
an axis that projects on this line in the plane of the sky. Such
a morpho-kinematic structure has also been observed in other
stars, notably R Dor (Vlemmings et al. 2018; Homan et al. 2018a;
Nhung et al. 2021). The angular resolution of the present data
does not allow for a detailed exploration of this region, which
prevents us from commenting on its possible cause. Neverthe-
less, the anti-symmetry axis of the velocity pattern projected on
the plane of the sky at a PA that approximately coincides with
the projected symmetry axis of the polar outflows (see Sect. 4.1)
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J. M. Winters et al.: Molecules, shocks, and disk in the axi-symmetric wind of the MS-type AGB star RS Cancri
Fig. 17. First-moment maps of different lines, indicating a possibly rotating structure (see Sect. 3.4). Left: HCN(3–2), middle left : SO 2(14(0,14)–
13(1,13)), middle right : SiO(v=1,6–5), right : SO(7(6)–6(5)). The black ellipses indicate the synthesized beam.
is remarkable and suggests that rotation is taking place about this
same polar axis in the inner CSE layer.
The line-of-sight velocities of these structures are small, on
the order of the velocities derived from CO for the equatorial
region, and we interpret them here as possible signs of rotation
(rather than indicating another bipolar outflow oriented perpen-
dicular to the larger scale outflow traced in CO and SiO ( v=0)
lines). We note that out of these four lines, the HCN(3–2) line
is detected with the highest S/N (S/N =233in the line peak, cf.
Table 1).
The mean Doppler velocity hvzi, averaged over the inner
0:500, of the HCN line can be fit in position angle !, measured
counter-clockwise from north, by
hvziHCN= 0:19 km s 1+1:0 km s 1sin(! 19); (1)
whereas the SiO( v=1, 6–5) velocity is well fit by
hvziSiO (v=1;6 5)= 0:37 km s 1+0:46 km s 1sin(! 26):(2)
The small offsets of 0:3km s 1on average are within
the uncertainty attached to the measurement of the star’s LSR
velocity. The coefficients of the sine terms measure the pro-
jected rotation velocity, namely the rotation velocity divided by
the sine of the angle made by the rotation axis with the line of
sight. Assuming that the rotation axis is the axi-symmetry axis of
the CSE, this angle is i30(see Sect. 4.1), meaning rotation
velocities of2and1km s 1for HCN and SiO respectively.
Observations of higher angular resolution are needed to confirm
the presence of rotation within a projected distance of 0:500from
the star and we prefer to summarize the results presented in this
section in the form of an upper limit to the mean rotation velocity
of a few km s 1.
3.5. Global outflow structure traced by CO and SiO
The detailed structure of the morpho-kinematics of the CSE has
been studied using observations of the12CO(1–0) and12CO(2–1)
molecular line emission. The analyses of Hoai et al. (2014) and
Nhung et al. (2015b) confirmed the interpretation of the two-
component nature of the Doppler velocity spectrum originally
given by Libert et al. (2010). The CSE is axi-symmetric about
an axis making an angle of i30with the line of sight and
projecting on the plane of the sky at a position angle !7east
of north (see also the sketch in Fig. 4). The expansion velocity
reaches8to9km s 1along the axis – we refer to this part of
the CSE as bipolar outflow – and 3to4km s 1in the plane
perpendicular to the axis – we refer to this part of the CSE as
equatorial enhancement. The transition from the equator to thepoles of the CSE is smooth. Section 4.1 below, using observa-
tions of the12CO(2–1) and13CO(2–1) molecular lines, confirms
and significantly refines this picture. The right panels of Fig. 20
show projections of the CSE on the plane containing the axis
and perpendicular to the plane of the sky, which give a good
qualitative idea of the global structure.
Velocity-integrated channel maps of the CO(2–1) and
SiO(6–5) observations analyzed in the present article are dis-
played in Fig. 18. They clearly show the bipolar outflows,
inclined toward the observer in the north and receding in the
south. We note that the red wings are brighter than the blue
wings as a result of absorption (see Sects. 4.1 and 4.2) The SiO-
emitting region is seen to be significantly more compact than the
CO-emitting region; this is in conformity with observations of
many other oxygen-rich AGB stars and is generally interpreted
as the result of SiO molecules condensing on dust grains and
being ultimately dissociated by the interstellar radiation at some
200 AU from the star, well before CO molecules are dissociated
(see e.g., Schöier et al. 2004).
3.6. Temperature and SO 2abundance
In this section, we use the 11 detected SO 2lines to derive
an approximate temperature and column density of the SO 2-
emitting region by means of a population diagram. Following
Goldsmith & Langer (1999), in the optically thin case, the col-
umn density of the upper level population Nuof a transition u->l
can be expressed as
Nu=8k2
hc3AulZ
Tbdv: (3)
Nuis the column density of the upper level population of the
transition, kandhare the Boltzmann and Planck constant,
respectively, is the line frequency, cthe speed of light, Aulis
the Einstein coefficient for spontaneous emission of the transi-
tion, andR
Tbdvis the velocity-integrated main-beam brightness
temperature. The latter is converted to the surface brightness
distribution of the source Sper beam, measured by the inter-
ferometer, by means of
Tb=2
2k
bS; (4)
where=c
is the observing wavelength, and
b=ab
4 ln 2witha
andbbeing the major and minor axis of the synthesized beam.
We determineR
S(v)dv=:WIfrom a circular Gaussian fit to
the velocity-integrated emission in the uv-plane, where the inte-
gration is taken from (vlsr,* 4:5)km s 1to(vlsr;+4:5)km s 1,
that is over the three central channels of the SO 2lines.
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about their formation paths during the past evolution of the core.
In particular, their degree of deuterium fractionation is a relic of
the conditions that were prevailing in earlier, colder stages (e.g.Taquet et al. 2012 ,2014 ;Aikawa et al. 2012 ).
Apart from methanol, relativ ely little is known about deuter-
ation of complex organic molecules in the interstellar medium,in particular in high mass star-forming regions. A few detec-
tions or tentative detections of deuterated (complex) organic
molecules have been reported toward Orion KL ( Gerin et al.
1992 ;Daly et al. 2013 ;Esplugues et al. 2013 ;Neill et al. 2013 ;
Coudert et al. 2013 ), but no systematic study of the deuteration
of complex organic molecules in high mass star-forming regionshas been reported so far.
Sagittarius B2, hereafter Sgr B2, is one of the most mas-
sive star-forming regions in the Galaxy. It is located in the cen-tral molecular zone, close to the Galactic center. Its current star
formation rate qualifies Sgr B2 as a mini-starburst region (see,
e.g., Appendix A of Belloche et al. 2013 ). The cloud contains
several sites of ongoing, high-mass star formation. One of these
sites, Sgr B2(N), contains two hot molecular cores that we des-
ignate as Sgr B2(N1) and Sgr B2(N2)
2. Their angular separation
is 5/prime/primein the north-south direction, corresponding to 0.2 pc in
projection at a distance of 8.3 kpc ( Reid et al. 2014 ). Their ve-
locities projected along the line of sight di ffer by 9–10 km s−1.
Both are characterized by extremely high H 2column densities
(>1025cm−2over few arcsec, see Belloche et al. 2008 ,2014 ;
Qin et al. 2011 ). They are both in an early stage of star forma-
tion when a (massive) protostar has already formed and startedto heat up its circumstellar envelope. The high kinetic temper-
atures of the hot cores ( ∼150–200 K) lead to the sublimation
of molecules that formed in the ice mantles of dust grains dur-ing the prestellar phase and the warming-up period of the proto-
stellar phase. As a result of both the high temperatures and col-
umn densities, numerous complex organic molecules have beendetected toward Sgr B2(N), many of these for the first time in
the interstellar medium, since the beginning of radio astronomy
nearly five decades ago.
Following up a molecular line survey of Sgr B2(N) per-
formed with the IRAM 30 m telescope that led to the first
detection in space of a few new complex organic molecules(Belloche et al. 2008 ,2009 ,2013 ), we performed a system-
atic line survey of Sgr B2(N) in the 3-mm atmospheric win-
dow at high angular resolution and sensitivity with the Atacama
Large Millimeter/submillimeter Array (ALMA) in its Cycles 0
and 1. This survey is called EMoCA, which stands for Exploring
Molecular Complexity with ALMA, and it aims to investigatemolecular complexity in the interstellar medium. One of the ini-
tial results of EMoCA was the first interstellar detection of a
branched alkyl molecule ( Belloche et al. 2014 ). Here, we take
advantage of this sensitive survey to explore, for the first time
in a systematic way, the deuterium fractionation of complex or-
ganic molecules in Sgr B2(N2). We focus on Sgr B2(N2) ratherthan the main hot core Sgr B2( N1) because the former has rel-
atively narrow linewidths ( ∼5k ms
−1) at the angular resolution
of EMoCA (∼1.8/prime/prime), while the latter still has prominent linew-
ings like in our previous single-dish survey. A companion paper
reports on the detection of alkanols and alkanethiols based on
EMoCA ( Müller et al. 2016b ).
The article is structured as follows. The observational setup
and the process of data reduction are described in Sect. 2.
Section 3explains the method employed to model the observed
2They were named P1 and P2 in Belloche et al. (2008 )a n dS M A 1a n d
SMA2 in Qin et al. (2011 ).spectra in the approximation of l ocal thermodynamic equilib-
rium (LTE) and Sect. 4gives some details about the spectro-
scopic predictions used to generate the synthetic spectra. Theresults of the analysis are reported in Sect. 5and discussed
in Sect. 6. Section 7gives our conclusions about deuterium
fractionation of complex organic molecules in Sgr B2(N2).
2. Observations and data reduction
2.1. Observations
We used ALMA to perform a complete spectral line survey to-ward Sgr B2(N) between 84.1 and 114.4 GHz. The field was cen-
tered at (α,δ)
J2000=(17h47m19.87s,−28◦22/prime16/prime/prime), halfway be-
tween Sgr B2(N1) and (N2), which are separated by 4 .9/prime/primein the
north-south direction. The size (HPBW) of the primary beam
of the 12 m antennas varies between 69/prime/primeat 84 GHz and 51/prime/prime
at 114 GHz ( Remijan et al. 2015 ).
The spectral line survey was divided into five spectral setups.
Each setup was observed in one polarization and delivered fourspectral windows, two per sideba nd. The separation between the
centers of the lower and upper sidebands is 12 GHz. Each spec-
tral window has a bandwidth of 1875 MHz and a channel spacingof 244.141 kHz, but the spectra were smoothed to a spectral res-
olution of 488.3 kHz (1.7 to 1.3 km s
−1). Each pair of adjacent
spectral windows has an overlap of about 50 MHz. Details aboutthe frequency coverage, the date of observation, the number of
antennas, the range of baselines, the on-source integration time,
and the bandpass, amplitude, and phase calibrators are given inTable 1. Setups S1 to S4 were observed in Cycle 0 while setup
S5 was observed in Cycle 1. As reported in Table 1, setups S1
and S5 were observed only once, but setups S2, S3, and S4 wereobserved on several days, between two and four times each.
2.2. Data reduction
The data was calibrated and imaged with the CommonAstronomy Software Applications package (CASA). We used
version 4.2.0 (r28322) for setups S1 to S4 and version 4.2.1
(r29047) for setup S5. We used the standard procedures providedby the Joint ALMA Observatory to apply the bandpass, ampli-
tude, and phase calibrations. The deconvolution was performed
with the csclean imager mode and a Briggs weighting scheme
with a robust parameter of 0.5. The cell size was set to 0 .3
/prime/prime.
In addition, three or four iterations of self-calibration were per-
formed using a strong spectral line detected toward Sgr B2(N1)
in each setup. This significantly improved the dynamical range
in the resulting images.
The spectra toward Sgr B2(N1) and (N2) are full of lines and
close to the confusion limit. It is thus di fficult to separate the line
emission from the continuum emission in a systematic way forthe full data cubes, but it is a necessary step to produce sepa-
rate line and continuum maps. For each spectral window of each
setup, we selected six groups of a few channels that seemed to befree of strong line emission. A first-order baseline was fitted to
these selected channels and the result of the fit was used to split
each data cube into two cubes: one for the line emission and onefor the continuum emission. Given the di fference in systemic ve-
locity between the two hot cores ( ∼10 km s
−1,s e e Belloche et al.
2013 ), we selected different sets of channels for the northern and
southern parts of the field. This process of baseline subtraction
was performed with the CLASS software3.
3Seehttp://www.iram.fr/IRAMFR/GILDAS
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Table 1. Observational setups of the EMoCA survey.
Setup Frequency range Date of tstartaNabBaseline tintdCalibratorsePeakf
LSB USB observation (UTC) rangecBA P ΔαΔδ
GHz GHz yyyy-mm-dd hh:mm m min/prime/prime /prime/prime
S1 84.1–87.8 96.2–99.8 2012-08-27 01:05 26 17–400 54.7 1 3 2 0.2 −2.4
S2 87.7–91.4 99.7–103.4 2012-06-05 09:03 20 14–392 24.2 1 3 2 1.2⋆−2.4
2012-07-01 07:04 13 25–393 40.0 1 3 2 1.2⋆−2.6
2012-07-03 06:36 21 14–395 48.4 1 3 2 0.6⋆−2.3
2012-09-28 21:57 25 20–387 44.1 1 4 2 0.2 −2.5
S3 91.4–95.1 103.4–107.1 2012-06-06 08:20 18 15–395 40.2 1 3 2 0.7⋆−2.4
2012-06-18 07:29 22 15–395 40.4 1 3 2 0.6⋆−2.2
S4 95.0–98.7 107.0–110.7 2012-07-04 05:38 21 17–398 8.1 1 3 2 0.1 −2.3
2012-08-01 02:32 24 19–442 34.9 1 3 2 0.1 −2.4
2012-08-10 00:45 26 21–400 35.0 1 3 2 0.2 −2.4
S5 98.7–102.4 110.7–114.4 2014-04-05 06:22 38 15–413 24.4 2 4 5 0.2 −2.4
Notes.(a)Start time of observation.(b)Number of ALMA 12 m antennas.(c)Minimum and maximum projected baseline separations.(d)On-source
integration time.(e)Bandpass (B), amplitude (A), and phase (P ) calibrators. The calibrators are: 1: B1730-130, 2: J 1700-2610, 3: Neptune, 4: Titan,
5: J1744-3116.(f)Offset of the continuum peak position of Sgr B2(N1) with respect to the phase center, in equatori al coordinate system (J2000).
Measurement sets with Δαdiffering from 0.1/prime/primeby more than 0.2/prime/prime(marked with a⋆) are believed to be a ffected by an astrometric problem.
We checked the accuracy of the relative astrometry between
the ten measurement sets by fitting the peak position of thecontinuum emission toward Sgr B2(N1) in selected channels of
the line+continuum data cubes that appeared to be free of line
emission. It turns out that the first three measurement sets ofsetup S2 and both measurement sets of setup S3 are a ffected
by an astrometric problem: the continuum peak of Sgr B2(N1)
is shifted by 0.6
/prime/primeto 1.2/prime/primein right ascension with respect to
all other measurement sets (see Table 1). The dispersion of
the peak position in declination is also a bit higher for the af-
fected measurement sets compared to the nona ffected measure-
ment sets. The average peak position of Sgr B2(N1) in all non-
affected measurement sets is at ( Δα,Δδ)=(0.15/prime/prime,−2.40/prime/prime), i.e.
(α,δ)J2000=(17h47m19.881s,−28◦22/prime18.40/prime/prime). The five affected
measurement sets were obtained after transit when the sourcewas setting and the phase calibrator was at low elevation, which
leads us to believe that the shift of the a ffected measurement sets
may be due to an inacurrate calibration of the atmospheric phasefluctuations. As a result, we ignored the a ffected measurement
sets of setup S2 and used only its fourth measurement set. For
setup S3, both measurement sets were used but the o ffset was
approximately compensated for by modifying the visibilities of
the phase calibrator with the CASA task fixvis before the phase
calibration. After this correcti on, the relative positional accuracy
of all measurement sets selected for this work is on the order
of±0.1
/prime/primein both right ascension and declination.
The measurement sets of setup S3 were merged into one sin-
gle measurement set with the CASA task concat before imag-
ing. The same was carried out for setup S4. Only one measure-
ment set was used for the other three setups. The size (HPBW)of the synthesized beam and the rms noise level in the final
cubes are given in Table 2. The noise level of each spectral win-
dow corresponds to the median of the noise levels measured inall channel maps using the procedure go noise in GREG
3.The
noise levels reported in Table 2were measured in the continuum-
subtracted datacubes. They are typically a factor ∼2 higher in the
line+continuum datacubes.
Based on the redundancies of the measurement sets and the
spectral overlap between the setups, we estimate the relative cal-ibration uncertainty on the flux density to be on the order of 15%.3. Radiative transfer modeling of the line survey
We used the input parameters of our LTE model of theIRAM 30 m spectrum of Sgr B2(N) ( Belloche et al. 2013 )a s
a starting point to assign the lines detected in the ALMA spec-
tra and model the emission of the detected molecules. Given the
high H
2densities of Sgr B2(N1) and (N2) ( ∼108cm−3at arc-
second scale, Belloche et al. 2008 ,2014 ;Qin et al. 2011 ), the
LTE approximation is appropriate. We used the software Weeds
(Maret et al. 2011 ) to produce synthetic LTE spectra that take
into account the radiative transfer and the (spectral-window- and
measurement-set-dependent) angular resolution of the observa-
tions. We performed the modeling for each species separately,and then we linearly added the contributions of all detected
species to the emitted spectra to obtain the final synthetic spec-
trum (hereafter called the full LTE model). This approximation
is valid for optically thin lines that overlap in frequency space orfor (optically thick or thin) lines of species that are emitted from
separated regions within the beam, but it is no longer correct for
frequency-overlapping optically thick lines of species that arecospatial or aligned along the line of sight. In such cases, the
synthetic spectrum overestimates the actual line flux density.
The model of each species is defined by five parameters:
angular size of the emitting region assumed to be Gaussian,
column density, rotational temperature, velocity o ffset with re-
spect to the assumed systemic velocity of the source, and
linewidth (FWHM). For a given species, the source size was de-
rived from two-dimensional Gau ssian fits to the integrated in-
tensity maps of all transitions that were well detected and found
to be free of contamination (based on the full LTE model). The
source size was set to the median deconvolved size of all suchtransitions. The other four parameters were optimized by eye.
We constructed population diagrams based on the transitions that
are well detected and not severe ly contaminated by transitions
of other species. In the case where a transition was partially con-
taminated, the contributions of the contaminating species was re-
moved from the measured integrated intensities, on the basis ofthe full LTE model. Each population diagram was also corrected
for optical depth following the method described in Goldsmith &
Langer (1999 ), using the opacities delivered by Weeds. We used
the population diagrams to verify that the rotational temperature
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Table 2. Beam sizes and noise levels.
Setup SPWaFrequency Synthesized beam rmsc
range HPBW PAbmJy
MHz/prime/prime×/prime/prime ◦beam−1K
S1 0 84 091–85 966 2 .1×1.5−85 3.0 0.16
1 85 904–87 779 2 .0×1.5−83 2.7 0.14
2 96 154–98 029 1 .8×1.4−85 3.0 0.16
3 97 904–99 779 1 .8×1.3−85 3.1 0.16
S2 0 87 729–89 604 1 .9×1.7 86 3.1 0.15
1 89 554–91 429 1 .8×1.6 52 2.8 0.15
2 99 728–101 602 1 .6×1.4 48 2.7 0.14
3 101 552–103 427 1 .6×1.4 49 2.7 0.14
S3 0 91 368–93 242 2 .9×1.5 84 3.4 0.12
1 93 193–95 067 2 .8×1.5 83 3.1 0.10
2 103 365–105 239 2 .5×1.3 82 3.4 0.11
3 105 189–107 064 2 .5×1.3 82 3.6 0.12
S4 0 95 021–S96 896 1 .9×1.4−82 1.9 0.10
1 96 846–98 720 1 .8×1.3−82 1.9 0.10
2 107 019–108 893 1 .7×1.2−83 2.2 0.11
3 108 843–110 718 1 .6×1.2−82 2.3 0.12
S5 0 98 672–100 546 1 .8×1.4−76 2.8 0.14
1 100 496–102 370 1 .7×1.4−76 2.7 0.13
2 110 669–112 543 1 .6×1.3−72 3.5 0.17
3 112 494–114 368 1 .6×1.2−77 4.9 0.24
Notes.(a)Spectral window.(b)Position angle east from north.(c)Median rms noise level measured in the channel maps of the continuum-removed
data cubes.
derived in the course of the (manual) modeling with Weeds made
sense.
In the population diagrams corrected for optical depth and
contamination, the residual dispersion of the synthetic data-points (red crosses) results in part from the frequency boundaries
set to integrate the intensity. These boundaries are a compromise
between covering the line as much as possible and limiting thecontamination from other species emitting at nearby frequencies
as much as possible. In addition, the correction for optical depth
is an approximation and may also introduce some bias. Finally,another limitation of this fit is that it can be biased by residualcontamination that remains even after removal of the contribu-
tion of the identified contamina ting species. Therefore, we be-
lieve that the formal errors on the rotational temperature derivedfrom the fit to the population diagrams do not necessarily rep-
resent the true errors on this temperature and should be viewed
with caution.
The emission of vibrationally excited states of a given
molecule were modeled independentely of the vibrational
ground state. The emission of isotopologues of a given moleculewere also modeled separately.
The physical structure of the source assumed for the model-
ing is uniform. This may sound simplistic given that temperature
and density gradients are expect ed in the envelope of Sgr B2(N2)
(e.g., Rolffs et al. 2011 ). It turns out that, even with such a sim-
ple assumption, the spectra of most complex organic molecules
detected toward Sgr B2(N2) can be well reproduced so we areconfident that the rotational temperatures and column densities
derived from our analysis are reliable.
In the following, we count a line of a given species as a de-
tected line if its frequency, peak intensity, and width are wellreproduced by our model and the line is not (or barely) con-
taminated by emission from other species. As a counter exam-
ple, a synthetic line that is consistent with the observed spec-trum, i.e., that has a peak intensity simply below the intensity ofthe detected signal, but would still remain consistent if it were
shifted by a frequency o ffset typically equal to its linewidth is not
counted as detected. We emphasize that our definition of a de-
tected line is very conservative but we believe that it is requiredto avoid unsecure molecule detections.
The complete list of transitions identified in our survey is
presently not available but the list of lines identified in our pre-
vious single-dish survey of Sgr B2(N) can be taken as reference
(Belloche et al. 2013 ).
4. Spectroscopic predictions
The origin of the spectroscopic predictions used to model the
emission of the species reported in Sect. 5is provided here.
Predictions for the three singly deuterated species of ethyl
cyanide were taken from the catalog of the Cologne Databasefor Molecular Spectroscopy (CDMS
4,Müller et al. 2001 ,2005 ;
tags 56 509, 56 510, and 56 511, all version 1). They are based
onMargulès et al. (2009 ). All other ethyl cyanide data were also
taken from the CDMS. The main species predictions are based
onBrauer et al. (2009 ) with published data in the range of our
survey from Fukuyama et al. (1996 ). Transition frequencies of
the isotopologues containing one13C were taken from Richard
et al. (2012 ), those for the15N isotopologue from Margulès et al.
(2009 ). Vibrational corrections to the rotational partition func-
tion, and thus to the column density, were derived for the main
isotopologue from Heise et al. (1981 ) and applied to all species.
Only limited isotopic data are available. It is safe to assume thatdifferences among the isotopologues are small, most likely not
exceeding a few percent because of the large number of heavy
atoms in the molecule.
Predictions for singly deuterated methyl cyanide were taken
from the CDMS catalog (tag 42 511, version 2). This entry is
4Seehttp://www.cdms.de
A91, page 4 of 66 | 10.1051_0004-6361_201527268 | page_0003 |
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based on Nguyen et al. (2013 ). Predictions for CH 3CN in its
/v18=1 and 2 excited states are based on preliminary results from
Müller et al. (2015 ), those in /v14=1 are preliminary data from
a subsequent study (Müller et al., in prep.). Transition frequen-
cies in the range of our study are from Bauer & Maes (1969 )
andBauer (1971 )f o r /v18=1 and 2, respectively. Predictions for
isotopic species with15N or one or two13C in their ground vibra-
tional states are from the CDMS. They are based on Müller et al.
(2009 ) with transition frequencies in the range of our survey
from Demaison et al. (1979 ). Predictions for13C isotopologues
in their /v18=1 states are based on preliminary data from Müller
et al. (2016a ). Vibrational corrections to the partition function
were included in the private entries for the main isotopic species.T h e ya r en o wa v a i l a b l ei n Müller et al. (2015 ). As the correc-
tions are small, the error using the values from the main isotopic
species for the other isotopologues as well is very small, evenfor CH
2DCN.
Predictions for deuterated vinyl cyanide CH 2CDCN were
taken from the molecular spectroscopic database of the Jet
Propulsion Laboratory (JPL5,Pickett et al. 1998 ; tag 54 004, ver-
sion 2). We prepared predictions for cis-CHDCHCN and trans -
CHDCHCN. All predictions are based on Colmont et al. (1997 ).
Predictions for C 2H3CN and isotopic species with one13Co r
with15N were taken from the CDMS and are based on Müller
et al. (2008 ). Transition frequencies in the range of our survey
are mostly from that study. For the main species, they are, toa large extent, also from Baskakov et al. (1996 ). Predictions
for excited states of vinyl cyanide used in the present work are
based on Cazzoli & Kisiel (1988 ) and unpublished data from
one of us (HSPM). These data included vibrational corrections
which are essentially complete at 200 K. The vibrational ener-
gies were gathered from several sources. A recent compilation
of low-lying vibrational states is available in Kisiel et al. (2015 ).
It is safe to assume that di fferences among the isotopologues are
small, most likely not exceedin g a few percent because of the
large number of heavy atoms in the molecule.
Predictions for deuterated c yanoacetylene were taken from
the CDMS catalog (tag 52 508, version 2). This entry is based on
Spahn et al. (2008 ). All other cyanoacetyl ene predictions were
also taken from the CDMS. The /v1
7=1 predictions of the main
species are based on Thorwirth et al. (2000 ) with data in the
range of our survey from Yamada & Creswell (1986 ). All pre-
dictions of isotopologues containing one or two13Ca r eb a s e d
onThorwirth et al. (2001 ), and those for HC15
3No n Fayt et al.
(2004 ). Ground state transition frequencies for singly substituted
species in the range of our survey were taken from Creswell
et al. (1977 ). Vibrational contributions to the partition functions
of HC 3Na n dD C 3N can be evaluated from the study of their
low-lying vibrational states by Uyemura et al. (1982 ). Isotopic
shifts, in particular of the lowest ν7mode, are much smaller for
13Co r15N species. Therefore, using vibrational corrections of
the main isotoplogue introduces small errors for these species.
Predictions for deuterated methanol CH 2DOH were taken
from the JPL catalog (tag 33 004, version 1). They are based on
Pearson et al. (2012 ) with rest frequencies almost entirely from
that study. With the use of torsional energies from Lauvergnat
et al. (2009 ), we estimate a vibrational correction factor to the
partition function of 1.15 at 160 K. For CH 3OD, we prepared
a catalog entry based on Anderson et al. (1988 ), with frequen-
cies updated to the values published in Duan et al. (2003 ).
We estimated the partition function to be 11 770 at 150 Kand 25 550 at 225 K, taking torsional energies of CH
3OD in
5Seehttp://spec.jpl.nasa.govAnderson et al. (1988 ) into account. Details on other methanol
isotopologues are given in Müller et al. (2016b ).
Predictions for all singly deuterated species of ethanol were
taken from the CDMS (tags 47 515 to 47 518, all version 1).
They are based on Walters et al. (2015 ) with rest frequencies
almost entirely from that study. All other ethanol analyses weretaken from Müller et al. (2016b ), and further details can be found
there. Conformational and vibrational corrections to the parti-
tion function were taken from the main isotopologue for whichonly data were available. This assumption is reasonable, though
errors may not be completely negligible. They are, however,
difficult to evaluate.
Predictions for both conformers of CH
2DOCHO were ex-
tracted from Table 7 of Coudert et al. (2013 ) and split into two
separate entries. The partition function was taken from theirTable 6. It is identical for both entries. Contrary to the CDMS en-
tries for CH
2DCH 2CN and CH 2DCH 2OH, this treatment means
that the two entries represent a single species with a statisticaldistribution (the out-of-plane conformer being twice as abun-
dant as the in-plane one). This means that the column density
derived for each conformer represents the total column densityof the molecule. However, we assumed a statistical distribu-
tion (2:1) to compute and report individual column densities in
Sect. 5. Predictions for the main isotopologue were taken from
the JPL catalog. The entry is based on Ilyushin et al. (2009 ).
Vibrational corrections to the partition function were derived
from the
13C species ( Favre et al. 2014 ). These authors pro-
vide rotational partition function values at di fferent temperatures
as well as detailed vibrational corrections that are complete up
to 300 K. The correction factors are 1.59 and 1.23 at 150 K forthe deuterated and main isotopic species, respectively. These val-
ues differ because values for the deuterated species refer to the
ground state only whereas contributions of the first excited stateswere already included for the main isotopologue.
5. Results
In this section, we report the detection or tentative detectionof deuterated complex organic molecules toward Sgr B2(N2).Column density upper limits are also reported for several non-
detections. Each subsection first presents the LTE model de-
rived for the main isotopologue and its
13Ca n d/or15N isotopo-
logues. This model is then used to obtain constraints on the col-
umn density of the deuterated species. The rotational tempera-
tures derived from fits to the population diagrams are reportedin Table 3and the parameters of the LTE model used to fit the
spectra are listed in Table 4. The analysis toward Sgr B2(N2)
was performed at the o ffset position (Δα,Δδ)=(−0.1
/prime/prime,2.6/prime/prime),
i.e. (α,δ)J2000=(17h47m19.86s,−28◦22/prime13.4/prime/prime).
5.1. Deuterated ethyl cyanide CH 2DCH 2CN and
CH3CHDCN
About 154, 54, 38, and 37 lines of ethyl cyanide and its singly
substituted13C isotopologues,13CH 3CH 2CN, CH 313CH 2CN,
and CH 3CH 213CN, respectively, are detected toward Sgr B2(N2)
(Figs. A.1–A.4). The15N isotopologue is also detected un-
ambiguously, with nine detected lines (Fig. A.5). The best-fit
LTE model fits very well all detected transitions, except the
very optically thick lines of the main isotopologue, which itsignificantly underestimates. We ignored the lines with opti-
cal depth higher than ∼2.5 to construct the population diagram
of this species (Fig. A.6), while all lines of the
13C isotopo-
logues that matched the criteria defined in Sect. 3were used
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Table 3. Rotational temperatures derived from population diagrams of
selected (complex) organic molecules toward Sgr B2(N2).
Molecule StatesaTfitb
(K)
CH 3CN /v18=1,/v18=2,/v14=1 253 (15)
13CH 3CN /v1=0,/v18=1 168 (13)
CH 313CN /v1=0,/v18=1 165.5 (3.3)
CH 2DCN /v1=0 136 (14)
C2H5CN /v1=0 137.3 (1.6)
13CH 3CH 2CN /v1=0 138.3 (7.5)
CH 313CH 2CN /v1=0 112 (11)
CH 3CH 213CN /v1=0 150 (40)
C2H3CN /v1=0,/v111=1,/v115=1,/v111=2 199.5 (3.4)
13CH 2CHCN /v1=0 255 (101)
CH 213CHCN /v1=0 140 (31)
CH 2CH13CN /v1=0 278 (126)
H13CCCN /v1=0,/v17=1 171.1 (3.2)
HC13CCN /v1=0,/v17=1 167.7 (5.5)
HCC13CN /v1=0,/v17=1 177 (18)
CH 3OCHO /v1t=0,/v1t=1 142.4 (4.4)
Notes.(a)Vibrational states that were taken into account to fit the popu-
lation diagram.(b)The standard deviation of the fit is given in parenthe-
ses. As explained in Sect. 3, these uncertainties should be viewed with
caution. They may be underestimated.
for their population diagrams (Figs. A.7–A.9). The results of the
linear fit to the population diagrams of all four isotopologues
are given in Table 3. The rotational temperature is well con-
strained to∼140 K for both C 2H5CN and13CH 3CH 2CN. This
value is consistent with the result of the fit for the two other iso-
topologues within the uncertainties. The temperature derived in
this way depends on the model used to make the opacity correc-tion. With an earlier best-fit model that assumed a temperature
of 170 K (instead of 150 K here), the fit to the population di-
agrams of both C
2H5CN and13CH 3CH 2CN yielded a tempera-
ture of∼150 K. This is the reason why we decided to assume
a rotational temperature of 150 K for ethyl cyanide and all its
isotopologues.
The median source size derived for the selected lines of
C2H5CN is about 1.15/prime/prime, but there seems to be a trend of de-
creasing size with increasing upper level energy, from ∼1.3/prime/primeat
low energy to∼0.8/prime/primeatEu∼700 K (Fig. 1). Similar results are
obtained for13CH 3CH 2CN, with a median size of ∼1.25/prime/primeand a
hint of a decrease down to ∼1.0/prime/primeatEu∼120 K. Our model does
not treat such gradients. As a compromise, we used a source size
of 1.2/prime/prime.
With this source size and a rotational temperature of 150 K,
we obtain an excellent fit to all emission lines of the four iso-
topologues, except for the very optically thick lines of C 2H5CN
(τmax∼60), as mentioned above. A better fit to these lines would
be obtained by increasing the temperature and /or assuming a
larger source size. Increasing the size to 1 .4/prime/primeturns out to be
insufficient. A larger size would be inconsistent with the mea-
sured sizes. Increasing the temperature to 200 K and the size
to 1.3/prime/primeyields peak temperatures of the optically thick lines sim-
ilar to those observed, but the synthetic lines look too saturatedcompared to the observed lines, and the fit to the optically thin
lines becomes worse; lines with high upper level energies be-
come overpredicted. A more complex model with nonuniformphysical parameters would probably be needed to reproduce the
intensity and shape of the very optically thick lines.
Assuming the same source size, rotational temperature,
linewidth, and velocity o ffset as derived for C
2H5CN and its13Ca n d15N isotopologues, we looked for emission of the singly
deuterated isotopologues, CH 3CHDCN and CH 2DCH 2CN. The
former is a chiral molecule b ecause the carbon atom in the
middle of the chain is linked to four di fferent atoms or func-
tional groups. Both isotopologues are tentatively detected to-
ward Sgr B2(N2) with 1 and 2 line(s), respectively (Figs. A.10
andA.11 ), the latter isotopologue in its out-of-plane conforma-
tion only. For the in-plane confomer of CH 2DCH 2CN, we derive
an upper limit only. This upper lim it is uncertain because the ap-
parent inconsistency between the synthetic spectrum and the ob-served one around ∼101 190 MHz may result from a slight over-
estimate of the baseline, at the 3 σlevel (Fig. A.12 ). Owing to the
limited signal-to-noise ratios, the source size derived from theintegrated intensity maps of the uncontaminated lines assigned
to CH
3CHDCN and CH 2DCH 2CN is uncertain, varying between
unresolved and∼2/prime/prime. The emission looks compact in the maps.
Thus, assuming the same source size as the other isotopologues
looks reasonable.
5.2. Deuterated methyl cyanide CH 2DCN
Methyl cyanide is clearly detected in its vibrational ground statetoward Sgr B2(N2) but its transitions are very optically thick
(τ
max∼50) and cannot be properly fitted in the framework of
our simple model (Fig. A.13 ). Transitions from within its vibra-
tionally excited states /v18=1a n d /v18=2 are also clearly detected,
withτmax∼2.7 and 0.3, respectively (Figs. A.14 andA.15 ). We
also find four transitions from within /v14=1 around 91 520 MHz
and 109 820 MHz ( τmax∼0.06), but they partially su ffer from
blends with other species (Fig. A.16 ). The assignment looks
reasonable, but the detection should be considered tentative.
The singly substituted13C isotopologues are very well de-
tected, both in their vibrational ground state and in their first
vibrationally excited state /v18=1( F i g s . A.17 –A.20 ). The fit
to their population diagrams yields rotational temperatures of
about 170 K (see Table 3and Figs. A.21 andA.22 ). The analysis
of the integrated intensity maps of the13C isotopologues deliv-
ers a source size of ∼1.4/prime/prime. For the main isotopologue, it seems
that the source size decreases with the vibrational energy ( ∼1.2/prime/prime
for/v18=1a n d∼0.8/prime/primefor/v18=2).
With the assumption of a source size of 1 .4/prime/primeand a temper-
ature of 170 K, our LTE modeling yields excellent and consis-
tent fits to the13C isotopologues (both /v1=0a n d /v18=1) and
to the /v18=1 transitions of the main isotopologue. However,
it was necessary to increase the column density and linewidth
to fit the transitions of the /v18=2a n d /v14=1 states. The fit
to the population diagram of the main isotopologue includingthe three vibrationally excited states suggests a temperature of
∼250 K (Fig. A.23 ). This explains why our 170 K model needs
higher column densities to reproduce the intensities of the /v1
8=2
and /v14=1 transitions. Here again, a more complex model with
a nonuniform physical structur e would be necessary to fit all
transitions in a consistent way. However, given that our simpleLTE model yields a good fit to the /v1
8=1 transitions of the main
isotopologue and all transitions of the13C isotopologues with a
single set of parameters, we consider that the derived12C/13C
column density ratios are reliable.
On the basis of the LTE model obtained above, we were
able to identify emission from the doubly substituted13C
isotopologue of methyl cyanide,13CH 313CN. One transition
at 107 108 MHz is well detected, and a group of transitions
at 89 270 MHz is relativel y well detected (Fig. A.24 ). Given
that the column density ratio of the singly to doubly substi-tuted isotopologues is very close to the ratio between the main
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A. Belloche et al.: Deuterated complex organic molecules in Sgr B2(N2)
Table 4. Parameters of our best-fit LTE model (or upper limit) of selected (complex) organic molecules toward Sgr B2(N2).
Molecule StatusaNdetbSizecTrotdNeCfΔVgVoffh Nref
Ni30 mj
(/prime/prime)( K ) ( c m−2)( k m s−1)( k m s−1)
CH 3CN, /v18=1⋆d 20 1.40 170 2.2 (18) 1.00 5.4 -0.5 1 y
/v18=2 d 8 1.40 170 7.5 (18) 1.00 6.5 –0.5 0.29 y
/v14=1 t 1 1.40 170 2.0 (19) 1.00 6.5 –0.5 0.11 y
13CH 3CN, /v1=0 d 8 1.40 170 1.1 (17) 1.18 5.4 –0.5 21 y
/v18=1 d 3 1.40 170 1.1 (17) 1.18 5.4 –0.5 21 y
CH 313CN, /v1=0 d 7 1.40 170 1.1 (17) 1.18 5.4 –0.5 21 y
/v18=1 d 9 1.40 170 1.1 (17) 1.18 5.4 –0.5 21 y
13CH 313CN d 1 1.40 170 4.7 (15) 1.18 5.4 –0.5 466 n
CH 3C15N t 0 1.40 170 8.3 (15) 1.18 5.4 –0.5 266 n
CH 2DCN d 6 1.40 170 8.3 (15) 1.18 5.4 –0.6 266 n
C2H5CN⋆d 154 1.20 150 6.2 (18) 1.38 5.0 –0.8 1 y
13CH 3CH 2CN d 54 1.20 150 1.9 (17) 1.38 5.0 –0.8 32 y
CH 313CH 2CN d 38 1.20 150 1.9 (17) 1.38 5.0 –0.8 32 y
CH 3CH 213CN d 37 1.20 150 1.9 (17) 1.38 5.0 –0.8 32 y
C2H5C15N d 9 1.20 150 1.2 (16) 1.38 5.0 –0.8 500 n
CH 2DCH 2CN (out of plane) t 2 1.20 150 3.0 (15) 1.38 5.0 –0.8 2045 n
CH 2DCH 2CN (in plane) n 0 1.20 150 <1.5 (15) 1.38 5.0 –0.8 >4091 n
CH 3CHDCN t 1 1.20 150 3.0 (15) 1.38 5.0 –0.8 2045 n
C2H3CN, /v1=0⋆d 44 1.10 200 4.2 (17) 1.00 6.0 –0.6 1 y
/v111=1 d 30 1.10 200 4.2 (17) 1.00 6.0 –0.5 1 y
/v115=1 d 20 1.10 200 4.2 (17) 1.00 6.0 –0.5 1 y
/v111=2 d 6 1.10 200 4.2 (17) 1.00 6.0 –0.5 1 y
13CH 2CHCN d 10 1.10 200 2.1 (16) 1.38 6.0 –0.6 20 y
CH 213CHCN d 9 1.10 200 2.1 (16) 1.38 6.0 –0.6 20 y
CH 2CH13CN d 8 1.10 200 2.1 (16) 1.38 6.0 –0.6 20 y
C2H3C15N n 0 1.10 200 <3.4 (15) 1.38 6.0 –0.6 >122 n
cis-CHDCHCN n 0 1.10 200 <3.4 (15) 1.38 6.0 –0.6 >122 n
trans- CHDCHCN n 0 1.10 200 <3.4 (15) 1.38 6.0 –0.6 >122 n
CH 2CDCN n 0 1.10 200 <2.1 (15) 1.38 6.0 –0.6 >203 n
HC 3N,/v17=1⋆d 6 1.30 170 3.5 (17) 1.44 5.0 –0.7 1 y
H13CCCN, /v1=0 d 2 1.30 170 1.7 (16) 1.44 5.0 –0.7 20 y
/v17=1 d 4 1.30 170 1.7 (16) 1.44 5.0 –1.0 20 y
HC13CCN, /v1=0 d 3 1.30 170 1.7 (16) 1.44 5.0 –0.7 20 y
/v17=1 d 3 1.30 170 1.7 (16) 1.44 5.0 –1.0 20 y
HCC13CN, /v1=0 d 3 1.30 170 1.7 (16) 1.44 5.0 –0.7 20 y
/v17=1 d 3 1.30 170 1.7 (16) 1.44 5.0 –1.0 20 y
H13C13CCN t 1 1.30 170 7.2 (14) 1.44 5.0 –0.7 480 n
H13CC13CN t 0 1.30 170 7.2 (14) 1.44 5.0 –0.7 480 y
HC13C13CN t 1 1.30 170 7.2 (14) 1.44 5.0 –0.7 480 n
HC 315N t 0 1.30 170 1.2 (15) 1.44 5.0 –0.7 300 y
DC 3N t 0 1.30 170 3.0 (14) 1.51 5.0 –0.5 1144 n
CH 3OH, /v1t=1⋆d 16 1.40 160 4.0 (19) 1.00 5.4 –0.2 1 y
CH 2DOH t 2 1.40 160 4.8 (16) 1.15 5.4 –0.5 828 n
CH 3OD n 0 1.40 160 <2.6 (16) 1.05 5.4 –0.5 >1524 n
C2H5OH⋆d 168 1.25 150 2.0 (18) 1.24 5.4 0.0 1 y
CH 3CH 2OD n 0 1.25 150 <3.0 (16) 2.96 5.4 0.0 >67 n
CH 3CHDOH n 0 1.25 150 <3.0 (16) 2.96 5.4 0.0 >67 n
CH 2DCH 2OH (out of plane) n 0 1.25 150 <3.0 (16) 2.96 5.4 0.0 >67 n
CH 2DCH 2OH (in plane) n 0 1.25 150 <2.1 (16) 2.96 5.4 0.0 >96 n
CH 3OCHO, /v1t=0⋆d 90 1.50 150 1.2 (18) 1.23 4.7 –0.4 1 y
/v1t=1 d 35 1.50 150 1.2 (18) 1.23 4.7 –0.4 1 y
CH 2DOCHO (out of plane) n 0 1.50 150 <2.5 (16) 1.07 4.7 –0.4 >50 n
CH 2DOCHO (in plane) n 0 1.50 150 <7.3 (15) 0.52 4.7 –0.4 >167 n
Notes.(a)d: detection, t: tentative detection, n: nondetection.(b)Number of detected lines (conservative estimate, see Sect. 3). One line of a given
species may mean a group of transitions of that species that are blended together.(c)Source diameter ( FWHM ).(d)Rotational temperature.(e)Total
column density of the molecule. X(Y) means X×10Y.(f)Correction factor that was applied to the column density to account for the contribution
of vibrationally or torsionally excited states or other conformers (e.g., gauche for ethanol), in the cases where this contribution was not included in
the partition function of the spectroscopic predictions. For deuterated methyl formate, it is the scaling factor used to compute the column densityof each conformer as if it were an independent species.
(g)Linewidth ( FWHM ).(h)Velocity offset with respect to the assumed systemic velocity of
Sgr B2(N2), Vlsr=74 km s−1.(i)Column density ratio, with Nrefthe column density of the previous reference species marked with a ⋆.(j)Detected
(y) or not detected (n) toward Sgr B2(N) (N1 and /or N2) with the IRAM 30 m telescope ( Belloche et al. 2013 ).
A91, page 7 of 66 | 10.1051_0004-6361_201527268 | page_0006 |
A&A 587, A91 (2016)
Fig. 1. Deconvolved major, minor, and mean sizes (FWHM) derived for uncontaminated C 2H5CN transitions detected toward Sgr B2(N2) and
plotted as a function of upper level energy. The symbols code for the spectral setup (S1 to S5, like in Table 2). In each panel, the dashed line
indicates the median value.
isotopologue and those that are singly substituted, we consider
the identification of13CH 313CN as secure.
Our LTE modeling indicates that the15N isotopologue con-
tributes significantly to the emission detected at 107 054 MHz
and 107 060 MHz (Fig. A.25 ). Since there is no clearly de-
tected line, we do not consider this identification as secure. Thederived column density is, therefore, relatively uncertain andshould rather be considered as an upper limit.
Finally, using the same parameters as for the other isotopo-
logues, we obtain a secure identification of singly deuteratedmethyl cyanide, CH
2DCN, with about six transitions clearly de-
tected (Fig. A.26 ). The rotation temperature derived from the
population diagram is consistent with the assumed temperaturewithin 2.4σ(Table 3and Fig. A.27 ). The source size can be
measured for three of the detected transitions and is found to
be consistent with the size derived from the
13C isotopologues.
5.3. Deuterated cyanoacetylene DC 3N
Cyanoacetylene is detected toward Sgr B2(N2) in its vibrational
ground state (Fig. A.28 ) as well as in many vibrationally excited
states: /v17=1( F i g . A.29 ),/v17=2( F i g . A.30 ),/v16=1( F i g . A.31 ),
/v15=1a n d /v17=3( F i g . A.32 ), and /v16=/v17=1( F i g . A.33 ).
In addition, emission from within the following excited states istentatively detected: /v1
4=1 (one detected line, Fig. A.34 ),/v17=4
and /v15=/v17=1 (significantly contributes to detected signal,
but no line individually detected, Fig. A.35 )6,a n d /v16=2 (one
detected line, Fig. A.36 ).
The three singly substituted13C isotopologues of
cyanoacetylene are also clearly detected in their vibrational
ground state (Figs. A.37 –A.39 )a n di n /v17=1( F i g s . A.40 –A.42 ).
HC13CCN is also detected in /v17=2( F i g . A.43 ) while the two
other isotopologues are only tentatively detected in this state(Figs. A.44 andA.45 ). HC
13CCN and HCC13CN are tentatively
detected in /v16=1 with one detected line each (Figs. A.46 and
6The current model is somewhat inconsistent with the observed spec-
trum at 92 129 MHz (blend of /v17=41 0−2–9 2and 10 4–9 4)a n d
100 431 MHz ( /v15=/v17=1l=0−110–1 0 0) but this is most likely
due to resonant interactions between /v17=4a n d /v15=/v17=1, which are
not well accounted for in the spectroscopic predictions. The frequen-cies of these transitions may well be o ffb yaf e wM H z( s e eC D M S
documentation and Sect. 4.4.33 of Belloche et al. 2013 ).A.47 ). Emission of H13CCCN in /v16=1 significantly contributes
to the detected signal, but this state cannot be unambiguously
identified (Fig. A.48 ).
Two doubly substituted13C isotopologues of cyanoacety-
lene, H13C13CCN and HC13C13CN are tentatively detected in
their vibrational ground state with one line each (Figs. A.49
andA.50 ). The third, H13CC13CN has no clearly detected line,
but the model using the same parameters as the former two iso-
topologues is fully consistent with the signal detected around
105 328 MHz (Fig. A.51 ). Therefore we consider this species as
tentatively detected too.
The15N isotopologue HC 315N is not unambiguously de-
tected in its vibrational ground state, but if we assume a
14N/15N isotopic ratio of 300, it contributes significantly to the
detected signal at 88 334 MHz and 105 999 MHz and is there-
fore included in our model (Fig. A.52 ). The column density of
this isotopologue should rather be considered as an upper limit.
The fits to the integrated intensity maps suggest that the size
of the emission decreases with increasing energy of the vibra-
tional state from within which the lines are emitted. Since our
model cannot account for a nonunifo rm physical structure, we
defined two groups of vibrational states: /v1=0a n d /v17=1
were modeled with a source size of 1 .3/prime/primewhile the higher ex-
cited states were modeled assuming 0 .9/prime/prime.
The fits to the population diagrams of the singly substituted
13C isotopologues including both /v1=0a n d /v17=1 yield rota-
tional temperatures of ∼170–180 K (Table 3,F i g s . A.53 –A.55 ).
With a temperature of 170 K and a source size of 1 .3/prime/prime,t h e
emission of all isotopologues reported above is well fitted up
to/v17=1, except for the vibrational ground state of HC 3N: its
transitions are very optically thick ( τmax∼30) and cannot be
reproduced with our simple model. For the vibrationally excited
states of the main and singly substituted13C isotopologues above
/v17=1, we assume a source size of 0 .9/prime/primeand obtain a very good
fit to the observed spectra with a temperature of 200 K and a
unique column density (divided by 20 for the13C isotopologues)
that is 1.5 times higher than for the model of the lower states.
Assuming the same parameters as derived above for the vi-
brational ground state, we looked for emission of deuterated
cyanoacetylene DC 3N. The molecule seems to contribute at a
level of∼70% to the signal detected at 101 315 MHz (Fig. A.56 ).
The rest of the emission comes from a transition of CH 2CO in its
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A. Belloche et al.: Deuterated complex organic molecules in Sgr B2(N2)
vibrationally excited state /v19=1. The detection of DC 3N is only
tentative, and its column density should rather be considered as
an upper limit.
5.4. Deuterated methanol CH 2DOH
Methanol and its13Ca n d18O isotopologues are well detected
toward Sgr B2(N2). The detected lines and detailed modeling of
these species is presente d in a companion paper ( Müller et al.
2016b ). We report in Table 4the parameters derived in that
paper for the main isotopologue based on the analysis of allisotopologues.
Assuming the same source size and rotational tempera-
ture, we obtain a tentative detection of CH
2DOH, with two
lines detected at 91 587 MHz (4 1,3e0–40,4e0) and 99 672 MHz
(61,5e0–60,6e0), two lines tentatively detected at 85 600 MHz
(62,4e1–61,6o1) and 94 563 MHz (1 1,0o1–10,1o1), and a
few other lines contributing significantly to the detected signal(Fig. A.57 ). The line appearing at 91 589 MHz in the full syn-
thetic model with no counterpart in the observed spectrum corre-
sponds to two transitions of acetone (23
18,6–23 17,7of the EE state
and 23 18,6–23 17,7of the AE state). While acetone is unambigu-
ously detected in our ALMA spectrum of Sgr B2(N2), a signif-
icant number of predicted lin es of acetone do not match the ob-
served spectrum. The spectrosc opic predictions are not accurate
enough for this set of problematic lines, the line at 91 589 MHz
being one of those. The ALMA spectrum suggests that the truefrequency could be 91 592 MHz for this acetone line. The source
size derived from the maps of the two detected CH
2DOH lines
is uncertain but the emission looks compact in the integrated in-tensity maps and is consistent with the source size assumed forthe modeling.
5.5. Upper limits
5.5.1. Deuterated methanol CH 3OD
CH 3OD is not unambiguously detected toward Sgr B2(N2).
It may significantly contribute to the emission detectedat 90 743 MHz (blend of 10
1,1–92,1and 2 1,0–11,0), 110 951 MHz
(41,0–40,0), 111 846 MHz (5 1,0–50,0), and 113 352 MHz (6 1,0–
60,0), but there is no clearly detected line (Fig. A.58 ). Assuming
the same parameters as for methanol (Sect. 5.4), we derive a col-
umn density upper limit that is a factor 1.8 times lower than the
column density tentatively derived for CH 2DOH (Table 4). This
upper limit corresponds to the synthetic spectrum shown in red
in Fig. A.58 .
5.5.2. Deuterated vinyl cyanide CHDCHCN and CH 2CDCN
Many lines of vinyl cyanide are detected in its ground state
and vibrationally excited states /v111=1,/v115=1, and /v111=2
(Figs. A.59 –A.62 ). The sizes derived from the corresponding in-
tegrated intensity maps tend to decrease with increasing energy,
from∼1.2/prime/primeforEup<100 K to∼0.8/prime/primefor higher energy tran-
sitions. As a compromise we adopt a source size of 1 .1/prime/prime. With
this source size, the analysis of the population diagram yields a
temperature of∼200 K (Table 3and Fig. A.63 ). Transitions from
within even higher vibrationally excited states are also detectedtoward Sgr B2(N2), but we do not report about these states.
Transitions of all three singly substituted
13C isotopologues
of vinyl cyanide are also clearly detected (Figs. A.64 –A.66 ;s e e
also Müller et al. 2008 for a previous single-dish detection).
Only a few lines are su fficiently free of contamination to allowfor a size measurement in the corresponding integrated inten-
sity maps. The outcome is more uncertain than for the main iso-
topologue, but is consistent with the source size adopted above.Because of the smaller number of detected lines, the population
diagrams have a higher dispersion than for the main isotopo-
logue and the rotational temperature is less well constrained butthe fits to all three diagrams are consistent with a temperature of
about 200 K (Figs. A.67 –A.69 ).
As a result of this analysis, we adopt a source size of 1 .1
/prime/prime
and a temperature of 200 K for vinyl cyanide and its isotopo-
logues. With these parameters, we do not detect the15Ni s o -
topologue. We also looked for the singly deuterated species cis-
CHDCHCN, trans -CHDCHCN, and CH 2CDCN, but did not de-
tect them. Column density upper limits are reported in Table 4.
5.5.3. Deuterated ethanol CH 3CH 2OD, CH 3CHDOH,
and CH 2DCH 2OH
Ethanol and its13C isotopologues are well detected toward
Sgr B2(N2). The detected lines and detailed modeling of these
species is presented i n a companion paper ( Müller et al. 2016b ).
We report in Table 4the parameters derived in that paper for the
main isotopologue based on the analysis of all isotopologues.
Assuming the same LTE parameters as for the main isotopo-
logue, we searched for all singly deuterated isotopologues ofethanol. None is detected. Upper limits to their column densities
are reported in Table 4.
5.5.4. Deuterated methyl formate CH 2DOCHO
Methyl formate is clearly seen toward Sgr B2(N2), with dozens
of transitions detected in both its ground and first torsionalstates (Figs. A.70 andA.71 ). We derive a median source size
of 1.5
/prime/primefrom fits to the integrated intensity maps of its numer-
ous uncontaminated lines. The formal fit to its population di-agram including both states yields a rotational temperature of
∼140 K (Fig. A.72 and Table 3). We used a temperature of
150 K in our model, which fits the ALMA spectrum very well,apart from a few discrepancies that we describe now. The rea-
son why the synthetic spectrum of the ground state poorly fits
the ALMA spectrum at 100 080 MHz is unclear. It may be dueto the nearby HC
3N 11–10 transition at 100 076 MHz, which
is probably affected by self-absorption and /or spatial filtering
and is by far overestimated by our simple LTE model. Thediscrepancy around 110 226 MHz is due to contamination by dif-
fuse cloud absorption in
13CO 1–0 that is not yet included in our
full model. Similar contamination by c-C3H2absorption features
not yet implemented in our full model likely explains the smalldiscrepancies for the /v1
t=1 transitions around 85 370 MHz.
Assuming the same LTE parameters as for the main isotopo-
logue, we searched for the in-plane and out-of-plane conformersof CH
2DOCHO toward Sgr B2(N2) but none of them is detected.
Upper limits to their individual column densities are reported in
Table 4.
6. Discussion
6.1. Comparison to other observations
The levels of deuterium fractionation derived in Sect. 5for (com-
plex) organic molecules toward Sgr B2(N2) are summarized inTable 5and shown in Fig. 2.
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A&A 587, A91 (2016)
Table 5. Deuterium fractionation of selected (complex) organic
molecules toward Sgr B2(N2) compared to predictions of astrochem-ical models.
Molecule Statusa[XD]/[XH]
N2bT14cA12d
%% %
CH 2DCN d 0.38 3.6–0.15 2.3–6.3
CH 2DCH 2CN (oop) t 0.05 – –
CH 2DCH 2CN (ip) n <0.024 – –
CH 3CHDCN t 0.05 – –
cis-CHDCHCN n <0.8 – –
trans- CHDCHCN n <0.8 – –
CH 2CDCN n <0.5 – –
DC 3N t 0.09 – 5.4–1.1
CH 2DOH t 0.12 5.5–0.51 2.4–2.4e
CH 3OD n <0.07 3.5–0.3 –e
CH 3CH 2OD n <1.5 – –
CH 3CHDOH n <1.5 – –
CH 2DCH 2OH (oop) n <1.5 – –
CH 2DCH 2OH (ip) n <1.0 – –
CH 2DOCHO (oop) n <2.0 14–0.43f–
CH 2DOCHO (ip) n <0.6 7–0.22f–
Notes. The notations oop and ip describe the position of the deuterium
and stand for out of plane and in plane, respectively.(a)d: detection,
t: tentative detection, n: nondetection.(b)Deuterium fractionation mea-
s u r e dt o w a r dS g rB 2 ( N 2 ) .(c)Deuterium fractionation predicted by the
model of Taquet et al. (2014 ) in the hot corino at the beginning and end
of the Class 0 phase.(d)Deuterium fractionation predicted by the model
ofAikawa et al. (2012 ) in the hot corino at the beginning and end of
the Class 0 phase.(e)The model of Aikawa et al. (2012 ) was not de-
signed to predict the abundance ratios of deuterated isomers: it assumesstatistical branching ratios.
(f)The model of T a q u e te ta l . (2014 ) does
not distinguish between the in-plane and out-of-plane conformers. Thevalues listed here assume a statistical distribution (2:1).
6.1.1. Deuterated methyl cyanide
The detection of CH 2DCN toward Sgr B2(N2) is the most se-
cure among the deuterated species reported here (Sect. 5.2and
Fig.A.26 ). On the basis of the LTE modeling of methyl cyanide
and its various isotopologues, we derive a deuterium fraction-ation of 0.4% for this molecule. This is a factor 2.6 lower
than the fractionation reported by Gerin et al. (1992 )t o w a r d
Orion KL (1%). Along with this first interstellar detection, theseauthors also reported a tentative detection toward the hot core
G34.26+0.15 that, if true, would indicate a similar level of deu-
terium fractionation as toward Orion KL. The di fference with the
level measured in Sgr B2(N2) is probably not significant because
the Orion KL and G34.26 +0.15 values may su ffer, as mentioned
by these authors, from a lack of knowledge of the source sizeand opacity of the lines of the main isotopologue.
A detection of deuterated methyl cyanide toward the Class 0
(low-mass) protostar IRAS 16293–2422 was also reported in
Taquet et al. (2014 ) based on an unpublished analysis. They
quote a deuterium fractionation of 1 .3%, a factor 3.4 higher than
the one obtained for Sgr B2(N2).
6.1.2. Deuterated ethyl cyanide
Both deuterated isotopologues of ethyl cyanide are tenta-tively detected toward Sgr B2(N2) (Sect. 5.1and Figs. A.10
andA.11 ). We derive a deuterium fractionation of ∼0.05% for
both CH
2DCH 2CN (in its out-of-plane conformation) and the
chiral molecule CH 3CHDCN. The upper limit obtained for theFig. 2. Deuterium fractionation of (complex) organic molecules toward
Sgr B2(N2). Secure detections are indicated with a filled square, ten-tative detections with an empty square, and upper limits with an arrowpointing to the left. The notations oop and ip describe the position ofthe deuterium and stand for out of plane and in plane, respectively.
in-plane conformer of CH 2DCH 2CN (Fig. A.12 ) is still consis-
tent with the expectation that it should be half as abundant asthe out-of-plane conformer. If we assume this expected ratio,then the total deuterium fractionation for CH
2DCH 2CN would
be∼0.075%, a factor 1.5 times higher than for CH 3CHDCN.
This would be consistent with th e statistical expectation because
the methyl group at the end of the carbon chain has three equiva-
lent hydrogen atoms while the middle chain group has only two.
The deuterium fractionation derived for ethyl cyanide to-
ward Sgr B2(N2) is nearly one order of magnitude lower thanfor methyl cyanide (0.4%), but similar within a factor two to
methanol (0.12%) and cy anoacetylene (0.09%).
Margulès et al. (2009 ) reported a detection of the
15Ni s o -
topologue of ethyl cyanide toward Orion KL but obtained onlyan upper limit for CH
2DCH 2CN. They derived a column density
ratio [CH 2DCH 2CN (oop)]/[C2H5C15N]<0.33, which trans-
lates into [CH 2DCH 2CN (oop)]/[C2H5CN]<0.2% using the
14N/15N isotopic ratio of 148 ±74 derived by Daly et al. (2013 ).
Daly et al. (2013 ) claimed tentative detections of both deuter-
ated isotopologues of ethyl cyanide with a deuterium fractiona-tion of 2% based on the same survey of Orion KL. No detected
transitions are shown in that study, though, and their Table 3 ac-
tually reports upper limits for the deuterated species. Given thelower deuterium fractionation obtained by Gerin et al. (1992 )
for methyl cyanide toward Orion KL (1%) and the order of
magnitude difference in deuterium fractionation between methyl
cyanide and ethyl cyanide obtained here toward Sgr B2(N2), a
deuterium fractionation of 2% for ethyl cyanide in Orion KL
sounds unlikely and questions the tentative detection of Daly
et al. (2013 ).
6.1.3. Deuterated methanol
CH 2DOH is tentatively detected toward Sgr B2(N2) (Sect. 5.4
and Fig. A.57 ). The deuterium fractionation we derive for this
isotopologue is 0.12%, a factor ∼3 lower than the value we
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A. Belloche et al.: Deuterated complex organic molecules in Sgr B2(N2)
obtain for methyl cyanide, the d euterated species of which
is securely identified in our ALMA spectrum of Sgr B2(N2)
(Sect. 6.1.1 ). Therefore, even if the di fference in deuterium
fractionation between methanol and methyl cyanide is a priori
surprising, the fact that it is lower for methanol gives us more
confidence in the detection of CH 2DOH. The deuterium frac-
tionation derived for CH 2DOH is a factor five lower than to-
ward the Compact Ridge in Orion KL (0.58%, Neill et al. 2013 ),
about one order of magnitude lower than toward the high-massprotostellar objects surveyed by Fontani et al. (2015 )a n dt h e
intermediate-mass protostar NGC 7129 FIRS 2 (2%, Fuente
et al. 2014 ), and more than two orders of magnitude lower
than toward Class 0 protostars which have values between 19%and 33% ( Parise et al. 2006 )
7.
Evidence for the presence of CH 3OD is too tenuous in our
ALMA spectrum of Sgr B2(N2) to claim a detection, even a
tentative one (Sect. 5.5.1 ). Still, we cannot completely exclude
that CH 3OD is present at the level indicated by our upper limit.
The synthetic spectrum shown in Fig. A.58 indicates that a
large fraction (>50%) of the flux density detected at 90 744,
99 964, 110 951, and 113 352 MHz may well be emitted by this
molecule. If this is true, the deuterium fractionation of methanolwould then be∼0.07% for CH
3OD. This would be nearly one
order of magnitude lower than toward the Compact Ridge in
Orion KL (0.5%, Neill et al. 2013 ) and about 50 times lower
than toward Class 0 protostars (1.6%–4.7%, Parise et al. 2006 ).
A detection of CH 3OD toward Sgr B2 was reported by
Gottlieb et al. (1979 ) with the 36 foot radio telescope of the
National Radio Astronomy Observatory at Kitt Peak ( HPBW∼
74/prime/prime). These authors detected a line at the frequency ex-
pected for the pair of partially blended transitions 2 −1–1−1E
(90 703.6 MHz, Eu/kB=11.3K )a n d2 0–10A (90 705.8 MHz,
Eu/kB=6.5 K), but they did not detect the nearby 2 1–11Et r a n -
sition (90 743.5 MHz, Eu/kB=15.6K ) ,w h i c hi si nf a c te x -
pected to be partially blended with the 10 1–92A transition
(90 741.7 MHz, Eu/kB=124 K). The former two transitions
are blended with deep HNC absorption features produced bydiffuse clouds along the line of sight in our ALMA spectrum
of Sgr B2(N2). This prevents th eir detection in our spectrum
(see Fig. A.58 ). Our LTE model shows that, for a temperature
of 160 K, the latter two transitions are expected to be as strong as
the former two. We conclude from this that either the assignment
of the 90 704 MHz line to CH
3OD in the Kitt Peak spectrum was
not correct, or the line reported by Gottlieb et al. (1979 ) traces
low-excitation emission of CH 3OD. Given that the line detected
in emission in the Kitt Peak sp ectrum dominates over the ab-
sorption features, opposite to what is seen in the ALMA spec-trum, this emission line, if real, must come from a region more
extended than the Sgr B2 continuum emission that is absorbed
by the diffuse clouds along the line of sight. Such an extended
emission would be filtered out in our ALMA spectrum.
Gottlieb et al. (1979 ) derived a ratio
[CH
3OD]/[13CH 3OH]∼0.18 for Sgr B2. This translates
into [CH 3OD]/[CH 3OH]∼0.7%, assuming a12C/13C isotopic
ratio of 25 as derived for methanol toward Sgr B2(N2) in the
companion paper Müller et al. (2016b ). This is an order of
7There was an issue with the spectroscopic predictions used in
the early studies reporting CH 2DOH column densities (B. Parise,
priv. comm.). We compared the Sμ2values listed in Table 1 of Parise
et al. (2002 ) ,w h i c hw e r ea l s ou s e di n Parise et al. (2006 ), with the cur-
rent JPL catalog. The new values of the selected transitions are a factor2.1±0.4 times higher on average than the old values. The partition func-
tion is the same in both cases. As a result, the column densities reportedfor CH
2DOH in both articles were overestimated by a factor of ∼2.magnitude higher than our upper limit of 0.07% derived in
Sect. 5.4. This discrepancy seriously questions the detection
of CH 3OD reported by Gottlieb et al. (1979 )t o w a r dS g rB 2 ,
unless deuteration of methanol is more e fficient by one order of
magnitude on large scales in the Sgr B2 cloud compared to the
embedded hot cores. Comito et al. (2003 ) derived an abundance
ratio [HDO]/[H2O]∼0.06% toward the Sgr B2 hot cores and
their T<100 K envelope, and even lower values of ∼0.013%
and∼0.02% (uncertain within a factor two) were obtained for
[DCN]/[HCN] and [DCO+]/[HCO+] in the molecular ridge
close to Sgr B2(M) ( Jacq et al. 1999 ). Deuterium fractionation
thus does not appear to be generally more e fficient on larger
scales in Sgr B2, which again questions the detection of CH 3OD
reported by Gottlieb et al. (1979 ).
6.1.4. Deuterated cyanoacetylene
The detection of DC 3N reported toward Sgr B2(N2) is only ten-
tative (Sect. 5.3and Fig. A.56 ). We obtain a deuterium fraction-
ation of 0.09%, similar to the values obtained for methanol and
ethyl cyanide. DC 3N was first detected toward TMC 1 with a
deuterium fractionation of 2–8% ( Langer et al. 1980 ), revised
to a lower value of 1.5% by Turner (2001 ). High values were
reported with single dish telescopes for a number of other cold
dense cores (5%–10%, Howe et al. 1994 )a sw e l la sf o rap r o t o -
star in a stage of “Warm Carbon-Chain Chemistry” ( ∼3%,Sakai
et al. 2009 ). A tentative detection toward the Compact Ridge
and the Hot Core of Orion KL was recently reported with a deu-terium fractionation of 1 .5%±0.9% ( Esplugues et al. 2013 ). A
tentative detection was also recently reported toward the high-
mass protostar NGC 2264 CMM3 (1.8% ±1.5%, Watanabe
et al. 2015 ). The deuterium fractiona tion of cyanoacetylene ten-
tatively derived toward Sgr B2(N2) is thus at least one order of
magnitude lower than in Orion and NGC 2264 CMM3 (if con-firmed) and even two orders of magnitude lower than in cold
dense gas.
6.1.5. Deuterated vinyl cyanide
The column density upper limits reported in Sect. 5.5.2
yield deuterium fractionations <0.8%,<0.8%, and<0.5%
for cis-CHDCHCN, trans- CHDCHCN, and CH 2CDCN,
respectively. We are not aware of any reliable detection of
deuterated vinyl cyanide in the interstellar medium.
6.1.6. Deuterated ethanol
The column density upper limits reported in Sect. 5.5.3 yield
deuterium fractionations <1.5%,<1.5%,<1.5%, and<1.0%
for CH 3CH 2OD, CH 3CHDOH, and the out-of-plane and in-
plane conformers of CH 2DCH 2OH, respectively. The latter
two translate into a total deuterium fractionation <2.5% for
CH 2DCH 2OH. These upper limits are about one order of mag-
nitude higher than the deuterium fractionation measured for
methanol (Sect. 6.1.3 ). They are thus not very constraining.
We are not aware of any detection of deuterated ethanol in theinterstellar medium.
6.1.7. Deuterated methyl formate
The column density upper limits reported in Sect. 5.5.4 yield
deuterium fractionations <2.0% and<0.6% for the out-of-plane
and in-plane conformers of CH 2DOCHO, respectively. This
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174901-3 P.-M. Lam and Y. Zhen J. Chem. Phys. 143, 174901 (2015)
g(f)+1
2Asin4α
r2+U(r)−sin 2α
2rM=0. (10)
Three equations (8)–(10) can be solved to obtain the remaining
three unknowns quantities α,r, and M.
In the high-force limit, Neukirch and Marko28have given
the solutions in closed form. Define a quantity Kas
K=
9π/8ν2LBkBT/g(f). (11)
The plectoneme radius rand angleαare given by
r=logK/(2κD), (12)
α=2r2g(f)/(3A)1/4. (13)
The torque Mis given by
M=2A
rsin3αcosα
cos 2α. (14)
A Taylor expansion of this expression for small αand
substituting the results, Eqs. (12) and (13), for αandryields
M≈[(32/27)A]1/4g(f)3/4/√κD
×
log
9π/8ν2LBkBT/g(f) 1+α2.(15)
Another quantity of experimental interest is the slope of
the average extension q=∂⟨X⟩/∂∆Lk=−∂2G/∂f∂∆Lk
=−2π∂M/∂f. Using Eq. (10) for M, this becomes q
=−4πrg′(r)/sin 2α. Taylor expanding this for small αand
substituting Eqs. (12) and (13) for αandryields
q=(6A
κD2g(f))1/4
log
9π/8ν2LBkBT/g(f)
×g′(f)(1+2α2/3). (16)
Using Eqs. (15) and (16) and g(f)=f−kBT
f/A, the
slope and torque calculated are in qualitative agreement with
experiment.28Experimental values of A/kBT=46, 47, 44,
45 nm at 50, 100, 200, and 500 nM salt and C/kBT=94 nm
are used in the calculation. We will show in Sec. III that using
a more accurate form of g(f)can significantly improve on the
agreement with experiment.
III. CALCULATION USING AN IMPROVED
FREE ENERGY
In this section, we give our calculation of the slope and the
torque using an improved form of the untwisted free energy.
The force-extension curve in the worm like chain (WLC)
model is given by the widely used interpolation formula26
f=(kBT)
LpX
L+1
4(
1−X
L)−2
−1
4, (17)
where Lphere is the persistence length, related to the bending
rigidity A, byA=kBT Lp, and Xis the extension. The negative
of the free energy per unit length g(f)is obtained by a
Legendre transform
Lg(f)=f X−W(X), (18)where
W(X)=X
0dX′f(X′) (19)
is the work done in extending the polymer. The functions
gandWdepend also on the persistence length Lp. From
Eq. (17), the extension Xis an implicit function of the force f.
Since the extension is a single-valued, monotonic increasing
function of f, we can define the inverse function Xf(f)which
gives the extension Xas a function of the force f. Even
though this function cannot be obtained analytically, it can be
calculated numerically to high accuracy. Substituting Eq. (17)
into Eq. (19), the function Wcan be calculated analytically,
W(X(f))
=LkBT
4LpXf(f)
L(
2Xf(f)
L−1)
+(
1−Xf(f)
L)−1.(20)
From Eq. (18), the negative of the free energy per unit length
is given as a function of the force fby
g(f)=1
Lf Xf(f)−kBT
4Lp
×Xf(f)
L(
2Xf(f)
L−1)
+(
1−Xf(f)
L)−1. (21)
We will use this form of the free energy in Eqs. (15) and (16)
to calculate the torque Mand slope q.
From Eq. (16), in order to calculate the slope q, the
derivative of gwith respect to fis needed. From Eqs. (18)
and (19), this is given by
Lg′(f)=Xf(f). (22)
In Fig. 2, we show our calculation of the slope of the
average extension q=∂⟨X⟩/∂∆Lkobtained using Eq. (16),
FIG. 2. Comparison of experimental and theoretical slopes q=∂⟨X⟩/∂∆Lk
of the average extension, as a function of the applied force, for 50, 100, 200,
and 500 mM salt (top to bottom). Circles are experimental data. Full lines are
our theoretical results using a better form of the free energy. Dashed lines are
theoretical results using approximate form of the free energy. | 10.1063_1.4934988 | page_0003 |
174901-4 P.-M. Lam and Y. Zhen J. Chem. Phys. 143, 174901 (2015)
FIG. 3. Comparison of experimental and theoretical torque as a function of
the applied force, for 50, 100, 200, and 500 mM salt (top to bottom). Circles
are experimental data. Full lines are our theoretical results using a better form
of the free energy. Dashed lines are theoretical results using approximate form
of the free energy.
withgandg′given by Eqs. (21) and (22), together with
results obtained using the approximate forms for gandg′. The
experimental data are directly taken from Fig. 2 of Ref. 28. The
data in Ref. 28 are obtained from Ref. 21. The slope in Ref. 21
is a dimensionless quantity defined as ˜ q=L−1∂⟨X⟩/∂σ, with
σ=(Lk−Lk0)/Lk0, where Lk0≈1500 is the linking number
of the DNA molecule under no external tension or torque. Our
slope qis related to ˜ qbyq=(L/Lk0)˜q=(5.4µm/1500 )˜q
=(3.6 nm )˜q. The experimental data given in Ref. 28 are
actually a factor (−3.6 nm )times the data in Ref. 21. In
Figure 3, we present the results of our calculation for the
torque M, using Eqs. (15) and (21), together with results
obtained using the approximate form, compared with the
experimental data, taken from Fig. 3 of Ref. 21. We can see that
this better form of the free energy improves significantly the
agreement with experiment. The agreement with experiment
is now surprisingly good, except for low salt concentrations.
IV. CONCLUSION
We have shown that by using a better form of the free
energy for the stretched but untwisted part of the DNA, the
Neukirch-Marko model can give quantitative agreement with
experimental results. There is still some disagreement at low
salt concentration, but this is probably due to the inadequacy of
the Debye–Hückel approximation of the Poisson-Boltzmann
equation, which results in imperfect screening of the elec-
trostatic potential at these low salt concentrations. It was
mentioned in Ref. 28 that the disagreement with experiment
may be due to the neglect of confinement entropy.36Since our
results using a better free energy already yield quantitative
agreement with experiment, the e ffect of confinement entropy
is probably small.
Our calculation is based on the model of Neukirch and
Marko.28This theory is an analytic theory, with analyticexpressions for the slope and torque as functions of the
tension. In order to arrive at this theory, several reasonable
simplications have been introduced. It does not incorporate
thermal fluctuations in plectoneme. The argument is that
at least at higher tensions, the fluctuations are small and
can as a consequence be neglected. It also neglects multi-
plectoneme e ffects. The use of a two-cylinder repulsion in
the Debye–Hückel regime is a rough approach not taking into
account the e ffect on plectoneme angle as was shown to be
important by Ubbink and Odijk.35More recent models37,38
have taken these e ffects into account. In Ref. 37, the authors
give results of the slope versus tension, in very good agreement
with experiment. However, for this quantity, the original
theory of Neukirch and Marko also gives good agreement
with experiment. It is the torque versus tension results in the
Neukirch-Marko theory that show the largest disagreement
with experiment, especially for low tension and low salt
concentrations. For the torque versus tension result, the result
of Ref. 37 is not so good. In more recent work,38Marko and
Neukirch have also incorporated the above mentioned e ffects
in their model, but unfortunately they do not give any new
torque versus tension results.
Notwithstanding the clearly better agreement between
theory and experiment achieved in this work, one notes, how-
ever, that it holds as far as the Debye–Hückel approximation
of the Poisson-Boltzmann theory remains valid, i.e., for high
screening /salt concentration only. As one can see from Figs. 2
and 3, the agreement with experiment deteriorates at low salt
concentration for both the slope and the torque.
A closer inspection of the q-f variation, shown in Fig. 2,
indicates that the agreement with experiment at higher applied
tensions (when f >3 pN at 500 mM and f >1 pN at 200 mM).
This is puzzling because the expressions for the free energy
g(f)and twist modulus Cs(f)should be correct for large fand
the fluctuations in plectoneme and multi-plectoneme e ffects
neglected in the model should also decrease with tension. Dhar
and Chaudhuri39and Samuel and Sinha40have explored e ffects
that go beyond the high force limit ( g(f)=f−kBT
f/A).
At these high forces, such e ffects may be relevant. It should
also be pointed out that the force-extension formula given in
Eq. (17) is only an interpretation formula which is convenient
for calculation and should not be considered as a substitute for
analytical or semi-analytic theoretical models in Refs. 39 and
40. In particular, the force-extension curve given by Eq. (19)
did not take into account the entropy of the chain, even when no
external force is applied, as pointed out by Neumann.41Also,
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of thermal fluctuations on DNA elasticity, as studied by Kulic
et al.42,43and Sinha and Samuel.40,44Finally, the Legendre
transform (Eqs. (18) and (19)) was used because we are
considering the long DNA limit. If one were to look at shorter
chains, with chain lengths comparable to the persistence length
of 50 nm, one would need to work with Laplace transforms
instead.41,45,46This is because such short chains are not in the
thermodynamic limit and one has to distinguish between the
isometric ensemble in which the chain ends are held fixed and
the applied force is allowed to fluctuate and the isotensional
ensemble in which the applied force is held fixed and the chain
lengths are allowed to fluctuate. Only in the thermodynamic | 10.1063_1.4934988 | page_0004 |
174901-5 P.-M. Lam and Y. Zhen J. Chem. Phys. 143, 174901 (2015)
limit in which the chain lengths are infinitely long, do the two
ensembles yield identical results.
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J. Chem. Phys. 145, 114901 (2016); https://doi.org/10.1063/1.4962516 145, 114901
© 2016 Author(s).On the influence of the intermolecular
potential on the wetting properties of
water on silica surfaces
Cite as: J. Chem. Phys. 145, 114901 (2016); https://doi.org/10.1063/1.4962516
Submitted: 17 June 2016 • Accepted: 29 August 2016 • Published Online: 16 September 2016
E. Pafong , J. Geske and B. Drossel
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THE JOURNAL OF CHEMICAL PHYSICS 145, 114901 (2016)
On the influence of the intermolecular potential on the wetting properties
of water on silica surfaces
E. Pafong,a)J. Geske, and B. Drossel
Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
(Received 17 June 2016; accepted 29 August 2016; published online 16 September 2016)
We study the wetting properties of water on silica surfaces using molecular dynamics (MD) simu-
lations. To describe the intermolecular interaction between water and silica atoms, two types of
interaction potential models are used: the standard BródkA and Zerda (BZ) model and the Gulmen
and Thompson (GT) model. We perform an in-depth analysis of the influence of the choice of the
potential on the arrangement of the water molecules in partially filled pores and on top of silica
slabs. We find that at moderate pore filling ratios, the GT silica surface is completely wetted by water
molecules, which agrees well with experimental findings, while the commonly used BZ surface is
less hydrophilic and is only partially wetted. We interpret our simulation results using an analytical
calculation of the phase diagram of water in partially filled pores. Moreover, an evaluation of the
contact angle of the water droplet on top of the silica slab reveals that the interaction becomes
more hydrophilic with increasing slab thickness and saturates around 2.5–3 nm, in agreement with
the experimentally found value. Our analysis also shows that the hydroa ffinity of the surface is
mainly determined by the electrostatic interaction, but the van der Waals interaction nevertheless
is strong enough that it can turn a hydrophobic surface into a hydrophilic surface. Published by AIP
Publishing. [http: //dx.doi.org /10.1063 /1.4962516]
I. INTRODUCTION
Water is an essential material in our everyday life and is
the most used solvent for chemical and biological reactions.
Water molecules are highly polar, forming hydrogen-bonded
networks and sharing hydrogen bonds with other molecules.
In particular, water confined within nanoscale geometries of
hydrophilic surfaces is subject to two competing interactions:
the hydrophilic interactions between water molecules and
those between water and surface molecules.
One of the standard systems for studying hydrophilic
interactions with water is silica nanopores such as sols-
gels,1mesoporous silica (MCM-41),2–7Vycor-glasses,8–10
controlled pore glasses (CPGs).11–15Water confined in
silica nanopores or near silica flat surfaces is a topic
which has attracted considerable attention,16–22mainly
because of the relevance of the water-silica interaction
in understanding the water transport in porous rocks,23
nanofluidic devices,24heterogeneous catalysis in mesoporous
materials,15,25and permeation through membrane channels.26
Experimental investigations of water in silica nanopores
have been carried out using NMR spectroscopy,2,12X-ray
and neutron di ffraction,5,6,9,10,27,28quasi-elastic neutron
scattering,3,4Small-angle neutron scattering (SANS),8and
optical Kerr-e ffect spectroscopy,1showing that the dynamics
of water in such pores is slow in comparison to the dynamics
of bulk water. This originates from the strong binding or
trapping of water molecules by silica surfaces as found by
experimental measurements conducted with MCM-41 as well
as CPG pores2,12resulting in a complete coverage of the pore
a)priscel@fkp.tu-darmstadt.desurface at even moderate hydration levels. Accordingly, the
intermolecular interactions between water and silica surfaces
in MD simulations should be set up such that the experimental
results are reproduced.
The influence of the filling ratios on the wetting properties
of water in silica nanopores has been studied by previous MD
research.29–32Such investigations are motivated by the fact that
in experiments the fluid is placed on top of a porous surface and
flows to enter the pores. In the mentioned MD simulations, it
was demonstrated that at all hydration levels water molecules
are absorbed by the Vycor material. However, they have not
shown to what extent the pore surface is wetted, whether
it is only partially wetted or rather completely wetted (as
expected from measurements2,12). Moreover, the confinement
near such hydrophilic surface was found to substantially alter
the dynamic behaviour of water, depending on the filling
ratio,19,33but it has not been checked how this relates to
the configurations that water can take inside the pore. In all
these previous MD analyses, the (12-6) Lennard-Jones (LJ)
potential and the partial charges assigned to each silica atom
site are chosen according to BródkA and Zerda (BZ).34In this
model, the LJ potential parameters for silica oxygen atoms are
approximated from the Kirkwood-Mueller formula,35while
no LJ interaction centers are assigned to silicon and hydrogen
(of the silanol groups) as they are small in size and possess
a low polarizability. In the present investigation, we have
found that water molecules do not completely wet the BZ
silica model surface at intermediate hydration levels. For this
reason, the silica model recently introduced by Gulmen and
Thompson36(GT) has been tested. The GT36potential is
defined similarly to the silica potential by BZ,34however,
a weak short-ranged interaction for silicon and hydrogen
0021-9606/2016/145(11)/114901/9/$30.00 145, 114901-1 Published by AIP Publishing.
| 10.1063_1.4962516 | page_0001 |
114901-2 Pafong, Geske, and Drossel J. Chem. Phys. 145, 114901 (2016)
atoms has been added and the partial charges on each
silica atom are increased. We probed the performance of
both silica models by analyzing the wetting behaviour of
water on silica surfaces and comparing to the experimental
results.2,12,37–39
In the following, we present the results of MD simulations
of water in a cylindrical silica nanopore of roughly 4 nm
diameter and 6 .1 nm height. Additionally, MD simulations of
water droplets wetting silica slabs of varying thicknesses were
performed. The silica nanopores and slabs were created in
our group, with the silanols molecules uniformly distributed
on the surface. For water in the silica pore, we evaluate the
minimum number of water layers necessary to completely
wet a silica surface by looking at the radial and angular
density distribution, as well as the number of hydrogen
bonds formed for di fferent filling ratios of water in the pore.
Furthermore, a phase diagram of the surface tension of the
different configurations adopted by water molecules in the
nanopore is calculated analytically, providing deeper insights
into the relation between the interaction energies and the water
arrangement in the pore.
To complete the work, the contact angle of a water droplet
on a silica flat slab is evaluated and compared between the
two model surfaces. Previous MD investigations have used
the contact angle investigation to approximate LJ parameters
between water and silica atoms40,41but they have not stated
clearly whether the simulations were performed in such a way
that the periodic images provided by the periodic boundary
conditions do not influence the contact angle evaluated. In
our investigation, we run the simulations without periodic
boundary conditions to avoid this issue. Previous experimental
results showed that the wetting properties do not only involve
atoms of layers in the vicinity of the interface but also
the atoms located deeply inside the slab material.37–39,42
Therefore, we measure how the contact angle changes with
the thickness of the slab, showing that a thickness of 2.5–3 nm
is sufficient for MD simulations. In order to disentangle the
contributions of the interfacial electrostatic and van der Waals
(VdW) interactions on the contact angle, we varied these two
contributions in our simulations, showing that the influence of
the electrostatic interaction is considerably larger than that of
the VdW interaction.
II. SIMULATION DETAILS
Classical MD simulations were performed with the
NAMD432.10 simulation package. An amorphous cylindrical
nanopore of roughly 4 nm of diameter and silica slabs of
different thicknesses were fabricated in our group. To create
the pore, a crystalline cell of SiO 2with a box length of
approximately 6 nm was built, the system was melted at
5000 K and cooled to room temperature with the method
described in Ref. 44, and then a cylindrical cavity of ∼4 nm
diameter was cut. The process of fabrication of the silica
cylindrical pore and the silica slab is explained in detail in a
separate paper.44The surface concentration of hydroxyl groups
on the surface is 7 .5 nm−2corresponding to highly hydrated
silica surfaces.34The silica slabs were created following a
similar procedure.TABLE I. LJ potential parameters for silica interaction centers.
Parameters Sites σ(nm) ε(kcal/mol) q (e)
BZ34Si 0.0178a0.000 00 1.283
OSi 0.27 0.457 056 94 −0.629
OH 0.3 0.457 056 94 −0.533
H 0.0178a0.000 00 0.206
GT36Si 0.25 0.000 1 1.28
OSi 0.27 0.457 −0.64
OH 0.307 0.17 −0.74
H 0.1295 0.000 365 7 0.42
aValues were not mentioned in the model and were chosen arbitrarily small.
The silica nanopore and slab contain two types of oxygen
atoms depending on the number of silicon atoms to which
they are connected. There are bridging oxygens (O Si) bonded
to two adjacent silicons and nonbridging oxygens (O H) on
the surface attached to only one silicon. Hydrogen atoms
are attached to the O Hin order to form the silanols groups
(SiOH, Si(OH) 2). The bonded interaction parameters for silica
atoms were obtained from Hill and Sauer.45Apart from the
hydrogen atoms of the silanols groups that are allowed to
rotate, all atoms in the silica pore and slab are immobile,
constrained to a fixed position, whereas water molecules are
free to move within the pore. Liquid water is defined using 2
models: a set of 3 rigid sites given by the SPC /E46model and a
set of 4 sites provided by the TIP4P200547model. The atoms
of the silica substrate are allowed to interact with the water
sites by means of the Coulomb potential and LJ potential in
Eq. (1),
ULJ=4ϵ*
,σ12
r12
i,j−σ6
r6
i,j+
-(1)
which implements the VdW interaction. LJ parameters and
fractional charges for the SiO 2sites are given in Table I.
All simulations were made with the NVT ensemble
with a fixed room temperature T=298 K using a Langevin
thermostat43with a coupling coe fficient of 1.0 ps−1and with
the hydrogen atoms included in the Langevin dynamics. An
integration time step of 2 fs was utilized and the simulations
were run for at least 20 ns. Periodic boundary conditions
were set for the simulations of water in the nanopore allowing
the calculation of the long-range Coulombic electrostatic
interactions with the particle-mesh Ewald sum, using a cut-o ff
of 1.2 nm. No periodic boundary conditions were defined for
the simulation of water wetting silica slabs in order to allow
the calculation of the full electrostatic and VdW interactions
between all the water droplet atoms and silica slab atoms.
III. RESULTS I: WATER IN PARTIALLY
FILLED SILICA PORES
In the following, we investigated the configuration of
water in a partially filled silica pore for the two di fferent
models using MD simulations. Furthermore, we performed an
analytical calculation of the di fferent possible phases of water
in a cylindrical pore that allows us to interpret the findings. | 10.1063_1.4962516 | page_0002 |
114901-3 Pafong, Geske, and Drossel J. Chem. Phys. 145, 114901 (2016)
FIG. 1. Top view of the two initial con-
figurations used in the MD simulations,
labelled in the subsequent figures with
“center” (a) and “surface” (b). Here the
hydration level is 30%. Si, O Si,H, H
are drawn in yellow, blue, and green,
while water atoms O, H are indicated
by red and white, respectively. The pic-
tures were generated using the VMD
program.48
A. MD simulation results
We evaluated the equilibrated configurations of water
in the pore for the GT and BZ surfaces, using di fferent
filling ratios and di fferent starting configurations. The pore
filling ratios are in the range 30%–97%, based on the
estimated number of molecules for 100% filling ratio, which
is 2700.30The equilibrium configurations were analyzed
by calculating the radial density profile, the distribution of
water molecules on the interior pore surface, and the number
of hydrogen bonds among water molecules and between
water and silica molecules. In order to see how far the final
configurations depend on the initial configuration, we used
the two di fferent initial configurations shown in Fig. 1, where
water is concentrated around the cylinder axis and at the pore
surface, respectively. There is thus a void between the water
droplet and the silica surface in the first configuration, and a
void in the pore center for the second configuration.
Fig. 2 shows the radial density profile of water molecules
inside the pore as a function of the distance to the pore center,
averaged over 15 ns after at least 5 ns of equilibration for each
simulation. One can see that water is closer to the GT surface.
The GT density profile shows only one peak for a filling ratio
of 30%, indicating that all water molecules are in contact
with the pore surface. Only after the first layer is completed,
a second layer is formed, as is visible for the curves for
filling ratios between 40% and 55%. At 65% filling ratio, thewater molecules can also be found in the interior of the pore,
indicating a configuration with a completely wetted surface
and a compact water droplet in the pore interior. The density
profiles for the BZ surface show several layers of water, with
a peak height that depends on the filling ratio. Furthermore,
the density profile depends on the initial configuration for
intermediate filling ratios, with the initial configurations at the
surface leading to final configurations with rather flat density
profiles. This suggests that for the initial configuration at the
boundary, the water droplet forms a “plug” in the pore interior,
while for the initial configuration in the center, water forms
some type of droplet sitting at the surface. Since the pore
surface is rough, some water molecules can also be found
inside the silica pore material.
In order to test the intuition obtained for the water
configurations based on the density profiles, we evaluated the
distribution of water molecules within a distance of 0.3 nm of
the surface. Fig. 3 shows the resulting surface density profiles,
using cylinder coordinates. This figure confirms that for the
GT surface, the water droplet first wets the surface completely,
before filling the interior. For the BZ surface, the pore surface
is only partially covered with water, and the final configuration
depends on the starting configuration for intermediate filling
ratios. For instance, for 40% filling ratio with the “center”
starting configuration, water molecules are concentrated in
one angular segment of the surface but are covering the whole
length, while for the “surface” starting configuration they
FIG. 2. Radial density profile of water in the silica pore for di fferent filling ratios and starting configurations, for the (a) BZ surface and the (b) GT surface. The
radius of the pore is 2 nm. The gray area indicates the silica pore surface and is arbitrarily scaled for a clear visibility. | 10.1063_1.4962516 | page_0003 |
114901-4 Pafong, Geske, and Drossel J. Chem. Phys. 145, 114901 (2016)
FIG. 3. The water density at the pore surface, showing water molecules that are within a distance of 0.3 nm of the silica surface. For the GT surface ((e)-(h)), only
filling ratios of 30% and 40% are shown, since for larger filling ratios the surface is completely wetted. For the BZ surface, the top ((a)-(b)) graphs correspond
to the “surface” starting configuration and the bottom graphs ((c)-(d)) correspond to the “center” starting configuration, (i) represents the density at 65% filling
ratio.
occupy only part of the zrange, but all angles. These final
configurations for intermediate filling ratios are in fact very
plausible if one tries to imagine how the initial configurations
can evolve with time in a situation where the water-surface
interaction is not strong enough that the entire surface is
wetted. When the initial configuration has a water cylinder
in the pore center, the entire cylinder gets attracted by the
silica molecules under the influence of electrostatic and VdW
interaction and moves as a whole towards the pore surface,
wetting a specific angular region of the surface. When the
initial configuration sits at the pore surface, the water film
may rupture along an angular line, and the water will contract
to form a plug. Even if one of the two final configurations has a
lower free energy, this free energy di fference will not be large,
and the transition between them will involve a barrier that is
so large that it is not overcome during the simulation time.
When the filling ratio is lower (as can be seen for 30%), the
plug is not observed for either initial configuration, indicating
that there is only one stable configuration. The two di fferent
final configurations merge also for larger filling ratios (as can
be seen for 65%), where the void left by the water droplet
takes the shape of a droplet that sits at the pore surface.
Finally, we evaluated the average number of hydrogen
bonds formed between water molecules, and between water
molecules and silica molecules. This shows to what extent the
stronger hydroa ffinity of the GT model a ffects the formationof molecular bonds. We considered two oxygen atoms to
be connected via a hydrogen bond if the angle between the
intramolecular O—H vector and the intermolecular O ···O
vector is less than 30◦, provided that the O ···O separation
is less than 0 .335 nm. The results are shown in Fig. 4. For
the BZ surface, the number of hydrogen bonds between water
molecules reaches the bulk value in the inner part of the pore
for a filling ratio larger than 40% with the “surface” initial
configuration. Also for the “center” initial condition, the bulk
value is reached for the water molecules in the interior of the
water droplet. In the GT surface, the bulk value is reached
only for filling ratios above 60%. This illustrates the fact that
the BZ surface disrupts the water structure more than the GT
surface. Accordingly, the number of hydrogen bonds formed
between the silica surface and the water molecules is larger
for the GT surface.
For both models, the maximum number of water-silica
hydrogen bonds is already reached at 40% filling ratio,
confirming that one and half layer of water molecules is
sufficient to completely wet the GT silica surface. It is at first
surprising that for the BZ surface, the number of water-silica
hydrogen bonds does not increase for filling ratios larger than
40% and stays considerably below the value of the GT surface.
This can only be explained by di fferent water orientations
near the surface in the two models. In the supplementary
material we show that near the BZ surface the OH bonds of | 10.1063_1.4962516 | page_0004 |
114901-5 Pafong, Geske, and Drossel J. Chem. Phys. 145, 114901 (2016)
FIG. 4. Average number of hydrogen bonds per water molecule for water–silica ((a)-(b)) and water–water ((c)-(d)) contacts, for di fferent initial conditions and
filling ratios, as indicated in the legends. The results for the GT silica surface are given on the left-hand side, and those for the BZ silica surface on the right-hand
side.
water molecules have a preferred orientation, while this is not
the case near the GT surface. This means that only part of the
water molecules can act as a hydrogen bond donor or acceptor
near a BZ silica molecule, while near the GT surface all the
water molecules can share hydrogen bonds with the surface
atoms.
B. Theoretical evaluation of the phase diagram
In order to better understand the dependence of the water
droplet configuration in the pore on the interaction energies
and the filling ratio, we performed a theoretical analysis that is
based on surface energy minimization. Denoting the surface
area between the water droplet and vacuum with A1, the
surface area between the water droplet and the pore material
with A2, andγ1as the surface tension between water and
vacuum,γ2as the di fference between the surface tension of
silica and water with the surface tension of silica and vacuum.
The total surface energy of the wetting droplet can be written
as
ES=γ1·A1+γ2·A2. (2)
If we assume that the entropy does not change much between
different phases, the configuration of the water droplet in the
pore can be obtained by minimizing ESfor a given filling
ratio. In order to perform the calculation mostly analytically,
we approximated the di fferent possible phases using simple
geometrical shapes, so that the energy minimization can be
performed by varying at most 2 parameters that characterize
the phase. We fixed the ratio of the pore radius and pore
length to the value R/L=2/6.1 used in the simulations. We
determined the phase diagram in dependence of the filling
ratio and the ratio between the two surface energies. We
allowed for hydrophilic ( γ2<0) as well as for hydrophobicsurfaces (γ2>0). The surface tension γ1is a positive
quantity.
Fig. 5 shows the eight phases and the phase diagram
obtained from minimizing ES.
Phases 1, 2, and 4 are translationally invariant along the
cylinder axis and represent the cases of partial, full, and no
wetting of the silica surface. Phase 3 represents a plug in the
shape of a cylinder that is shorter than the pore. Phases 5-8
describe the cases where the water or the vacuum forms a
spherical droplet in the interior or one that intersects with the
pore surface.
The calculation of the surface energy for phases 1-6
is a straightforward analytical calculation. For phase 1, we
had to use mathematica to evaluate the final expression.
In order to evaluate phases 7 and 8, we had to resort
to a numerical evaluation. We first created a database by
FIG. 5. (a) The eight di fferent phases used for energy minimization and
(b) the phase diagram in dependence of the ratio of the water-vacuum and
water-silica surface energies and of the filling ratio. The aspect ratio r/l
between radius and length of the cylindrical pore is 2 /6.1. | 10.1063_1.4962516 | page_0005 |
114901-6 Pafong, Geske, and Drossel J. Chem. Phys. 145, 114901 (2016)
calculating numerically the volume and surface of the cut
droplet for over 1 ×106different combinations of the sphere
radius and the distance of the sphere center from the cylinder
axis. Then, we used this database to find for a given filling
ratio the values that minimize ES.
The phase diagram shows clearly three qualitatively
different regions that depend on the ratio γ2/γ1. For
γ2/γ1.−1, the energy is minimized by having maximum
surface area with the pore surface. The water wets the pore
completely. Correspondingly, the phases 2 and 6 occur. With
increasing filling ratio, the volume of the vacuum becomes
smaller, and eventually a free volume that does not touch the
surfaces fits into the pore. For su fficiently large filling ratio, the
droplet clearly has the smaller surface area with the vacuum
and therefore the lower energy. (Our simple calculation did
not take into account that the droplet could be stretched, and
therefore the position of the phase boundary between phases
2 and 6 should in fact be at a lower filling ratio.)
Forγ2/γ1&1, the pore material is highly hydrophobic,
and the phases 4 and 5, which have no contact between
water and silica, have the lowest energy, depending on the
filling ratio. The phase boundary between phases 5 and 4
moves downwards with decreasing aspect ratio r/l, because
a vacuum droplet that does not touch the pore wall takes a
smaller proportion of the total volume when r/lis smaller.
(See the supplementary material for phase diagrams with other
aspect ratios.)
In the intermediate parameter region −1.γ2/γ1.1, we
observe phases 7, 1, and 8 as the filling ratio is increased. These
are the phases that have surfaces with the pore and with the
vacuum. Since the (absolute value of) water-vacuum energy is
larger than that of the water-silica energy, these phases are to
a large extent a ffected by the condition that the water-vacuum
interface shall be minimum. The transition from phase 7 to
phase 1 occurs for lower values of γ2/γ1at smaller filling ratios
than for larger γ2/γ1, because a larger surface area to the pore
is energetically favorable for negative γ2. For the same reason,
phase 8 wins over phase 1 for high filling ratios and negative
γ2, because phase 8 has more surface area between water and
the pore. The phase boundary to phase 8 moves upwards and
the boundary to phase 7 moves downwards with decreasing
aspect ratio r/l, because droplets that touch the pore wall
only at one side take a smaller proportion of the total volume
when r/lis smaller. The droplet phases will also vanish when
the ratio r/lbecomes large, as the system then is e ffectively
two-dimensional and shows only the three phases that are
translationally invariant along the z-axis. (See supplementary
material for phase diagrams with other aspect ratios.)
Phase 3 does not occur in the phase diagram. It will
certainly occur when the aspect ratio r/lbetween the radius
and length of the pore becomes smaller, because it has then
smaller surface area than phase 1. (See the supplementary
material.) In our simulations with the BZ potential, we found
this phase for intermediate filling ratios, where it coexists with
phase 1. Phase 3 thus might well be metastable. On the other
hand, it is also possible that phase 3 is indeed stable in part
of the phase diagram due to entropic e ffects, which were not
taken into account when calculating the phase diagram. Since
in the canonical NVT ensemble the free energy F=E−T Shas to be minimized, phases with larger entropy become more
favored when entropy is taken into account. This will shift
the phase boundaries somewhat. For instance, when phase 2
contains only two layers of water molecules, its entropy per
molecule is smaller than in bulk water. Similarly, the entropy
per water molecule is larger in phase 3 than in phase 1, since
the water in phase 3 is more bulk-like.
With the insights gained from these analytical calcula-
tions, we can interpret the results of the MD simulations
shown in Figs. 2–4: For the BZ surface, the water wetted
the silica surface only partially for all simulated filling ratios,
and we observed the phases 1, 3, and 8 depending on the
filling ratio. The transition to phase 8 occurs at a filling ratio
of approximately 60%. For smaller filling ratios below 15%,
we also see phase 7 (see the supplementary material). This
means that the ratio of surface energies γ2/γ1is in the interval
(−1,0). (Since the surface is hydrophilic, we have γ2<0.)
With the GT surface, we observed a complete wetting of the
silica surface (phases 2 and 6) for all simulated filling ratios,
with a transition between these two phases at a filling ratio
around 60%. This means that γ2/γ1<−1. This appears to be
the more realistic scenario, as it agrees well with experimental
results.2
In order to obtain an additional perspective on the di fferent
interaction between water and a silica surface in the two
models, we will in Sec. IV investigate the contact angle of
water on top of a flat silica slab using both models.
IV. RESULTS II: WATER ON TOP OF A SILICA SLAB
A good tool to examine the performance of silica
potentials is the evaluation of the contact angle of a water
droplet wetting the surface. We performed MD simulations
of a water droplet on a flat surface of amorphous silica
and measured the contact angle. We did not use periodic
boundary conditions in order to remove the influence of the
neighbouring water periodic images. Instead, the Coulombic
and the VdW (LJ) interaction energies between all atoms
in the water droplet and the silica slab were calculated
exactly.
In order to evaluate the contact angle θ, the density
profile of all horizontal water layers of 0 .05 nm thickness was
determined, and from these a contour plot of the density was
obtained. The contour plot was fitted to a circular segment, and
the contact angle was deduced from the tangential line to the
base of the circular segment. The result is shown in Fig. 6 for
both types of potentials, with a slab of thickness t=2.5 nm.
For the GT model, the droplet covers the entire surface and
has a very small contact angle of 7◦. When we performed the
same simulation with periodic boundary conditions, the water
layer became completely flat. In contrast, the contact angle
of the water droplet on top of the BZ surface is 25◦. These
results confirm the findings of Subsection III B, that the GT
silica surface is so hydrophilic that water wets it completely,
while the BZ surface is less hydrophilic.
The contact angle is closely related to the surface tensions
that we used for evaluating the phase diagram. The condition
that the total surface energy ( ES) of water wetting a silica
surface must be minimal for an equilibrated droplet of constant | 10.1063_1.4962516 | page_0006 |
A&A 641, A54 (2020)
Fig. 6. Abundances relative to H2of MF, DE, F, and EC (Table 10) as
a function of the total luminosity/mass ratio (see Sect. 6.3 for details)
for the sources of our sample. The linear best-fit to the data is shown for
each molecule.
luminosity and is not affected by any distance-induced observa-
tional bias, since we have checked that molecular abundances are
independent from source mass and distance. PC and most HMS-
FRs are in very good agreement with the trend observed in our
sample, while hot corinos, IMSFRs and some of the other HMS-
FRs show slightly higher values. Since the results of the latter
are based on interferometric data, this discrepancy could be due
to the different angular resolution. Although we accounted for
beam dilution effects as consistently as possible (see Sect. 4),
lower resolution (single-dish) observations may still result in
slightly underestimated molecular column densities.
Figure 8 summarises the main result of this analysis, showing
the average abundances of the four molecules with respect to the
evolutionary stage of the sources. For molecules detected at mul-
tiple stages (MF, DE, and EC), average values increase with the
evolution, namely from protostellar to intermediate until UCHII
regions, preserving the mutual molecular ratios. The increasing
trend is particularly evident for MF and DE. Average abundances
increasing with time were also found by Gerner et al. (2014) for
less complex molecules CH 3OH(methanol), CH 3CN(methyl
cyanide), and other simpler molecules, and were predicted by
Choudhury et al. (2015) for COMs including MF and DE through
evolutionary models of HMCs.
6.4. Implications for the chemistry of COMs
The abundances of MF, DE, and EC are very well correlated
(r0:92, Fig. 2) and their mutual molecular ratios are nearly
constant (Figs. 3–4). The result is very robust since it is based
on a sample with good statistics (20 sources in our sample plus
59 sources from literature overall), covering several orders of
magnitude in abundance and source luminosity.
In some cases, this may indicate a chemical link between
the species. This is most likely the case of MF and DE, show-
ing the strongest correlations in many parameters (abundance,
source size, and FWHM) and a constant 1ratio over a remark-
able9orders of magnitude in source luminosity (Fig. 3, upper
panel), with a limited scatter both in a large sample of low- to
high-mass star-forming regions and among different interstellar
environments (Fig. 4). The link may consist in a common forma-
tion pathway or in one species being the precursor of the other.
Fig. 7. Same as Fig. 6, but for individual molecules MF ( upper panel ),
DE (middle panel ), and EC ( lower panel ). The evolutionary classifica-
tion is shown for the sources of our sample (different colours), while
black symbols represent different interstellar sources taken from litera-
ture for comparison (see Table F.1 for references). The black lines fit the
data of the sources included in this work.
The first scenario is indeed predicted by the theoretical model of
Garrod & Herbst (2006) and Garrod et al. (2008), who propose
a common formation route through surface chemistry on dust
grains at low temperatures ( 50K), from the methoxy precursor
CH 3O(see also Allen & Robinson 1977):
CH 3O+HCO !CH 3OCHO; (MF)
CH 3O+CH 3 !CH 3OCH 3: (DE)
A54, page 12 of 25 | 10.1051_0004-6361_202038212 | page_0011 |
A. Coletta et al.: Evolution of COMs in star-forming regions
Fig. 8. Average abundances relative to H2(with respective standard
errors) of MF, DE, F, and EC (different colours), as a function of the
evolutionary stage.
Balucani et al. (2015) present instead a gas-phase route able
to efficiently form MF from DE at low temperatures ( 10K)
through reactions involving the radical CH 3OCH 2:
CH 3OCH 3+F !CH 3OCH 2+HF;
CH 3OCH 3+Cl !CH 3OCH 2+HCl;
CH 3OCH 2+O !CH 3OCHO +H:
In addition, the correlated FWHM of the lines (middle panel
of Fig. 5), the similar overall range of excitation temperatures
(Sect. 5.3), and the spatial coexistence derived from interfero-
metric observations (e.g. Brouillet et al. 2013; Bøgelund et al.
2019; El-Abd et al. 2019) suggest that MF and DE could trace
the same gas in various environments and evolutionary stages.
However, also in the case of species for which a chemical
link is not so clear (EC and MF, or EC and DE, showing slightly
higher dispertion in molecular ratios, Fig. 3, bottom two panels)
a clear abundance trend is observed. A potential link between
these molecules may involve the methyl radical CH 3as a com-
mon precursor. EC could indeed form through a sequence of
gas-phase and grain-surface reactions mainly involving the CN
andCH 3radicals (Garrod et al. 2017). We cannot exclude either
the existence of a chemical link with formamide, consistent with
the abundance correlations ( >0:9) found in Sect. 6.2.1, but the
poor statistics obtained for this molecule prevents conclusive
considerations, and needs to be improved by further targeted
observations. Although the formation paths of formamide are
still under debate (see e.g. Bisschop et al. 2007; Barone et al.
2015; Codella et al. 2017; Skouteris et al. 2017; Ligterink et al.
2018; Quénard et al. 2018; López-Sepulcre et al. 2019), recent
works propose that it would form more efficiently on icy dust
grains during the cold phases of star formation (Jones et al.
2011; López-Sepulcre et al. 2015; Fedoseev et al. 2016). It
has to be noted, however, that abundance correlations between
molecules do not necessarily imply the existence of a chemical
link, as recently proved by Quénard et al. (2018) for formamide
andHNCO (isocyanic acid), and confirmed by Belloche et al.
(2020) in a sample of hot corinos. These observational corre-
lations seem to be a necessary but not sufficient condition to
claim a chemical link. Nevertheless, observations are needed
to test models and understand how molecules are formed. This
work shows, in fact, that between molecules whose chemistry isexpected to be related (such as MF and DE) the correlations are
tighter. Furthermore, a clear trend of increasing molecular abun-
dances with L=M(mainly governed by L) emerges for all species,
spanning up to4orders of magnitude in abundance and 6in
L=M, which implies also a trend with the evolutionary stage of
the sources (Figs. 6–8).
Besides suggesting potential individual links between the
COMs, these results allow us to formulate a general, most likely
scenario for their formation and evolution. The fact that the
molecular ratios are nearly constant across the whole star forma-
tion process and among different types of sources is particularly
interesting, because the physical conditions in these environ-
ments (especially in the case of MF/DE, Fig. 4) are different:
pre-stellar cores, shock-dominated regions (protostellar shock
and GC clouds), thermal-dominated regions (cores in low- to
high-mass star-forming regions), and comets (whose chemical
composition is thought to be presolar, see e.g. Rivilla et al.
2020). This seems to reveal a rather universal chemistry for
COMs, mainly developed at the cold earliest stages of star for-
mation and then essentially preserved through the evolution,
being only marginally altered by the evolving physical condi-
tions. In more detail, molecules may be formed in pre-stellar
cores, possibly in gas phase or on the surface of dust grains,
from which they can desorb thanks to non-thermal mechanisms
such as cosmic rays (see e.g. Shingledecker et al. 2018; Bonfand
et al. 2019; Willis et al. 2020). This would explain the detec-
tion and the relative (low) abundances in the pre-stellar cores
and the comets. The lack of molecular detections (at least at
2mm) among our 11 HMSCs may be due to the fact that they
are tipically much more distant than the observed PCs (which
can be resolved even with relatively low resolutions, see e.g.
Jiménez-Serra et al. 2016), and thus more affected by beam
dilution. Later on, in star-forming regions and GC molecular
clouds, other mechanisms are able to massively (and more effi-
ciently) desorb the molecules formed on grains: thermal heating
and shock-induced heating. This has the effect to significantly
increase the observed gas-phase molecular abundances and thus
the expected number of detections. This scenario is consistent
with the trend we find between abundances and L=M(proxy for
the evolutionary stage), as well as with the number of detections
we report for each evolutionary group (Sect. 5.1). Moreover,
while low luminosity sources (pre-stellar and hot corinos) are
usually isolated (or at most binary) systems, high-mass star-
forming regions are clustered environments. In these regions,
the thermal and shock energy injected to the medium strongly
increases with time due to the protostellar activity (heating and
protostellar outflows). This produces more and more desorption,
accordingly increasing the gas-phase abundances of COMs with
evolution. Therefore, the proposed scenario supports the forma-
tion of COMs on grain surfaces, indicating that the majority of
COMs observed in star-forming regions could be produced by
the desorption from icy grain mantles. However, it is still possi-
ble that gas-phase formation pathways (see e.g. Balucani et al.
2015; Codella et al. 2017; Skouteris et al. 2019), though not
expected to significantly affect the molecular ratios (based on
our results), could contribute to the abundance of COMs in cold
regions.
Moreover, our results suggest that O- and N-bearing COMs
may behave similarly in star-forming regions at all stages, shar-
ing the same physical conditions (or even direct chemical links)
for their formation. This has been found also by Fontani et al.
(2007) in hot cores, whereas other authors noticed differences
between O- and N-bearing COMs in both the spatial distribution
(e.g. Liu 2005; Csengeri et al. 2019) and the radial velocities
A54, page 13 of 25 | 10.1051_0004-6361_202038212 | page_0012 |
A&A 641, A54 (2020)
(Blake et al. 1987). We also note that, given the increasing abun-
dance trend, molecular destruction routes seem to be less effi-
cient than formation/desorption mechanisms, especially at later
evolutionary stages (i.e. higher luminosities). However, destruc-
tion routes represent a less investigated but non-negligible topic,
as they can in principle affect the predicted molecular abun-
dances (see e.g. Garrod 2013; Shingledecker et al. 2019; Ascenzi
et al. 2019 and refs. therein).
Lastly, we stress that the angular resolution of our data
(Table 2) is larger than the size of the observed sources.
Although this issue has been taken into account through the
beam dilution factor applied in the line fitting procedure (see
Sect. 4), we are still not able to spatially resolve the inner struc-
ture of the targets, which is often fragmented into multiple
smaller objects in potentially diverse evolutionary stages. The
observed emission could hence include contributions from both
the inner hot core and its cooler outer envelope, preventing a
clear distinction between nearby emission zones, and causing
sometimes potentially misleading correlations among differently
distributed molecules. High angular resolution interferometric
observations would be able to confirm more robustly the pro-
posed scenario for the formation of COMs, as they can more
accurately identify spatial correlations and resolve the poten-
tial protostellar multiplicity within a region (see e.g. Murillo
et al. 2018). Nevertheless, we do not find relevant differences
by comparing our results to interferometric data from literature,
seemingly indicating that the observed chemistry is almost the
same across different spatial scales within star-forming regions.
7. Summary and conclusions
In this work we have analysed spectra at 3,2, and 0:9mm of 39
selected high-mass star-forming regions at different evolution-
ary stages (HMSCs to UCHIIs) obtained with the IRAM-30m
telescope, searching for rotational transitions of the complex O-
bearing molecules CH 3OCHO (MF) and CH 3OCH 3(DE), and
N-bearing molecules NH 2CHO (F) and C2H5CN(EC). We have
reported molecular detections in 20 sources, performing a line
fitting procedure to derive the main physical parameters for each
molecule. We summarise below the main results of this study:
– The highest number of detections was reported in UCHII
regions ( 45%, 9 out of 20 sources). DE was detected in
19 sources, while MF in 13, EC in 9, and F in 5.
– We observe relevant discrepancies between the total molec-
ular column densities obtained at different wavelengths (up
to 2 orders of magnitude between 0:9and 3mm), so
that in all sources N3(3mm)>N2(2mm)>N1(0:9mm)and
N2=N1>N3=N2. This can be interpreted as an effect of the
differential attenuation caused by dust opacity at each fre-
quency ( d/ ), proving that dust properties have indeed to
be considered when dealing with young, tipically dust-rich
star-forming regions at multiple wavelengths. Therefore, we
chose the 2mm data for our analysis (being the band that
reported the most detections) and found source-averaged col-
umn densities ranging from 1015to1018cm 2for MF,
DE, and EC, and from 1014to1017cm 2for F.
– The derived abundances with respect to H2are10 10 10 7
for MF and DE, 10 12 10 10for F, and10 11 10 9
for EC. For all species we find a consistent overall range
of linewidths (2 10km s 1) and excitation temperatures
(20 220K).
– We find very strong correlations ( r0:92) between the
abundances of MF, DE, and EC, spanning 3orders of
magnitude in abundance, uniformly covered by our sample.We have compared our results with heterogeneous sources
from literature (including low-, intermediate- and high-mass
star-forming regions, a protostellar shock region, pre-stellar
cores and Galactic centre clouds), which confirmed and
expanded the correlations to 4orders of magnitude in abun-
dance for all tracers. We also find nearly constant molecular
ratios with respect to source luminosity across all evolution-
ary stages and among different types of sources, indicating
that the chemistry of COMs is mainly developed at early
stages and then preserved during the evolution, barely altered
by the changing local physical conditions. These results may
suggest a potential link between MF, DE, and EC, whereas
for F, though consistent with correlations ( r>0:9), we can-
not draw conclusions due to the poor statistics. In particular,
we claim that MF and DE are most likely chemically linked,
since they show the strongest correlation in most parame-
ters (abundance, FWHM, and source size) and a remarkably
constant ratio of1across a wide variety of sources at all
evolutionary stages (also including comets), spanning a strik-
ing9orders of magnitude in luminosity. The link may
consist in a common formation pathway, such as from pre-
cursor CH 3Oas predicted by Garrod & Herbst (2006) and
Garrod et al. (2008), or in one species being the precursor
of the other, as proposed by Balucani et al. (2015) with MF
forming from DE. MF-EC and DE-EC may share CH 3as
common precursor instead (see e.g. Beuther et al. 2007).
Although observational correlations alone are not enough to
prove a chemical link, this work shows that they are tighter
among molecules whose chemistry is expected to be related
(e.g. MF and DE).
– We have also evaluated the variation of molecular abun-
dances with the evolutionary stage of the source (traced by
the luminosity/mass ratio) finding a clear increasing trend for
all species over up to 6 orders of magnitude in L=M, ranging
from pre-stellar cores and hot corinos to UCHIIs.
– Based on correlations, molecular ratios and evolutionary
trend, we propose a general scenario for the formation and
evolution of COMs, which involves a prevalent formation
at low temperatures in the earliest phases of star forma-
tion (likely mainly on frozen dust grains) followed by a
growing desorption powered by the progressive thermal and
shock-induced heating of the core with evolution. This would
explain the increasing observed gas-phase abundances and
number of molecular detections. Moreover, these results sug-
gest that O- and N-bearing COMs might have a similar
behaviour in star-forming regions at all stages. Interestingly,
this analysis also points out that molecular abundances might
serve as evolutionary tracers within the whole star formation
process.
In conclusion, we stress that the physical parameters derived in
our sample represent average values across the whole clumps,
and could therefore include also contributions from outside the
cores. Relevant improvements to this work will come from high
angular resolution observations, able to resolve the inner struc-
ture of these regions and hence to better locate the molecular
emission, allowing to more accurately identify spatial correla-
tions between COMs. In particular, interferometric observations
of a large sample of star-forming regions in different evolution-
ary stages, like the one studied in this work, will be able to
confirm and improve the proposed scenario for the formation and
evolution of COMs.
Acknowledgements. We thank the IRAM-30m staff for the precious help during
the different observing runs. V.M.R. has received funding from the European
A54, page 14 of 25 | 10.1051_0004-6361_202038212 | page_0013 |
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