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10.1051_0004-6361_202141662 | page_0000 | 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: [email protected]
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_0001 | 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
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10.1051_0004-6361_202141662 | page_0002 | 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_0003 | 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
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10.1051_0004-6361_202141662 | page_0004 | 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
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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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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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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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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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Fig. 18. Velocity-integrated intensity maps of the12CO(2–1) line ( upper row ) and the vibrational ground-state line of SiO(6–5) ( lower row ),
covering three velocity intervals. Left: blue line wing [ vlsr; 10,vlsr; 2] km s 1,middle : line center [ vlsr; 2,vlsr;+2] km s 1,right : red line
wing [vlsr;+2,vlsr;+10] km s 1. North is up and east is to the left. We note the different color scales. Contours are plotted every 5for CO and
every 20for SiO, where ( from left to right )1=14:6;22:0;19:2mJy beam 1km s 1for CO(2–1) and 1=11:1;16:7;16:4mJy beam 1km s 1
for SiO(6–5). The black ellipse in the lower left corner indicates the synthesized beam.
Fig. 19. Population diagram for SO 2. The three data points in brackets
correspond to the three lowest frequency SO 2lines observed with setup
1, which, due to a different uvcoverage, resulted in a comparably larger
beam than the setup 2 observations (see Table 2 and Eq. (6)).
For the population diagram, we then get
ln Nu
gu!
=ln uWI
gu!
=ln NSO2
QSO2;rot!
Eu
kT; (5)
where we define uas
u=4:78410 7
hcAul1
ab: (6)
In Eq. (5), WIis expressed in Jykm s 1,aandbare given
in arcsec, Euis the upper level energy, guthe statistical weight of
the upper level, and Tis the excitation temperature. All relevant
parameters of the SO 2transitions used here are listed in Table 2.In fitting a straight line to the population diagram (shown
in Fig. 19) to determine a rotational temperature according to
Eq. (5), we assume that the SO 2level populations are dominated
by collisions, i.e., that LTE holds for the rotational excitation
of SO 2, and that the lines are optically thin. The assumption of
LTE populations may be questionable for SO 2(see Danilovich
et al. 2016), and essentially could result in underestimation of
the kinetic gas temperature in the SO 2-emitting region (cf. the
discussion in Goldsmith & Langer 1999, their Sect. 5). The effect
on the derived column density is more difficult to assess without
a detailed non-LTE modeling. However, we note that our result is
consistent with the SO 2abundance derived for similar objects by
means of a comprehensive non-LTE description (see below). On
the other hand, the assumption that the lines are optically thin is
justified by the results of our XCLASS modeling; see below and
Appendix D.
With the temperature of T320K resulting from a lin-
ear fit to the population diagram shown in Fig. 19, we get
the partition function QSO2;rot(interpolated from values given
in the CDMS), from which an effective SO 2column density
ofNSO2=3:51015cm 2is determined by means of Eq. (5).
The SO 2source is compact (see Table 1 and Fig. B.4, FWHP
0:500, corresponding to 75 AU, or 70R), which is consistent
with the estimated temperature in this inner (possibly rotating)
region. Assuming a mass-loss rate of 110 7M yr 1in the
equatorial region (cf. Sect. 4.1), an outflow velocity of at max-
imum 8 km s 1as indicated by the line widths (but excluding
the high-velocity wings discussed in Sect. 3.3), an inner radius
of1014cm, and an outer radius of that region of 1015cm,
corresponding to 0:500, we estimate upper limits of the SO 2
abundance of X(SO 2=<H>) = 7:310 7, or, if hydrogen were
completely bound in H 2,X(SO 2/H2) =1:510 6. For compari-
son, Danilovich et al. (2016) find an SO 2abundance of510 6
for the low-mass-loss-rate ( 1–210 7M yr 1) oxygen-rich
stars R Dor and W Hya, about a factor of approximately 3higher
than the value found here for the MS-type star RS Cnc. We note
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Fig. 20. CO data and 3D reconstruction. Left panels : flux density averaged over 0:400<R<2:500in thevzvs.!plane for12CO(2–1) ( left) and
13CO(2–1) ( center-left ).Right panels : de-projected flux density projected on the plane perpendicular to the sky and containing the polar outflow
axis, shown as black lines, for12CO(2–1) ( center-right ) and13CO(2–1) ( right ).
that Decin et al. (2008) and De Beck & Olofsson (2020) do not
detect SO 2in the S-type star W Aql. Our result therefore appears
to be consistent with an intermediate chemical state of RS Cnc.
In Appendix D, an XCLASS modeling is presented that
results in the same SO 2column density of 3:51015cm 2as
derived from the population diagram, and in a slightly higher
rotational temperature of 350 K, still within the uncertainties
of50 K derived here (see Fig. 19). The XCLASS modeling
of the 11 SO 2lines results in an average optical depth of 0.1,
confirming that the lines are optically thin.
4. Discussion
4.1.12CO(2–1) and13CO(2–1): morpho-kinematics of the
circumstellar envelope
Rotational CO lines in the vibrational ground state are known to
probe the circumstellar envelope of AGB stars up to distances on
the 1000 AU scale, where the CO molecules are dissociated by
the interstellar UV radiation (Mamon et al. 1988). In this section,
we use observations of the12CO(2–1) and13CO(2–1) lines to
probe the morpho-kinematics of the wind at distances from the
star in excess of50AU, in a region where the wind is expected
to evolve smoothly toward the constant expansion regime.
Both12CO(2–1) and13CO(2–1) data have a Doppler veloc-
ity (vz) spectrum that clearly shows a two-component structure,
where the blueshifted wing of the12CO line is partly absorbed,
very similar to the corresponding situation in EP Aqr (Tuan-
Anh et al. 2019). CO rotational lines from higher J levels (5–4
and 9–8) observed with Herschel (Danilovich et al. 2015) show
triangular profiles consistent with the double-component wind
structure that we are proposing.
In the spatial distribution of the CO emission, a clear sep-
aration is observed between the equatorial region and the polar
outflows. This is illustrated in Fig. 20, where we show the maps
of the flux density in the Doppler velocity ( vz) versus position
angle (!) plane. The flux density is integrated over an interval of
projected distance ( R) from the star between 0.400and 2.500. The
equatorial region is seen as an intense oscillation at low values
ofjvzjwhile the polar outflows are seen as emission at larger jvzj
values, in phase opposition. From these maps, we estimate, in
agreement with earlier findings, that the outflow axis projects on
the plane of the sky at a position angle of !=75, at which
the equatorial and bipolar outflow oscillations are maximal and
minimal, respectively. Figure 20 also shows de-projections of the
data cubes projected on the plane perpendicular to the plane ofthe sky that contains the polar outflow axis. These are drawn
assuming a dependence of the wind velocity on stellar latitude
of the form vterm=4+5 sin4 km s 1, increasing from 4 to
9 km s 1from the equator to the poles. The velocity field is
assumed to be radial and to have reached its terminal value in
theRinterval considered here.
In order to interpret these observations, in particular possi-
ble differences in the12CO/13CO ratio between the equatorial
region and polar outflows, we need to take into account the
effect of absorption. We choose to consider only regions outside
0.40060 AU from the star, which allows for major simplifica-
tions: we can ignore the very complex kinematics that governs
the inner CSE layers, including shocks and possible rotation. As
we cannot expect the data to strongly constrain the temperature
distribution, we take it of the form T=T0exp( r=r0)and fit the
observed data cubes by means of a 2minimization scheme for
different values of the ( T0;r0) pair consistent with earlier esti-
mates (Nhung et al. 2015a). We find that the morpho-kinematics
is best described by modeling the polar outflows and equatorial
region separately, with a separation at stellar latitude 030.
We parametrize the radial dependence of the wind velocity as
v=vtermr=(r+r1=2): it increases from 0 at r=0tovtermatr=1,
reaching1
2vtermatr=r1=2. In order to account for different open-
ing angles of the polar outflows and different flaring angles of
the equatorial enhancement, we allow, within each region, for
latitudinal dependencies of the velocity described as Gaussian
functions in sin in the equatorial region and in cos in the
polar outflows with adjustable Gaussian widths .
We do the same for the number densities, which vary radi-
ally as0(vterm=v)r 2with different 0values for the equatorial
region and the polar outflows, and of course for12CO and13CO.
The radiative transfer equation is integrated in a sphere of 1000
radius and the calculated flux densities are then smeared with
the synthesized beam of the observations. Reasonably good fits
of the data cubes are obtained given the crudeness of the model
(see Fig. 21).
We find that the best fits to the morpho-kinematics of the
two lines are relatively insensitive to the exact form assumed for
the temperature structure. For r0=200, we find that values of T0
between 70 K and 170 K in the equatorial region and between
100 K and 200 K in the polar outflows are acceptable. Chang-
ing the value of r0modifies the values of T0accordingly but
does not improve the quality of the fit. Parameters of the best-fit
model include an angle of the polar outflow axis with the line of
sight i30as expected, a separation in latitude between polar
and equatorial regions, 0=294 deg , terminal velocities of
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Fig. 21. Best-fit results for CO. Left panels : same as in Fig. 20, but for the model best fit. Right panels : modeledvzspectra (red) compared with
observations (black) for12CO(2–1) ( center-right ) and13CO(2–1) ( right ).
Table 3. Parameters of the best-fit model for CO.
Region vterm r1=2 T0 r0 Opening angle ()(v)0(12CO)0(13CO)
( km s 1) (arcsec) (K) (arcsec) (FWHM) (deg) (cm 3) (cm 3)
Equator 3:50:7 0:60:2 100 2.0 30 0:210:03>0:4 8610 4:20:4
Poles 8:60:5 0:290:10 130 2.0 70 0:500:02 0:700:04 706 2:90:4
Notes. The quoted uncertainties correspond to a 10% increase in the best fit 2, leaving all other parameters fixed at their best-fit value: they should
not be understood as uncertainties but as indicators of the sensitivity of the quality of the fit to each separate parameter.
3–4 km s 1in the equatorial region, and 8–9 km s 1in the polar
outflows, outflow opening angle and equatorial flaring angle of
70and30, respectively ( FWHM =2:35arccos (())and
2:35arcsin (()), respectively); these are listed in Table 3.
The wind is still being accelerated (the escape velocity of
a1:5M star at a distance of 150 AU ( 100for RS Cnc) is
4.2 km s 1) – having reached half terminal velocity at the inner
edge of the observed radial range – earlier in the poles than in the
equatorial region. The number densities of CO molecules corre-
spond to mass-loss rates of 1:010 7M yr 1in the equatorial
region and 2:010 7M yr 1in the outflows6for a CO/H 2ratio
of210 4. The12CO/13CO ratio is measured to be 20on aver-
age, but larger in the polar outflows ( 242) than in the equatorial
region ( 193). This is a barely significant difference, but a sim-
ilar asymmetry seems to be present in EP Aqr (Tuan-Anh et al.
2019): such a result is unexpected and needs to be confirmed by
higher sensitivity observations before being accepted. Indeed, if
it were confirmed, this might suggest that the polar outflows are
fed in part from material freshly produced in the 3- process
and mixed into the atmosphere by the third dredge-up follow-
ing a He shell flash. This process would not only increase the
12C abundance in the atmosphere, but also the12C/13C isotope
ratio, as indicated for example by Smith & Lambert (1990); see
in particular their Fig. 9.
The presence of an equatorial density enhancement with a
rather small flaring angle, 30FWHM, suggests that it may
rather be a disk, which might be expected to be rotating and
to have an inner rim. However, the size of the beam is too
large to study this reliably. From a close inspection of the hvzi
distribution near the star, using the method described in Sect. 3.4
6This is about a factor 2 larger than the values quoted in Hoai et al.
(2014). Their data were affected by a pointing offset of the old 30m
OTF maps that lead to an underestimation of the CO line flux of about
a factor 2.for HCN and SiO, we infer a rotation velocity at r0:500of
vrot=jvzj=sini2:5km s 1. However, this is a very crude
estimate given the size of the beam and the lack of precise
knowledge of the morpho-kinematics in the innermost radial
range.
The blob of enhanced12CO(2–1) line emission that had been
identified in Hoai et al. (2014) as possibly suggesting the pres-
ence of a companion is seen on the channel maps in the vlsr=6
to 7 km s 1range as an elongation in the west–northwest to east–
southeast direction (Fig. 22). Projections of the data cube on
different planes ( vzvs.!,vzvs.R;and!vs.R) in its neigh-
borhood show that it can be described as a pair of elongations
at position angles of 120and270, the latter being signifi-
cantly more intense than the former and covering a broad range
ofRbetween 1and200. While these features provide no justifica-
tion for a possible identification of a companion, they cannot be
used either as arguments against the presence of an unobserved
companion.
4.2. SiO(5–4) and SiO(6–5): evidence for strong absorption
In the present section, we compare the SiO(5–4) and SiO(6–5)
line emission with the12CO results described in the previous
section. In contrast to CO, the SiO emission does not resolve the
equatorial region from the polar outflows, as illustrated in the
leftmost panels of Fig. 23. Part of the reason for this is the much
smaller radial range being probed, as illustrated in the right panel
of Fig. 23. As mentioned earlier in Sect. 3.5, the radial extent of
the SiO emission is often significantly smaller than that of the
CO emission, which is usually interpreted as evidence for the
progressive condensation of SiO molecules on dust grains (e.g.,
Schöier et al. 2004). This would cause the progressive decline of
the SiO/CO ratio observed in the right panel of Fig. 23 up to
R1:500, followed by a more abrupt cut-off around R200
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Fig. 22. Enhanced12CO(2–1) emission at vlsr6:75km s 1.Upper panels : channel maps of the12CO(2–1) line emission between 6.25 and
7.25 km s 1.Lower panels : projection of the flux density multiplied by Ron thevlsrvs.Rplane for 250<!< 330(left), on thevlsrvs.!plane for
0.5<R<2 arcsec ( middle ), and on the !vs.Rplane for 5.75 <vlsr<7:25km s 1(right ).
Fig. 23.vzvs.!maps for 0:500<R<1:500.Left: SiO(5–4), middle : SiO(6–5), octant intervals in !as discussed in the text are indicated. Right :
intensity ratio SiO(5–4)/12CO(2–1) (black) and SiO(6–5)/12CO(2–1) (red) as a function of Rforjvzj<8km s 1.
caused by the dissociation of the SiO molecules by the inter-
stellar UV radiation.
Another striking difference is the presence of high-velocity
wings in the SiO data close to the star, that are mostly absent
in the CO data (see Figs. 24 and 16). This may be understood
as the SiO data probing the close neighborhood of the star much
more efficiently, where pulsation shocks and possibly convection
cells are known to play an important role, as demonstrated by a
host of observations at shorter wavelengths, from far-infrared to
near-UV, and in agreement with theoretical modeling (see, e.g.,Hinkle et al. 1982; Winters et al. 2000a; Richter et al. 2003;
Nowotny et al. 2005; Freytag et al. 2017; Montez et al. 2017;
Höfner & Olofsson 2018, and references therein). Also worth
noting in Fig. 24 is the significant absorption in front of the
stellar disk seen in the SiO data at 6km s 1, reminiscent
of similar observations in stars such as R Dor (Nhung et al.
2021), W Hya (Takigawa et al. 2017), and oCeti (Wong et al.
2016). Of these three stars, two are found to be surrounded by
an optically thick SiO layer that extends well beyond the stellar
disk, while in the third, oCeti, SiO emission decreases abruptly
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Fig. 24. Doppler velocity spectra integrated over 0:2<R<2:5arcsec (black) and within R<0:2arcsec (red) for SiO(5–4), SiO(6–5), and12CO(2–
1)from left to right .
beyond some 10to50AU from the center of the star. In order
to understand the mechanism of condensation of SiO molecules
on dust grains, it is therefore important to study the SiO emis-
sion region in oxygen-rich AGB stars. Accordingly, we devote
the remainder of the present section to this task. In a first part,
we make some qualitative comments that help with unraveling
the general picture; in a second part, we account for radiative
transfer using the model of the morpho-kinematics developed for
CO emission in the preceding section. The morpho-kinematics
of the SiO(5–4) and SiO(6–5) lines are so similar that we cannot
expect their comparison to be very sensitive to temperature. At
temperature T, in the optically thin LTE approximation, the ratio
RTof the SiO(5–4)/SiO(6–5) line emission depends only on the
ratio of the Einstein coefficients, 5:210 4=9:110 4=0:57;
and the ratio of the level populations, (2J+1)(exp( Eu=T),
where the upper level energies Euare31:3K and 43:8K,
respectively (line parameters from the CDMS, based on
Müller et al. 2013).
Hence, we have
RT=0:48 exp( 31:3=T)=exp( 43:8=T); (7)
from which we obtain
T[K]=12:5=(ln(RT)+0:74: (8)
Figure 25 (left) displays the observed dependence of RTonR.
If the SiO layer is optically thin, the value of RTprovides a direct
measure of the temperature; if it is optically thick, the emis-
sion probes only the outer part of the SiO layer and measures
a temperature that is representative of larger values of r. When
Rincreases, the observed value of RTremains nearly constant at
0:65up to R100and then increases to a value of 0:8at1:500,
corresponding to temperatures of 40K and24K, respectively.
The value of 40K, associated with R<100, is close to the lower
value of the temperature obtained from the CO model for r=100
(TCO[K]=70 exp( r=200)=42K for r=100) in Sect. 4.1. This
suggests that for low values of the projected distance from the
star,R, the distance in space from the star, r, effectively probed
by the SiO emission stays approximately constant and of the
order of 100. Indeed, the strong self-absorption causes the region
probed by the SiO emission to be confined beyond r100(cor-
responding to SiO1), but not to probe the volume beneath this
surface. For larger values of the projected distance R>100, we
expect the distance in 3D space, r, of the effective SiO-emittingsurface to increase progressively as a result of the elongation of
the emission volume along the line of poles, a pure geometrical
effect (Fig. 20).
Qualitatively, we describe this trend in Fig. 25 (left) by
assuming that rstays at the 100level for R<100and increases
approximately from 100to2:500when the projected Rincreases
from 100to200. Such a trend, when translated in terms of tem-
peratures using the CO model relation TCO[K]=70 exp( r=200)
gives a fair description of the observed dependence of RTonR
given the important approximations that have been made (Fig. 25
left).
The ratio"= of the emissivity to optical depth is a measure
of the lower limit of the emission of a self-absorbing layer. In
the LTE approximation and to first order in E=T, where E
is the energy of the transition, ("= )=(T2)is a constant, where
is the frequency of the emission. Therefore, at the same tem-
perature, ("= )[SiO(5–4)] =0:88("= )[12CO(2–1)]. The value of
("= )isT=26:3Jy arcsec 2for CO and T=29:5Jy arcsec 2for
SiO. Taking as reference T=100K for SiO and 50 K for CO,
the corresponding values of ("= )are 1.9 Jy arcsec 2for CO
and 3.4 Jy arcsec 2for SiO. The observed values (Fig. 25 center-
right) are2:5and 6 Jy arcsec 2, respectively at R0. This is
less than a factor 2 above the reference values, showing that the
optical thickness is close to that of the self-absorption regime. A
similar result has been observed for other AGB stars with mass-
loss rates on the order of 10 7M yr 1(R Dor, Nhung et al. 2021,
W Hya, Takigawa et al. 2017).
To gain further insight into this issue, having obtained qual-
itative evidence for strong absorption, we need to properly
account for radiative transfer. To do so, we use the model devel-
oped in Sect. 4.1 to describe the morpho-kinematics of the CO
component of the CSE: in Fig. 26 we compare Doppler veloc-
ity spectra of SiO and CO in octants of position angle (the first
one defined as 7<!< 52, then counter-clockwise for increas-
ing numbers, as indicated on Fig. 23) in a ring 100<R<1:500.
This range of Ris far enough from the star to be relatively inde-
pendent of modeling the star neighborhood, which contributes
to the high-velocity wings of SiO spectra but our current data
do not offer significant constraints on this region. We only show
SiO(5–4) but the results are essentially the same for SiO(6–5).
The CO data are seen to trace the polar outflows from the equa-
torial region, the SiO data do not. To adapt the CO model to
a description of the SiO data, we keep all parameters as listed
in Table 3 with the only exception being the radial profile: we
divide the CO density parameter 0by three, and we further
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10.1051_0004-6361_202141662 | page_0016 | J. M. Winters et al.: Molecules, shocks, and disk in the axi-symmetric wind of the MS-type AGB star RS Cancri
Fig. 25. Analysis of SiO and comparison with CO. Left: ratio RTof SiO(5–4) to SiO(6–5) line emitted fluxes as a function of Rforjvzj<8km s 1.
Corresponding temperature values using the relation T[K]=12:5=(ln(RT)+0:74are shown in red on the scale of the ordinate. The red dashed
line indicates constant RTof 0.64 ( T42K) for R100and a linear increase of RTto 0.89 ( T20K) from 100to200.Center-left : Doppler
velocity spectrum of the SiO(5–4) data for R<0:100.Center-right :Rdistribution of the SiO(5–4) (red) and12CO(2–1) (black) emission averaged
over position angle !, measured in Jy arcsec 2, and averaged over 2< v z<6km s 1as shown by the arrow in the center-left panel. Right :R
dependence of the12CO(2–1)/13CO(2–1) ratio (black) and of the28SiO(5–4)/29SiO(5–4) ratio (red).
Fig. 26.12CO(2–1) and28SiO(5–4) Doppler velocity spectra in the ring 100<R<1:500. The data are shown in black and the best-fit model results
are shown in red (see text). Octant intervals in position angle !are numbered as 1=[7;52];2=[52;97];:::8=[322;7], these are indicated
on the left and central panels of Fig. 23.
multiply it by exp( r=1:6), and set it to zero beyond r=1:600,
in qualitative accordance with the distributions displayed in the
right panel of Fig. 23. These modifications result in a ratio of
SiO/CO=0:18atr=100, in agreement with the estimate of
Van de Sande et al. (2018a), who obtain a SiO/CO ratio of
0.17–0.19 for this type of star.
Apart from this major modification of the radial distribution
of the density, we use the same morpho-kinematics and same
temperature distribution as for the best fit to the CO data. In
order to adapt to SiO, we change the parameters defining the
transition, in particular with Einstein coefficients three orders
of magnitude larger than for the CO transitions. The result, dis-
played in Fig. 26, describes the data surprisingly well given the
crudeness of the exercise; in addition to offering an understand-
ing of the large difference between CO and SiO emission, it
provides confirmation of the validity of the description of the
morpho-kinematics given by the model. What happens is that
the SiO emission in the modeled annular ring between 100and
1:500probes only the outer layer of the (confined) SiO volume
because of the very large absorption, while CO probes the lower
density gas at much larger distances from the star where the
equatorial region and the polar outflows are well separated. We
refrain from attempting to adjust parameters to obtain a better
fit: modeling the inner region could not be done reliably with the
limited angular resolution of the present data.Another illustration of the stronger absorption of the SiO
line compared to the CO line is displayed in the right panel of
Fig. 25. It compares the (projected) radial distribution of the ratio
28SiO(5–4)/29SiO(5–4) with that of the ratio12CO(2–1)/13CO(2–
1). The29SiO data are obtained with a similar beam size to
the28SiO and CO data, but with a spectral resolution of only
3 km s 1, preventing us from a detailed study of their Doppler
velocity spectra. We expect the28SiO/29SiO isotopic ratio to be
12or lower (De Beck & Olofsson 2018, 2020), but this line
ratio is reached only at large enough values of R, where the
optical depth has decreased sufficiently for absorption to be less
important. In the limit of complete self-absorption (i.e., emission
at the"= level), the line ratio is unity. In contrast, the CO ratio is
much less affected by absorption, staying at 80% of the value
evaluated in Sect. 4.1 ( 20) over the whole radial range.
4.3. MHD wind models
An important feature of the morpho-kinematics of RS Cnc is the
latitudinal dependence of the velocity, which is larger towards
the pole than along the equatorial plane. On the other hand, the
modeling of Hoai et al. (2014) leads to an almost spheroidal
distribution of matter (their Fig. 6), which implies an isotropic
radiation field within the circumstellar shell (assuming position
coupling between dust and gas). In these conditions, a driver
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10.1051_0004-6361_202141662 | page_0017 | A&A 658, A135 (2022)
other than radiation is needed to accelerate matter preferentially
along the polar axis.
Axi-symmetric models have been developed on the assump-
tion that a companion disturbs the gravitational field (Theuns
& Jorissen 1993; Mastrodemos & Morris 1999; Decin et al.
2020). These models have been successful in explaining sev-
eral observed features, such as the presence of spiral structures,
although the preferential acceleration along the polar axis seems
more difficult to reproduce.
In RS Cnc, we do not find evidence for the presence of a com-
panion. While this negative result does not necessarily mean that
there is no companion, we are considering here another mecha-
nism that could play a role: the presence of a magnetic field. In
this section, we argue that magnetic fields are one possible can-
didate to explain a significant pole-to-equator velocity contrast
of>1.
Indeed, magnetic fields are an appealing way to explain
some of the axi-symmetric shapes of planetary nebulae, such as
polar jets or equatorial winds. Early simulations of winds with
dipole fields and rotation showed that excess magnetic pressure
could be able to repel the wind towards both the equator and/or
the poles (Washimi & Shibata 1993). Similar simulations also
showed the formation of equatorial disks with enhanced outflow
velocities in the equatorial region (Matt et al. 2000). In a more
toroidal configuration, Matt & Balick (2004) showed that both
jets and equatorial disks could be produced depending on the
magnitude of the rotation. Finally, García-Segura et al. (2005)
showed that magnetically driven winds yield strongly anisotropic
outflows with highly collimated polar jets.
Observational polarimetric studies (Greaves 2002) revealed
ordered magnetic fields in planetary nebulae, with various
degrees of toroidal configurations depending on the target. Using
a handful of SiO masers (Herpin et al. 2006) or CN Zeeman
measurements, Duthu et al. (2017) later attempted to further
characterize the magnitude and the radial dependence of the
magnetic field in the winds of AGB stars. These latter authors
concluded that the field is on the order of a few Gauss near
the stellar surface, and consistent with a 1=rdependence on the
distance rfrom the star (see their Fig. 6).
In this section, we report results of simplistic calculations
which integrate magnetized fluid parcel trajectories from the
surface of an AGB star up to 10 stellar radii. We integrate
the acceleration due to gravitational and Lorentz forces over
time (pressure gradients become quickly negligible after the
sonic point is crossed):
¨r=( 1)GM
r3r+1
JB; (9)
where ris the position of the fluid parcel, is the ratio between
the radiative and the gravitational force, Gis the universal grav-
ity constant, Mis the stellar mass, and J=1
4rBis the
current vector. The mass density and the magnetic field Bare
prescribed, while we solve for the position and velocity of the
fluid parcels. We parametrize our equations with ( 1)GM=
v1R2
and=˙M
4r2v1. We assume ˙M=1:2410 7M yr 1;and
R=1:61013cm as reasonable values for RS Cnc (Hoai et al.
2014). Our choice of parametrization allows us to easily explore
nondimensional values of the parameters independently of the
absolute observational constraints. After we obtain a suitable
contrast between polar and equatorial velocities, we retrieve the
physical value for the velocity scale – here v1=5:6km s 1–
in order to obtain a given polar outflow velocity of 8 km s 1at
r=10R. The initial velocity vector is set with a small uniform
Fig. 27. Magnetized fluid parcel trajectories from a simplified model of
RS Cnc (see text). Red trajectories meet on the polar axis, where they
will likely generate a jet.
Fig. 28. Radial velocity at 10 stellar radii depending on the latitude for
the same simplified model of magnetized wind as shown in Fig. 27.
radial velocity and we probe starting trajectories at the surface
with a uniformly distributed initial latitude.
This simple setup allows us to quickly investigate various
magnetic field configurations. Figure 27 displays the trajecto-
ries in the meridional plane obtained for a toroidal magnetic
field with a 1=r1:1decline from B=0:5G at the stellar surface:
B =Bcos()=(r=R)1:1whereis the latitude ( 1=r1:1gives a
more pronounced velocity contrast between pole and equator
than 1=r). The Lorentz force JBin this case is directed toward
the symmetry axis and acts as a focusing agent. All trajecto-
ries eventually end up on the axis where they would presumably
launch a jet: this focuses mass loss towards the poles. Figure 28
shows the resulting “terminal” velocity at 10 stellar radii, where
we have separated the latitudinal and the radial components.
The flow velocities at this radius are dominated by their radial
component, but with a clearly slower wind at the equator com-
pared to the pole, as indicated by observations of, for instance,
RS Cnc and EP Aqr. We note that rotation tends to produce
the opposite effect (faster radial flow at equator compared to
poles, due to centrifugal acceleration). We find similar behav-
ior for toroidal magnetic field configurations closer to what Matt
& Balick (2004) found ( B =3Bcos() sin()2=(r=R)2with a
1=r2dependence and a concentration of Bat intermediate lati-
tudes). We investigated additional dipolar fields which are able
to generate some amount of rotation in the wind. Thanks to the
versatility of the present setting, we can quickly explore various
A135, page 18 of 27 |
10.1051_0004-6361_202141662 | page_0018 | J. M. Winters et al.: Molecules, shocks, and disk in the axi-symmetric wind of the MS-type AGB star RS Cancri
configurations, linear combinations between them, several mag-
netic field decay exponents, but have not yet investigated them
systematically. The purpose of our investigation here is simply to
show that a magnetic field is a valid candidate to produce pole-
to-equator velocity ratios of significantly greater than 1. Finally,
we note that our termination radius of r=10Ris arbitrary, and
a pertinent match to the observations could be considered at var-
ious distances depending on where the given tracer is expected
to be concentrated. These crude models are still far from quan-
titatively matching the observational constraints from RS Cnc
or EP Aqr, which require a broader polar outflow and a thinner
and denser equatorial disk. This could be adjusted by providing a
sharper toroidal magnetic barrier to funnel the wind at the appro-
priate places. However, such fine-tuning would overcome the
limits of this crude exercise which still lacks self-consistency as
the density profile remains radial and unaffected by the magnetic
constraints (themselves blind to the wind), and shocks gener-
ated by the crossings of trajectories at the polar axis are not
accounted for. We plan to investigate further with such simpli-
fied models in future work as they might provide a useful means
to constrain the magnetic field configuration from the morpho-
kinetics.
4.4. HCN in M- to S-type stars
Cherchneff (2006) recognized that the formation of CN/HCN
depends on the high activation barrier of the H + C 2!CH + C
reaction, followed by rapid CN formation via N + CH !CN+H.
Their abundance therefore depends on thermal excursions in
shocks, or inhomogeneities of temperature. In addition, both the
total rate of formation of the pair CN/HCN and the respective
share between CN and HCN depend on the H/H 2ratio which
itself depends on out-of-equilibrium chemistry because of the
slow conversion between H and H 2. Cherchneff (2006) was thus
able to show that the shocks produced by the pulsations close to
the stellar photosphere could produce highly increased yields of
the HCN molecule in M or S-type stars, despite their high O/C
ratio. We note here that magnetic fields produce shocks on the
symmetry axis which might also help to boost HCN production
in the polar jet.
HCN has long been detected and surveyed in M-type and
S-type stars (e.g., Deguchi & Goldsmith 1985; Lindqvist et al.
1988; Bujarrabal et al. 1994; Olofsson et al. 1998; Schöier et al.
2013). RS Cnc on the other hand has never been detected in
ground-state or vibrationally excited HCN despite various obser-
vational efforts with different telescopes (Lucas et al. 1988;
Sopka et al. 1989; Nercessian et al. 1989; Lindqvist et al. 1992;
Bujarrabal et al. 1994; Bieging & Latter 1994; Olofsson et al.
1998). Adopting a mass-loss rate of 310 7M yr 1, Bujarrabal
et al. (1994) estimated an upper limit to the HCN abundance
in RS Cnc of 4:510 7. This upper limit becomes 1:3510 6
if we adopt ˙M=110 7M yr 1. Schöier et al. (2013) pre-
sented a comprehensive analysis of the HCN abundance in a
sample of 59 AGB stars, including 25 carbon-rich, 19 S-type, and
25 M-type stars, by means of a non-LTE radiative trans-
fer modeling. For M-type and S-type stars, these authors
derived a median HCN/H 2abundance of order 110 7and
710 7, respectively, with a large spread between 510 8and
510 6.
By an XCLASS modeling of the HCN(3–2) line detected
here (see Appendix D), and assuming a rotational temperature of
350 K, we derive an HCN column density of 1:61015cm 2;
see Fig. 29. With the same assumptions as those made in
Sect. 3.6, this translates to HCN abundances of X(HCN/hHi)=
1.0" 0.5" 0.0" -0.5" -1.0"1.0"
0.5"
0.0"
-0.5"
-1.0"
R.A. Offset (arcsec)Dec. Offset (arcsec)HCN (3-2)
0.20.40.60.81.01.21.4Ntot (cm2)
1e15Fig. 29. Map of the HCN column density as derived by an XCLASS
modeling (see Appendix D). The black ellipse in the lower left corner
indicates the synthesized beam.
3:310 7, or, if hydrogen were completely bound in H 2,
X(HCN/H 2)=6:610 7. This abundance perfectly fits in the
range found by Schöier et al. (2013) for M- to S-type stars and is
also consistent with the upper limit derived by Bujarrabal et al.
(1994) corrected for the mass-loss rate.
Clumpy and porous winds help UV photons to penetrate
closer to the star, thus photodissociating CO and N 2to release
more of the C/NO and the N/CS pairs of reactants, which both
produce CN: this process was shown to considerably enhance
the HCN abundances close to the star (Van de Sande et al. 2018b,
2020). Rather than uniformly distributed random clumpiness and
porosity, one can also imagine ordered density distributions in
the wind, which could let UV photons penetrate through low-
density channels. These structures could sometimes be hard to
witness due to line of sight confusion. In fact, our simplified
magnetized wind models (see Fig. 27 with scarcity of trajec-
tories around the equator) or more sophisticated magnetized
wind models (e.g., Matt et al. 2000; Washimi & Shibata 1993)
allow for lower column-density channels at certain angles. These
may result in increased HCN abundance, but chemical post-
processing in magnetized models will be necessary to assess
whether this is a viable interpretation of the observations.
5. Conclusions
Using NOEMA equipped with PolyFiX, we obtained high-
spatial resolution ( 0.300) images of RS Cnc in several lines
of different molecules. We detect, and in most cases are able
to map, 32 lines of 13 molecules and isotopologs (CO,13CO,
SiO,29SiO, SO,34SO, SO 2, H 2O, HCN, H13CN, PN), includ-
ing several transitions from vibrationally excited states, and a
tentative identification of Si17O and possibly29Si17O. HCN as
well as millimeter vibrationally excited H 2O, SO, SO 2, and PN
and their isotopologs are first detections in RS Cnc. From their
first-moment maps, some of the lines, SiO( v=1,6–5), HCN,
SO, SO 2, show signs of rotation in the close vicinity of the star.
A population diagram analysis for the 11 observed SO 2lines
provides a rotational temperature of about 320 K in the region
that shows signs of rotation. Temperatures of this order are also
found from an XCLASS modeling of the SO 2lines. For SO 2
and HCN, we find column densities from the XCLASS mod-
eling of NSO23:51015cm 2andNHCN1:61015cm 2,
A135, page 19 of 27 |
10.1051_0004-6361_202141662 | page_0019 | A&A 658, A135 (2022)
which translate to abundance ratios of X(SO2=H2)=1:510 6
andX(HCN/H 2)=6:610 7, respectively, well within the range
expected for an MS-type star.
We find broad wings in the spectral line profiles of vibra-
tional ground-state transitions of SiO and SO and in first
vibrationally excited transitions of SiO, which indicate radial
velocities of about twice the terminal outflow velocity as probed
by CO. As high velocities very close to the star are also seen in
similar objects, such as EP Aqr, oCet, and R Dor, the presence
of these broad line wings calls for a mechanism common to the
class of pulsating AGB stars. We interpret these high-velocity
line wings as the imprints of pulsation shocks acting in the very
inner region around these stars.
The spatially resolved images allow us to trace the morpho-
kinematics of the wind around RS Cnc at different scales. In the
inner part ( <0.500, or 75 AU), we find a rotating structure well
traced by the less abundant molecules (HCN, SO, SO 2), and by
SiO in (v=1) lines. Outside 75 AU, we find an expanding axi-
symmetric outflow, with velocities 4km s 1in the equatorial
plane, and9km s 1along the polar axis. This polar axis coin-
cides with the axis of the internal rotating structure. A model
that fits the data cubes obtained on the12CO(2–1),13CO(2–1)
and SiO(v=0, 5–4 and 6–5) lines gives a mass-loss rate of
110 7M yr 1for the equatorial region (latitude <30) and
of210 7M yr 1for the polar outflows (latitude >30). The
12CO/13CO ratio is measured to be 20on average, 242in the
polar outflows and 193in the equatorial region.
Although we cannot exclude the possibility that an unseen
stellar or substellar companion shapes the circumstellar environ-
ment of RS Cnc, we also consider the possibility of a magnetic
field playing this role. In particular, a toroidal magnetic field
configuration would provide a mechanism able to produce the
significant velocity contrast between high polar-outflow veloci-
ties and low expansion velocities in the equatorial region that is
observed in RS Cnc and other similar stars.
Acknowledgements. We thank the staff at the NOEMA and Pico Veleta obser-
vatories for their support of these observations. The authors are grateful to
the anonymous referee for a very detailed and valuable report that helped
improving the presentation of the material. This work is based on observations
carried out under project numbers W16BE, D17AE, W19AX with the IRAM
NOEMA interferometer and under project ID 136-19 with the IRAM 30m tele-
scope. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN
(Spain). The Ha Noi team acknowledges financial support from the World Lab-
oratory, the Odon Vallet Foundation and VNSC. This research is funded in
part by the Vietnam National Foundation for Science and Technology Devel-
opment (NAFOSTED) under grant number 103.99-2019.368. This work was
supported by the Programme National “Physique et Chimie du Milieu Interstel-
laire” (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES. This
work has made use of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia ), processed by the Gaia Data Process-
ing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/
gaia/dpac/consortium ). Funding for the DPAC has been provided by national
institutions, in particular the institutions participating in the Gaia Multilateral
Agreement.
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A135, page 21 of 27 |
10.1051_0004-6361_202141662 | page_0021 | A&A 658, A135 (2022)
Appendix A: Resolved out flux
Fig. A.1. Effect of missing short spacing information on the CO
lines. Left:12CO(2–1). Right:13CO(2-1). A-configuration and D-
configuration are merged, the spectral resolution is 0.5 km s 1and the
CO emission is integrated over the central 22002200, i.e., over the full
field of view of the NOEMA antennas at 230 GHz. Black profiles: OTF
data (i.e., the short-spacing information that is filtered out by the inter-
ferometer) are added. Red profiles: A+D configuration interferometer
data, only.
The effect on the flux of filtering out large-scale structure
with the interferometer is shown in Fig. A.1 for the CO and13CO
lines. These two are the only lines discussed in this paper that are
affected by the short-spacing problem.
Appendix B: Intensity maps
Here we present velocity-integrated intensity maps in three
velocity ranges for HCN and H13CN (Fig. B.1), the four detected
SO lines (Fig. B.3), and three out of the 11 SO 2lines (Fig. B.4).
These are the SO 2line with the lowest upper level energy, the
strongest SO 2line detected here, and the SO 2line with the high-
est upper level energy, respectively. All these nine lines display
kinematic structure in east-west direction. Also shown are zeroth
moment maps for the (unresolved) H 2O lines (Fig. B.2) and for
the (weak) PN line (Fig. B.5).
Appendix C: SO 2line profiles
In this section, we present the line profiles of all the 11 SO 2lines
detected with our setups (see Fig. C.1).
Appendix D: XCLASS modeling of HCN and SO 2
The HCN(3-2) line and the 11 detected SO 2emission lines
were modeled using the eXtended CASA Line Analysis Soft-
ware Suite (XCLASS7, Möller et al. 2017). XCLASS models and
fits molecular lines by solving the 1D radiative transfer equa-
tion with the assumption of LTE and of an isothermal source.
Here, 1D means that the radiative transfer equation is integrated
along the line of sight. Spectral lines are fitted with Gaussian
profiles, and optical depth effects and source size are considered
in the calculations. Molecular properties (e.g., Einstein coeffi-
cients, partition functions, etc.) are taken from an embedded
SQLite database containing entries from the Cologne Database
for Molecular Spectroscopy (CDMS, Müller et al. 2001, 2005)
and from the Jet Propulsion Laboratory database (JPL, Pickett
7https://xclass.astro.uni-koeln.deet al. (1998)) using the Virtual Atomic and Molecular Data Cen-
ter (VAMDC, Endres et al. 2016). The fit parameter set for each
line component consists of the source size source , the rotation
temperature Trot, the total column density Ntot, the line width
v, and the velocity offset v o (given here in the LSR system).
The XCLASS package offers various algorithms to find the
best-fit parameters by minimizing the 2value, and here we uti-
lized the Levenberg-Marquardt (LM) method. To obtain maps
of the physical parameters, we use the myXCLASSMapFIt func-
tion to fit HCN(3-2) and the 11 detected SO 2emission lines (see
Fig. C.1) pixel by pixel.
For SO 2, we modeled and fitted 11 lines simultaneously with
a threshold of 18 and a single Gaussian component. All fit
parameters are regarded as free parameters in the fitting process.
The XCLASS models for SO 2result in a temperature of Trot
350K (Fig. D.1), somewhat higher than the result from our pop-
ulation diagram analysis, but within the error bars (see Sect. 3.6).
It also results in an average line optical depth of 0.1, confirming
that the assumption of the lines being optically thin is justi-
fied when constructing the population diagram. Assuming LTE,
the derived rotation temperature equals the kinetic gas temper-
ature Tkin. For the SO 2column density, the XCLASS modeling
results in a value of NSO23:51015cm 2, almost identical
to the result from the population diagram analysis presented in
Sect. 3.6, resulting in an abundance X(SO2=H2)=1:510 6.
The respective results are shown in Figs. D.1 and D.2.
For HCN(3-2), we applied the same threshold of 18 as for
SO2and fitted Gaussian components to the line profiles on each
pixel, taking into account the hyperfine structure of the line. The
velocity map and line widths displayed on Fig. D.3 are due to
the intrinsic (thermal and rotational) broadening only, whereas
the profile shown in Fig. D.4 represents the sum of the hyper-
fine components of HCN(3-2). As only one HCN rotational line
is available, the HCN rotational temperature cannot be deter-
mined. We therefore fixed the rotation temperature at a value
of 350 K, the same temperature as we find from the SO 2mod-
eling based on the similar emission region of SO 2and HCN,
see Figs. 17, B.1, and B.4. The HCN results are displayed in
Fig. D.3. In particular, we derive an HCN column density of
1:61015cm 2, which translates to an HCN abundance of
X(HCN/H 2)=6:610 7.
A135, page 22 of 27 |
10.1051_0004-6361_202141662 | page_0022 | J. M. Winters et al.: Molecules, shocks, and disk in the axi-symmetric wind of the MS-type AGB star RS Cancri
Fig. B.1. Velocity-integrated intensity maps of the HCN(3-2) (upper row) and H13CN(3-2) lines (lower row), covering three velocity intervals.
Left: Blue line wing [v lsr; 10,vlsr; 2] km s 1, Middle: line center [v lsr; 2,vlsr;+2] km s 1, Right: Red line wing [v lsr;+2,vlsr;+10] km s 1.
North is up and east is to the left. We note the different color scales. Contours are plotted every 10for HCN and every 3for H13CN, where
(from left to right) 1=5:7;7:2;7:2mJy/beam km s 1for HCN(3-2) and 1=5:2;5:0;5:6mJy/beam km s 1for H13CN(3-2). The black ellipse
in the lower left corner indicates the synthesized beam. We note that the HCN maps were produced using robust weighting, whereas for the H13CN
maps, we applied natural weighting.
Fig. B.2. Zeroth moment maps of the H 2O 232 GHz (left) and H 2O 263 GHz (right) lines. North is up and east is to the left. We note the different
color scales. Contours are plotted every 5where 1=13:8mJy/beamkm s 1for the 232 GHz line and 1=13:92mJy/beamkm s 1for the
263 GHz line. The black ellipse in the lower left corner indicates the synthesized beam.
A135, page 23 of 27 |
10.1051_0004-6361_202141662 | page_0023 | A&A 658, A135 (2022)
Fig. B.3. Velocity-integrated intensity maps of the SO(6(6)-5(5)) (upper row), SO(5(5)-4(4)) (second row), SO(6(5)-5(4)) (third row) and SO(7(6)-
6(5)) (lower row) lines covering three velocity intervals. Left: Blue line wing [v lsr; 10,vlsr; 2] km s 1, Middle: Line center [v lsr; 2,vlsr;+2]
km s 1, Right: Red line wing [v lsr;+2,vlsr;+10] km s 1. North is up and east is to the left. We note the different color scales. Contours are
plotted every 10, where (from left to right) 1=10:0;10:4;10:3mJy/beamkm s 1for SO(6(6)-5(5)), 1=7:3;7:6;7:4mJy/beamkm s 1for
SO(5(5)-4(4)), 1=7:6;8:1;7:4mJy/beamkm s 1for SO(6(5)-5(4)), and 1=8:7;9:6;8:7mJy/beamkm s 1for SO(7(6)-6(5)). The black ellipse
in the lower left corner indicates the synthesized beam.
A135, page 24 of 27 |
10.1051_0004-6361_202141662 | page_0024 | J. M. Winters et al.: Molecules, shocks, and disk in the axi-symmetric wind of the MS-type AGB star RS Cancri
Fig. B.4. Velocity-integrated intensity maps of SO 2(9(3, 7)-9(2, 8)) (lowest E u, upper row), SO 2(14(0,14)-13(1,13)) (strongest SO 2line, second
row), and SO 2(34(4,30)-34(3,31)) (highest E u, lower row), covering three velocity intervals. Left: Blue line wing [v lsr; 10,vlsr; 2] km s 1,
Middle: line center [v lsr; 2,vlsr;+2] km s 1, Right: Red line wing [v lsr;+2,vlsr;+10] km s 1. North is up and east is to the left. We note
the different color scales. Contours are plotted every 3, where (from left to right) 1=6:5;6:7;6:6mJy/beamkm s 1for SO 2( 9(3, 7)- 9(2,
8))1=5:9;6:2;6:3mJy/beamkm s 1for SO 2(14(0,14)-13(1,13)), 1=7:8;7:8;7:7mJy/beamkm s 1for SO 2(34(4,30)-34(3,31)) . The black
ellipse in the lower left corner indicates the synthesized beam.
Fig. B.5. Zeroth moment map of the PN(N=5-4,J=6-5) line. Contours are plotted every 3, where 1=9:6mJy/beamkm s 1. North is up and
east is to the left. The black ellipse in the lower left corner indicates the synthesized beam.
A135, page 25 of 27 |
10.1051_0004-6361_202141662 | page_0025 | A&A 658, A135 (2022)
Fig. C.1. Profiles of all the 11 detected SO 2lines. A-configuration and
D-configuration data are merged, the spectral resolution is 3 km s 1,
and the emission is integrated over the central 200200square aperture.
The lines are ordered by decreasing frequency from top to bottom and
left to right.
0.5" 0.0" -0.5"0.6"
0.4"
0.2"
0.0"
-0.2"
-0.4"
R.A. Offset (arcsec)Dec. Offset (arcsec)SO2
1.01.52.02.53.03.5Ntot (cm2)
1e15
0.5" 0.0" -0.5"0.6"
0.4"
0.2"
0.0"
-0.2"
-0.4"
R.A. Offset (arcsec)Dec. Offset (arcsec)SO2
240260280300320340Trot (K)
0.5" 0.0" -0.5"0.6"
0.4"
0.2"
0.0"
-0.2"
-0.4"
R.A. Offset (arcsec)Dec. Offset (arcsec)SO2
6.006.256.506.757.007.257.507.758.00Voff (km s1)
0.5" 0.0" -0.5"0.6"
0.4"
0.2"
0.0"
-0.2"
-0.4"
R.A. Offset (arcsec)Dec. Offset (arcsec)SO2
7.07.58.08.59.09.5Line width(km s1)
Fig. D.1. Maps of total column density, rotation temperature, velocity
offset (in the LSR system), and line width for SO 2are derived with a
threshold of 18 and fitting one Gaussian component to the line profiles.
A135, page 26 of 27 |
10.1051_0004-6361_202141662 | page_0026 | J. M. Winters et al.: Molecules, shocks, and disk in the axi-symmetric wind of the MS-type AGB star RS Cancri
0.5" 0.0" -0.5"0.6"
0.4"
0.2"
0.0"
-0.2"
-0.4"
R.A. Offset (arcsec)Dec. Offset (arcsec)SO2
1.01.52.02.53.03.5Ntot (cm2)
1e15
20
0 200.000.020.04Flux [Jy/pixel]SO2 (16(3,13)16(2,14))
20
0 200.000.010.020.030.04SO2 (22(2,20)22(1,21))
20
0 200.000.010.020.030.04Flux [Jy/pixel]SO2 (28(3,25)28(2,26))
20
0 200.000.020.040.06
SO2 (14(0,14)13(1,13))
20
0 200.000.010.020.03Flux [Jy/pixel]SO2 (10(3,7)10(2,8))
20
0 200.000.010.020.03SO2 (15(2,14)15(1,15))
20
0 200.000.010.020.03Flux [Jy/pixel]SO2 (32(4,28)32(3,29))
20
0 200.000.010.020.03SO2 (9(3,7)9(2,8))
20
0 200.000.010.020.030.04Flux [Jy/pixel]SO2 (30(4,26)30(3,27))
20
0 20
LSR velocity (km/s)0.000.010.020.03SO2 (30(3,27)30(2,28))
20
0 20
LSR velocity (km/s)0.000.010.020.03Flux [Jy/pixel]SO2 (34(4,30)34(3,31))
Fig. D.2. Profiles of the 11 SO 2emission lines (in black) extracted on
the central pixel and XCLASS modeled lines (in red) at the position
of the continuum at RA = 09:10:38.77 and Dec = +30:57:46.68 (see
Sect. 3.1) as marked on the upper diagram.
1.0" 0.5" 0.0" -0.5" -1.0"1.0"
0.5"
0.0"
-0.5"
-1.0"
R.A. Offset (arcsec)Dec. Offset (arcsec)HCN (3-2)
0.20.40.60.81.01.21.4Ntot (cm2)
1e15
1.0" 0.5" 0.0" -0.5" -1.0"1.0"
0.5"
0.0"
-0.5"
-1.0"
R.A. Offset (arcsec)Dec. Offset (arcsec)HCN (3-2)
6.256.506.757.007.257.507.758.00Voff (km s1)
1.0" 0.5" 0.0" -0.5" -1.0"1.0"
0.5"
0.0"
-0.5"
-1.0"
R.A. Offset (arcsec)Dec. Offset (arcsec)HCN (3-2)
3.03.54.04.55.05.56.0Line width (km s1)
Fig. D.3. Maps of total column density, velocity offset (= v lsr), and line
width of HCN(3-2) (see text for details). The black ellipse in the lower
left corner of each map indicates the synthesized beam.
5
0 5 10 15 20
VLSR [km s1]
0.00.10.20.30.40.50.60.7Flux [Jy/pixel]HCN (32)
Fig. D.4. Profile of the HCN(3-2) emission line (in black) extracted
on the central pixel and XCLASS modeled line (in red) at the position
of the continuum at RA = 09:10:38.77 and Dec = +30:57:46.68 (see
Sect. 3.1) as marked on the upper diagram of Fig. D.3.
A135, page 27 of 27 |
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