# Evidence for episodic and patchy mass ejection in the circumstellar envelope
of AGB star R Leonis

D.T. Hoai , P.T. Nhung , M.N. Tan, P. Darriulat, P.N. Diep, N.B. Ngoc, T.T.
Thai and P. Tuan-Anh
Department of Astrophysics, Vietnam National Space Center, Vietnam Academy of
Science and Technology,
18, Hoang Quoc Viet, Nghia Do, Cau Giay, Ha Noi, Vietnam E-mail:
<EMAIL_ADDRESS><EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

The morpho-kinematics of the circumstellar envelope of oxygen-rich AGB star R
Leonis is probed using ALMA (Atacama Large Millimeter/submillimeter Array)
observations of the emission of molecular lines, including in particular
CO(2-1) and 29SiO(5-4). Evidence is found for an episode of enhanced mass
loss, a few centuries ago, that produced a broad expanding shell of mean
radius $\sim$6 arcsec and mean radial expansion velocity $\sim$5.5 km s-1.
Detailed scrutiny of its structure, as displayed by the emission of the
CO(2-1) line, reveals strong inhomogeneity and patchy morphology. Evidence is
also found, in particular from the morpho-kinematics of the emission of SiO,
SO and SO2 lines probing the close neighbourhood of the star, for distinct gas
outflows covering broad solid angles in the south-eastern, south-western and
north-western quadrants, suggesting significant contribution of the convective
cell granulation in defining the pattern of mass ejection. A study of relative
molecular abundances in these outflows suggests that a Local Thermal
Equilibrium (LTE) description applies approximately beyond $\sim$10 stellar
radii from the centre of the star but not at the smaller angular separations
where the SO and SO2 molecules are found to be confined. Near the stellar
disc, masers of the vibrationally excited SiO lines are found to probe north-
western parts of a layer of hot gas, consistent with the earlier observation
of an asymmetric expanding shell within 1-2 stellar radii from the centre of
the star. Globally, a picture dominated by episodic and patchy mass ejections
is found to prevail.

###### keywords:

stars: AGB and post-AGB – circumstellar matter – stars: individual: R Leonis –
radio lines: stars

††pubyear: 2022††pagerange: Evidence for episodic and patchy mass ejection in
the circumstellar envelope of AGB star R Leonis–Evidence for episodic and
patchy mass ejection in the circumstellar envelope of AGB star R Leonis

##  1 Introduction

High resolution observations of the circumstellar envelopes of oxygen rich AGB
stars, in particular using the Very Large Telescope (VLT) or the Atacama Large
Millimeter/submillimeter Array (ALMA), have revealed very complex structures.
Recent state-of-the art hydro-dynamical simulations (Höfner & Freytag, 2019;
Freytag et al., 2017; Liljegren et al., 2018) suggest that such complexity is
the result of shocks induced by a combination of convection and stellar
pulsations. They induce an effective line broadening for ALMA observations of
the emission of molecular lines in the close neighbourhood of the star.
Typical examples are R Dor (Hoai et al., 2020; Nhung et al., 2021), $o$ Cet
(Nhung et al., 2022a) or R Hya (Nhung et al., 2022b). In the present article
we study the case of R Leo, for which ALMA observations of the emissions of
the 12CO($\nu$=0,$J$=2-1) and 29SiO($\nu$=0,$J$=5-4) (hereafter abbreviated as
CO(2-1) and 29SiO(5-4) respectively) lines have been the subject of
preliminary studies by Fonfría et al. (2019a, b). We contribute additional and
complementary analyses of the same data as well as new analyses of other ALMA
observations, including the emissions of molecular lines
28SiO($\nu$=1,$J$=5-4), 28SiO($\nu$=1,$J$=8-7), 28SiO($\nu$=2,$J$=5-4),
SO(${}^{3}\Sigma$,$\nu$=0,$N_{J}$=55-44),
SO2($\nu$=0,$J_{\text{Ka,Kc}}$=222,20-221,21) and
SO2($\nu$=0,$J_{\text{Ka,Kc}}$=132,12-121,11), hereafter abbreviated as
SiO($\nu$=1,5-4), SiO($\nu$=1,8-7), SiO($\nu$=2,5-4), SO(55-44),
SO2(222,20-221,21) and SO2(132,12-121,11) respectively.

R Leo is an oxygen-rich AGB star. Its distance to Earth is not well measured,
varying from 71 pc (Gaia Collaboration, 2018) to 114 pc (van Leeuwen, 2007).
In our analysis we use 114 pc, a value consistent with the distance obtained
from the period-luminosity relation (Haniff et al., 1995). We note that after
submission of the present paper for publication, an article of utmost
relevance to this issue has been published (Andriantsaralaza et al., 2022),
arguing in favour of a distance of 100$\pm$5 pc. The pulsation period is 310
days (Feast, 1996; Watson et al., 2006) and the mass-loss rate, evaluated from
single dish observations, is $\sim$1.0 10-7 solar masses per year (Danilovich
et al., 2015). The star effective temperature is $\sim$2500-3000 K and its
angular diameter is 25-30 mas (Perrin et al., 1999; Fedele et al., 2005;
Wittkowski et al., 2016; Matthews et al., 2018). Vlemmings et al. (2019) using
ALMA observations to probe the extended atmosphere within 1-2 stellar radii,
measured an asymmetric, radial expansion of the radio photosphere at a mean
velocity of 10.6$\pm$1.4 km s-1 at stellar phases between 0.41 and 0.46.

The close neighbourhood of the star has been observed in the near-infrared by
Fedele et al. (2005) using VLTI/VINCI and in the mid-infrared by Paladini et
al. (2017) using VLTI/MIDI. SiO masers have been the subject of numerous VLBA
observations of outstanding quality by Soria-Ruiz et al. (2007), Cotton et al.
(2004, 2008); Cotton et al. (2009) and Desmurs et al. (2014). Herpin et al.
(2006), using the IRAM 30 m telescope, have analysed single-dish SiO maser
Zeeman observations to estimate the value of the magnetic field in the near
CSE at the level of 4.2-4.6 G; quasi-periodic polarization fluctuations have
been interpreted as resulting from a precessing planetary magnetosphere,
suggesting the presence of an evaporating Jovian planet (Wiesemeyer et al.,
2009). Using the Stratospheric Observatory for Infrared Astronomy (SOFIA),
Fonfría et al. (2020) have detected the fluorescence of hot carbon dioxide in
the extended atmosphere of the star.

Millimetre observations of the expanding gas have measured a terminal velocity
of 6-9 km s-1 (De Beck et al., 2010; Ramstedt & Olofsson, 2014) and have
detected significant abundances of CO, H2O, OH, SiO, SO, SO2 and HCN molecules
(Hinkle & Barnes, 1979; Bujarrabal et al., 1994; Etoka & Le Squeren, 1997;
Bieging et al., 2000; González Delgado et al., 2003; Ohnaka, 2004; Schöier et
al., 2013; Danilovich et al., 2020).

Of particular relevance to the present work are the ALMA observations of
29SiO(5-4) and CO(2-1) molecular emissions reported by Fonfría et al. (2019a,
b). They interpret the observed morpho-kinematics in terms of an expanding,
thin and dense partial shell behind the star that is being shocked by a
faster, collimated matter ejection coming from the star. This shell would have
been ejected in an apparently single strong event during the last 700 yr. Its
thickness ($\sim$1 arcsec) suggests a mass-loss rate enhancement lasting for
about 50 yr. They remark that the 29SiO(5-4) emission around the systemic
velocity resembles a deformed spiral structure that suggests the existence of
a companion of R Leo. Within $\sim$0.17 arcsec from the centre of the star,
they find evidence for the presence of hot gas, elongated along the NE/SW
direction, contributing to continuum emission. They remark that the molecular
emission displays prominent red-shifted absorption in front of the star,
typical of material in-fall, and lateral gas motions compatible with the
presence of a possibly rotating torus-like structure.

##  2 Observations and data reduction

The present work uses archival observations of R Leo from ALMA projects
ADS/JAO.ALMA#2016.1.01202.S (PI. J. Fonfría) in Band 6 and
ADS/JAO.ALMA#2017.1.00862.S (PI Kamiński) in Band 7.

The Band 6 (211-275 GHz) observations were made on 1 October 2016, 22 March
and 3 May 2017 with low angular resolution ($\sim$0.2 arcsec) and on 21
September and 27 October 2017 with high angular resolution ($\sim$0.03
arcsec). The baselines were between 15 m and 13.9 km long. The total time on
source of the observations was $\sim$80 min.

The Band 7 (275-373 GHz) observations were made on 16 November 2017 with
configuration C43-8 which has baselines between 92 m and 8.5 km. The total
time on source of the observations was $\sim$22 min. Both Band 6 and Band 7
observations were made shortly after the minimum of the light curve, the
stellar phase of the former being $\sim$0.50 (Fonfría et al., 2019b).

The data were calibrated using CASA111https://casa.nrao.edu/ with the standard
script provided by the ALMA staff. The images of CO(2-1) in Section 4 were
produced from the merged data of Band 6 observations using
GILDAS222https://www.iram.fr/IRAMFR/GILDAS//IMAGER333https://imager.oasu.u-bordeaux.fr/
with robust weighting (threshold value of 1.5). The images of the continuum
and the lines at high resolution in Band 6 were produced from the data
observed on 27 October 2017 with baselines between 191 m and 13.9 km and total
time on source of $\sim$15 min. The phase centre was shifted to the centre of
the continuum emission and the visibilities were changed accordingly. Phase
self-calibration was done for the continuum data and the results were applied
to the line data. The cleaned images were produced using CASA with uniform
weighting for the continuum and natural weighting for the lines. We also used
CASA for imaging the data of Band 7 with robust parameter of 0.5. In all cases
of line emission imaging, continuum emission has not been subtracted at
visibility level in order to preserve the possibility to account properly for
its contribution in the image plane.

Relevant parameters are listed in Tables 1 and 2.

We use coordinates centred on the peak of continuum emission, $x$ pointing
east, $y$ pointing north and $z$ pointing away from Earth. The projected
angular separation to the star is calculated as $R$=$\sqrt{x^{2}+y^{2}}$.
Position angles, $\omega$, are measured counter-clockwise from north. The
Doppler velocity $V_{\text{z}}$ spectrum is centred on a star systemic
velocity of $-$0.5 km s-1 (Teyssier et al., 2006), which, however, is not
known to better than $\sim$$\pm$0.5 km s-1.

Table 1: Observations: relevant parameters | Line | Beam | Pixel size | Channel spacing (km s-1) | Noise (mJy beam-1)
---|---|---|---|---|---
Band 6 |  29SiO(5-4) | 47$\times$44 mas2, PA=40∘ | 5$\times$5 mas2 | 1.36 | 0.7
SiO($\nu$=1,5-4) | 46$\times$38 mas2, PA=34∘ | 5$\times$5 mas2 | 1.36 | 0.6
SiO($\nu$=2,5-4) | 47$\times$44 mas2, PA=39∘ | 5$\times$5 mas2 | 1.36 | 0.8
SO(55-44) | 46$\times$38 mas2, PA=34∘ | 5$\times$5 mas2 | 1.36 | 0.5
SO2(222,20-221,21) | 46$\times$37 mas2, PA=34∘ | 5$\times$5 mas2 | 1.36 | 0.8
CO(2-1) extended | 43$\times$36 mas2, PA=33∘ | 5$\times$5 mas2 | 0.635 | 0.8
Continuum | 28$\times$26 mas2, PA=34∘ | 5$\times$5 mas2 | $-$ | 0.06
CO(2-1) merged | 106$\times$86 mas2, PA=71∘ | 30$\times$30 mas2 | 0.635 | 0.5
Band 7 | SiO($\nu$=1,8-7) | 49$\times$44 mas2, PA=$-$12∘ | 7.4$\times$7.4 mas2 | 0.85 | 2.1
SO2(132,12-121,11) | 49$\times$44 mas2, PA=$-$11∘ | 7.4$\times$7.4 mas2 | 0.85 | 2.1
Continuum | 45$\times$40 mas2, PA=$-$38∘ | 7.4$\times$7.4 mas2 | $-$ | 0.33
Table 2: Line parameters (Müller et al., 2005): frequency $f$, Einstein coefficient $A_{\text{ji}}$, energy $E_{\text{u}}$ and angular momentum $J$ of the upper level. The factors $k$ are the ratio of the temperature to the partition function $Q$. In general they depend on temperature and we give their values at 100 and 1000 K.  Line |  $f$ [GHz] |  $A_{\text{ji}}$ [10-3 Hz] |  $E_{\text{u}}$ [K] | 2$J$+1 |  $k$ (100 K) |  $k$ (1000 K)
---|---|---|---|---|---|---
CO(2-1) | 230.5380 | 0.69 10-3 | 16.6 | 5 | 2.75 | 2.63
29SiO(5-4) | 214.3858 | 0.50 | 30.9 | 11 | 1.03 | 0.85
SiO($\nu$=1,5-4) | 215.5959 | 0.50 | 1789 | 11 | 1.01 | 0.85
SiO($\nu$=1,8-7) | 344.9165 | 2.2 | 1844 | 17 | 1.01 | 0.85
SiO($\nu$=2,5-4) | 214.0885 | 0.51 | 3552 | 11 | 1.04 | 0.86
SO(55-44) | 215.2206 | 0.12 | 44.1 | 11 | 0.37 | 0.35
SO2(132,12-121,11) | 345.3385 | 0.24 | 93 | 27 | 0.087 | 0.021
SO2(222,20-221,21) | 216.6433 | 0.093 | 248.4 | 45 | 0.087 | 0.021
H13CN(4-3) | 344.2001 | 1.9 | 41.4 | 9 | 2.04 | 0.87

##  3 Continuum emission

While Band 7 data display a nearly circular continuum emission (Figure 1), as
do lower frequency data (e.g. Matthews et al., 2018, at VLA frequencies), Band
6 data were shown by Fonfría et al. (2019b) to display clear elongation in the
NE/SW direction, which they interpreted as evidence for hot gas and dust
around the star, probably in a nearly edge-on torus configuration. However,
this elongation is caused by a significant offset of the phase-centre and
disappears after having corrected for it (Figure 1). The coordinates of the
origin are: RA=09h47m33.492315s and Dec=11∘25’42.9081536”. This confirms
results obtained by Vlemmings et al. (2019). These authors performed a very
careful and detailed analysis of ALMA Band 6 observations and found evidence
for asymmetric expansion with significant residuals from a uniform stellar
disc towards the north-east. They describe it in terms of an increased opacity
layer that might in reality be a directional shock wave propagating through
the extended atmosphere. They argue that the observed motion is likely due to
density or ionisation changes and remark that it means an expansion of
material with a size of up to a quarter of the stellar disc, not inconsistent
with the size of a large convective cell.

Figure 1: Continuum intensity maps for Band 7 (panel (a), beam of 45$\times$40
mas2) and Band 6 (uniform weighting with beam of 28$\times$26 mas2; panel (b)
before phase-centre correction, panel (c) after phase-centre correction and
panel (d) after self-calibration). The contour shown in panel (d) is at
3-$\sigma$ noise level.

##  4 CO(2-1) line emission: a radially expanding shell

Channel maps of the CO(2-1) emission are displayed in Figure 2. The bulk of
the emission is well contained within $R$<6 arcsec and |$V_{\text{z}}$|<10 km
s-1. Figure 3 gives evidence for a significant enhancement of emission in a
shell having a mean radius of some 6 arcsec and expanding at a mean velocity
of some 5.5 km s-1, namely having been ejected 6-7 centuries ago. Panel (a)
displays the $R$ distribution of the intensity integrated over
|$V_{\text{z}}$|<10 km s-1 and panel (b) an intensity map on the
$V_{\text{z}}$ vs $R$ plane, integrated over position angles. The latter
illustrates clearly the shell structure: the data are compared with three
ellipses defined as
$\rho$=$\sqrt{(V_{\text{z}}/5.5)^{2}+(R/6)^{2}}$=1/$\sqrt{2}$, 1 and
$\sqrt{2}$, respectively; they correspond to spherical shells of radius
$6\times\rho$ arcsec and expansion velocities $5.5\times\rho$ km s-1. Panel
(c) displays the $\rho$ distribution of the emission for each of the blue- and
red-shifted hemispheres separately as well as for the whole range of Doppler
velocities. The shape is the same in both hemispheres, the blue-shifted
emission being some 30% weaker than the red-shifted one. It gives evidence for
a clear enhancement at $\rho$$\sim$0.8-1.2. The Doppler velocity spectrum,
shown in panel (d), displays the double hump profile expected from the shell
structure. Globally, Figure 3 illustrates and quantifies the qualitative
interpretation of the channel maps that Fonfría et al. (2019a) had suggested.

However, when inspecting in more detail the morpho-kinematics governing the
structure of the shell, one finds evidence for very important inhomogeneity,
the shell being in fact made of a collection of individual patches. Figures 4
and 5 illustrate the main features. Figure 4 displays PV maps, $V_{\text{z}}$
vs $\omega$, of the CO(2-1) emission in three different intervals of $R$: 1 to
2, 2 to 3 and 3 to 4 arcsec, respectively. It gives evidence for the very
irregular distribution of Doppler velocities in the shell, and for the patchy
nature of its emission, in particular in the blue-shifted hemisphere.
Moreover, patches of emission are seen inside the shell. In particular, at
$V_{\text{z}}$$\sim$$-2$ km s-1, $\omega$$\sim$260∘ (diamond) for 1<$R$<2
arcsec; at $V_{\text{z}}$$\sim$2-3 km s-1, $\omega$$\sim$300∘ (circle) for
2<$R$<3 arcsec; and at $V_{\text{z}}$$\sim$2-3 km s-1, $\omega$$\sim$120∘
(rectangle) for 3<$R$<4 arcsec. The first of these (diamond) corresponds to a
blue-shifted gas flow that is further illustrated in Figure 5 and starts being
clearly identified at $R$$\sim$0.4 arcsec. The second (circle) is a blob of
emission that is visible on the 0-3 km s-1 intensity map (centre-right panel
in the lower row of Figure 4). The third (rectangle) is located near an arc of
emission that can be seen on both the red-shifted and the 0-3 km s-1 intensity
maps. A similar arc is visible on the blue-shifted intensity map. It is
tempting to associate these arcs with possible spirals revealing the presence
of a companion (Fonfría et al., 2019a). However, when mapping the
$V_{\text{z}}$ vs $\omega$ map of the intensity along such a presumed spiral
(right panel of the lower row of Figure 4), one sees that one cannot make
simply sense of such an interpretation.

Figure 2: Channel maps of the CO(2-1) line emission. The circles are drawn for
$\rho$=0.85 and 1.15, respectively. The colour scale is in units of Jy beam-1.

Figure 3: CO(2-1) emission. (a): $R$ distribution of the intensity integrated
over |$V_{\text{z}}$|<10 km s-1. (b): $V_{\text{z}}-R$ map of intensity (Jy
arcsec-1) integrated over position angles. Three ellipses are defined by
$\rho$=1/$\sqrt{2}$, 1 and $\sqrt{2}$. (c): dependence on $\rho$ of the
intensity averaged and multiplied by $R$ over the surface area of the red-
shifted (red) hemisphere, blue-shifted (blue) hemisphere and the whole
velocity range (black). (d): Doppler velocity spectrum integrated over the
circle $R$<6 arcsec. Note that on the pair of leftmost panel the contribution
of continuum emission is clearly visible.

Figure 5 displays PV maps on the $V_{\text{z}}$ vs $\omega$ plane at shorter
distances from the star, between 0.2 and 1 arcsec. In addition to the
previously identified gas flow (diamond), it shows, within $R$$\sim$0.4
arcsec, a blob of emission (ellipse) covering between 0 and 5 km s-1 at mean
position angle $\omega$$\sim$270∘, which is associated with a western, red-
shifted mass ejection that we study in detail in the next section. Absorption
in the blue-shifted part of the shell is seen to possibly extend up to
$R$$\sim$0.5 arcsec, but cannot be invoked to explain its weaker emission when
compared with the red-shifted part over a much broader range of $R$.

In order to quantify the inhomogeneity of the shell structure, we have
compared the $\rho$ distributions of the CO(2-1) intensity measured in twelve
sectors of position angle, each 30∘ wide, with the mean distribution in Figure
6. In each sector we measure the resulting rms deviation from unity of their
ratio, evaluated in two different intervals of $\rho$. The results are listed
in Table 3. On average, they reach 37% and 73% for |$\rho-1$|<0.25 and
|$\rho-1$|<0.5, respectively, illustrating the importance of inhomogeneity.

Table 3: Rms deviations from a uniform expanding spherical shell. In each 30∘ sector (labelled 1 to 12 counter-clockwise, starting from 0<$\omega$<30∘) we calculate $\Delta$=$\sqrt{\frac{\sum_{\text{i}}(f_{\text{i}}/<f_{\text{i}}>-1)^{2}}{n}}$, where the sum runs over the $n$ bins of the relevant $\rho$ interval (first column) and where $f_{\text{i}}$ is the intensity measured in bin $i$. Sector | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12
---|---|---|---|---|---|---|---|---|---|---|---|---
$\Delta$(0.5<$\rho$<1.5) [%] | 109 | 104 | 54 | 109 | 25 | 36 | 47 | 92 | 67 | 61 | 43 | 132
$\Delta$(0.75<$\rho$<1.25) [%] | 57 | 60 | 16 | 28 | 10 | 30 | 41 | 29 | 56 | 57 | 24 | 39

Figure 4: CO(2-1) emission. Upper row: PV maps, $V_{\text{z}}$ vs $\omega$ for
1<$R$<2 arcsec (left), 2<$R$<3 arcsec (centre) and 3<$R$<4 arcsec (right).
Lower row: intensity maps (Jy arcsec-2 km s-1): from left to right, red-
shifted, blue-shifted, 0<$V_{\text{z}}$<3 km s-1 and $V_{\text{z}}$ vs
$\omega$ map (Jy degree-1) on the eastern “spiral” (10∘<$\omega$<180∘ &
4.5”$-\omega$/60∘<$R$<7.0”$-\omega$/45∘, as shown on the centre-right lower
panel).

Figure 5: CO(2-1) emission. Maps of intensity on the $V_{\text{z}}$ vs
$\omega$ plane for $R$ between 0.2 and 0.4 (a), 0.4 and 0.6 (b), 0.6 and 0.8
(c) and 0.8 and 1.0 (d) arcsec.

##  5 The close neighbourhood of the star

In the present section we study the emission of lines that probe the close
neighbourhood of the star, within $\sim$ 0.3 arcsec angular separation from
its centre. In addition to the high resolution CO(2-1) data, this includes the
vibrational ground state emission of the 29SiO(5-4) line and the emissions of
the sulphur oxide lines, SO(55-44), SO2(222,20-221,21) and SO2(132,12-121,11).
The latter is blended with a contribution of H13CN($\nu$=0,$J$=4-3) (hereafter
abbreviated as H13CN(4-3)) emission, which we discuss below. In the remaining
of the article, we refer to it as the SO2-HCN line. Figures 7 to 11 illustrate
the main features using a common format: channel maps and PV maps in both
$V_{\text{z}}$ vs $\omega$ and $V_{\text{z}}$ vs $R$, the latter being
displayed in four separate quadrants.

Figure 6: CO(2-1) distributions of $\rho$ in twelve 30∘ wide sectors of
position angle, $\omega$. In each panel, the range of $\omega$ is inserted and
the mean distribution is shown in red.

###  5.1 Observational results

The 29SiO(5-4) emission (Figure 7) is seen from the channel maps to be
dominantly west and slightly red-shifted. The $V_{\text{z}}$ vs $\omega$ map
locates the bulk of the emission between 0 and 4 km s-1 in $V_{\text{z}}$ and
between 200∘ and 340∘ in $\omega$. Two blobs of emission, separated by
$\sim$50-60∘ in $\omega$ and sharing a common mean Doppler velocity of $\sim$2
km s-1, are clearly identified from the channel maps and the $V_{\text{z}}$ vs
$\omega$ map. The south-western blob reaches maximum at $R$$\sim$0.1 arcsec
and the north-western blob at $R$$\sim$0.2 arcsec. The CO(2-1) emission
(Figure 8) displays a qualitatively similar pattern as the 29SiO(5-4)
emission, with red-shifted enhancements in the south-western and north-western
quadrants. The SO(55-44) (Figure 9), SO2(222,20-221,21) (Figure 10) and
SO2-HCN (Figure 11) emissions are relatively stronger in the blue-shifted
south-eastern quadrant. In summary, and qualitatively, the five lines display
clear enhancements of emission in three angular ranges, well separated from
each other, one slightly blue-shifted in the south-eastern quadrant and two
slightly red-shifted in the western hemisphere, one south-west and the other
north-west. We have checked that such strong anisotropy is not an artefact of
the imaging process by simulating visibilities, for the same observational
coverage, for a disc source having a radius of 0.5 arcsec and an isotropic
brightness decreasing radially as 1/$R$. The brightness of the image, obtained
with natural weighting, was found to deviate from the source brightness by
less than a few percent.

In order to compare quantitatively the emissions of the five lines, we define
three regions, called SE, SW and NW, with angular separations from the centre
of the star between 60 and 300 mas, covering $V_{z}$ and $\omega$ ranges
listed in Table 4. They have a same data cube volume of 0.48 arcsec2 km s-1
and are indicated by rectangles on the $V_{\text{z}}$ vs $\omega$ maps of
Figures 7 to 11. They contain well the features observed in these figures and
take due account of the sizes of the beams and of the continuum emission.
Figure 12 displays, for each line emission, its intensity map integrated over
the interval |$V_{\text{z}}$|<6 km s-1 and the Doppler velocity spectra
measured in each of the three regions defined above. Table 4 lists the mean
and rms values of the Doppler velocity and position angle distributions
measured in each region for each line, together with the associated intensity.

Table 4: Main features of the distributions displayed in Figure 12. The mean and rms values of $V_{\text{z}}$ are in km s-1 and the intensities in Jy km s-1. In all cases a 3$\sigma$ cut has been applied to the data. The lower rows are a reminder of the beam dimensions (in mas) and of the noise (in mJy beam-1). For each of the three regions and of the five lines we list the mean values of the Doppler velocity and position angle, <$V_{\text{z}}$> and <$\omega$> calculated over the region using the flux density as weight. Similarly, we list the root-mean-square deviations, Rms($V_{\text{z}}$) and Rms($\omega$) calculated the same way. Region |  | CO(2-1) |  29SiO(5-4) | SO(55-44) | SO2(222,20-221,21) | SO2(132,12-121,11) | Mean
---|---|---|---|---|---|---|---
| <$V_{\text{z}}$> |  $-$1.2 |  $-$0.3 |  $-$0.4 |  $-$1.4 |  $-$1.1 |  $-$0.8
SE | Rms($V_{\text{z}}$) | 1.8 | 1.5 | 1.6 | 1.8 | 1.3 | 1.5
$-$5<$V_{\text{z}}$<2 km s-1 | <$\omega$> | 129∘ | 137∘ | 130∘ | 132∘ | 133∘ | 133∘
90∘<$\omega$<180∘ | Rms($\omega$) | 25∘ | 25∘ | 24∘ | 23∘ | 24∘ | 24∘
| Intensity | 0.35 | 0.71 | 0.13 | 0.08 | 0.81 | $-$
| <$V_{\text{z}}$> | 1.2 | 1.1 | 1.7 | 1.4 | 0.6 | 1.1
SW | Rms($V_{\text{z}}$) | 1.7 | 1.5 | 1.7 | 1.8 | 1.7 | 1.6
$-$2<$V_{\text{z}}$<5 km s-1 | <$\omega$> | 232∘ | 230∘ | 220∘ | 214∘ | 216∘ | 227∘
180∘<$\omega$<270∘ | Rms($\omega$) | 24∘ | 23∘ | 19∘ | 24∘ | 24∘ | 22∘
| Intensity | 0.59 | 2.19 | 0.12 | 0.04 | 0.61 | $-$
| <$V_{\text{z}}$> | 0.6 | 1.0 | 1.0 | $-$ | 0.5 | 0.8
NW | Rms($V_{\text{z}}$) | 1.6 | 1.5 | 1.0 | $-$ | 1.7 | 1.5
$-$2<$V_{\text{z}}$<5 km s-1 | <$\omega$> | 305∘ | 305∘ | 306∘ | $-$ | 312∘ | 305∘
270∘<$\omega$<360∘ | Rms($\omega$) | 25∘ | 21∘ | 12∘ | $-$ | 25∘ | 22∘
| Intensity | 0.62 | 2.19 | 0.02 | $-$ | 0.53 | $-$
Beam | 43$\times$36/33∘ | 47$\times$44/40∘ | 46$\times$38/34∘ | 46$\times$37/34∘ | 49$\times$44/$-$11∘ | $-$
Noise | 0.8 | 0.7 | 0.5 | 0.8 | 2.1 | $-$
Total intensity | 1.56 | 5.09 | 0.27 | 0.12 | 1.95 | $-$
Share SE/SW/NW (%) | 22/38/40 | 14/43/43 | 48/44/7 | 67/33/0 | 42/31/27 | $-$

In order to comment on these results, and to suggest plausible
interpretations, we shall use the predictions of a local thermal equilibrium
(LTE) regime as a reference with which to compare our results. We recall the
relevant arithmetic in the following sub-section.

Figure 7: 29SiO(5-4) emission without continuum subtraction. Upper row: Left,
channel maps. The crosses show the position of the star. The colour scale is
in units of Jy beam-1. Right, PV map, $V_{\text{z}}$ vs $\omega$, for
0.04<$R$<0.3 arcsec. The rectangles delineate the regions defined in Table 4,
from left to right, SE, NW and SW. Lower row: PV maps, $V_{\text{z}}$ vs $R$,
for 0∘<$\omega$<90∘, 90∘<$\omega$<180∘, 180∘<$\omega$<270∘ and
270∘<$\omega$<360∘, from left to right.

Figure 8: CO(2-1) emission. Same as Figure 7.

###  5.2 LTE approximation and temperature dependence

In the LTE approximation, for a given velocity $V_{\text{z}}$ and a brightness
$I_{0}$ [Jy arcsec-2] on the entrance side of a slab of thickness
d$z$[arcsec], density $n$[molecules cm-3] and temperature $T$[K], the
brightness $I$ [Jy arcsec-2] at the exit side, reads

$I=I_{0}e^{-\tau}+\varepsilon(1-e^{-\tau})/\tau=\varepsilon/\tau+(I_{0}-\varepsilon/\tau)e^{-\tau}$
(1)

where $\varepsilon$ describes the unabsorbed emission of the slab, and $\tau$
its opacity.

$\displaystyle\varepsilon$
$\displaystyle={(hc)/(4\pi\Delta{V})}A_{\text{ji}}f_{\text{pop}}n\text{d}z$
(2) $\displaystyle=\frac{0.558\,10^{6}}{\Delta{V}\text{[km
s${}^{-1}$]}}A_{\text{ji}}\text{[Hz]}f_{\text{pop}}n\text{[mol.
cm${}^{-3}$]}\text{d}z\text{[arcsec]}d\text{[pc]}$ (3)

Here, $h$ is the Planck constant, $c$ the light velocity, $\Delta{V}$ the FWHM
of the line profile, $A_{\text{ji}}$ the Einstein coefficient, $n$ the density
and $d$ the distance of the star from Earth;

$f_{\text{pop}}=(2J+1)e^{-E_{\text{u}}/T}/Q$ (4)

where $J$ and $E_{\text{u}}$[K] are the angular momentum quantum number and
energy of the upper level and $Q=T/k$ is the partition function. Parameters
$A_{\text{ji}}$, $E_{\text{u}}$ and $k$ are given in Table 2 together with the
frequency $f$. The opacity is given by the relation ($\Delta{E}$ is the energy
of the transition):

$\displaystyle\tau$ $\displaystyle=\frac{c^{2}}{2h}\varepsilon\frac{e^{\Delta
E/T}-1}{f^{3}}$ (5) $\displaystyle=2.88\,10^{7}\varepsilon\mbox{[Jy
arcsec${}^{-2}$]}\frac{e^{\Delta E/T}-1}{f\mbox{[GHz]}^{3}}.$ (6)

Figure 9: SO(55-44) emission. Same as Figure 7.

Figure 10: SO2(222,20-221,21) emission. Same as Figure 7.

Figure 11: SO2(132,12-121,11)+H13CN(4-3) emission. Same as Figure 7.

Neglecting opacity and the temperature dependence of $k$, the temperature
dependence of $\varepsilon$ is governed by a factor
$f_{\text{T}}=e^{-E_{\text{u}}/T}/T$: for $T>>E_{\text{u}}$, $f_{\text{T}}\sim
1/T$ independently from $E_{\text{u}}$. When comparing two lines, the ratio of
the two factors is
$f_{\text{T1}}/f_{\text{T2}}$=e${}^{(E_{\text{u2}}-E_{\text{u1}})/T}$. To the
extent that we deal with temperatures in excess of $\sim$200 K, this ratio is
between $\sim$0.7 and 1 for most lines: we cannot expect temperature to cause
important differences between the relative line emissions. The only exception
is the SO2(222,20-221,21) line, for which
$f_{\text{T}}$(SO2)/$f_{\text{T}}$(CO)=e-231/T, namely $\sim$0.3 at 200 K and
$\sim$0.1 at 100 K.

We also remark that the ratio of opacity to unabsorbed emissivity,
$\tau/\epsilon$, is proportional to (e${}^{\Delta{E}/T}-1$)/$f^{3}$. For
$\Delta{E}<<T$, $\tau/\epsilon$ is therefore inversely proportional to
temperature and to the square of the frequency, namely $\sim$2.5 times smaller
for Band 7 than for Band 6 data.

###  5.3 Discussion of the results

We are now in a position to discuss the results summarised in Table 4.
Averaging over the five lines, the mean velocity <$V_{z}$> of the emission of
the SE region is blue-shifted by 0.8 km s-1, that of the SW region red-shifted
by 1.1 km s-1 and that of the NW region red-shifted by 0.8 km s-1. Even if the
outflows are inclined by as little as 10∘ with respect to the plane of the
sky, their mean space velocity does not exceed $\sim$6 km s-1: we are dealing
with slow streams, which barely overcome the star gravity (the escape velocity
from a 0.7 solar mass star at an angular distance of 300 mas from its centre
is $\sim$6 km s-1). In each region, the rms deviations of $V_{z}$ and $\omega$
from their mean is $\sim$80% of the value corresponding to a uniform
distribution, showing that the selected regions cover well the observed
outflows.

A first important remark is that emission is shared very differently between
the different regions. While the CO(2-1) and 29SiO(5-4) lines display similar
shares between the three regions (on average, 18%/41%/41% in SE/SW/NW,
respectively), the shares of the SO and SO2 lines are very different, with
strong dominance in the SE region and, in the case of the Band 6 lines
(SO(55-44) and SO2(222,20-221,21)), near absence in the NW region. Such
important differences challenge interpretation.

The Band 7 SO2-HCN line is a blend of the SO2(132,12-121,11) line with the
H13CN(4-3) line, which is blue-shifted by $\sim$1.1 km s-1 with respect to the
SO2 line. Figure 13 displays the observed radial dependence of the intensities
of the SO2(222,20-221,21) and SO2-HCN emissions. While the latter remains at
an approximate level of 2-5 Jy arcsec-2 km s-1 over the whole $R$ range (60 to
300 mas) in each of the three regions, the former drops rapidly when $R$
increases and nearly vanishes in the NW region. This suggests that HCN
emission dominates over SO2 emission over most of the $R$ range and that SO
and SO2 emissions are both strongly depressed in the western hemisphere,
nearly absent in the NW region. In the remaining of the article, we take it as
granted that such is the case. Accordingly, we interpret the emission of the
SO2-HCN line as dominated by emission of the H13CN(4-3) line for
$R$>$\sim$0.15 arcsec and the emissions of the SO(55-44), SO2(222,20-221,21)
and SO2(132,12-121,11) lines as being confined within $\sim$0.15 arcsec from
the centre of the star, as illustrated in the lower panels of Figure 13. Such
confinement is at strong variance with the much broader radial distributions
assumed by Danilovich et al. (2016), Van de Sande et al. (2020) and Massalkhi
et al. (2020) and its vicinity from continuum emission prevents a reliable
study. The similarity between the SO and SO2 emissions supports the assumption
that SO2 is essentially produced (Cherchneff, 2006) via the reaction:

$\text{SO+OH}\longrightarrow\text{SO}_{2}+\text{H}$ (7)

and suggests that SO and SO2 molecules are destroyed by the same mechanism.
However, the observed confinement is not expected. As remarked by Massalkhi et
al. (2020) photodissociation by UV radiation is equally probable for SO and
SiO molecules: Figure 13 excludes an interpretation of the confinement in
terms of photodissociation of the SO and SO2 molecules. Confinement within 1-2
stellar radii (60-150 mas) is predicted by chemical models for carbon-rich
stars, the absence of OH molecules at larger distances preventing formation of
SO molecules via the reaction (Cherchneff, 2006):

$\text{S+OH}\longrightarrow\text{SO+H}$ (8)

However, as soon as C/O falls below unity, SO formation extends well beyond 5
stellar radii (60-150 mas). Agúndez et al. (2020) use a chemical equilibrium
model that predicts confinement within 5-10 stellar radii for Mira stars,
however with uncertainties at the level of an order of magnitude.

To get some insight into the effect of opacity, we display in Figure 14
Doppler velocity spectra observed over the stellar disc ($R$<30 mas) and
around it (30<$R$<50 mas). In the ring around the stellar disc, where the
continuum level is $\sim$17% of its value over the stellar disc, absorption is
weak and indicates that opacity corrections in the radial range covered by
Table 4 are small. As expected, absorption is much stronger over the stellar
disc. In percentage of the continuum level, it reaches $\sim$70% at
$V_{z}$$\sim$$-$3 km s-1 for 29SiO(5-4) and $\sim$24% at $V_{z}$$\sim$6 km s-1
for CO(2-1). These differences reveal different contributions from out-flowing
and in-falling gas, depending on the radial range being probed and are briefly
discussed in the next subsection.

In order to perform a more quantitative analysis of the observed intensities
listed in Table 4, we use the LTE description as reference. In the radial
range covered by Table 4, 60 to 300 mas, we expect the temperature to decrease
from $\sim$1300-1500 K to $\sim$300-500 K (Fonfría et al., 2020) and the
factor e-Eu/T is close to unity. We calculate accordingly, for each of the
three regions and for each line, the ratio between the observed intensity
(Table 4) and the factor $F=A_{ji}(2J+1)k\text{e}^{-Eu/T}$ calculated at
$T$=1000 K using the line parameters listed in Table 2. In the LTE
approximation, neglecting absorption, this ratio is proportional to the
abundance of the excited molecule, namely to the global density in each region
and to the relative molecular abundances. The latter are particularly
informative as they reveal important differences between the different lines.
We list in Table 5, for each region and for each line, the calculated ratio of
the relevant molecular abundance to the 29SiO abundance chosen as reference.
We also list, in the same table, abundances obtained from single dish
observations using broad and isotropic radial distributions. The main results
can be summarized as follows:

(i) The observed CO/SiO abundance ratios are within $\pm$30% equal to the
abundance ratios obtained from single dish observations, 30% larger in the SE
region, 30% smaller in the SW and NW regions. This implies that within the
large uncertainties attached to these evaluations, absorption and deviations
from an LTE regime do not much influence the evolution of the outflows. Namely
the presence of shocks suggested by studies of continuum emission and
molecular abundances is confined to the very close neighbourhood of the star,
well within 60 mas. Yet, small differences between different regions of the
CO/SiO abundance ratio would not be surprising as the SiO emission is more
sensitive to temperature than the CO emission, making SiO a good shock tracer.

(ii) The observed SO/SiO and SO2/SiO abundance ratios are much smaller in the
western hemisphere, and particularly in the NW region, than in the SE region.
However, the confinement of the SO and SO2 molecules within $\sim$0.15 arcsec
from the centre of the star, for which strong evidence has been obtained,
makes a reliable quantitative analysis difficult. As clearly illustrated in
Figures 9 and 10, the emission of these molecules does not extend radially
much beyond continuum emission: better angular resolution and sensitivity
would be required for a reliable analysis.

(iii) The observed H13CN/29SiO abundance ratio, evaluated by assuming that
H13CN emission dominates over SO2 emission in the NW region, is $\sim$7%. It
corresponds to a relative abundance of H12CN of $\sim$10-6, $\sim$4 times
larger than obtained from single dish analyses. This is consistent with
observations in the other regions, but a reliable evaluation of the HCN
abundance in the SE region would require observing the emission of other,
unblended, lines.

Table 5: Comparison between observations and LTE predictions for the $\nu$=0 line emissions in the SE, SW and NE regions. Single dish abundances relative to H2 are from (a) González Delgado et al. (2003), (b) Schöier et al. (2013) and (c) Danilovich et al. (2016) (value obtained for R Dor) and (g) Massalkhi et al. (2020). Isotopic ratios are from (e) De Beck & Olofsson (2018) and (f) Ramstedt & Olofsson (2014). The factors $F=A_{\text{ji}}(2J+1)k\text{e}^{-Eu/T}$ are calculated at $T$=1000 K. Relative abundances normalised to the 29SiO value, $A_{\text{SiO}}$, are listed for single dish observations and for the present work in regions SE, SW and NW separately. For the HCN line we quote the values obtained using the observed blended line intensities as upper limits. Line | CO(2-1) |  29SiO(5-4) | H13CN(4-3) | SO(55-44) | SO2(222,20-221,21) | SO2(132,12-121,11)
---|---|---|---|---|---|---
Abundance | 2$\times$10-4 (a) | 13$\times$10-6 (a) | 2.5$\times$10-7 (b) | 6.7$\times$10-6 (c) | 5$\times$10-6 (c) | 5$\times$10-6 (c)
($f_{0}=n/n_{H2}$) |  $\times$0.08 (e) |  $\times$0.08 (e) | 6.6$\times$10-7 (g) | <1.1$\times$10-7 (g) | <1.1$\times$10-7 (g)
$A_{\text{SiO}}$ Single dish | 192 | 1 | 0.019 | 6.4 (c)/0.6 (g) | 4.8 (c)/<0.11 (g) | 4.8 (c)/<0.11 (g)
$F$ | 8.92$\times$10-3 | 4.53 | 14.3 | 0.44 | 0.069 | 0.124
A${}_{\text{SiO}}$ this work | SE | 250 | 1 | < 0.36 | 1.9 | 7.2 |
SW | 140 | 1 | <0.089 | 0.6 | 1.2 |
NW | 140 | 1 | <0.076 | 0.1 | 0 |

Finally, we remark that the complexity of the observed morpho-kinematics
prevents confirmation of two predictions made earlier by Fonfría et al.
(2019b) and Wiesemeyer et al. (2009). The former authors speculated that the
high resolution CO(2-1) observations might suggest the presence of rotation in
the close neighbourhood of the star. It is difficult, however (see Figure 8),
to separate a possible effect of rotation from the contribution of the south-
western outflow and evidence for a possible rotation cannot be stated with
reasonable confidence. The latter authors have given arguments in favour of
the presence of an evaporating Jovian planet orbiting R Leo at some 30 mas
from its centre. According to their definition of the orbit parameters, such a
planet would have been south-east of the star at the time of the present
observations and blue-shifted by some 4-5 km s-1, in a region where we observe
no feature that might be revealing its presence: again, speculation about the
possible presence of a planet cannot be made with reasonable confidence from
the present observations.

Figure 12: Intensity maps for |$V_{\text{z}}$|<6 km s-1 (up) and line spectra
in the ($R$,$\omega$) ranges of the regions SE, SW and NW (down). The position
of the star and the radii of 0.1 and 0.2 arcsec are indicated by crosses and
black circles respectively. The colour scales are in units of Jy arcsec-2 km
s-1.

Figure 13: Radial dependence of the intensities (continuum substracted) of the
SO2(222,20-221,21) (red) and SO2-HCN (black) lines (upper panels) and of the
SO2(222,20-221,21) (red), SO(55-44) (blue) and 29SiO(5-4) (black) lines (lower
panels) in the SE, SW and NW regions defined in Table 4.

###  5.4 Summary

In summary, within 300 mas from the centre of the star, we observe a very
complex morpho-kinematics giving evidence for anisotropic emission and, within
40 mas from the centre of the star, we find evidence for simultaneous presence
of outflowing and in-falling gas. Similar features have been observed
previously in several other oxygen-rich AGB stars, such as R Dor (Hoai et al.,
2020; Nhung et al., 2021), W Hya (Hoai et al., 2021; Vlemmings et al., 2017)
and $o$ Ceti (Wong et al., 2016; Khouri et al., 2018; Nhung et al., 2022a).
The angular and radial distributions of the pattern of in-falling and out-
flowing gas, its evolution as a function of stellar phase, and how it is
influenced by anisotropy, cannot be accurately predicted in the present state
of our understanding. In particular the radial range over which the
simultaneous presence of in-falling and out-flowing gas contributes to line
broadening cannot be precisely defined. In the present case of R Leo, Figure
14 has shown that Doppler velocities reaching beyond 10 km s-1 are observed
over the stellar disc for the 29SiO(5-4), CO(2-1) and SO(55-44) lines. They
decrease to $\sim$10 km s-1 for $R$ between 30 and 50 mas and reach terminal
values of $\sim$5 km s-1 for $R$ beyond $\sim$100 mas (Figure 15). In the case
of $o$ Ceti (Nhung et al., 2022a), at a distance of 100 pc instead of 114 pc
for R Leo, a similar decrease is observed, from $\sim$20 km s-1 to $\sim$6 km
s-1 between $\sim$ 50 mas and $\sim$ 150 mas. However, while $o$ Ceti displays
approximate isotropy in this radial range, R Leo shows important anisotropy,
with much stronger emission in the southern than northern hemisphere.

The diversity of patterns displayed in Figure 14 suggests that the
SO2(222,20-221,21) line probes too high temperatures and/or too small
abundances to reveal significant absorption, while the CO(2-1) line probes too
large distances to reveal important anisotropy. The different patterns
displayed by in-falling gas are more difficult to interpret. Fonfría et al.
(2019b) have commented on the cases of the CO(2-1) and 29SiO(5-4) lines, both
in the $\nu$=0 and $\nu$=1 lines, and underscored the complexity of the
implied morpho-kinematics.

Figure 14: Doppler velocity spectra observed above the stellar disc (black,
$R$<30 mas) and around it in four different quadrants (30<$R$<50 mas, colour
code in the insert of the left panel). Lines are specified on top of each
panel. Each spectrum, evaluated from cubes without continuum subtraction, has
been shifted downward to have the flux density cancel outside the line.

Three slow gas streams have been identified, covering projected angular
distances from the centre of the star of up to $\sim$400 mas with rms spread
in $V_{z}$ and $\omega$ of typically 1.5 km s-1 and 22∘, respectively. Beyond
40 mas angular separation from the centre of the star, the emissions of the
CO(2-1), 29SiO(5-4) and H13CN(4-3) molecular lines do not reveal major anomaly
when compared with LTE predictions, showing neither strong absorption
contributions nor important deviations from an LTE regime. This is at variance
with the regime at stake within 40 mas, known to host shocks and turbulences
from the study of continuum emission (Vlemmings et al., 2019) and of the non-
equilibrium chemistry required to explain the molecular abundances of species
formed in this radial range (Bieging et al., 2000; Schöier et al., 2013;
Massalkhi et al., 2020). In contrast with the CO(2-1), 29SiO(5-4) and
H13CN(4-3) line emissions, the SO(55-44) and SO2(222,20-221,21) line emissions
display features, which current chemical models fail to explain. While the
evidence for similar confinement of both SO and SO2 molecules within
$\sim$0.15 arcsec from the centre of the star in each of the three outflows
can be stated with confidence, a reliable quantitative study would require new
observations and a better understanding of the chemistry at stake.

Figure 15: Doppler velocity spectra of the CO(2-1) and 29SiO(5-4) line
emissions in 50 mas wide rings as indicated in the insert.

##  6 Vibrationally excited SiO lines

The emissions of the vibrationally excited SiO lines, 28SiO($\nu$=1,5-4) and
28SiO($\nu$=2,5-4) in Band 6 and 28SiO($\nu$=1,8-7) in Band 7, when compared
to that of the 29SiO($\nu$=0,5-4) line, probe higher temperature regions
closer to the star (Table 2). Accounting for the 29SiO/28SiO isotopic ratio,
the LTE values of the $J$=5-4 line intensities for $\nu$=0 and $\nu$=1 are
equal for a temperature $T$$\sim$700 K and in a ratio $\sim$1/5 for $T$=2000K.
Figures 16 to 18 display the same information for these lines as Figure 7 does
for the ground state. The emission of the $\nu$=1 lines is dominantly north,
evolving from north-east in the blue-shifted hemisphere to north-west in the
red-shifted hemisphere, and is largely confined within 100 mas from the centre
of the star, reaching up to 200 mas for the $J$=8-7 line. The emission of the
$\nu$=2 line is limited to a small region of the emission of the $\nu$=1
lines, north of the star, with a mean Doppler velocity of $\sim$$-$5 km s-1
and confined within $\sim$80 mas. When inspected along $V_{\text{z}}$, the
emission is seen to consist of three different components at mean Doppler
velocities of $\sim$$-$8 to $-$2 km s-1, $\sim$$-$2 to 2 km s-1 and $\sim$4 to
8 km s-1, respectively.

Figure 16: 28SiO($\nu$=1,5-4) emission. Upper row: Left, channel maps. The
crosses show the position of the star. The colour scale is in units of Jy
beam-1. Right, PV map, $V_{\text{z}}$ vs $\omega$, for 0.04<$R$<0.3 arcsec.
Lower row: PV maps, $V_{\text{z}}$ vs $R$, for 0∘<$\omega$<90∘,
90∘<$\omega$<180∘, 180∘<$\omega$<270∘ and 270∘<$\omega$<360∘, from left to
right.

Figure 17: 28SiO($\nu$=2,5-4) emission. Same as Figure 16.

Figure 18: 28SiO($\nu$=1,8-7) emission. Same as Figure 16.

Figure 19 (left) illustrates the peculiarity of the 28SiO($\nu$=1,5-4)
emission by comparing its Doppler velocity spectrum, integrated within $R$<0.3
arcsec, with those of the $\nu$=0 and $\nu$=2 lines: its emission is an order
of magnitude more intense and it covers a much broader interval of Doppler
velocities, reaching beyond $\sim$$\pm$16 km s-1. From Table 2, the LTE
approximation predicts the intensity of the $\nu$=1, $J$=8-7 line to be a
factor $\sim$7 larger than that of the $\nu$=1, $J$=5-4 line in the optically
thin limit and $\sim$2.5 times larger in the optically thick limit, while in
fact it is over 3 times smaller (Figure 19, centre). Such features are
evidence for masing (Gray et al., 2009), the latter probably being an effect
of the wavelength dependence of the stimulated emission probability.

Indeed, the emission of the $\nu$>0 lines is known to host strong masers, the
amplitude of which is highly variable. As was mentioned in the introduction,
they have been the subject of numerous outstanding VLBA observations. As
remarked by Cotton et al. (2009), they appear within a few stellar radii of
the stellar surface, typically $\sim$30 mas from the centre of the star,
between the hot inner envelope and the cooler region where the dust forms.
They tend to occur in clumpy, partial rings centred on the star.

The presence of masers does not simply trace local SiO abundance but is a
function of the conditions for population inversion and the direction of maser
beaming. Their amplification depends on the length of the path over which they
can develop, and therefore takes values that are difficult to predict. The
blue-and red-shifted emissions observed in the present case may reveal the
presence of an expanding layer of gas reminiscent of the contemporaneous
observation (October 3 and 11 instead of September 21 and October 27) of the
extended atmosphere made by Vlemmings et al. (2019) within 1-2 stellar radii.
These authors model the continuum emission with a uniform elliptical stellar
disc and find a temperature of $\sim$1900$\pm$100 K at an angular separation
of $\sim$22 mas from the centre of the star. The continuum emission probes the
same radial range as do the $\nu$=1 and $\nu$=2 SiO lines and these authors
model their observations as emission from an increased opacity layer expanding
at a radial velocity of $\sim$10.6 km s-1. If the actual expansion velocity of
the SiO masers seen on the $\nu$=1 line is the same as the 10.6 km s-1
inferred for the continuum, then a $|V_{z}|\sim$6 km s-1 would place the
masing clumps at an inclination angle of 30-40∘ with respect to the plane of
the sky. The right panel of Figure 19 sketches the corresponding geometry. The
maximum SiO velocity (Figure 15 and left panels of Figure 19) is $\sim$10 km
s-1, which is consistent with this picture. The clumpy nature of the emission
(north in the blue-shifted hemisphere and north-west in the red-shifted
hemisphere) cannot be simply interpreted in terms of gas density but simply
reveals regions where masers are more intense.

No significant absorption can be revealed above and around the stellar disc
(Figure 20), in strong contrast with the $\nu$=0 lines (Figure 14), the
$\nu$>0 lines probing a region where masing is important and where the gas is
too hot to absorb strongly, as was already the case for the SO2(222,20-221,21)
line (Section 5.2).

Figure 19: Left: Doppler velocity spectra of the SiO(5-4) line emissions
integrated in the circle $R$<0.3 arcsec. Centre: Doppler velocity spectra of
the SiO($\nu$=1,5-4) and SiO($\nu$=1,8-7) line emissions integrated in the
circle $R$<0.2 arcsec (continuum subtracted). Right: schematic of the
suggested geometry.

Figure 20: Same as Figure 14 for transitions from vibrationally excited
states.

##  7 Conclusions

A global view of the morpho-kinematics of the circumstellar envelope of R Leo
has been presented, which complements earlier studies. In short, it
distinguishes between four regions covering different radial ranges: within
$\sim$2 stellar radii, using continuum emission and $\nu$>0 maser lines as
probes, evidence is found for an expanding shell with a radial velocity of
$\sim$10 km s-1; between $\sim$2 and $\sim$10 stellar radii, in a region
probed in particular by the emission of SO and SO2 $\nu$=0 molecular lines and
hosting in its inner part both in-falling and outflowing gas, evidence is
found for a non-LTE regime suggesting that shocks play an important role;
between $\sim$10 and $\sim$30 stellar radii, in a region probed in particular
by the $\nu$=0 emission of SiO, CO and HCN molecules and hosting three
distinct outflows, LTE becomes progressively dominant; beyond $\sim$30 stellar
radii, in a region probed by the emission of CO molecules, evidence is found
for patchy and episodic mass ejection, with an enhanced layer of emission
having a mean radial velocity of $\sim$5.5 km s-1 and a mean angular
separation from the centre of the star of $\sim$6 arcsec.

At variance with preliminary analyses presented by Fonfría et al. (2019a, b),
we have shown that continuum emission is nearly circular and gives
insufficient evidence to claim, or refute, the possible presence of an
evaporating Jovian planet and/or of rotation in the close neighbourhood of the
star. Instead, we give evidence for three distinct outflows, each covering a
solid angle at steradian scale,which have been described in detail in Section
5. As they cover nearly 400 mas in projected angular distance from the centre
of the star, and have a space velocity expected to not significantly exceed
$\sim$6 km s-1, they have been present for several decades. While it is
tempting to associate such outflows with possible convective cells on the
surface of the star, this seems an order of magnitude longer time than the
expected lifetime of a given granulation pattern, underscoring the lack of
detailed understanding of the mechanism at stake. A study of the relative
abundances of the molecular species present in these outflows has revealed an
unexpected confinement of SO and SO2 molecules within $\sim$0.15 arcsec from
the centre of the star, suggesting a complex competition between chemical
reactions contributing to the formation and destruction of the parent SO
molecules. The similar morpho-kinematics at stake for the emission of the SO
and SO2 molecules has given support that the latter are dominantly produced by
oxygenation of the former. Evidence for different SO/SiO ratios in each of the
three outflows is strong (lower panels of Figure 13) suggesting that at the
short distances probed by the SO and SO2 molecules, LTE does not apply and
shocks are likely to play a significant role.

In contrast with SO and SO2 molecules, the relative abundances of the CO, SiO
and HCN molecules are consistent, within large uncertainties, with
expectation.

Very close to the star, evidence for the simultaneous presence of expanding
and in-falling gas, reminiscent of observations made in several other oxygen-
rich AGB stars, has been presented and commented. A study of vibrationally
excited SiO lines, expected to host important masers, has been shown in
Section 6 to probe an expanding layer of hot gas, just above the photosphere,
consistent with earlier studies by Vlemmings et al. (2019).

At larger distances from the star, where depletion of the SiO molecules by
condensation on dust grains and photo-dissociation of the SiO, SO and SO2
molecules are expected to be significant, the CO line emission traces the mass
loss history over the past few centuries, giving evidence for a very patchy
morpho-kinematics with inhomogeneity at the level of $\sim$40%, and revealing
an episode of enhanced mass-loss seen as a layer of increased emission at a
mean distance of 6 arcsec from the centre of the star and an expansion
velocity reaching up to 9 km s-1 and having an average value of $\sim$5.5 km
s-1. An escape velocity of 6 km s-1 from a 0.7 solar mass star is reached at
$\sim$300 mas: some acceleration is therefore necessary after the initial
boost. Understanding its nature requires independent information about dust
formation. The dust emission coefficient in the mid-infrared is known to be
low (Sloan & Price, 1998) and Paladini et al. (2017), using VLTI/MIDI
observations, remark that R Leo displays no significant 8 $\mu$m silicate
feature in its spectrum and speculate that the important brightness asymmetry
supports a large grain scenario of dust formation.

We noted the presence of patches of emission inside the shell, in particular
of some arcs that may suggest the presence of spirals associated with the wake
emission of a companion; however, we have shown that such an interpretation
cannot be reliably supported or refuted from the present data alone.

The complexity of the observed morpho-kinematics, which had been underscored
by all earlier studies, together with the strong anisotropy of line emission
ratios, provide evidence for non-equilibrium chemistry, supporting the role
played by shocks and/or density and temperature inhomogeneity in the
generation of the nascent wind. But it also makes it hard to develop accurate,
comprehensive models with confidence, restricting reliable interpretations to
considerations based on very crude and approximate modelling. When observed in
sufficient detail, the inner layers of the circumstellar envelopes of oxygen-
rich AGB stars are all different. Their observation shows the importance of
collecting a sufficient sample to be able to interpret reliably their
diversity in terms of state-of the art simulations such as proposed by Höfner
& Freytag (2019), in particular for being able to describe more precisely the
role played by convective cells in defining the pattern of mass ejections.
While such simulations provide a useful framework in which to describe the
mechanisms at stake in the genesis of the nascent wind, many questions remain
unanswered, requiring new observations: How does the pattern of outflows
depend on the stellar phase? What distinguishes outflows lasting for a few
decades from mass ejections covering only a few years? What causes the CSE to
retain, in some cases, a same axial symmetry over centuries? An accurate model
of the morpho-kinematics of the observed line emissions in the neighbourhood
of the star should be able to define precisely the angular size and time
duration of the patches of emission associated with the convective cell
granulation, but we are still far from such achievement.

## Acknowledgements

We are deeply indebted and grateful to the referee, Dr Anita Richards, for a
very careful reading of the manuscript and pertinent comments that helped
greatly with improving both the form and the substance of the present article.
We thank Dr Stéphane Guilloteau for guidance in producing Table 2. This paper
makes use of the following ALMA data: ADS/JAO.ALMA#2016.1.01202.S,
ADS/JAO.ALMA#2017.1.00862.S. ALMA is a partnership of ESO (representing its
member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST
and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the
Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and
NAOJ. We are deeply indebted to the ALMA partnership, whose open access policy
means invaluable support and encouragement for Vietnamese astrophysics.
Financial support from the World Laboratory, the Odon Vallet Foundation and
the Vietnam National Space Center is gratefully acknowledged. This research is
funded by the Vietnam National Foundation for Science and Technology
Development (NAFOSTED) under grant number 103.99-2019.368.

## Data Availability

The raw data are available on the ALMA archive: ADS/JAO.ALMA#2016.1.01202.S
and ADS/JAO.ALMA#2017.1.00862.S. The calibrated and imaged data underlying
this article will be shared on reasonable request to the corresponding author.

## References

  * Agúndez et al. (2020) Agúndez M., Martínez J. I., de Andres P. L., Cernicharo J., Martín-Gago J. A., 2020, A&A, 637, A59
  * Andriantsaralaza et al. (2022) Andriantsaralaza M., Ramstedt S., Vlemmings W. H. T., De Beck E., 2022, arXiv e-prints, p. arXiv:2209.03906
  * Bieging et al. (2000) Bieging J. H., Shaked S., Gensheimer P. D., 2000, ApJ, 543, 897
  * Bujarrabal et al. (1994) Bujarrabal V., Fuente A., Omont A., 1994, A&A, 285, 247
  * Cherchneff (2006) Cherchneff I., 2006, A&A, 456, 1001
  * Cotton et al. (2004) Cotton W. D., et al., 2004, A&A, 414, 275
  * Cotton et al. (2008) Cotton W. D., Perrin G., Lopez B., 2008, A&A, 477, 853
  * Cotton et al. (2009) Cotton W. D., Ragland S., Pluzhnik E., Danchi W. C., Traub W. A., Willson L. A., Lacasse M. G., 2009, ApJ, 704, 170
  * Danilovich et al. (2015) Danilovich T., et al., 2015, A&A, 581, A60
  * Danilovich et al. (2016) Danilovich T., De Beck E., Black J. H., Olofsson H., Justtanont K., 2016, A&A, 588, A119
  * Danilovich et al. (2020) Danilovich T., Richards A. M. S., Decin L., Van de Sande M., Gottlieb C. A., 2020, MNRAS, 494, 1323
  * De Beck & Olofsson (2018) De Beck E., Olofsson H., 2018, A&A, 615, A8
  * De Beck et al. (2010) De Beck E., Decin L., de Koter A., Justtanont K., Verhoelst T., Kemper F., Menten K. M., 2010, A&A, 523, A18
  * Desmurs et al. (2014) Desmurs J. F., Bujarrabal V., Lindqvist M., Alcolea J., Soria-Ruiz R., Bergman P., 2014, A&A, 565, A127
  * Etoka & Le Squeren (1997) Etoka S., Le Squeren A. M., 1997, A&A, 321, 877
  * Feast (1996) Feast M. W., 1996, MNRAS, 278, 11
  * Fedele et al. (2005) Fedele D., Wittkowski M., Paresce F., Scholz M., Wood P. R., Ciroi S., 2005, A&A, 431, 1019
  * Fonfría et al. (2019a) Fonfría J. P., Santander-García M., Cernicharo J., Velilla-Prieto L., Agúndez M., Marcelino N., Quintana-Lacaci G., 2019a, in ALMA2019: Science Results and Cross-Facility Synergies. p. 85, doi:10.5281/zenodo.3585368
  * Fonfría et al. (2019b) Fonfría J. P., Santander-García M., Cernicharo J., Velilla-Prieto L., Agúndez M., Marcelino N., Quintana-Lacaci G., 2019b, A&A, 622, L14
  * Fonfría et al. (2020) Fonfría J. P., Montiel E. J., Cernicharo J., DeWitt C. N., Richter M. J., 2020, A&A, 643, L15
  * Freytag et al. (2017) Freytag B., Liljegren S., Höfner S., 2017, A&A, 600, A137
  * Gaia Collaboration (2018) Gaia Collaboration 2018, VizieR Online Data Catalog, p. I/345
  * González Delgado et al. (2003) González Delgado D., Olofsson H., Kerschbaum F., Schöier F. L., Lindqvist M., Groenewegen M. A. T., 2003, A&A, 411, 123
  * Gray et al. (2009) Gray M. D., Wittkowski M., Scholz M., Humphreys E. M. L., Ohnaka K., Boboltz D., 2009, MNRAS, 394, 51
  * Haniff et al. (1995) Haniff C. A., Scholz M., Tuthill P. G., 1995, MNRAS, 276, 640
  * Herpin et al. (2006) Herpin F., Baudry A., Thum C., Morris D., Wiesemeyer H., 2006, A&A, 450, 667
  * Hinkle & Barnes (1979) Hinkle K. H., Barnes T. G., 1979, ApJ, 234, 548
  * Hoai et al. (2020) Hoai D. T., Nhung P. T., Darriulat P., Diep P. N., Ngoc N. B., Thai T. T., Tuan-Anh P., 2020, Communications in Physics, 30, 85
  * Hoai et al. (2021) Hoai D. T., Tuan-Anh P., Nhung P. T., Darriulat P., Diep P. N., Ngoc N. B., Thai T. T., 2021, JKAS, 54, 171
  * Höfner & Freytag (2019) Höfner S., Freytag B., 2019, A&A, 623, A158
  * Khouri et al. (2018) Khouri T., Vlemmings W. H. T., Olofsson H., Ginski C., De Beck E., Maercker M., Ramstedt S., 2018, A&A, 620, A75
  * Liljegren et al. (2018) Liljegren S., Höfner S., Freytag B., Bladh S., 2018, A&A, 619, A47
  * Massalkhi et al. (2020) Massalkhi S., Agúndez M., Cernicharo J., Velilla-Prieto L., 2020, A&A, 641, A57
  * Matthews et al. (2018) Matthews L. D., Reid M. J., Menten K. M., Akiyama K., 2018, AJ, 156, 15
  * Müller et al. (2005) Müller H. S. P., Schlöder F., Stutzki J., Winnewisser G., 2005, Journal of Molecular Structure, 742, 215
  * Nhung et al. (2021) Nhung P. T., Hoai D. T., Tuan-Anh P., Darriulat P., Diep P. N., Ngoc N. B., Phuong N. T., Thai T. T., 2021, MNRAS, 504, 2687
  * Nhung et al. (2022a) Nhung P. T., Hoai D. T., Tuan-Anh P., Darriulat P., Diep P. N., Ngoc N. B., Thai T. T., 2022a, ApJ, 927, 169
  * Nhung et al. (2022b) Nhung P. T., Hoai D. T., Tuan-Anh P., Darriulat P., Diep P. N., Ngoc N. B., Thai T. T., 2022b, JKAS, submitted
  * Ohnaka (2004) Ohnaka K., 2004, A&A, 424, 1011
  * Paladini et al. (2017) Paladini C., et al., 2017, A&A, 600, A136
  * Perrin et al. (1999) Perrin G., Coudé du Foresto V., Ridgway S. T., Mennesson B., Ruilier C., Mariotti J. M., Traub W. A., Lacasse M. G., 1999, A&A, 345, 221
  * Ramstedt & Olofsson (2014) Ramstedt S., Olofsson H., 2014, A&A, 566, A145
  * Schöier et al. (2013) Schöier F. L., Ramstedt S., Olofsson H., Lindqvist M., Bieging J. H., Marvel K. B., 2013, A&A, 550, A78
  * Sloan & Price (1998) Sloan G. C., Price S. D., 1998, ApJS, 119, 141
  * Soria-Ruiz et al. (2007) Soria-Ruiz R., Alcolea J., Colomer F., Bujarrabal V., Desmurs J. F., 2007, A&A, 468, L1
  * Teyssier et al. (2006) Teyssier D., Hernandez R., Bujarrabal V., Yoshida H., Phillips T. G., 2006, A&A, 450, 167
  * Van de Sande et al. (2020) Van de Sande M., Walsh C., Danilovich T., 2020, MNRAS, 495, 1650
  * Vlemmings et al. (2017) Vlemmings W., et al., 2017, Nature Astronomy, 1, 848
  * Vlemmings et al. (2019) Vlemmings W. H. T., Khouri T., Olofsson H., 2019, A&A, 626, A81
  * Watson et al. (2006) Watson C. L., Henden A. A., Price A., 2006, Society for Astronomical Sciences Annual Symposium, 25, 47
  * Wiesemeyer et al. (2009) Wiesemeyer H., Thum C., Baudry A., Herpin F., 2009, A&A, 498, 801
  * Wittkowski et al. (2016) Wittkowski M., Chiavassa A., Freytag B., Scholz M., Höfner S., Karovicova I., Whitelock P. A., 2016, A&A, 587, A12
  * Wong et al. (2016) Wong K. T., Kamiński T., Menten K. M., Wyrowski F., 2016, A&A, 590, A127
  * van Leeuwen (2007) van Leeuwen F., 2007, A&A, 474, 653