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\DOI{10.5802/crphys.185}
\datereceived{2023-11-17}
\daterevised{2024-03-05}
\dateaccepted{2024-03-20}
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%\begin{noXML}

\CDRsetmeta{articletype}{review}

\title{On the nascent wind of oxygen-rich AGB stars: scrutiny of a
sample of nearby stars}

\alttitle{Gen\`{e}se du vent des \'{e}toiles riches en oxyg\`{e}ne de
la branche AGB : examen d'un \'{e}chantillon d'\'{e}toiles proches}

\author{\firstname{Pierre} \lastname{Darriulat}\CDRorcid{0000-0002-8979-6898}\IsCorresp}
\address{Department of Astrophysics, Vietnam National Space Center, 
Vietnam Academy of Science and Technology, 18, Hoang Quoc Viet, 
Nghia Do, Cau Giay, Ha Noi, Vietnam}
\email[P. Darriulat]{darriulat@vnsc.org.vn}

\author{\firstname{Do Thi} \lastname{Hoai}\CDRorcid{0000-0002-3816-4735}}
\addressSameAs{1}{Department of Astrophysics, Vietnam National Space Center, 
Vietnam Academy of Science and Technology, 18, Hoang Quoc Viet, 
Nghia Do, Cau Giay, Ha Noi, Vietnam}
\email[D. T. Hoai]{dthoai@vnsc.org.vn}

\author{\firstname{Pham Thi Tuyet} \lastname{Nhung}\CDRorcid{0000-0002-0311-0809}}
\addressSameAs{1}{Department of Astrophysics, Vietnam National Space Center, 
Vietnam Academy of Science and Technology, 18, Hoang Quoc Viet, 
Nghia Do, Cau Giay, Ha Noi, Vietnam}
\email[P. T. Nhung]{pttnhung@vnsc.org.vn}

\author{\firstname{Pham Ngoc} \lastname{Diep}\CDRorcid{0000-0002-2808-0888}}
\addressSameAs{1}{Department of Astrophysics, Vietnam National Space Center, 
Vietnam Academy of Science and Technology, 18, Hoang Quoc Viet, 
Nghia Do, Cau Giay, Ha Noi, Vietnam}
\email[P. N. Diep]{pndiep@vnsc.org.vn}

\author{\firstname{Nguyen Bich} \lastname{Ngoc}\CDRorcid{0000-0002-5913-5554}}
\addressSameAs{1}{Department of Astrophysics, Vietnam National Space Center, 
Vietnam Academy of Science and Technology, 18, Hoang Quoc Viet, 
Nghia Do, Cau Giay, Ha Noi, Vietnam}
\email[N. B. Ngoc]{ntbngoc@vnsc.org.vn}

\author{\firstname{Tran Thi} \lastname{Thai}\CDRorcid{0000-0002-8408-4816}}
\addressSameAs{1}{Department of Astrophysics, Vietnam National Space Center, 
Vietnam Academy of Science and Technology, 18, Hoang Quoc Viet, 
Nghia Do, Cau Giay, Ha Noi, Vietnam}
\email[T. T. Thai]{ttthai@vnsc.org.vn}

\author{\firstname{Pham Tuan} \lastname{Anh}\CDRorcid{0000-0002-3773-1435}}
\addressSameAs{1}{Department of Astrophysics, Vietnam National Space Center, 
Vietnam Academy of Science and Technology, 18, Hoang Quoc Viet, 
Nghia Do, Cau Giay, Ha Noi, Vietnam}
\email[P. T. Anh]{ptanh@vnsc.org.vn}

\shortrunauthors

\keywords{\kwd{AGB stars}
\kwd{Circumstellar envelope}
\kwd{Radio lines}
\kwd{Visible/infrared emission}
\kwd{Gas/dust}
\kwd{Pulsation/convection}}

\altkeywords{\kwd{\'{E}toiles AGB}
\kwd{Enveloppe circumstellaire}
\kwd{Raies d'\'{e}mission radio}
\kwd{\'{E}mission visible/infrarouge}
\kwd{Gaz/poussi\`ere}
\kwd{Pulsation/convection}}

\thanks{Vietnam Academy of Science and Technology under grand number
THTETN.03/24-25, World Laboratory, Odon Vallet Foundation
and Vietnam National Space Center}

\begin{abstract}
The 
commonly accepted mechanism governing the formation of the nascent
wind in oxygen-rich AGB stars combines an initial boost above the
photosphere, given by shock waves resulting from stellar pulsations and
convective cell partition, with a subsequent acceleration fuelled by
the radiation pressure of the star on dust grains. We use six nearby
stars, for which detailed studies of visible and infrared observations
at the VLT and millimetre observations at ALMA are available, to assess
the extent to which the validity of this picture is currently
corroborated. We show that while providing a very useful guide to
current research and having received general support and suffered no
contradiction, it still requires many additional observations to be
reliably validated. In particular, observations of the highest possible
angular resolution at both millimetre and visible/infrared wavelengths,
performed in conjunction with measurements of the light curve, are
necessary to tell apart the respective roles played by convection and
stellar pulsations. The observed concurrence of high variability near
the photosphere with persistence over decades, or even centuries, of
the global anisotropy displayed by the CSE needs to be understood. New
observations of the close neighbourhood of the star are required to
elucidate the mechanism that governs rotation, in particular in the
cases of R Dor, L\textsubscript{2} Pup and EP Aqr. We argue that the presence of
stellar or planetary companions does not seriously impact the formation
of the nascent wind and only modifies its subsequent\unskip\break
evolution. 
\end{abstract}

\begin{altabstract}
Le m\'{e}canisme couramment accept\'{e} comme pr\'{e}sidant \`{a} la
formation du vent des \'{e}toiles AGB riches en oxyg\`{e}ne combine
deux effets : un \'{e}lan initial qui projette le gaz au-dessus de la
photosph\`{e}re, donn\'{e} par des ondes de choc produites par
pulsations stellaires et cellules de convection, suivi d'une
acc\'{e}l\'{e}ration aliment\'{e}e par la pression de radiation
stellaire sur des grains de poussi\`{e}re. Nous examinons dans quelle
mesure ce mod\`{e}le est corrobor\'{e} par les observations de six
\'{e}toiles proches faites dans les domaines du visible/infrarouge par
le VLT et dans le domaine millim\'{e}trique par ALMA. Nous montrons que
bien que g\'{e}n\'{e}ralement corrobor\'{e}, n'ayant souffert aucune
contradiction et servant utilement de guide aux recherches actuelles,
il a encore besoin de nombreuses observations compl\'{e}mentaires pour
\^{e}tre valid\'{e} de mani\`{e}re fiable. En particulier, afin de
mieux pr\'{e}ciser les r\^{o}les jou\'{e}s par pulsations stellaires et
mouvements de convection, il faudra mesurer la courbe de lumi\`{e}re en
m\^{e}me temps qu'on observera, avec la meilleure r\'{e}solution
angulaire possible, les \'{e}missions des domaines millim\'{e}trique et
visible/infrarouge. Il faudra clarifier comment la grande
variabilit\'{e} r\'{e}v\'{e}l\'{e}e par les observations de la
photosph\`{e}re est compatible avec la persistance sur des
d\'{e}cennies, voire des si\`{e}cles, de l'anisotropie de l'enveloppe.
De nouvelles observations du gaz proche de l'\'{e}toile seront
n\'{e}cessaires pour pr\'{e}ciser le m\'{e}canisme pr\'{e}sidant \`{a}
sa rotation, en particulier pour R~Dor, L\textsubscript{2} Pup et EP~Aqr. Nous
sugg\'{e}rons que la pr\'{e}sence de compagnons stellaires ou
plan\'{e}taires n'a pratiquement pas d'impact sur la gen\`{e}se du vent
et ne fait que modifier son \'{e}volution ult\'{e}rieure.
\end{altabstract}
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\maketitle

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\vspace*{-3pt}

\section{Introduction}\label{sec1}

\subsection{State-of-the-art}\label{sec1.1}
Much progress has been made over the past decade in understanding the
mechanisms at stake in the formation of the nascent wind of oxygen-rich
AGB stars. The most salient features have recently been described, in
particular by B. Freytag, S. H\"{o}fner, S. Liljegren and H. Olofsson
in a series of recent papers, in terms that we summarise below; we
refer the reader to these  articles~\cite{1,2,3,4} for a list of
relevant references. For simplicity, in the remainder of this article,
we refer to such description as ``the current model''.  

In contrast to carbon-rich, oxygen-rich AGB stars have a dusty envelope
that is more transparent in the visible and near-infrared, giving a
better view of the innermost dust-forming atmospheric layers. Their
study supports a scenario where the radiation pressure, which triggers
the outflows, is caused by photon scattering on highly transparent
iron-free dust grains, which condense at shorter distances than
iron-bearing silicate grains. As long as they are of a size comparable
to the radiation wavelength, ${\sim}0.1\ndash1.0~\rmmu\mathrm{m}$, they
uphold sufficient radiation pressure. Studies of dust 
formation~\cite{5,6,7,8,9} suggest that the condensation of corundum
(Al$_{2}$O$_{3}$), forming a thin dust layer close to the stellar
photosphere, precedes the formation of silicate dust, the condensation
of silicate mantles on top of corundum cores speeding up grain growth
to the critical size.

Recent high-resolution imaging of nearby AGB stars at visible and
infrared wavelengths has revealed complex, non-spherical distributions
of gas and dust in the close circumstellar environment, with changes in
morphology and grain sizes occurring over the course of weeks or
months. Such inhomogeneous distribution of atmospheric gas emerges
naturally in 3-D hydrodynamical models, as a consequence of large-scale
convective flows below the photosphere and the resulting network of
atmospheric shock waves, the dynamical patterns in the gas being
imprinted on the dust in the close stellar environment. Global AGB star
models~\cite{10} are characterised by giant convection cells, which can
span over a steradian, and have a lifetime of many years. The
photospheric layers have a complex, variable appearance due to smaller,
shorter-lived cells, which form close to the surface of the convection
zone. In addition to the convective flows, radial pulsations occur with
typical periods at year scale. These dynamical processes generate waves
of various frequencies and spatial scales, which quickly develop into
shock waves as they propagate outward through the atmosphere with its
steeply declining density. The shocks give rise to ballistic gas
motions, which typically peak around 2 stellar radii. As the shock
waves interact and merge, they produce large-scale regions of enhanced
densities in their wakes. 

As remarked by H\"{o}fner and Freytag~\cite{3}, the basic formation
mechanism of the dust cloud precedes wind acceleration. Its study is
therefore a necessary preliminary to the understanding of the mass-loss
mechanism;
in this context, the acceleration of the wind, its possible
subsequent interaction with\vadjust{\pagebreak}  
planetary or stellar companions, and more
generally the evolution towards the planetary nebula phase, appear as
complications that can be ignored. This early phase of formation of the
nascent wind appears instead as fundamental and its study deserves
being dedicated major effort on both theoretical and observational
fronts. Recently, two main approaches have been pursued towards this
aim: observations in the visible and infrared, essentially using the
VLT, and millimetre observations, essentially using ALMA.

The former, using the VLT in single-dish or interferometer mode, take
advantage of the high performance of instruments such as SPHERE-ZIMPOL.
Particularly remarkable are observations  of $\rmpi^1$~Gruis~\cite{11}
using PIONIER, which show evidence for the presence of large
granulation cells on the stellar surface. In this context, using the
same instrument, one must recall the observation of granulation on the
surface of  Betelgeuse~\cite{12} and its confirmation from
spectro-polarimeter observations~\cite{13} using NARVAL at Pic du~Midi;
the latter give evidence for slow evolution of the granule pattern on a
2 to 3 years timescale, accompanied by a much faster variability with
small amplitude variations of a week-to-month time scale. NARVAL
observations have also given evidence for asymmetric shocks in
$\rmchi$~Cygni, induced by the interplay between pulsation and
convection, suggesting the presence of a highly anisotropic and
variable velocity field near the surface of the  star~\cite{14}.  

In general, evidence for clumpy dust clouds near the star has been
obtained from the detection of scattered light and multi-epoch
observations have shown changes in morphology on month time scales.
They have provided evaluations of the dust grain size consistent with
the picture described above.

Millimetre observations have concentrated on three fronts: (1)~study of
the continuum emission of the stellar disc and surrounding hot dust,
giving occasional evidence for hot spots and variability; (2)~
measurements of the radial dependence of the abundance of molecular
species giving evidence, in particular, for the early formation of
aluminium-rich dust grains;  (3)~measurements of the morpho-kinematics
of the inner CSE layer using the emission of molecular
lines. 

\subsection{Six selected stars}\label{sec1.2}
We have selected a sample of six well-studied oxygen-rich AGB stars to
illustrate the most salient features displayed by the morpho-kinematics
of their inner CSE layers. All stars in the sample are oxygen-rich
nearby stars, with spectral type M and within 100~pc or so from the
Sun. Their masses cover between  ${\sim}$0.7 and ${\sim}$2~solar
masses. Most are long period variables with periods at year 
scale~\cite{15}, with the exception of EP~Aqr and L$_2$~Pup, which have
periods of only 110 and 141~days, respectively. The period-luminosity
relation shows that EP~Aqr pulsates on the first overtone while all
others pulsate in the fundamental mode. They are shared between Mira
and semi-regular types, but the separation between the two classes is
sometimes unclear (e.g. W~Hya). None shows a clear technetium signal in
its  spectrum~\cite{16} but \textit{o}~Cet~\cite{17,18} and
L$_2$~Pup~\cite{19} may display some. All have low mass-loss rates, not
exceeding ${\sim}2\times10^{-7}$~solar masses per year. \textit{o}~Cet
has a clearly identified companion of mass 0.7~solar masses with a
separation of  ${\sim}$80~au and displays features characteristic of
symbiotic systems. Kervella  \etal~\cite{20} have claimed the presence
of a planetary companion distant by only 2~au from the centre of
L$_2$~Pup but this needs to be confirmed. Important parameters are
listed in  Table~\ref{tabA1} of the Appendix~\ref{appA}, together
with references of relevance to the present article.  Table~\ref{tabA2}
lists molecular lines considered in the present review and observed
with high angular resolution, together with relevant parameters and
associated beam sizes.

At first glance, each of the oxygen-rich AGB stars that have been
studied in some detail displays properties of its own making it appear
as somewhat singular: unveiling common properties that can be
considered as characteristic of the whole family is therefore very
challenging. The aim of the present article is to make a step in this
direction.

\section{The stellar disc and its immediate environment}\label{sec2}
ALMA observations of continuum emission have provided images of the
stellar disc and of its immediate environment at millimetre
wavelengths, often displaying variability and hot spots interpreted as
the effect of shocks induced by pulsations and convective cell
partition. 

The disc of \textit{o}~Cet has been shown to have a 10\% to 20\%
ellipticity in early measurements using  JVLA~\cite{21,22},
ISI~\cite{23} and IOTA~\cite{24}, but was found circular later 
on~\cite{25,26}. Kam\'{i}nski \etal~\cite{27}, also using APEX and
Herschel observations, have given evidence for strong inhomogeneity
(hot spot) and irregular variability in the emission of AlO molecules.
Spectro-polarimeter observations using NARVAL at Pic  du~Midi~\cite{28}
have given evidence for shock-induced polarised hydrogen emission
lines, suggesting their association with convective cells.

Strong hot spots have been observed on W~Hya, with lifetimes at the
scale of  weeks~\cite{26,29} and on R~Dor~\cite{26}, correlated with
dust structures observed in the visible. However, no hot spot has been
directly observed on R~Leo and EP~Aqr; in the former case, Vlemmings 
\etal~\cite{26} have given evidence for a radial asymmetric expansion
with mean velocity of $10.6\pm1.4~\mathrm{km}{\cdot}\mathrm{s}^{-1}$
within 1--2~stellar radii; in the latter case,  Homan \etal~\cite{30}
have given evidence for a 20\% flux density increase between 2016 and
2019, suggesting variability and sporadic contributions on scales
larger than the stellar disc. 

Observations using the VLT, at optical and infrared wavelengths, have
given evidence for a dusty layer surrounding the photosphere, commonly
displaying both inhomogeneity and variability. In particular
SPHERE/ZIMPOL polarisation measurements are available for 
L$_2$~Pup~\cite{31}, for \textit{o}~Cet~\cite{32}, for
W~Hya~\cite{9,33,34},  for R~Dor~\cite{35} and for EP~Aqr~\cite{30}.
The degree of linear polarisation usually reaches high values, well in
excess of 10\%, except for \textit{o}~Cet, where it does not exceed
4\%, dust being confined at the border of a dense gas reservoir, within
100--200~mas (10--20~au) from the centre of the star. In the case of
W~Hya, together with observations using  NACO~\cite{36},
AMBER/VLTI~\cite{9,33,37} and MIDI/VLTI~\cite{38}, evidence is obtained
for a clumpy and dusty layer, displaying significant variability at
short time scale. In the case of R~Dor, Khouri  \etal~\cite{35} find
evidence for variability and asymmetry, with outflwing dust of steeply
decreasing radial density and Ohnaka  \etal~\cite{39}, using
VLTI/AMBER, find evidence for sudden outward acceleration to
$7\ndash15~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ at radial distances
between 1.5 and 1.8~stellar radii. In the case of  EP~Aqr~\cite{30},
the linearly polarised flux map suggests the presence of a torus of
dust with an axis close to the known axi-symmetry axis of the CSE.
Finally, the close neighbourhood of R~Leo has been observed in the 
near-infrared~\cite{40} using VLTI/VINCI, giving evidence for
significant deviation from a uniform disc profile, and in the
mid-infrared by  Paladini \etal~\cite{41} using VLTI/MIDI, showing
unusually large spectral shape variations and giving evidence for
brightness inhomogeneity appearing already in the dust-forming region.

The case of L$_2$~Pup is outstanding. Its light curve~\cite{42,43,44}
has been undergoing a major dimming episode in ${\sim}$1994. NACO
observations together with VINCI  observations~\cite{45}, and together
with AMBER/VLTI observations~\cite{46,47}, have revealed a dust disc,
oriented east--west and inclined by ${\sim}82\text{\textdegree}$ with
respect to the plane of the sky, with approximate projected size of 
$180\times50~\mathrm{mas}^2\; (11.5\times3.2~\mathrm{au}^{2})$.  Ohnaka
\etal~\cite{47} and Bedding \etal~\cite{43} assume that dust clouds
were ejected at the end of the past century, causing the formation of
the circumstellar disc. Others assume instead that it existed before
the dimming event and, in 1994, simply started obscuring significantly
the star. ALMA observations of continuum  emission~\cite{20} show a
slight E--W elongation caused by hot dust in the circumstellar disc.
Finally, using SPHERE ZIMPOL observations,  Kervella \etal~\cite{31}
have claimed the presence of a companion at ${\sim}$2.1~au west of the
star, but the NACO images and the VINCI interferometer observations do
not see trace of it.   

One generally finds evidence for the presence of large transparent dust
grains very close to the photosphere, in agreement with the seminal
paper of  Norris \etal~\cite{36} where VLT/NACO observations of W~Hya,
R~Dor and R~Leo were reported; in particular, dust grains surrounding
W~Hya, mostly aluminium  composites~\cite{7}, are found to have sizes
ranging between 0.1 and 0.5~$\rmmu$m. 

Finally, Khouri \etal~\cite{48} have detected emission from highly
excited OH lines $(E_{\mathrm{up}}>4800~\mathrm{K})$ within a very few
au from the centres of W~Hya and R~Dor, giving evidence for the
presence of strong shock fronts. 

\section{Molecular line spectra: absorption over the stellar
disc}\label{sec3}
High angular resolution millimetre observations have revealed strong
absorption of molecular line emission over the stellar disc.  Wong
\etal~\cite{25} were first to give a detailed description in the case
of \textit{o}~Cet. Such absorption is particularly large for SiO lines
and is often found to extend beyond the stellar disc in the form of
self-absorption. Absorption spectra observed over the stellar disc
provide important information on the morpho-kinematics of the inner
layer, in particular giving evidence for in-falling gas. They probe the
central line of sight independently from maximal recoverable scale
constraints and the explored radial range depends only on the radial
distribution of the abundance of the molecule being studied and on the
range of temperatures associated with the particular transition. 

\begin{figure}
\includegraphics{fig01}
\caption{\label{fig1}Doppler velocity spectra observed over the stellar
disc. From left to right and up-down:  L$_2$~Pup~\cite{49},
$\mbox{}^{12,13}$CO(3--2) and  $\mbox{}^{29}$SiO(8--7), 27 mas (1.7 au)
FWHM beam;  \textit{o}~Cet~\cite{25}, $\mbox{}^{28,29}$SiO(5--4), 32 mas
(3.2 au) FWHM beam;  W~Hya~\cite{50}, $\mbox{}^{29}$SiO(8--7), 47 mas
(4.9 au) FWHM beam; R~Leo~\cite{51}, CO(2--1), $\mbox{}^{29}$SiO(5--4)
and SO(5$_{5}$--4$_{4}$), 42 mas (4.8 au) FWHM beam; R~Dor~\cite{52}, 
$\mbox{}^{29}$SiO(8--7) and SO$_{2}$(34$_{3,31}$--34$_{2,32}$), 38 mas (2.2 au) 
FWHM beam; EP~Aqr~\cite{53}, SiO(5--4), 32 mas (3.8 au) FWHM
beam.}
\end{figure}

Figure~\ref{fig1} displays such spectra measured on the six stars
studied in the present article. In all cases, and in the whole article,
they are referred to the systemic star velocity. They show an
absorption peak on the blue-shifted side, at terminal velocity,
revealing the opacity of the CSE layer farther away from the star. In
the case of L$_2$~Pup, where this layer is dominated by an edge-on
rotating gravitationally bound disc, the absorption peak is centred at
the origin. In the case of \textit{o}~Cet, where SiO molecules are
confined within  ${\sim}$0.5~arcsec (50~au) from the centre of the
star, the terminal velocity is probed by the emission of CO lines but
not by that of SiO lines. 

With the exception of EP~Aqr, all show absorption on the red-shifted
side, accounting for a significant fraction of the continuum emission,
usually interpreted as evidence for in-falling gas. The dominance of
red-shifted absorption is qualitatively consistent with the remark that
the spectra illustrated in  Figure~\ref{fig1} are generally measured
near the minimum of the light curve: the phases for \textit{o}~Cet,
W~Hya, R~Leo and R~Dor are 0.45, 0.3, 0.5 and 0.5, respectively.
L$_2$~Pup is outstanding: the spectra were measured on November~5,
2015, approximately one month after the expected maximum light, which,
however, did not  occur~\cite{20}: the magnitude stayed near minimum,
regular oscillations resuming in early 2016 with smaller amplitude 
than\unskip\break
in 2014.

Finally, there exists no measurement of the EP~Aqr light curve,
unfortunately preventing a reliable interpretation of the absence of
red-shifted absorption. As the beam is usually larger than the stellar
disc, some emission from gas located farther away from us than the star
is leaking into the spectrum. In case of dominant infall, it is seen as
blue-shifted, in case of dominant outflow, it is seen as red-shifted.
In the present case, the ratio between the beam FWHM and the diameter
of the stellar disc is  $13.5/12\sim1.1$, $16/21\sim0.8$, 
$23.5/26\sim0.9$, $21/21\sim1$,  $19/32\sim0.6$ and $16/8\sim2$ for
L$_2$~Pup, \textit{o}~Cet, W~Hya, R~Leo, R~Dor and EP~Aqr,
respectively. Its large value in the case of EP~Aqr weakens the
significance of the absence of red-shifted absorption. All spectra show
evidence for significant wings of large velocities that are discussed
in  Section~\ref{sec5}.

\section{Outflowing gas}\label{sec4}

\subsection{Close to the star}\label{sec4.1}
Gas escaping the central gravitationally bound reservoir does so in the
form of outflows covering solid angles at steradian scale and having
mean radial velocities of a few  $\mathrm{km}{\cdot}\mathrm{s}^{-1}$.
This is a common feature observed in all six stars but taking different
forms in each of them.

\textit{o}~Cet, R~Leo and R~Dor display particularly complex
morpho-kinematics seen as patchy emission in the close neighbourhood of
the stars. On \textit{o}~Cet  (Figure~\ref{fig2}), ALMA
observations~\cite{54,55} of SiO(5--4) and $\mbox{}^{12,13}$CO(3--2) line
emissions have given evidence for three ongoing CO outflows: one
blowing south-east towards Mira B and two blowing north-east and
south-west with Doppler velocities
$V_z\sim{-}3~\mathrm{km}{\cdot}\mathrm{s}^{-1}$. Moreover, evidence is
also found for recent ejections of a north-eastern arc at
$V_z\sim{+}2~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ and a south-western
outflow in the plane of the sky. A soft X-ray outburst was observed in 
2003~\cite{56} using CHANDRA/ACIS-S, probably caused by a magnetic
flare followed by a large mass ejection. 

\begin{figure}
\vspace*{2pt}
\includegraphics{fig02}
\vspace*{4pt}
\caption{\label{fig2}\fontsize{9.6}{12}\selectfont
Outflows from \textit{o}~Cet~\cite{54}.
Left: map of the $\mbox{}^{12}$CO(3--2) intensity 
$(\mathrm{Jy}{\cdot}\mathrm{km}{\cdot}\mathrm{s}^{-1}
{\cdot}\mathrm{arcsec}^{-2})$
integrated over $\vert V_z\vert<4~\mathrm{km}{\cdot}\mathrm{s}^{-1}$. 
Middle and right:  $\mbox{}^{13}$CO(3--2) PV maps, $V_z$ vs 
$x^{\prime}$ (middle) and $V_z$ vs $y^{\prime}$ (right) defined in the
left panel. The labels SWS, NEA, SWO and NEO stand for south-western
stream, north-eastern arc, south-western outflow and north-eastern
outflow, respectively; the arrow and the blue lines refer to the
south-eastern outflow (SEO) dominated by the wind blowing from Mira A
to Mira B. The colour scales are in units of Jy${\cdot}$arcsec$^{-1}$.} 
\vspace*{8pt}
\end{figure}

R~Leo has been studied~\cite{51} using ALMA observations of
$\mbox{}^{29}$SiO(5--4), CO(2--1), SO(5$_{5}$,4$_{4}$) and
SO$_{2}$(22$_{2,20}$--22$_{1,21}$) line emissions, giving evidence for
three ongoing outflows covering broad solid angles in the
south-eastern, south-western and north-western quadrants with low
Doppler velocities at $\mathrm{km}{\cdot}\mathrm{s}^{-1}$ scale
(Figure~\ref{fig3}). The study of the relative abundance of different
molecules in these outflows suggests that Local Thermal Equilibrium is
violated close to the star, between  ${\sim}$2 and  ${\sim}$10 stellar
radii, and is progressively restored when moving outward to ${\sim}$30
stellar radii. In addition, like in \textit{o}~Cet, detached patches of
emission are observed, the one closest to the star having Doppler
velocity $V_z=2\ndash3~\mathrm{km}{\cdot}\mathrm{s}^{-1}$, position
angle ${\sim}260{\text{\textdegree}}$ and projected distance from the
star between 1 and 2~arcsec.

\begin{figure}
\vspace*{2pt}
\includegraphics{fig03}
\caption{\label{fig3}Outflows from R~Leo~\cite{51}. PV maps, Doppler
velocity  $V_z$ vs position angle $\omega$,  integrated over projected
distances from the star $0.04< R<0.30$~arcsec (4.6 to 34.2~au). From
left to right: SiO, CO, SO and SO$_{2}$ emissions. The black rectangles
locate three regions of enhanced emission associated with different
intervals of  $R$.}
\vspace*{5pt}
\end{figure}

In the case of R~Dor (Figure~\ref{fig4}), multiline ALMA
observations~\cite{57} have shown that projected distances between
${\sim}$20 and  ${\sim}$100~au host a radial wind with Doppler
velocities reaching up to
${\sim}6~\mathrm{km}{\cdot}\mathrm{s}^{-1}$, characterised
by strong inhomogeneity, both in angle and radially, as had been noted
earlier by De~Beck and Olofsson~\cite{58}. In particular, observations
of the emission of the SO(6$_{5}$--5$_{4}$) line show that the presence
of separate cores, of which seven have been identified and studied; at
short distances from the star, the combined effect of expansion and
rotation complicates the analysis of the morpho-kinematics.
Particularly outstanding is a blue-shifted stream observed at 
${\sim}140\text{\textdegree}$ position angle to extend radially from 
${\sim}$10  to ${\sim}$30~au~\cite{52}, which can be interpreted as a
mass ejection that took place 5 to 10 years ago with a mean radial
velocity of  $15\pm5~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ but not as
evidence for an evaporating planetary companion, as had been 
suggested\unskip\break 
earlier~\cite{6,59,60}.

\begin{figure}
\vspace*{3pt}
\includegraphics{fig04}
\caption{\label{fig4}Outflows from R~Dor, SO(6$_{5}$--5$_{4}$)
emission~\cite{57}. Left: P-V map (Doppler velocity  $V_z$ vs position
angle $\omega$) integrated over projected distances from the star
$0.2<R<1.2$~arcsec (11.8 to 71.8~au). Middle: $P$--$V$ map of the product
brightness $\times$ angular distance $R$ in the  $V_z$ vs $R$ plane,
averaged over $\omega$, showing toroidal cavity K$_1$ (and possibly 
K$_2$), giving evidence for a recent episode of enhanced mass loss.
Right: the blue-shifted stream seen in\unskip\break 
$\mbox{}^{29}$SiO(8--7)
emission~\cite{52}. The intensity map is integrated over
${-}18.7<V_z<{-}6.3~\mathrm{km}{\cdot}\mathrm{s}^{-1}$.}
\vspace*{8pt}
\end{figure}

The cases of W~Hya and L$_2$~Pup are different, with a single ongoing
outflow identified in each case  (Figure~\ref{fig5}). W~Hya has been
shown~\cite{50}, using ALMA observations of  $\mbox{}^{12}$CO(3--2) and
\mbox{$\mbox{}^{29}$SiO(8--7)}
emissions, to host a recent mass ejection
covering a broad cone with an axis making an angle of some
30\textdegree\ with the line of sight, and a blob of enhanced emission
located some 0.2~arcsec (20~au) above the plane of the sky. Within the
cone, and within radial distances confined to less than 25 au from the
centre of the star, the number density is increased by an order of
magnitude, with a SiO/CO ratio larger by at least a factor~2, and the
effective line width is also about twice as large. The mean radial
velocity inside the cone is 
$6\ndash7~\mathrm{km}{\cdot}\mathrm{s}^{-1}$. The cone geometry matches
the dust distribution observed using SPHERE/ZIMPOL at the 
VLT~\cite{33}. 

\begin{figure}
\vspace*{3pt}
\includegraphics{fig05}
\vspace*{5pt}
\caption{\label{fig5}Outflows from W~Hya (left,~\cite{50}) and
L$_{2}$~Pup (right,~\cite{49}). Left: schematic geometry of the mass
ejection from W~Hya. Right: PV map of the $\mbox{}^{12}$CO(2--1)
emission of L$_{2}$~Pup in the $V_z$ vs  $y$ plane integrated over the
wedge $\vert\sin\omega\vert<0.5$. The central gas-and-dust disc
is indicated as G/D disc and the ongoing outflow mentioned in the text
is indicated as X. The colour scale is in units of 
$\mathrm{Jy}{\cdot}\mathrm{arcsec}^{-1}$.}
\vspace*{5pt}
\end{figure}

Close to the star, the CSE of L$_2$~Pup is dominated by a gas-and-dust
disc in rotation, nearly edge-on. It may be slightly expanding at a
rate of  $0.8\pm0.5~\mathrm{km}{\cdot}\mathrm{s}^{-1}$. It has been
studied using ALMA observations of  $\mbox{}^{29}$SiO(8--7) 
emission~\cite{20}, of
$\mbox{}^{12,13}$CO(3--2)
emission~\cite{61} and
\mbox{$\mbox{}^{29}$SiO(8--7),}\ 
$\mbox{}^{12,13}$CO(3--2) and
$\mbox{}^{28}$SiO(5--4)  emissions~\cite{49}. An ongoing northern
outflow with $V_z$ between  ${-}5$ and
${-}3~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ is visible in $\mbox{}^{12}$CO
and  $\mbox{}^{28}$SiO emissions and probably associated with a feature
seen in NACO infrared  images~\cite{45}; it is the only candidate mass
ejection that can be clearly identified~\cite{49}.

The case of EP~Aqr is outstanding (Figure~\ref{fig6}). In addition to
two broad outflows observed in SiO(5--4) line emission, of a similar
nature as those observed in the other stars of the sample, a
circumstellar disc in rotation, displaying emission dominated by CO
lines, is observed to be formed very close to the photosphere. While
Homan  \etal~\cite{30,62} have proposed an interpretation in terms of a
white dwarf companion orbiting the star at an angular distance of
${\sim}$400~mas (48~au), a recently published  interpretation~\cite{53}
relies on a different mechanism for the formation of the circumstellar
disc and describes the observed morpho-kinematics of the CSE and the
apparent formation of polar outflows as the result of collimation
produced by the interaction between the circumstellar disc and a
standard stellar wind. 

\begin{figure}
\vspace*{4pt}
\includegraphics{fig06}
\vspace*{4pt}
\caption{\label{fig6}EP~Aqr~\cite{53}. PV maps (Doppler velocity vs
position angle) integrated over five successive intervals of angular
distance as indicated on top of the panels in arcsec. In the upper row
CO(2--1) emission is dominated by a disc, in the lower row SiO(5--4)
emission is dominated by a pair of outflows.}
\vspace*{4pt}
\end{figure}

In all cases, the radial extension of the outflows and the distance
between separated patches are at the scale of some 100 au, a distance
covered in 50 years at a velocity of
$10~\mathrm{km}{\cdot}\mathrm{s}^{-1}$. Such a time scale is more than
two orders of magnitude larger than the typical variability observed on
the stellar disc. Whatever is causing these outflows to blow in a same
direction over several years must have a lifetime at the same scale.   

\subsection{Farther away}\label{sec4.2}
A similar comment applies to the CSE's at larger distances, where the
history of the mass-loss mechanism is explored at century scale. They
are mostly studied using ALMA observations of the emission of CO lines,
most SiO molecules having either been dissociated by UV radiation or
adsorbed on dust grains. While covering the whole $4\rmpi$ solid angle,
they display strong inhomogeneity and deviate significantly from
spherical envelopes, taking rather the form of radially expanding
oblate volumes more or less inclined with respect to the plane of the
sky and hosting significant localised emission enhancements. Such are
the cases of  R~Dor~\cite{52,57,59,63}, L$_{2}$~Pup~\cite{49} and
possibly \textit{o}~Cet~\cite{54,55}. The oblate CSE of R~Dor 
(Figure~\ref{fig7}) displays enhanced emissions in two back-to-back
directions, each dominated by a pair of cores. The CSE of L$_2$~Pup
probes the mass-loss history preceding the 1994 dimming event and hosts
three directions of enhanced emission. The CSE of 
EP~Aqr~\cite{30,62,64} is characterised by broad bipolar outflows along
the disc axis, the two-component morpho-kinematics being clearly
revealed by the Doppler velocity spectrum  (Figure~\ref{fig8}); 
a recently proposed interpretation assumes that it is the interaction of
a standard wind with the circumstellar disc that causes the wind
expansion velocity to decrease from
${\sim}10~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ on the disc axis down to
${\sim}2~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ in the disc plane,
producing the appearance of two polar  outflows~\cite{53}. Very patchy
emission is observed in the CSEs of R~Leo and \textit{o}~Cet 
(Figure~\ref{fig9}). In the cases of R~Leo~\cite{51} and
R~Dor~\cite{57}, episodes of enhanced mass loss are revealed by
elliptical depressions of the observed emission in the $V_z$ vs  $R$
plane. The observed terminal velocities  (Table~\ref{tabA1}) never
exceed ${\sim}12~\mathrm{km}{\cdot}\mathrm{s}^{-1}$, reaching such a
value in the only case of the bipolar outflows of EP~Aqr, for which the
terminal expansion velocity of the circumstellar disc is only
${\sim}2~\mathrm{km}{\cdot}\mathrm{s}^{-1}$; the mean terminal velocity
of the five other stars is $5.4~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ with
a rms deviation of only $0.8~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ with
respect to the mean. 

\begin{figure}
\vspace*{4pt}
\includegraphics{fig07}
\vspace*{4pt}
\caption{\label{fig7}R~Dor CSE. Upper panels: schematic of the
morpho-kinematics~\cite{57}. Lower panels, SO(6$_{5}$--5$_{4}$) line
emission~\cite{52}: (a)~intensity in the Doppler velocity  $V_z$ vs
position angle $\omega$ plane integrated over 12
$\mathrm{au}<R<60~\mathrm{au}$;  (b)~intensity projected on P1;
(c)~intensity projected on P2; planes P1 and P2 are defined in the
upper-left panel. In both panels (b) and (c) NEB stands for
north-east-blue-shifted and SWR for south-west-red-shifted and a cut
$R>0.3$~arcsec (18~au) has been applied.}
\end{figure}

\begin{figure}
\includegraphics{fig08}
\caption{\label{fig8}EP~Aqr. Left: schematics of the morpho-kinematics
of the CSE. Middle~\cite{64}: two-component structure of the Doppler
velocity spectra of  $\mbox{}^{13}$CO(3--2) emission. The narrow
component (equatorial density enhancement) is shown in blue and the
broad component (bipolar outflow) in red. Right: PV map in the $V_z$ vs
$R$ plane of the projection of the data cube defined as
$1.2<R<5.2$~arcsec (140 to 620~au) and $\vert
V_z\vert<8~\mathrm{km}{\cdot}\mathrm{s}^{-1}$.}
\end{figure}

\begin{figure}
\includegraphics{fig09}
\caption{\label{fig9}Left: the \textit{o}~Cet emissions of the CO(3--2)
(colour) and SiO(5--4) (contours) lines integrated over
$1.0<R<3.7$~arcsec (100 to 370~au) are shown in the Doppler velocity 
$V_z$ vs position angle $\varphi$ plane~\cite{55}. The colour scale is
in Jy. NEA, SWO, SA and NEO stand for outflows identified in other
projections of the data cube. The full (dashed) sinusoidal lines are
the traces of an isotropic radial wind of 2.8 
$(2.0)~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ velocity blowing in the plane
of Mira B orbit using systemic velocities of 47.7 
$(46.7)~\mathrm{km}{\cdot}\mathrm{s}^{-1}$. Middle: the R~Leo emission
of the CO(2--1) line~\cite{51} integrated over the position angle and
displayed in the Doppler velocity vs  $R$ plane gives evidence for
enhanced emission in a shell emitted 5 to 6 centuries ago. The lines
show ellipses  $\rho=1/\sqrt{2}$, 1 and $\sqrt{2}$ with
$\rho=([V_z/5.5~\mathrm{km}/\mathrm{s}]^2+
[R/6^{\prime\prime}]^2)^{1/2}$.  The right panel displays the
dependence on $\rho$ of the intensity integrated over each of the blue-
and red-shifted hemispheres separately as well as over the whole range
of Doppler velocities (blue, red and black respectively).} 
\end{figure}

It is tempting to infer from these observations that whatever is
causing ejection of gas from the extended atmosphere of the star, as do
probably shocks induced by pulsations and convective cells, while
displaying rapid variations at the scale of months, retain a same broad
deviation from sphericity at century scale. However, such a conclusion
is weakened by the remark that other mechanisms contribute to shaping
the CSE away from the star. Such is particularly the case of the
presence of stellar or planetary companions. In the present sample, the
case of EP~Aqr is the most  compelling~\cite{53}, the presence of polar
outflows being understood as resulting from effective collimation by
the continuous formation of a slowly expanding circumstellar\break disc.

\section{High Doppler velocity wings and possible rotation in the inner
CSE layer}\label{sec5}

\subsection{General comments}\label{sec5.1}
All six stars give evidence for significant effective line broadening,
in particular of SiO lines, at distances from the star below
${\sim}$15~au, the less convincing case being of W~Hya, for which clear
line broadening is only seen over the stellar disc. It is observed in
the form of high Doppler velocity wings above continuum level and
confined to the vicinity of the line of sight crossing the star at its
centre; they extend to some
${\pm}10\ndash20~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ in velocity and to
some 15~au in radius.\unskip\break 
They receive negligible contributions from
thermal broadening and are understood as being in fact the result of
the simultaneous observation of high-velocity blue-shifted and
red-shifted gas flows on an angular scale smaller than the beam size.
We recall that the maximal distance reached by a volume of gas launched
with velocity  $V_0$ at distance $r_0$ is $r_{\mathrm{max}}=
r_0V_{\mathrm{esc}}^2/(V_{\mathrm{esc}}^{2}-V_0^2)$ where the escape
velocity  $V_{\mathrm{esc}}=(2GM/r_0)^{1/2}$,  $G$ being Newton's
gravity constant and  $M$ the mass of the star. Namely for a radial
boost of velocity at the star photosphere equal to a fraction  $f$ of
the escape velocity, it will reach  $1/(1-f^2)$ stellar radii: it
remains below  ${\sim}$5 stellar radii for $f<0.9$ and then blows up
rapidly when  $f$ approaches unity. For a solar mass star of radius~1
au, the escape velocity is  $42~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ and
a $20~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ boost will therefore produce a
maximal distance of  ${\sim}$1.3\unskip\break
stellar radii. 

The presence of high velocity wings had been noticed early in single
dish observations~\cite{65}, suggesting that the emission occurs close
to the star, where SiO grains have not yet fully formed, and is somehow
related to star pulsations. Their ALMA observation was first mentioned
by  Decin \etal~\cite{6} and early attempts at interpreting them as
bipolar gas streams flowing along the line of sight in the case of 
EP~Aqr~\cite{67} or as the effect of rotation in the case of
L$_2$~Pup~\cite{20,61} have been published. However, it has been later
understood, following the study of other stars, that they are in fact
confined to the close neighbourhood of the star and are essentially
radial, although occasionally combining with  rotation~\cite{53,66}. As
first remarked by Decin \etal~\cite{6}, it is the high sensitivity of
ALMA observations, rather than their high angular resolution, which
made it possible to reveal their presence. Indeed, to the extent that
their source is confined to the close neighbourhood of the star and
that no other source of such high Doppler velocities exists, low
angular resolution observations are able to detect them as long as
their sensitivity is sufficient: their emission is a minor fraction of
the total emission detected within the broad beam, but they have no
competition in the extreme Doppler velocity region that they populate.
That does not mean that high angular resolution observations are
unnecessary. They are indeed essential to measure the radial extension
of the source and to explore the details of its morphology projected on
the plane of the sky. 

Even with an excellent angular resolution, the observed line profile
receives contributions from all sources located on the line of sight;
the opacity of the layers crossed at the line frequency suppresses part
of their emission but, at extreme Doppler velocities, the density can
be expected to be low enough for absorption to be small. Several
effects contribute to the dependence of the line emission on radial
distance: depletion of the gas phase by adsorption on dust grains, as
is the case for SiO and AlO; mode of excitation, by collision with
other molecules, mostly hydrogen, or absorption of stellar UV
radiation; photodissociation by interstellar radiation or by radiation
emitted by the star itself or by a nearby white dwarf companion;
dissociation produced by possible shocks; dependence on temperature,
the relevant parameters being the emission parameter $\varepsilon$,
which measures the emissivity in the absence of absorption, and the
optical\unskip\break depth $\tau$. 

Absorption, particularly strong over the stellar disc but also
extending well beyond it in some cases (see  Section~\ref{sec3}),
complicates the study of line broadening, the line profile being
interrupted over a significant interval of Doppler velocity. Its
contribution needs to be taken in a proper account. The complexity of
the physics mechanisms at stake is particularly well illustrated by the
analyses of  Wong \etal~\cite{25} for \textit{o}~Cet and Vlemmings
\etal~\cite{29} for W~Hya.

Evidence for rotation in the inner region of the CSE, at distances from
the star comparable with those covered by significant effective line
broadening, has been found in four stars of the present sample,
particularly strong in L$_2$~Pup and R~Dor, but absent in W~Hya 
and\unskip\break 
R~Leo.

The presence of rotation in the same radial range as line broadening
requires disentangling the two effects, which can be done by
considering separately four quadrants of position\unskip\break 
angle: near the
projection of the rotation axis on the plane of the sky, the effect of
rotation cancels, while it is maximal in the perpendicular direction.
Similarly, the possible presence of expansion in this radial range
complicates the analysis of the line broadening and needs to be
properly taken into account. A detailed discussion of disentangling the
effects of line broadening, rotation and expansion has been given by 
Nhung \etal~\cite{66} using the case of R Hya as an\unskip\break 
illustration.

\subsection{Selected sample}\label{sec5.2}

\subsubsection{L$_2$~Pup}\label{sec5.2.1}
Hoai \etal~\cite{49} and Homan \etal~\cite{61} have given evidence for
high $\vert V_z\vert$ wings in the $\mbox{}^{29}$SiO(8--7) and
$\mbox{}^{12,13}$CO(3--2) emissions of the inner CSE of L$_2$Pup: over
${\sim}$60~mas (3.8~au) from the centre of the star, the effective line
width increases (FWHM) from ${\sim}5~\mathrm{km}{\cdot}\mathrm{s}^{-1}$
to ${\sim}20~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ (Figure~\ref{fig10},
upper row). The rotation of the gas and dust disc is seen on all
observed lines  (Figure~\ref{fig10}, lower row) with a projected
rotation velocity increasing from
${\sim}4~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ to
${\sim}8~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ (Figure~\ref{fig10}, upper
row) when $R$ decreases from 120--150~mas to  30--60~mas~\cite{49}.
However, ignoring line broadening, Kervella \etal~\cite{20} claim
instead a projected rotation velocity of
${\sim}15~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ in the 30--60~mas
interval. 

\begin{figure}
\includegraphics{fig10}
\caption{\label{fig10}Upper row, left pair of panels: line broadening
in L$_{2}$~Pup measured on the  $y$ axis where contribution from
rotation cancels as seen from $\mbox{}^{13}$CO(3--2) line emission
(left,~\cite{49}) and $\mbox{}^{12}$CO(3--2) line emission
(right,~\cite{61}); the left panel shows the evolution of the FWHM line
width (blue and red correspond to south and north, respectively) and
the right panel the maximal velocity. Upper row, right triplet of
panels: L$_{2}$~Pup~\cite{49}, dependence on position angle of the
Doppler velocity averaged over $\vert
V_z\vert<20~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ in successive rings as
indicated in the inserts (in arcsec); the lines show sine wave fits.
Lower row: maps of the mean Doppler velocity measured for several
L$_{2}$~Pup lines observed with high angular resolution by Kervella
\etal~\cite{20}.}
\end{figure}

\subsubsection{\textit{o}~Cet}\label{sec5.2.2}
Hoai \etal~\cite{55} and Nhung \etal~\cite{54} give strong evidence for
the line width of the SiO emission to increase from $\vert
V_z\vert\sim{}5~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ to
${\sim}20~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ when $R$ decreases from
${\sim}$0.17 to  ${\sim}$0.05~arcsec (17 to 5~au) and for rotation
about an axis projecting $40\text{\textdegree}\pm15\text{\textdegree}$
east of north with a projected velocity of 
$0.7\pm0.2~\mathrm{km}{\cdot}\mathrm{s}^{-1}$, in agreement with
results obtained from the observation of SiO  masers~\cite{68,69}. The
low rotation velocity and the absence of absorption outside the stellar
disc make this case relatively easy to analyse  (Figure~\ref{fig11}).

\begin{figure}
\includegraphics{fig11}
\vspace*{4pt}
\caption{\label{fig11}Line broadening and rotation in the SiO(5--4) line
emission of \textit{o}~Cet~\cite{54,55}. Upper row: Doppler velocity
spectra averaged in quadrants of 3 au broad annular rings centred on
Mira A with mean radii increasing from 2.5~au (blue) to 21.5~au (red)
in steps of 1 au. The dependence on  $R$ of the full-width at 1/5
maximum of the spectra is shown in the lower-left panel. Lower right:
dependence of the mean Doppler velocity on position angle $\omega$ in
the ring  $3~\mathrm{au}<R<10~\mathrm{au}$. The lines are sine wave
best fits.}
\end{figure}

\subsubsection{W~Hya}\label{sec5.2.3}
The study of line broadening in W~Hya~\cite{29,50} is made difficult by
the presence of a recent mass ejection in the blue-shifted northern
octant; outside the region of the sky plane covered by this mass
ejection, observations of the $\mbox{}^{29}$SiO(8--7) line emission
using a 45~mas (4.7~au) FWHM beam show that the largest Doppler
velocities are observed within ${\sim}$75~mas (7.8~au) projected
distance from the centre of the star and reach only
${\sim}10~\mathrm{km}{\cdot}\mathrm{s}^{-1}$, less than twice the
terminal velocity. The clearer evidence for larger Doppler velocities
is from the absorption spectra measured over the stellar disc, reaching
${\sim\pm}20~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ and showing evidence
for in-falling gas reaching high Doppler velocity.  Vlemmings
\etal~\cite{29}, using a beam of only  ${\sim}$16~mas FWHM, have
observed the CO($v=1$,3--2) line emission of W~Hya, which, with an
upper level at 3120~K, probes efficiently the warm extended atmosphere.
Their analysis reveals the presence of a warm molecular layer close to
the stellar surface, with temperatures nearing 3000~K, surrounded by a
cooler layer at ${\sim}$900~K, extending to radial distances of 
${\sim}$50~mas and hosting both infall and outflow components 
(Figure~\ref{fig12}). These reach larger velocities in the eastern
hemisphere than in the western hemisphere where a hot spot of continuum
emission is observed. No evidence for rotation has been reported.

\begin{figure}
\vspace*{2pt}
\includegraphics{fig12}
\vspace*{4pt}
\caption{\label{fig12}Doppler velocity spectra of the CO($v=1$,3--2)
line emission of W~Hya~\cite{29} extracted towards the eastern (A) and
western (B) stellar hemisphere as well as in an annulus between 2.9 and
5~au off the star (C). The beam size is ${\sim}16~\mathrm{mas}$ FWHM
and the spectral resolution
${\sim}1~\mathrm{km}{\cdot}\mathrm{s}^{-1}$. The red lines show model
results. The lower-right panel maps the brightness temperature of the
stellar surface as observed with ALMA continuum emission at 338~GHz.
The rms noise in the image is 18~K and the peak is 3560~K. The red
ellipse indicates the size of the fitted, uniform, stellar disc with a
brightness temperature of $2495\pm125$~K. The effective temperature of
the photosphere is  ${\sim}2500$~K.} 
\vspace*{6pt}
\end{figure}

\subsubsection{R~Leo}\label{sec5.2.4}
In the case of R~Leo, Hoai \etal~\cite{51} observe Doppler velocities
reaching beyond $10~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ over the stellar
disc for the $\mbox{}^{29}$SiO(5--4), CO(2--1) and SO(5$_{5}$--4$_{4}$)
lines. They decrease to ${\sim}10~\mathrm{km}{\cdot}\mathrm{s}^{-1}$
for $R$ between 30 and 50~mas (3.4 and 5.7~au) and reach terminal
values of  ${\sim}5~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ for $R$ beyond 
${\sim}$100~mas (11.4~au). They show significant anisotropy, with
stronger emission in the southern than the northern hemisphere. 
Fonfr\'{i}a \etal~\cite{70} have observed the emission of the CO(2--1)
and $\mbox{}^{29}$SiO(5--4) lines over the stellar disc 
(Figure~\ref{fig13}) giving evidence for in-falling gas in front of the
star and for most of the emission coming from directions that do not
enclose the star; they comment on the possibility for the
$\mbox{}^{29}$SiO($v=1$,6--5) line to show maser emission. They argue
that the red-shifted absorption may be produced by radial movements of
photospheric layers (or convective cells) due to the stellar pulsation
and that the spectra suggest the presence of random gas movements in
the stellar photosphere and/or of periodic shocks. They also suggest
the possible presence of rotation, which, however, cannot be confirmed
when the outflows described by  Hoai \etal~\cite{51} are taken in due
account. Higher angular resolution observations would be necessary to
better explore the close environment of R~Leo.

\begin{figure}
\includegraphics{fig13}
\caption{\label{fig13}High velocity wings in R~Leo. Upper pair of
panels: Doppler velocity spectra~\cite{70} in the central pixel of the
$\mbox{}^{12}$CO(2--1) and $\mbox{}^{29}$SiO(5--4) lines ($v=0$ in blue
and  $v=1$ in red). The different line styles correspond to different
beam sizes as indicated in the insert. The grey vertical bands indicate
the gas expansion velocity derived from single-dish observations. Lower
pair of panels: Doppler velocity spectra~\cite{51} of the CO(2--1) and 
$\mbox{}^{29}$SiO(5--4) line emissions in 50~mas (5.7~au) wide rings as
indicated in the insert.}
\end{figure}

\subsubsection{R~Dor}\label{sec5.2.5}
In the case of R~Dor, near the centre of the star, the presence of high
Doppler velocity wings reaching 
$15\ndash20~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ had been noted early by 
Decin \etal~\cite{6} and Hoai \etal~\cite{63}  (Figure~\ref{fig14});
Nhung \etal~\cite{52}, using observations of the line emissions 
of\,~$\mbox{}^{29}$SiO(8--7) and SO$_{2}$(34$_{3,31}$--34$_{2,32}$) and
accounting for the contribution of rotation, have shown that such a
significant line broadening occurs within ${\sim}$12~au from the centre
of the star. In this region evidence for rotation was first obtained by
Vlemmings \etal~\cite{60} using high angular resolution observations of
\mbox{SiO($v=3$,5--4),}
SO$_{2}$(16$_{3,13}$--16$_{2,14}$) and
$\mbox{}^{29}$SiO($v=1$,5--4) emissions and, farther away from the star,
by Homan \textit{et~al.}~\cite{59} 
using observations of the SiO($v=1$,8--7)
emission. The former authors gave evidence for solid-body rotation with
velocity increasing from ${\sim}1~\mathrm{km}{\cdot}\mathrm{s}^{-1}$
near the stellar surface and the latter authors for sub-Keplerian
rotation with velocity cancelling beyond 15 au from the centre of the
star.  Nhung \etal~\cite{52,57} have later shown that rotation reaches
a maximal velocity of  ${\sim}$5 to
$7~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ at some  $8\pm2$~au from the
centre of the star, where the Keplerian orbital velocity around a solar
mass star is ${\sim}11~\mathrm{km}{\cdot}\mathrm{s}^{-1}$. Its axis
projects on the plane of the sky at a position angle of
$10\pm5\text{\textdegree}$ and makes an unknown angle with the plane of
the sky; yet, qualitative considerations favour a low value, typically
$20\text{\textdegree}\pm20\text{\textdegree}$ as suggested by the
analysis of  Homan \etal~\cite{59}. The morphology of the rotating
volume does not show strong anisotropy and, in particular, fails to
provide evidence for a disc-like flattening about the equator as
observed in the case of L$_2$~Pup. 

\begin{figure}
\vspace*{2pt}
\includegraphics{fig14}
\vspace*{4pt}
\caption{\label{fig14}R~Dor inner CSE layer~\cite{52}. Left pair of
panels: Doppler velocity distributions of the $\mbox{}^{29}$SiO(8--7)
emission observed for $\vert
V_z\vert>8~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ using different datasets.
Right pair of panels: dependence on position angle $\omega$ of the mean
Doppler velocity averaged over $50< \mathrm{R}<100~\mathrm{mas}$ (3 to 6~au,
black), $100< \mathrm{R}<150~\mathrm{mas}$ (6 to 9~au, red) and
$150<R<200~\mathrm{mas}$ (9 to 12~au, blue) for $\mbox{}^{29}$SiO(8--7)
and $\mathrm{SO}_{2}(34_{3,31}\ndash34_{2,32})$ line emissions.}
\vspace*{8pt}
\end{figure}

\begin{figure}
\includegraphics{fig15}
\vspace*{4pt}
\caption{\label{fig15}EP~Aqr~\cite{53}. Left: radial dependence of the
full width at 10\% of the maximum of the Doppler velocity spectrum
measured in a ring of radius $R$ centred on the star. Four rightmost
panels: PV maps of $\vert V_z\vert$ vs  $R$ for both hemispheres and
both CO(2--1) and \mbox{SiO(5--4)}
lines separately as indicated on top of each panel.} 
\vspace*{4pt}
\end{figure}

\subsubsection{EP~Aqr}\label{sec5.2.6} 
High Doppler velocity wings, reaching
${{\sim}{\pm}}~20~\mathrm{km}{\cdot}\mathrm{s}^{-1}$, have been 
observed~\cite{53} on both \mbox{SiO(5--4)} and CO(2--1) line emissions and
shown to be confined within  ${\sim}$150~mas (18~au) from the centre of
the star  (Figure~\ref{fig15}). The simultaneous presence of large
radial wind velocities, reaching above
$12~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ complicates their study.
Evidence for rotation within some  100--200~mas (12 to 24 au) from the
centre of the star, with a rotation velocity at
$\mathrm{km}{\cdot}\mathrm{s}^{-1}$ scale, has been obtained from the
observation of the emissions of the CO(2--1) and
SO$_{2}$(16$_{6,10}$--17$_{5,13}$) lines, consistent with observations
of the dust induced polarisation of the  550--750~nm emission observed
at the VLT using  SPHERE-ZIMPOL~\cite{30}. This suggests that such
rotation may be related to the precocious formation of the equatorial
disc. Unfortunately, the orientation of the disc, inclined by only
${\sim}10\text{\textdegree}$ with respect to the plane of the sky,
makes its study particularly difficult and additional high sensitivity
and angular resolution observations are necessary to clarify 
this\unskip\break
point.

\section{Discussion and conclusion}\label{sec6} 

\subsection{Rotation and the role of planetary or stellar
companions}\label{sec6.1}
Evidence for rotation in the close neighbourhood of the star is
generally ascribed to the presence of planetary or stellar companions.
Indeed, while it is recognised that the initial angular momentum of the
star must produce negligible velocities on the surface of the AGB star,
which has expanded by over two orders of magnitude, planetary
companions, whether orbiting the star above the photosphere or 
having
been recently  engulfed~\cite{71}, can be expected to transfer 
a significant part of their angular momentum to the inner CSE. In
contrast to protostars, the complex shock dynamics at stake near the
photosphere is likely to prevent the radial distribution of the
velocity of such rotating gas from being Keplerian. While some
carbon-rich evolved stars, such as LL  Pegasi~\cite{72}, display very
clear spiral features revealing the presence of a companion,
oxygen-rich stars do not. Attempts at identifying such structures have
always proven difficult. A well-documented recent example was given by 
Randall \etal~\cite{73} in the case of GX Monocerotis. In the
particular sample of nearby stars considered in the present article,
claims for the presence of spiral structures have been made by 
Ramstedt \etal~\cite{74} in the case of \textit{o}~Cet and by Homan
\etal~\cite{30,62} in the case of EP~Aqr. However, the former has been
shown by  Hoai \etal~\cite{55} to wind in the wrong direction and
serious doubts have been shed by  Nhung \etal~\cite{53} on the reality
of the latter. While the validity of the observation of possible spiral
structures must be critically assessed, the failure to obtain reliable
evidence should not be understood as a denial of the presence of
planetary companions, which are obviously expected to be there. The
question, which has currently received no satisfactory answer, is of
their precise role in the generation of the wind. In the present
sample, the only star, which has a well-established companion, in this
case probably a white dwarf (Mira B), is \textit{o}~Cet. It plays a
clear, but modest, role in focusing the wind of the main 
star~\cite{54,55}. 

The case of EP~Aqr is outstanding. The evidence for the precocious
formation of a nearly face-on circumstellar disc is strong, the disc
interacting with the nascent wind, giving the CSE its two-component
appearance, with a pair of polar outflows. In such a case, the question
to be answered is not the nature of the generation of the wind, assumed
to obey the current state-of-the-art ideas developed in the current
model, but the mechanism that governs the formation of the disc, which
is unknown but might very well imply the presence of a planetary
companion near the photosphere. 

In the present sample, the two stars, which display clearer evidence
for significant rotation, are R~Dor and L$_2$~Pup. In the former 
case~\cite{52,60,62}, rotation reaches a maximal velocity of
${\sim}6~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ at some 4 stellar radii
from the centre of the star, and cancels beyond ${\sim}$8 stellar
radii, suggesting the presence of a planetary companion close to the
photosphere or having been recently engulfed. The lack of significant
oblateness disproves the presence of a thin circumstellar disc. There
is no apparent relation between the geometry of the rotation (an axis
projecting  ${\sim}10\text{\textdegree}$ east of north on the plane of
the sky) and that of the median plane of the global CSE (with a normal
projecting  ${\sim}120\text{\textdegree}$ east of north), probably
implying that the observed rotation does not play an important role in
the formation of the nascent wind.  

The case of L$_2$~Pup~\cite{20,49,61} is different: the rotating volume
is a nearly edge-on disc of gas and dust covering radial distances
between 30 and 400~mas (2 to 26~au) from the centre of the star and
rotation velocities reaching
${\sim}8~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ near the inner rim (the
latter evaluation taking proper account of the effective line
broadening in the vicinity of the star). As a result, at strong
variance with the disc of EP~Aqr, the velocities are accurately
measured but the radial distribution is not. This makes it difficult to
compare the two circumstellar discs. The L$_2$~Pup disc seems, however,
to be of a different nature: its outer diameter is much smaller, it
hosts line emissions from both CO and SiO molecules while the EP~Aqr
disc is formed near the photosphere, where it is revealed exclusively
by the emission of CO molecules and extends to large distances; in
contrast with the EP~Aqr disc, the L$_2$~Pup disc does not seem to play
a role in shaping the CSE: farther away from the star, the wind
oblateness is unrelated to the orientation of the disc and no evidence
has been found for outflows collimated by the disc. This implies that
for L$_2$~Pup, as for R~Dor, the observed rotation does not play an
important role in the formation of the nascent wind. But understanding
the mechanism that governed the formation of the rotating circumstellar
disc is complicated by the presence of the strong dimming episode that
the light curve underwent at the end of the past century, inviting
different speculations. Yet, it is generally assumed that an orbiting
planetary companion is responsible for the observed rotation and 
Kervella \etal~\cite{20} claim to have obtained evidence for it,
although their analysis suffers from ignoring effective 
line\unskip\break
broadening. 

In summary, while rotation is present within a few stellar radii of the
centre of several oxygen-rich AGB stars, there is no evidence for it to
play an important role in the generation of the nascent wind. There is
no reason to doubt the presence of planetary companions orbiting AGB
stars at short distances from their centre or having been recently
engulfed, but their role seems limited to their impact on shaping the
gravity field and to the production of rotation by dragging gas, with
no significant incidence on the generation proper of the nascent wind.
When based on the observation of an apparent spiral wake, claiming
evidence for the presence of a companion requires a critical analysis,
sufficiently rigorous to be credible. Cases where the presence of a
companion is well established, such as \textit{o}~Cet in the present
sample or  R~Aqr~\cite{75,76,77} and $\rmpi^1$~Gru~\cite{78} may
display spectacular symbiotic phenomena, but the role of the companion
is limited to its impact on shaping a pre-existing wind, with no
incidence on its preliminary formation. Yet, more detailed studies of
the mechanism governing the formation of rotation in the inner layers
of the CSE, complicated by the presence of effective line broadening,
are required in order to better specify the role played by possible
companions.

\subsection{Effective line broadening and the role played by stellar
pulsations and convective cell partition}\label{sec6.2} 
The commonly accepted ideas of the current model about the mechanisms
governing the formation of the nascent wind of oxygen-rich AGB stars,
outlined in the Introduction, are proving very useful in guiding
current research and helping with the interpretation of the results.
They have not suffered any significant contradiction. Yet, their
validity is far from being confirmed and their conformity with
observations is mostly qualitative. 

Indeed, the present ALMA observations may suggest identifying the
region where the wind gets its initial boost within the radial range
over which effective line broadening is observed. The complexity of the
morpho-kinematics at stake in this region is described by essentially
just two numbers: its mean radius, measured from the centre of the
star,  $r_{\mathrm{boost}}$, and the extreme velocity reached by the
high  $V_z$ wings,  $V_{\mathrm{boost}}$.  Table~\ref{tab1} lists their
values together with the terminal velocity $V_{\mathrm{term}}$, the
stellar radius $r_{\mathrm{star}}$ and the mass-loss rate, $\dot{M}$.
The values and uncertainties retained for W~Hya,
$V_{\mathrm{boost}}=15\pm5~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ and
$r_{\mathrm{boost}}=40\pm30$~mas ($4.2\pm3.1$~au) reflect the
difficulty to summarise in only two numbers the complex
morpho-kinematics revealed by  Vlemmings \etal~\cite{29} and Hoai
\etal~\cite{50}. As illustrated in  Figure~\ref{fig16}, the values of
$V_{\mathrm{boost}}$ are similar, with a mean value of 
$15.3~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ and a rms deviation of
$2.6~\mathrm{km}{\cdot}\mathrm{s}^{-1}$ with respect to the mean. The
case of EP~Aqr is outstanding, with a value of
$V_{\mathrm{term}}\;(12\pm2~\mathrm{km}{\cdot}\mathrm{s}^{-1})$ more
than twice that of the other stars of the sample
$(5.4\pm0.8~\mathrm{km}{\cdot}\mathrm{s}^{-1})$ and a ratio
$r_{\mathrm{boost}}/r_{\mathrm{star}}\sim12$,  four times as large,
resulting from a very small stellar radius,  ${\sim}$7~mas (0.8~au),
and a relatively broad line broadening region, reaching over 150~mas
(18~au)  from the centre of the star. For the other stars,
$r_{\mathrm{boost}}$ increases in near proportion to
$r_{\mathrm{star}}$, with a ratio
$r_{\mathrm{boost}}/r_{\mathrm{star}}\sim3$;  it is higher for
\textit{o}~Cet, probably because of the larger mass of the star causing
the mass-loss rate to be small in spite of the large value of 
$r_{\mathrm{boost}}$. L$_2$~Pup, with the smallest values of both
$r_{\mathrm{boost}}$ and $\dot{M}$, stands out as being particularly
quiet. The crudeness of these considerations prevents us from making
deeper comments and illustrates well the oversimplification implied by
such description. 

\begin{figure}
\vspace*{4pt}
\includegraphics{fig16}
\vspace*{4pt}
\caption{\label{fig16}Location of the stars of the selected sample in
the $V_{\mathrm{boost}}$ vs $V_{\mathrm{term}}$ (left),
$r_{\mathrm{boost}}$ vs $r_{\mathrm{star}}$ (centre) and
$r_{\mathrm{boost}}$ vs  $\dot{M}$ (right) planes.} 
\vspace*{6pt}
\end{figure}

\begin{table}
\caption{\label{tab1}Parameters of relevance to the region of effective
line broadening\vspace*{3pt}}
\begin{tabular}{ccccccc} 
\thead
 & L$_2$~Pup & \textit{o}~Cet & W~Hya & R~Leo & R~Dor & EP Aqr \\ 
\endthead
$V_{\mathrm{boost}}~(\mathrm{km}{\cdot}\mathrm{s}^{1})$\raisebox{1.2em}{} &
$17\pm3$\0 & $12\pm2$\0 & $15\pm5$\0 & $13\pm3$\0 & $15\pm3$\0 & $20\pm2$ \\ 
$V_{\mathrm{term}}~(\mathrm{km}{\cdot}\mathrm{s}^{1})$ & 
$4\pm2$ & $5\pm2$ & $6\pm2$ & $6\pm2$ & $6\pm1$ & $12\pm2$ \\ 
$r_{\mathrm{boost}}~(\mathrm{au})$ & 
$2.2\pm0.6$ & $10.5\pm1.5$\0 & $4.2\pm3.1$ & $5.7\pm2.3$ &
$5.9\pm1.2$ & $10.1\pm1.8$ \\ 
$r_{\mathrm{star}}~(\mathrm{au})$ &
$0.7\pm0.1$ & $1.8\pm0.3$ & $2.4\pm0.3$ & $1.9\pm0.5$ &
$1.8\pm0.1$ & \0$0.8\pm0.2$ \\ 
$d~(\mathrm{pc})$ & 
${\sim}64$ & ${\sim}100$ & ${\sim}104$ & ${\sim}114$ & 
${\sim}59$ & ${\sim}119$ \\ 
$\dot{M}~(10^{-7}~\mathrm{M}_{\mathrm{Sun}}/\mathrm{year})$ & 
$0.12\pm0.07$ & $0.7\pm0.2$ & $1.3\pm0.2$ & $1.6\pm0.2$ &
\0$2\pm0.2$ & \0$1.6\pm0.4$
\botline
\end{tabular}
\vspace*{5pt}
\end{table}

Ideally, one would like to tell apart, in correlation with the
oscillations of the light curve, regions of the stellar disc over which
gas is in-falling from regions where it is outflowing. Such detailed
information is still lacking, with the exception of  W~Hya~\cite{29}
where it is, however, only partial. Available Doppler velocity spectra
measured over the stellar disc lack a systematic study of their
dependence over the stellar phase and the ratio between the diameters
of the beam and of the stellar disc are often too large. 

Nearly fifty years have elapsed since Schwarzschild~\cite{79} estimated
the size of convective cells in red giants and mentioned the
possibility that they might play a role in generating mass loss. Later,
Templeton and Karovska~\cite{80,81} and Kiss, Szab\'{o}, and
Bedding~\cite{82} presented indirect evidence for granulation of the
photosphere from Fourier analyses of the light curves. But it was only
five years ago that  Paladini \etal~\cite{11}, using PIONIER on the
VLT, presented clear evidence for the presence of large granulation
cells on the surface of $\rmpi^1$~Gruis. Such evidence has also been
obtained, using PIONIER and NARVAL, for the red supergiant 
Betelgeuse~\cite{12,13} and, using the latter instrument, for
\textit{o}~Ceti  and $\rmchi$~Cygni~\cite{11,19}. While it is still
lacking for the six stars of the present sample, ALMA observations of
the continuum emission and VLT observations of the stellar disc and of
its close surroundings have produced images of very high angular
resolution, which support the validity of the general picture outlined
by the current model. Yet, clear evidence for strong inhomogeneity has
been obtained for only three stars of the sample, W~Hya, \textit{o}~Cet
and R~Dor, and its relation with possible convective cell partition 
is not clear. 

The study by Vlemmings \etal~\cite{29} of the stellar disc of W~Hya and
its immediate neighbourhood offers a remarkable example of
inhomogeneity. The observation of continuum emission gives evidence for
a small $({\sim}2\times3~\mathrm{mas}^{2})$ spot having a brightness
temperature in excess of ${\sim}$53,000~K, consistent with the
temperature expected in a strong shock, correlated with a significant
excess of in-falling gas seen from its CO($v=1$,3--2) emission. Two
years later,  observations~\cite{26} using a broader beam
$(48\times40~\mathrm{mas}^2)$, while still giving evidence for strong
inhomogeneity, did not see any trace of the hot spot.  Ohnaka
\etal~\cite{9,33} using SPHERE/ZIMPOL observations at two epochs, have
resolved three clumpy dust clouds at a projected distance of
${\sim}$1.4--2~stellar radii, displaying clear time variations (in
particular formation of a new dust cloud and disappearance of an
earlier one) and correlated with the recent mass ejection described 
by\unskip\break  
Hoai \etal~\cite{50}. 

The case of \textit{o}~Cet is not particularly convincing when
considering only VLTI/AMBER  observations~\cite{83} and ALMA
observations~\cite{26} of continuum emission using a beam of
$33~\times23~\mathrm{mas}^{2}$. However, Kaminski  \etal~\cite{27},
using ALMA observations of the emission of the AlO(6--5) line with a
similar beam $(33\times24~\mathrm{mas}^2)$, have given evidence for the
presence of two strong blobs of emission, at projected distances of 2.9
and 4.4~stellar radii in the NNW and E directions, respectively,
revealing in-falling AlO gas having inward velocity of 4 to
$7~\mathrm{km}{\cdot}\mathrm{s}^{-1}$. However, these blobs show no
obvious correlation with the outflows displayed in  Figure~\ref{fig2}. 

In the case of R~Dor, there is evidence for clumpy emission, both from
continuum with a beam of  $25\times18~\mathrm{mas}^2$~\cite{26} and
from dust~\cite{35}. The continuum emission of L$_2$~Pup, observed by 
Kervella \mbox{\etal}~\cite{20} with a beam of  $18\times15~\mathrm{mas}^2$,
displays some elongation along the dust disc with a western excess that
the authors interpret as evidence for a planetary companion at 
$2.0\pm0.2$~au; but it shows no feature that might suggest the presence
of granulation. SPHERE/ZIMPOL  ${\sim}$650~nm observations of the disc
of  EP~Aqr~\cite{30} show evidence for light scattered by an inclined
dust disc, but the observed intensity fluctuations are too small to
claim the presence of granulation. The continuum emission of R~Leo,
observed by  Vlemmings \etal~\cite{26} with a beam of
$19\times19~\mathrm{mas}^{2}$, reveals the outward motion of a shock
wave, but no sign of hot spots; other observations 
(VLTI/AMBER~\cite{83}; VLTI/MIDI~\cite{41}; VLTI/VINCI~\cite{40})
suggest the presence of inhomogeneity and variability, but without firm
evidence. 

In summary, while the general features displayed by ALMA continuum and
VLT optical/infrared observations unanimously support a model where the
presence of large convection cells play an essential role in the
generation of shocks responsible for the observed effective line
broadening, direct evidence for the existence of such convective cells
is scarce. When inhomogeneity is observed, usually with significant
variability, in the form of hot spots of emission on the stellar disc
or of clumpy dust emission, relating it to the presence of convective
cells remains speculative and a detailed understanding of such a
relation is still lacking. New VLT and ALMA observations of high
sensitivity and angular resolution are still required, in particular in
relation with the stellar phase, to progress towards a more
quantitative description. 

\subsection{On the nature of the gas outflows}\label{sec6.3}
An observation that suffers no exception is of the presence of a
reservoir of molecular gas gravitationally bound to the star within
${\sim}$2 stellar radii from its centre. As remarked by  Vlemmings
\etal~\cite{29} for W~Hya, its total mass is over three orders of
magnitude larger than the mass lost by the star in the course of one
pulsation period. Thus, the gas spends at least $10^3$ years in this
region or even closer to the photosphere, in a shock-heated environment
that significantly affects the chemistry at stake. In no case does gas
escape from this reservoir in a spherical flow; it does it instead in
the form of outflows covering typical solid angles at steradian scale
and displaying radial distributions showing that they last several
decades. An interpretation in terms of the current model would suggest
associating each such outflow with a giant convective cell having a
lifetime of several decades, which contrasts with the millimetre
continuum and VLT observations of variability on a much shorter time
scale. A similar concurrence of two different time scales was observed
on Betelgeuse using spectro-polarimeter  observations~\cite{13}. In
some cases, as for W~Hya and R~Leo, the global morphology of the CSE
displays modest anisotropy, suggesting that on a time scale of
centuries the outflows might be emitted over $4\rmpi$ steradians and
anisotropy might somewhat average out. This may also be the case of
EP~Aqr, for which the interaction of the wind with the circumstellar
disc dominates and prevents a reliable evaluation. In the cases of the
higher mass-loss rate, R~Dor, and of the lower mass-loss rates,
\textit{o}~Cet and L$_2$~Pup, the global CSE seems to retain
significant anisotropy, possibly related to the orbit of Mira~B in the
case~of~\textit{o}~Cet. 

Smaller and more episodic outflows, as observed in \textit{o}~Cet, are
more prone to dissociation by interstellar UV radiation, causing SiO
abundance, in contrast to CO abundance, to be confined near the star. 
Nhung \etal~\cite{54} have discussed this issue in some detail but
presently available observations do not allow for a reliable conclusion
to be reached. 

Other outflows seem to be of a different nature, looking more like mass
ejections occurring over a short period of time. An extreme case is the
mass ejection, which followed the magnetic flare that produced a soft
X-ray burst in \textit{o}~Cet in  2003~\cite{56}; this seems, however,
to be rather the exception. It is not clear whether the mass ejections
observed on W~Hya (left panel of  Figure~\ref{fig5}) and on R~Dor
(right panel of  Figure~\ref{fig4}), which look like having occurred
recently over a short period of time, are of a same or different nature
as the former outflows; in particular, it is not clear whether they
should be described in the framework of the same hydrodynamical models.
More generally, these remarks raise the question of a possible
continuity, as opposed to a completely different nature, between the
mass ejection observed in \textit{o}~Cet in 2003 and the outflows
observed in the other stars of the sample. Granulation, magnetic flares
and coronal mass ejections are related phenomena and, in the case of
the Sun, the details of these relations are still raising unanswered 
questions~\cite{84}.  

\subsection{Magnetic fields}\label{sec6.4}
The generally accepted picture described by the current model offers a
framework in which to study the role played by magnetic fields in
generating the nascent wind and, later, shaping it towards the
planetary nebula phase. While little is known about such a possible 
role~\cite{85}, the presence of magnetic fields near the stellar
surface has been suggested by events such as UV emission from a
majority of AGB  stars~\cite{86}, the occurrence of a soft X-ray
outburst on \textit{o}~Cet~\cite{56} or the ephemeral presence of a
small and very hot spot on the surface of  W~Hya~\cite{29}. An abundant
literature addresses topics of direct relevance to the role possibly
played by magnetic fields in relation to convections, pulsations and
shock  waves~\cite{14,28,87,88,89,90,91}, illustrating the importance
of devoting to it increased observational attention. 

Of direct relevance to the present sample of selected stars are
measurements and observations made on \textit{o}~Cet, W~Hya and R~Leo.
Significant polarisation of maser emission from vibrationally excited
SiO  lines~\cite{68,69,92,93} has been measured using VLBA
observations, complemented by VLTI/MIDI interferometry at 10~$\rmmu$m
wavelength, and 30~m IRAM single dish observations. While giving clear
evidence for the presence of magnetic fields of a few Gauss, they are
difficult to interpret in terms of their structure, radial or toroidal.
Recently, using CARMA observations,  Huang \etal~\cite{94} have
measured linear polarisations from the Goldreich--Kylafis effect on the
CO(2--1) emission of R~Leo at the level of  ${\sim}$9.7\%. The effect
reveals unequal populations of the sublevels of the final state of the
transition and gives reliable evidence for the presence of magnetic
field. Finally, using NARVAL mounted on the 2~m telescope at Pic
du~Midi Observatory,  Fabas \etal~\cite{28} have observed variability
and structures on the polarised Balmer line emission of \textit{o}~Cet,
which they interpret in terms of shock waves suggesting the presence of
magnetic field. Also worth mentioning is a magneto-hydrodynamic model
of \textit{o}~Cet proposed by Thirumalai and  Heyl~\cite{89}, which
describes how an equatorial magnetic field could contribute to the
production of a dust-driven wind. 

\subsection{Conclusion}\label{sec6.5}
We have presented a brief review of the current knowledge of the
properties displayed by the CSEs of a sample of six well-studied nearby
oxygen-rich AGB stars. The aim has been to illustrate difficulties
experienced when comparing observations with current models and
possibly identify ways to overcome them, or at least to progress in
such a direction. The scope of the article is accordingly limited, and
we list below a few points of relevance in this
respect.

\begin{enumerate}[(i)]
\item 
We use as reference the simulations published by Freytag, H\"{o}fner
and coworkers (references 1 to 4). These should not be understood as
one model out of many possible, but as providing a useful and
convenient summary of the current understanding of the mechanisms
governing the genesis of the wind, including pulsations, convections,
shocks, dust formation and radiation pressure. We take it as granted
that there is no question that these are indeed the main contributions
to the genesis of the nascent wind. There exist, of course, many other
publications addressing the issue from a theoretical or
phenomenological point of view, but reviewing, or even simply
mentioning these would not alter the general picture and is outside the
scope of the present
article. 
\item
One may find frustrating, or at least disappointing, that the many
observations reported in the article, making use of the outstanding
performance of instruments such as VLT or ALMA, leave so many questions
unanswered. Their diversity, each star appearing as a singular case,
makes it difficult to identify common features with confidence.
Moreover, the intrinsic limitations inherent to astronomical
observations, with only two position coordinates and a single velocity
component being accessible to measurement, must be kept in mind:
experience shows that when more accurate measurements become available,
some of our earlier preconceptions may need to be abandoned, or at
least modified. In such a context, it is important to clarify which are
the main open questions and, if possible, to seek ways to progress
towards answering them. 
\item 
We have limited our study to M-type stars, oxygen-rich, having a small
mass-loss rate and displaying no clear technetium signal. The
occurrence of third-dredge-up events is obviously a major step in the
evolution of AGB stars. It adds a further complication to the
mechanisms governing the genesis of the nascent wind and would deserve
being scrutinised in a separate study including the evolution to S-type
and carbon stars. It leaves many new questions unanswered, such as why
Tc-rich and Tc-poor stars populate different regions of the
period-luminosity  diagram~\cite{136,137} or of a possible relation
between third-dredge-ups and specific features of the light 
curves~\cite{138}.
\item 
We have deliberately excluded considerations on the fate of the wind
following its genesis, such as the nature of the superwind that
precedes the formation of planetary nebulae, or the possible presence
of spiral structures revealing the shaping of the wind by distant
companions. It was usual, in the early literature, to assume that the
wind was isotropic in the early stage of the AGB, and it was therefore
natural to see such phenomena as being the cause of the breaking of
spherical symmetry observed in planetary nebulae. But the high angular
resolution observations that instruments such as ALMA and VLT have now
made possible have shown that spherical symmetry is in fact already
broken in the early stage of the AGB, making it advisable to understand
the genesis of the nascent wind at this stage before addressing its
subsequent evolution.
\end{enumerate}

In summary, we have identified a few domains that deserve particular
attention and a continued, or even increased effort on both
observational and phenomenological fronts:
\begin{enumerate}[(i)]
\item 
The role played by shocks. Their impact is important and one tends to
blame them whenever an unexpected feature is observed. Yet, few
observations allow for a reliable identification of the exclusive
effect of shocks and, in particular, for a quantitative evaluation of
its importance. A characteristic property of shocks is to induce a
specific chemistry, a result of the very high temperatures that they
are hosting. Shock chemistry allows for the production of molecules
such as OH or HCN at rates very different from those possible without 
shocks~\cite{139,140,141}. An abundant literature addresses this topic
and we mentioned in the text the case of OH molecules detected in the
neighbourhood of W~Hya and  R~Dor~\cite{48}. Systematic measurements of
abundance ratios such as HCN/SiO close to the star would therefore help
with understanding why they seem to play a significantly more important
role in some stars than in others. Similarly, emission ratios from a
same line allow for a quantitative evaluation of the deviation from LTE
predictions and of the role played by shocks. An example is the
SiO(5--4)/SiO(6--5) emission ratio predicted to be ${\sim}$0.5 and
measured in R~Dor to be  0.77~\cite{58}. Systematic measurements of
such abundance and emission ratios would make it possible to look for
correlations with other parameters characteristic of the star and
should be encouraged.
\item
The role played by stellar pulsations. Over four decades ago, Hinkle
and coworkers presented an analysis of infrared spectroscopic
observations of $\chi$~Cygni covering more than three periods of the
light  curve~\cite{142}
and gave evidence for the presence of a wave
driven by the stellar pulsation and travelling outward in the stellar
atmosphere. Since that time, much progress has been achieved in
understanding the role played by stellar pulsations in the generation
of the nascent wind and in the study of the light curves of Mira's
and Long Period Variables. Yet, correlated observations of the light
curve and of either optical/infrared or millimetre emissions are
scarce. This is very much lacking and should be given much more
attention than it currently is. Moreover, a quantitative understanding
of the ballistic up-down excursions experienced by the gas above the
photosphere is also badly needed. As was illustrated  in 
Section~\ref{sec6.2} and  Figure~\ref{fig16}, we are still a long way
from it. Systematic very high-resolution measurements of the line
broadening observed in the close neighbourhood of the star, together
with careful analyses of Doppler velocity spectra above the stellar
disc should be encouraged with the aim to reveal correlations with
properties characteristic of the star. 
\item
The role played by convection cells. The evidence for convection cells
to play an important role is strong and we had many opportunities to
illustrate it. Yet, we fail to quantify critically the degree of
agreement between observations and model simulations. Images of the
star surface of the same quality as obtained  on
$\rmpi^1$~Gru~\cite{11} using PIONIER should be sought for other stars
and a similar comment can be made concerning continuum maps of the same
quality as obtained on W~Hya using  ALMA~\cite{29}. One tends to blame
convection cells for any deviation from spherical symmetry at steradian
scale: we need a more rigorous approach to the problem, in particular
with understanding the
diversity of time scales that seem to govern the
variability of the observed properties. We fail to understand clearly
what is causing the modulation of the gas outflow, both in time, with
episodes of enhanced mass loss, and in space, with steradian like
enhancements that we tend to blame on convection cells. A considerable
effort in obtaining many more high-resolution observations of the
emission of several molecular lines is needed on a large sample of
nearby stars in order to progress. In particular, as mentioned in the
text, the precise nature of blobs of gas emission as observed in R~Dor
and W~Hya needs to be
clarified.
\item
Rotation and disc formation. As we mentioned in the text, the question
of what is the cause of the slow rotations observed near the surface of
some stars, star rotation or close-by planetary companion, remains
open. Moreover, what is causing the formation of a circumstellar disc
on stars such as L$_2$~Pup, EP~Aqr or RS~Cnc needs to be clarified.
This calls for an increased effort in high angular resolution
observations of the emission of several molecular lines.
\item 
Magnetic fields. As discussed in  Section~\ref{sec6.4}, we know of the
presence of magnetic fields near the surface of some stars, but it
seems that they do not play a significant role in the genesis of the
nascent wind, at least in the early AGB phase discussed in the article.
Yet, we need to be much clearer on this point than we currently are,
but how precisely one should proceed is not clear to us.
\item
Finally, one must keep in mind that the primary cause of the nascent
wind is located inside the star, where nuclear reactions occur.
Ultimately, we shall need to understand it before being able to claim
that we understand the genesis of the wind. In this context,
understanding the evolution of the stars from M to S and C types,
including the precise role played by third-dredge-up events and by
mixing is obviously essential.
\end{enumerate}

The contribution of the present article to the progress of the field is
both modest and limited in scope. It does not do more than illustrating
the complexity of the issues that need to be addressed and of the
problems that need to be solved. Such complexity calls for a
multidisciplinary effort requiring familiarity with nuclear, atomic,
molecular, plasma and condensed matter physics as well as with
chemistry. This is highly challenging and we hope that the article has
at least shed light on questions that need to be answered in priority
in order to progress. The outstanding performance of the VLT and of
ALMA in terms of angular resolution and sensitivity will still allow
for major progress over many years to come.

\section*{Declaration of interests}
The authors do not work for, advise, own shares in, or receive funds
from any organization that could benefit from this article, and have
declared no affiliations other than their research organizations.

\section*{Funding}
This research is funded by Vietnam Academy of Science and Technology
under grand number THTETN.03/24-25. Financial support from the World
Laboratory, the Odon Vallet Foundation and the Vietnam National Space
Center is gratefully acknowledged. 

\section*{Acknowledgements}
We thank Dr.~Bernd Freytag, Dr.~Ward Homan,  Dr.~Iain McDonald, 
Dr.~Stefan Uttenthaler and Dr.~Albert Zijlstra for sharing with us
their understanding of the issues developed in the present article.
This paper
makes use, in particular, of many archival ALMA data. 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.

\CDRGrant[VAST]{THTETN.03/24-25}

\back{}

\appendix{}

\gdef\appendixlabel{Appendix A}

\setcounter{table}{0}
\renewcommand\thetable{A\arabic{table}}

\section{}\label{appA}
See Tables~\ref{tabA1} and~\ref{tabA2}.

\begin{table}[ht!]
\caption{\label{tabA1}Parameters and references of relevance to the six
selected stars}
\fontsize{8}{9.6}\selectfont\tabcolsep=2pt
\begin{tabular}{ccccccc} 
\thead
 & 
\parbox[t]{3pc}{\centering 
L$_2$ Pup HD56096} & 
\parbox[t]{3pc}{\centering
\textit{o} Cet HD14386} & 
\parbox[t]{3pc}{\centering
W~Hya HD120285} &
\parbox[t]{3pc}{\centering
R Leo HD84748} &
\parbox[t]{3pc}{\centering
R Dor HD29712} & 
\parbox[t]{3pc}{\centering
 EP Aqr HD207076} 
\vspace*{2pt}\\ 
\endthead

\parbox[t]{5pc}{\centering
Type (spectral\ubreak/variable)} &
M5IIIe/SRb & 
\parbox[t]{2.5pc}{\centering
M7-IIIe\ubreak/Mira} &
M7.5-9/SRa & M7-9/Mira &
M8/SRb & M7-8/SRb 
\vspace*{4pt}\\ 

$d$ (pc) & $64\pm4$~\cite{98} & $\sim$100~\cite{98} & 104~\cite{98} & 114~\cite{98} & 
59~\cite{102} & 119~\cite{98,101} 
\vspace*{4pt}\\ 

\parbox[t]{4.5pc}{\centering
$R_{\mathrm{star}}$~(au)\unskip\break
continuum/NIR} & 
\parbox[t]{3pc}{\centering
0.58/0.64\unskip\break
\cite{45,47}} & 
2.1/1.5~\cite{26} & 2.7/2.1~\cite{26} & 2.4/1.6~\cite{26} & 1.9/1.7~\cite{26} &
\parbox[t]{3pc}{\centering
1.0/0.7\unskip\break
\cite{30,103}} 
\vspace*{4pt}\\ 

Period $(d)$ & 141~\cite{42,43} & 333~\cite{80,81} & 361~\cite{96} & 
310~\cite{105} & 175/332~\cite{104} & 110~\cite{113,114} 
\vspace*{4pt}\\ 

Mass $(\mathrm{M}_{\mathrm{Sun}})$ & $\sim$0.7~\cite{20} & 
\parbox[t]{3.5pc}{\centering
$A\sim2.0$,\unskip\break
$B\sim0.7$~\cite{106}} &
\parbox[t]{4.2pc}{\centering
1.0--1.5\unskip\break
\cite{107,109,110}} &
\parbox[t]{4pc}{\centering
$\sim$0.7~\cite{108}} & 0.7--1.0~\cite{39} & 
$\sim$1.7~\cite{30} 
\vspace*{4pt}\\ 

\parbox[t]{4.2pc}{\centering
Mass-loss rate\unskip\break
$(10^{-7}~\mathrm{M}_{\mathrm{Sun}}/\mathrm{yr})$} & 
\parbox[t]{3pc}{\centering
$0.12\pm0.07$\unskip\break 
\cite{49}} &
\parbox[t]{3.4pc}{\centering
$0.7\pm0.2/2.5$\unskip\break 
\cite{54,111}} & 
1.3~\cite{109,110} & ${\sim}$1.6~\cite{112} & 
${\sim}$2~\cite{58} & $1.6\pm0.4$~\cite{64}
\vspace*{4pt}\\ 

\parbox[t]{4.6pc}{\centering
Terminal\unskip\break 
velocity~$(\mathrm{km}{\cdot}\mathrm{s}^{-1})$} &
$3.4\pm1.7$~\cite{49} & 2.5~\cite{111} & 5~\cite{50} &
5.5~\cite{51} & 6--9~\cite{57} & 2--11~\cite{64}
\vspace*{4pt}\\ 

\parbox[t]{4.2pc}{\centering
VLT NACO\Lbreak VLTI VINCI} & 
\cite{45,46,47} & & \cite{36} & \cite{36,40} &
\cite{36} &
\vspace*{4pt}\\ 

\parbox[t]{4pc}{\centering
VLT SPHERE} & \cite{31} & \cite{32} & \cite{9,33,34} & & 
\cite{35} & \cite{30} 
\vspace*{4pt}\\ 

\parbox[t]{4pc}{\centering
VLTI AMBER} & \cite{47} & \cite{83} & \cite{9,33,37} & \cite{83} &
\cite{39} & 
\vspace*{4pt}\\ 

\parbox[t]{4pc}{\centering
VLTI MIDI} & \cite{45} & & \cite{38,115} & \cite{41} & &  
\vspace*{4pt}\\ 

Others & & 
\parbox[t]{4pc}{\centering
\cite[ISI]{23},\unskip\break
\cite[IOTA]{24}\Lbreak
\cite{117},\unskip\break
\cite[Keck]{118}\Lbreak
\cite[ISI]{120}} & 
\parbox[t]{4.2pc}{\centering
\cite{117},\unskip\break
\cite[Keck]{118}\Lbreak
\cite[ISO]{121}} & 
\parbox[t]{4.2pc}{\centering
\cite[IOTA]{116}\Lbreak
\cite{117},\unskip\break
\cite[Keck]{118}\Lbreak
\cite[SAO]{119},\unskip\break
\cite[ISI]{120}} &  & 
\vspace*{4pt}\\ 

\parbox[t]{3pc}{\centering
ALMA\unskip\break
continuum} & \cite{20} & 
\parbox[t]{3.8pc}{\centering
\cite{21,22,25,26}\Lbreak
\cite{27,32,106}} & 
\cite{26,29} & \cite{26} & \cite{26} & \cite{30} 
\vspace*{4pt}\\ 

\parbox[t]{6pc}{\centering
ALMA and APEX 
Abundances} & & \cite{27,135} & \cite{7,48,107,123} & & 
\cite{5,48,122} &  
\vspace*{4pt}\\ 

\parbox[t]{4.7pc}{\centering
ALMA\unskip\break
molecular lines} & \cite{20,49,61} & 
\parbox[t]{3.5pc}{\centering
\cite{25,32,54}\Lbreak
\cite{55,127,128}} &
\cite{7,29,50,126} & 
\cite{51,70,124} & 
\parbox[t]{3.5pc}{\centering
\cite{6,52,57,59}\Lbreak
\cite{60,63}} & 
\parbox[t]{3.5pc}{\centering
\cite{30,33,62}\Lbreak
\cite{64,67}} 
\vspace*{4pt}\\ 

Others &  &
\cite[JVLA]{22} & & 
\parbox[t]{3pc}{\centering
\cite[VLA]{129}\Lbreak
\cite[JVLA]{130}} & 
\cite[APEX/SEPIA]{58} &  
\vspace*{4pt}\\ 

Masers & \cite{44} & \cite{68,69,92,131} &
\parbox[t]{4.2pc}{\centering
\cite{92,93,121}\Lbreak
\cite{125,131}} & 
\parbox[t]{4.2pc}{\centering
\cite{68,92,93,131}\Lbreak
\cite{132,133,134}} &  &
\vspace*{2pt}
\botline
\end{tabular}
\tabnote{Spectral and variability types are taken from standard
catalogues~\cite{95,96,97}. Distance $(d)$ measurements are typically
reliable to within ${\pm}$10\%, with the exception of R Leo for which
we retain the Hipparcos value of 114 pc~\cite{98} rather than the Gaia
value of 71 pc~\cite{99,100}. Stellar radii $(R_{\mathrm{star}})$
measurements span broad samples of values, depending on stellar phase
and wavelength. We retain values~\cite{26} (continuum at millimetre
wavelengths and near infrared) quoted in a reliable and critical review
of four of the stars in our sample. For the other two stars (L$_2$ Pup
and EP Aqr), the continuum values are poorly measured. The period of EP
Aqr is poorly known and often quoted as 55 $d$ while it is in fact more
like 110 days. Masses are not precisely measured and are mostly crude
estimates.}
\end{table}

\begin{table}
\caption{\label{tabA2}Molecular lines observed and studied with high
angular resolution (beam FWHM $< {\sim}200$~mas) in
the selected sample of six stars}
\fontsize{9}{10.8}\selectfont\tabcolsep=3.3pt
\begin{tabular}{cccccccccc}  
\thead
Line & $A$~[Hz] & $E_{\mathrm{up}}$~[K] & $f$~[GHz] & 
L$_2$~Pup & \textit{o}~Cet & W~Hya & R~Leo & 
R~Dor & EP Aqr \\ 
\endthead
$\mbox{}^{12}$C$\mbox{}^{16}$O($v=0$,2--1)\raisebox{1.2em}{} &
$6.91\times10^{-7}$ &
16.6 & 230.5 &  &  &  & 40 &  & \025 \\ 
$\mbox{}^{13}$C$\mbox{}^{16}$O($v=0$,2--1) & 
$6.04\times10^{-7}$ & 
15.9 & 220.4 &  &  &  &  &  & \023 \\ 
$\mbox{}^{12}$C$\mbox{}^{16}$O($v=0$,3--2) & 
$2.50\times10^{-6}$ & 33.2 & 345.8 & 21 &  & 46 &  & 160 &  \\ 
$\mbox{}^{12}$C$\mbox{}^{16}$O($v=1$,3--2) & 
$1.45\times10^{-6}$ & 3120 & 342.6 &  &  & 17 &  &  &  \\ 
$\mbox{}^{13}$C$\mbox{}^{16}$O($v=0$,3--2) & 
$2.18\times10^{-6}$ & 31.7 & 330.6 & 22 &  &  &  &  &  \\ 
$\mbox{}^{28}$Si$\mbox{}^{16}$O($v=0$,5--4) &
$5.91\times10^{-4}$ & 31.3 & 217.1 &  & 32--45 &  &  &  & \024 \\ 
$\mbox{}^{28}$Si$\mbox{}^{16}$O($v=1$,5--4) & 
$0.50\times10^{-3}$ & 1800 & 215.6 &  & 32 &  & 42 &  &  \\ 
$\mbox{}^{28}$Si$\mbox{}^{16}$O($v=1$,8--7) & 
$2.20\times10^{-3}$ & 1844 & 344.9 &  &  &  & 47 & 150 &  \\ 
$\mbox{}^{28}$Si$\mbox{}^{16}$O($v=2$,5--4) & 
$0.51\times10^{-3}$ & 3552 & 214.1 & & 32 &  & 46 &  &  \\ 
$\mbox{}^{28}$Si$\mbox{}^{16}$O($v=3$,5--4) &
$5.08\times10^{-4}$ & 5287 & 212.6 &  &  &  &  & \036 &  \\ 
$\mbox{}^{29}$Si$\mbox{}^{16}$O($v=0$,5--4) &
$0.50\times10^{-3}$ & 30.9 & 214.4 &  & 32 &  & 46 &  &  \\ 
$\mbox{}^{28}$Si$\mbox{}^{16}$O($v=0$,8--7) & 
$2.20\times10^{-3}$ & 75.0 & 347.3 &  &  &  &  & \030 &  \\ 
$\mbox{}^{29}$Si$\mbox{}^{16}$O($v=1$,5--4) & 
$4.93\times10^{-4}$ & 1789 & 212.9 &  &  &  &  & \036 &  \\ 
$\mbox{}^{29}$Si$\mbox{}^{16}$O($v=0$,8--7) & 
$2.10\times10^{-3}$ & 74.1 & 343.0 & 20 &  & 35--45 &  & \030 &  \\ 
$\mbox{}^{30}$SiO($v=0$,8--7) & 
$2.05\times10^{-3}$ & 73.2 & 338.9 &  &  &  &  & 150 &  \\ 
$\mbox{}^{28}$Si$\mbox{}^{32}$S($v=1$,19--18) & 
$6.89\times10^{-4}$ & 1236 & 343.1 & 20 &  &  &  &  &  \\ 
$\mbox{}^{32}$S$\mbox{}^{16}$O(5$_5$,4$_4$) & 
$0.12\times10^{-3}$ & 44.1 & 215.2 &  &  &  & 42 &  &  \\ 
$\mbox{}^{32}$S$\mbox{}^{16}$O(6$_5$,5$_4$) & 
$1.96\times10^{-4}$ & 50.7 & 251.8 &  &  &  &  & 150 &  \\ 
$\mbox{}^{32}$S$\mbox{}^{16}$O($v=0$,8$_8$--7$_7$) &
$5.19\times10^{-4}$ & 87.5 & 344.3 & 20 &  &  &  &  &  \\ 
$\mbox{}^{32}$S$\mbox{}^{16}$O($v=0$,8$_9$--7$_8$) & 
$5.38\times10^{-4}$ & 78.8 & 346.5 &  &  &  &  & 150 &  \\ 
$\mbox{}^{32}$S$\mbox{}^{16}$O$_2$(34$_{3,31}$,34$_{2,32}$) &
$3.45\times10^{-4}$ & 581.9 & 342.8 &  &  &  &  & \038 &  \\ 
$\mbox{}^{32}$S$\mbox{}^{16}$O$_2$(16$_{3,13}$,16$_{2,14}$) & 
$9.90\times10^{-5}$ & 147.8 & 214.7 &  &  &  &  & \036 &  \\ 
$\mbox{}^{32}$S$\mbox{}^{16}$O$_2$(16$_{6,10}$,17$_{5,13}$) & 
$2.35\times10^{-5}$ & 213.3 & 234.4 &  &  &  &  &  & 175 \\ 
$\mbox{}^{32}$S$\mbox{}^{16}$O$_2$(13$_{2,12}$,12$_{1,11}$) & 
$2.38\times10^{-4}$ & 92.8 & 345.3 &  &  &  & 47 &  &  \\ 
$\mbox{}^{32}$S$\mbox{}^{16}$O$_2$(22$_{2,20}$,22$_{1,21}$) & 
$9.30\times10^{-5}$ & 248.4 & 216.6 &  &  &  & 42 &  &  \\ 
$\mbox{}^{32}$S$\mbox{}^{16}$O$_2$(4$_{2,2}$--3$_{1,3}$) & 
$7.69\times10^{-5}$ & 19.0 & 235.2 &  &  &  &  &  & \025 \\ 
H$_2\mbox{}^{16}$O($v_2=1$,5$_{5,0}$,6$_{4,3}$) &
$4.77\times10^{-6}$ & 3462 & 232.7 &  & 30 &  &  &  &  \\ 
H$\mbox{}^{12}$C$\mbox{}^{14}$N(4--3) & 
$2.06\times10^{-3}$ & 42.5 & 354.5 &  &  &  &  & 151 &  \\ 
H$\mbox{}^{13}$C$\mbox{}^{14}$N(4--3) &
$1.90\times10^{-3}$ & 41.4 & 344.2 &  &  &  & 45 &  &  \\ 
$\mbox{}^{27}$Al$\mbox{}^{16}$O($N=9$,8) & 
\multicolumn{2}{c}{See~\cite{7}} & 344.4 &  &  & 34 &  &  &  \\ 
\multicolumn{4}{c}{$\mbox{}^{16}$OH Many (see~\cite{48})} &
&  & ${\sim}$30\mn &  & \0${\sim}$30\mn & 
\botline
\end{tabular}
\tabnote{Emission related parameters (Einstein coefficient  $A$, energy
of the upper level $E_{\mathrm{up}}$ and frequency  $f$ of the
transition) are listed in the first columns. For each star the mean
beam size (FWHM) associated with the highest angular resolution is
listed in mas in the last columns. We recall that the emissivity
$\varepsilon$ and the optical depth $\tau$ are obtained from the
relations $\varepsilon[\mathrm{Jy}\times\mathrm{arcsec}^{-2}]/
N[\mathrm{mol}{\cdot}\mathrm{cm}^{-3}{\cdot}\mathrm{arcsec}]=
5.5\times10^3\times d[\mathrm{pc}]\times
A[\mathrm{s}^{-1}]f_{\mathrm{pop}}$ with $f_{\mathrm{pop}}=
k(2J+1)\mathrm{e}^{-Eu/T}/T$ and $\varepsilon/\tau=
0.34\times10^{-7}f^3/(\mathrm{e}^{\Delta E/T}-1)$ where $N$ is the density,  $d$
the distance from Earth to the star and $k$ is the product of
the partition function by the temperature.}
\end{table}

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\end{document}
