# Morpho-kinematics of the wind of AGB star L2 Pup

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

###### Abstract

Single dish observations of AGB star L2 Pup have revealed exceptionally low
mass loss rate and expansion velocity, challenging interpretations in terms of
standard wind models. Recent VLT and ALMA observations have drawn a detailed
picture of the circumstellar envelope within $\sim$20 au from the centre of
the star: a nearly edge-on rotating disc of gas and dust, probably hosting a
planetary companion near the star. However, these observations provide no
direct information on the wind escaping the gravity of the star. The present
article uses ALMA observations of the 12,13CO(3-2), 29SiO(8-7), 12CO(2-1) and
28SiO(5-4) line emissions to shed new light on this issue. It shows the
apparent normality of L2 Pup in terms of the formation of the nascent wind,
with important line broadening within 4 au from the centre of the star, but no
evidence for a wind flowing along the disc axis. At larger distances, up to
some 200 au from the centre of the star, the wind morpho-kinematics is
dominated by a disc, or equatorial enhancement, expanding isotropically and
radially with a velocity not exceeding some 5 km s-1, inclined in the north-
west/south-east direction with respect to the plane of the sky. In addition,
outflows of lower density are observed on both sides of the disc, covering
large solid angles about the disc axis, contributing about half the flux of
the disc. Such morphology is at strong variance with the expectation of a pair
of back-to-back outflows collimated by the central gas-and-dust disc.

###### keywords:

stars: AGB and post-AGB – circumstellar matter – stars: individual: L2 Pup –
radio lines: stars

††pubyear: 2021††pagerange: Morpho-kinematics of the wind of AGB star L2 Pup–A

##  1 Introduction

Over the past decade, a host of new observations of the circumstellar envelope
(CSE) of oxygen-rich AGB stars have considerably improved our understanding of
the formation of the nascent wind, yet leaving an important number of
questions unanswered (Höfner & Olofsson, 2018). From infrared to millimetre
wavelengths, the latter probing the proximity of the stellar surface with
vibrationally excited molecular lines or continuum emission, they show the
importance of pulsation- and shock-induced dynamics in levitating the
molecular atmosphere. They reveal a complex dynamics and grain chemistry,
influenced by variability, displaying significant inhomogeneity and suggesting
the presence of shocks related to star pulsations: evidence is found for short
time variability, occasional gas in-fall, hot spots covering a small fraction
of the stellar disc, radial velocities at the 10 km s-1 scale. A consequence
on the millimetre observation of the emission of molecular lines is the
presence of large Doppler velocity wings near the line of sight crossing the
stellar disc in its centre.

Recently, ALMA observations of the 12,13CO(3-2) and 29SiO(8-7) emissions of
the CSE of such a star, the nearby L2 Pup, have been reported by Homan et al.
(2017) and Kervella et al. (2016), respectively. Both analyses offer a
detailed description of the CSE in terms of a nearly edge-on rotating disc of
gas and dust, suggesting the presence of a planetary companion at $\sim$2.4 au
from the centre of the star. These analyses predict the presence of radial
outflows collimated by the disc and do not explicitly account for an important
line broadening in the inner region of the CSE, in contrast with what is
usually observed in other similar AGB stars. These are the two main issues
that the present article is addressing.

L2 Pup is a semi-regular pulsating variable (P$=$141 days Bedding et al.,
2005) of spectral type M5III corresponding to an effective temperature of
$\sim$3500 K. Hipparcos locates it at 64$\pm$4 pc (van Leeuwen, 2007). Its
mass was first estimated as 1.7 M⊙ by Dumm & Schild (1998), 2 M⊙ by Kervella
et al. (2015) and 0.7 M⊙ by Lykou et al. (2015); it is now measured as
0.66$\pm$0.05 M⊙ by Kervella et al. (2016) from the Keplerian motion of the
gas orbiting it.

The light curve (Bedding et al., 2002, 2005; McIntosh & Indermüehle, 2013) has
been undergoing a major dimming episode at the end of the past century, in
$\sim$1994\. This event has triggered detailed studies of the CSE using high
angular resolution VLT observations at visible and infrared wavelengths. Using
NACO observations, Kervella et al. (2014), Lykou et al. (2015) and Ohnaka et
al. (2015), the latter authors combining these with AMBER/VLTI observations,
have detected and resolved a dust disc, oriented east-west and inclined by 82∘
with respect to the plane of the sky, with approximate projected size of
180$\times$50 mas2. While agreeing on the general picture, these authors
mention several small differences between their observations. Some of them
(Ohnaka et al., 2015; Bedding et al., 2005) assume that dust clouds were
ejected at the end of the past century, causing the appearance of the disc.
Others assume that the disc existed before the dimming event and that in 1994
it simply started obscuring significantly the star. Kervella et al. (2015),
using VLT/SPHERE-ZIMPOL observations in the visible, have revealed the
possible 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.
There had been many earlier speculations about a possible binarity (Goldin &
Makarov, 2007; Bedding et al., 2002; Jorissen et al., 2009; McIntosh &
Indermüehle, 2013).

Single dish observations of the CSE use mostly ground based telescopes, with
the exception of the most recent, Danilovich et al. (2015), that uses data
from Herschel/HIFI; they quote a mass loss rate of 1.4$\times$10-8 M⊙ yr-1
obtained from a radiative transfer modelling of the emission of CO lines. A
similarly low value of 2$\times$10-8 M⊙ yr-1 had been obtained by Olofsson et
al. (2002). Typical terminal velocities of $\sim$2 to 3 km s-1are quoted
(Winters et al., 2002; González Delgado et al., 2003). However these models
are crude, in particular they assume a spherically symmetric wind, which is
probably far from being the case: they can only provide an order of magnitude
estimate of the mass loss rate. Neither the terminal velocity nor the mass
loss rate has been measured directly.

The extensions of the CO and SiO line emissions have been evaluated by Schöier
et al. (2004) using Australia Telescope Compact Array (ATCA) observations with
an angular resolution at the scale of 2 arcsec and by Ramstedt et al. (2020)
using the Atacama Compact Array (ACA). But the morpho-kinematics of the CSE
has now been studied in detail using ALMA long baseline millimetre
observations of 29SiO(8-7) and continuum emissions (Kervella et al., 2016) and
of the 12CO(3-2) and 13CO(3-2) line emissions (Homan et al., 2017). These
authors draw a detailed picture of the morpho-kinematics of the disc; they
find that between 2 au and 6 au from the star, there is only gas and the
rotation is Keplerian, while between 6 au and some 25 au from the star, there
is both gas and dust and the rotation is sub-Keplerian. Evidence for rotation
had already been obtained earlier from the study of SiO masers (McIntosh &
Indermüehle, 2013). Homan et al. (2017) use a radiative transfer model to
study the distribution of temperature and density within the disc; they find
that the inner rim of the disc has a thickness of $\sim$1.5 au and evaluate a
disc mass of $\sim$2$\times$10-4 M⊙ and a 12CO/13CO abundance ratio of
$\sim$10, however with a large uncertainty. Continuum emission confirms the
presence of a likely planetary companion orbiting at only 2.4 au from the
centre of the star (Kervella et al., 2016); Homan et al. (2017) estimate its
mass at Jupiter mass scale. Chen et al. (2016) have presented a hydro-
dynamical modelling of these observations and Haworth et al. (2018) have
studied their implication on the dust properties.

Finally, we note that Little et al. (1987) and Lebzelter & Hron (1999) have
both reported possible detections of technetium in the atmosphere of L2 Pup,
none of which, however, could be firmly established.

##  2 Overall picture

We use archival ALMA observations from project ADS/JAO.ALMA#2015.1.00141.S (PI
P. Kervella) which cover emissions of the 12CO(3-2), 13CO(3-2) and 29SiO(8-7)
lines in the close neighbourhood of the star and of the 12CO(2-1) and
28SiO(5-4) lines farther away. The first set of observations was previously
analysed by Kervella et al. (2016) and Homan et al. (2017). We refer the
reader to these publications for details concerning the observations and their
calibration. We used CASA111https://casa.nrao.edu/ to produce clean maps with
natural weighting and no continuum subtraction. The second set was observed on
April 29 and August 13, 2016 with 42 and 38 antennas in configurations C36-2
and C36-5, respectively. The phase centres were shifted to the corresponding
peaks of the continuum ($\alpha$$=$07:13:32.4820, $\delta$$=$$-$44:38:17.6336
for April 29 and $\alpha$$=$07:13:32.4835, $\delta$$=$$-$44:38:17.5728 for
August 13) before merging; these data have been calibrated using standard
scripts of ALMA without continuum subtraction and cleaned using
GILDAS222https://www.iram.fr/IRAMFR/GILDAS/ with natural weighting.

Figure 1 shows the baseline distribution and the $uv$ coverage for the first
set of observations. Baselines smaller than 500 m are sparse and unevenly
distributed, limiting the range of reliable imaging to projected distances
from the star $R$$<$$\sim$0.2 arcsec. A more detailed evaluation is obtained
by producing the $uv$ map of an isotropic wind and inspecting its clean image.
The right panel of Figure 1 displays the resulting distributions of the
position angle $\omega$ in successive intervals of $R$: important distortions
are already seen in the 0.15$<$$R$$<$0.20 interval.

Figure 1:  Left: distribution of the decimal logarithm of the baselines
measured in metres. Middle: central $uv$ coverage; the red circle has a radius
of 500 m. Right: position angle $\omega$ distributions of the image of an
isotropic wind in intervals 0.05$<$$R$$<$0.10 arcsec (black),
0.10$<$$R$$<$0.15 arcsec (red) and 0.15$<$$R$$<$0.20 arcsec (blue).

The main relevant parameters are listed in Table 1. They include, for each of
the line emissions studied in the article, intensities $f_{1000}$, $f_{100}$
and $f_{10}$ calculated at temperatures of 1000 K, 100 K and 10 K,
respectively for an optically thin layer having a column density of 1 molecule
cm-3 arcsec. They are given in units of Jy arcsec-2 km s-1 and are calculated
as $f$$=$$hc/(4\pi)NA_{ji}f_{pop}$ with $f_{pop}$$=$$(2J+1)\exp(-E_{up}/T)/Q$
where $Q=T/k$ is the partition function, $h$ the Planck constant, $c$ the
light velocity, $N$ the column density and $A_{ji}$ the Einstein coefficient.
The beam diameters (FWHM) are typically 20 mas (1.3 au) for the first set of
observations and 340 mas (22 au) for the second. The brightness distributions
are shown in Figure 2. We use orthonormal coordinates with $x$ pointing east,
$y$ pointing north and $z$ pointing away from us. The projected distance from
the star is $R=\sqrt{x^{2}+y^{2}}$ and the position angle $\omega$ is measured
counter-clockwise from north. Doppler velocities $V_{z}$ are referred to the
same radial velocity relative to the Local Standard of Rest as used by Homan
et al. (2017), $V_{lsr}$=33.3 km s-1.

In a first step we study the close neighbourhood of the star using the first
set of observations. We analyse the second set in Section 5. Figure 3 displays
intensity maps, mean Doppler velocity <$V_{z}$> (moment 1) maps and Doppler
velocity spectra for each of the CO(3-2) and 29SiO(8-7) line emissions. They
are shown as a reminder: the reader is referred to the detailed analyses of
Kervella et al. (2016) and Homan et al. (2017), which give interpretations in
terms of a nearly edge-on rotating disc.

Figure 4 compares the radial distributions of the 12,13CO(3-2) and 29SiO(8-7)
line emissions. The contribution of continuum emission is seen to extend to
$\sim$0.03 arcsec ($\sim$1.9 au) as expected (Kervella et al., 2016), beyond
which 12CO and SiO emissions have similar intensities. The 13CO emission is
nearly optically thin (Homan et al., 2017). All three line intensities
decrease very steeply with $R$, illustrating the confinement of the CO and SiO
molecules to the gas and dust disc described by Homan et al. (2017) and
Kervella et al. (2016). The steeper decrease of the 13CO emission reveals the
stronger absorption of the optically thicker 12CO and SiO line emissions when
approaching the star.

Figure 2:  From left to right: brightness distributions of the 12CO(3-2), 13CO(3-2) and 29SiO(8-7) line emissions in the region of $|x|$, $|y|$$<$0.5 arcsec and $|V_{z}|$$<$25 km s-1; of the 12CO(2-1) line emission in the region of $R$$<$4 arcsec and $|V_{z}|$$<$32 km s-1; and of the 28SiO(5-4) line emission in the region of $R$$<$4 arcsec and $|V_{z}|$$<$5 km s-1. Table 1: Main parameters related to the line emissions studied in the article. The intensities $f$ listed in the lower rows are for an optically thin layer having a column density of 1 molecule cm-3 arcsec at temperatures of 1000 K, 100 K and 10 K, respectively. They are given in units of Jy arcsec-2 km s-1.  Line |  12CO(3-2) |  13CO(3-2) |  29SiO(8-7) |  28SiO(5-4) |  12CO(2-1)
---|---|---|---|---|---
Beam (mas2) | 24$\times$18 | 25$\times$19 | 24$\times$18 | 370$\times$330 | 320$\times$310
Frequency (GHz) | 345.796 | 330.588 | 342.981 | 217.105 | 230.538
Noise ($\sigma$, mJy beam-1) | 2.4 | 2.2 | 1.5 | 10 | 2.5
d$V_{z}$ (km s-1) | 0.212 | 0.222 | 0.427 | 0.337 | 0.159
Pixel size (mas2) | 2.52 | 2.52 | 2.52 | 502 | 502
$E_{up}$ (K) | 33.19 | 31.73 | 74.08 | 31.26 | 16.60
$A_{ji}$(10-6 s-1) | 2.5 | 2.2 | 2100 | 520 | 0.69
$k$ | 2.77 | 2.65 | 1.03 | 1.04 | 2.77
$f_{1000}$ | 0.016 | 0.014 | 12.2 | 2.0 | 0.0034
$f_{100}$ | 0.13 | 0.11 | 62.6 | 15.6 | 0.029
$f_{10}$ | 0.062 | 0.061 | 0.80 | 9.3 | 0.065

##  3 Absorption over the stellar disc

High angular resolution observations of the emission of molecular lines
resolve the stellar disc and reveal the absorption of its continuum emission
by the surrounding gas. Wong et al. (2016) were first to present a detailed
study of this feature using ALMA observations of Mira Ceti. It has since been
observed on several other oxygen-rich AGB stars: we show in the left panel of
Figure 5 the case of R Dor, the other nearby such star, measured inside a
circle of 35 mas radius (Nhung et al., 2021). The absorption spectrum over the
stellar disc is a rich source of information. In particular, it probes the
whole CSE, unaffected by maximal resolvable scale constraints: it provides a
direct measure of the terminal velocity in the form of a narrow absorption
peak, visible at $V_{z}$$\sim$$-$4 km s-1 in the case of R Dor; moreover, it
probes the very close environment of the star, where pulsations and convective
cell ejections produce shocks, providing direct evidence for Doppler
velocities in excess of 10 km s-1.

The absorption spectra measured inside a circle of 12 mas radius centred on L2
Pup are shown in the right panel of Figure 5 for both 12,13CO(3-2) and
29SiO(8-7) emissions. They are located well within the inner rim of the gas
disc, evaluated at $R$$\sim$31 mas by Homan et al. (2017) and should receive
no contribution from rotation. Their comparison with the R Dor spectrum
invites several comments.

The L2 Pup spectra peak at 0, giving evidence for the absence of significant
wind along the line of sight crossing the star in its centre. This observation
suggests that the wind of L2 Pup, contrary to that of R Dor, lacks spherical
symmetry, as will be quantitatively confirmed in Section 5. At first glance,
this result is not surprising, the CSE consisting essentially in this
direction of a gravitationally bound disc of gas and dust. In the present
state of the evolution of L2 Pup, if there is a wind escaping its gravity, it
must mostly be in a broad cone around the disc axis, close to the plane of the
sky and, therefore, displaying a low mean Doppler velocity. We shall come back
to this point in Section 5. However, in the past, before the 1994 dimming
episode, there might have been significant mass loss along the line of sight
crossing the star in its centre. No trace of it is to be seen on the
absorption spectra displayed in Figure 5, however. The 12CO line emission must
be probing the CSE over several arcseconds away from the star and this is
therefore evidence for the absence of significant wind, with a velocity in
excess of $\sim$1 km s-1, along the line of sight crossing the star in its
centre.

Figure 3: Left: Intensity maps integrated over $|V_{z}|$$<$20 km s-1. Middle:
maps of the mean Doppler velocities (moment 1); a 3-$\sigma$ cut has been
applied. A circle of radius 0.25 arcsec is shown on each map to indicate the
region over which the spectra in the right panels are integrated. Right:
Doppler velocity spectra integrated over $R$$<$0.25 arcsec (16 au). The upper
row is for 12CO(3-2) emission, the middle row for 13CO(3-2) emission and the
lower row for 29SiO(8-7) emission. The units of the colour bars are Jy beam-1
km s-1 in the left panels and km s-1 in the middle panels. Figure 4: Radial
distributions of 12CO(3-2) (black), 13CO(3-2) (blue) and 29SiO(8-7) (red)
emissions averaged over position angles and integrated over $|$$V_{z}$$|$$<$20
km s-1. The line at $R$$=$30 mas indicates the region beyond which the
contribution of the continuum is negligible (Kervella et al., 2016). Note that
the size of the beam is nearly the same for each of the three lines.

The L2 Pup spectra reveal a more important component of gas in-fall than for R
Dor; they reach Doppler velocities of $\sim$20 km s-1in absolute value,
suggesting comparable levels of activity in the close neighbourhood of each
star. In both R Dor and L2 Pup absorption of the SiO line is nearly complete
over the stellar disc, a result of the important optical thickness. The
absorptions of the CO lines are slightly less important, larger for 12CO than
for 13CO as expected. The continuum levels of both stars are similar once
accounting for slightly different frequencies and normalisation to a same
area, a result to be expected to the extent that both stars have similar
temperatures.

Figure 5: Absorption spectra over the stellar disc, integrated over
$R$$<$0.035 arcsec (2.1 au) for R Dor (left) and over $R$$<$0.012 arcsec (0.8
au) for L2 Pup (right). 29SiO(8-7) data are shown for both stars and CO(3-2)
data for L2 Pup only. The slightly different continuum levels of the L2 Pup
emission of the two CO isotopologues is the result of the associated frequency
difference.

The important optical thickness of the gas and dust disc revealed by the
absorption spectra observed over the stellar disc brings up the question of
its extension beyond the stellar disc. In other oxygen-rich AGB stars,
absorption is usually observed to extend well beyond the stellar disc for
28SiO emission, in the form of self-absorption, as well as, to a lesser
extent, for 29SiO and 12CO emissions while being nearly confined to the
stellar disc for 13CO emission. Figure 6 displays PV maps of $V_{z}$ vs $R$
for each of the northern, eastern, southern and western quadrants separately.
Significant absorption over $\sim$1 km s-1 below systemic velocity is seen to
persist up to $\sim$15 au in most quadrants for both 12CO and 29SiO lines. Its
slightly negative Doppler shift (also visible on the 29SiO absorption spectrum
of Figure 5) may reveal a possible expansion of the disc, at the level of
0.8$\pm$0.5 km s-1. This is smaller than the expansion velocity generally
assumed in the earlier literature, of the order of 3 km s-1 (Winters et al.,
2002). In contrast, absorption of the 13CO line is limited to the stellar
disc.

Figure 6: PV maps of $V_{z}$ vs $R$ for each of the north, east, south and
west quadrants (from left to right). The upper row is for 12CO(3-2) emission,
the middle row for 13CO emission and the lower row for 29SiO(8-7) emission.
The colour scales are in units of Jy arcsec-1.

##  4 High Doppler velocity wings

The absorption spectra observed over the stellar disc and discussed in the
preceding section give evidence for large velocities in the neighbourhood of
the star, in line with the standard picture of a region dominated by shocks
from pulsations and convection cell ejections, boosting the gas to distances
where acceleration from dust grains becomes effective. These high velocities
are known to be seen as high Doppler velocity wings on the profiles of
molecular lines observed on lines of sight crossing the star near its centre.
Their evolution when moving away from the star centre provides an estimate of
the thickness of the layer where shocks are important. Such an evaluation was
done in the case of Mira Ceti (Hoai et al., 2020), locating the layer between
5 and 15 au from the centre of the star. In the case of R Dor, a confinement
of the layer within $\sim$12 au from the centre of the star has been obtained
(Nhung et al., 2021).

Figure 7: Evolution of the Doppler velocity spectrum when scanning at $x$$=$0
in 10 mas steps of $y$ (see text). The northern and southern scans are
illustrated separately in the upper and lower rows, respectively. From left to
right: 12CO(3-2), 13CO(3-2) and 29SiO(8-7). Colours evolve from blue to red
when $|y|$ increases from 10 to 90 mas.

The present section aims at obtaining such an evaluation in the case of L2
Pup, but the presence of high rotation velocities reaching close to the star
makes the exercise more difficult. The inner rim of the gas disc is located at
$\sim$2 au from the centre of the star (Homan et al., 2017) and the diameter
of the beam (FWHM) is $\sim$1.2 au: when staying on the $x$$=$0 line, one may
then expect to be free of significant contribution from rotation. Figure 7
illustrates the evolution of the line profile when scanning along this line in
steps of $y$$=$10 mas (0.64 au). Very strong distortions caused by absorption
illustrate the difficulty of making a faithful radiative transfer modelling of
a very complex reality: speaking of a line width is but a crude approximation.
Yet, to be free of the effect of the strong red-side absorption, we evaluate
its evolution from the value $V_{z,20}$ of $V_{z}$ at which 20% of the maximal
flux density is reached on the blue side. In both south and north directions,
Figure 8 shows that, for both 29SiO(8-7) and 12CO(3-2) emissions, this value
increases by $\sim$8 km s-1when $|y|$ increases from 0.8 au to 4 au, confining
broad effective line widths within $\sim$4 au from the centre of the star,
slightly beyond the inner cavity of the gas disc as measured by Homan et al.
(2017). Uncertainties at the scale of $\pm$1 km s-1are estimated from the
results obtained using different methods to evaluate the values of $V_{z,20}$.
We have checked that this evaluation is consistent with the results obtained
on the red side and with a scan made at $y$$=$0 in small steps of $x$ (Figure
8). The evolution of $V_{z,20}$ depicted in Figure 8 is reminiscent of similar
results presented by Homan et al. (2017) in their Figures 4 and 12. These
authors have studied critically the detailed configuration of the velocity
field in the inner disc; however their interpretation differs from ours. To
quantify the line broadening is made difficult by the importance of
absorption. In the approximation of Gaussian line profiles, we estimate that
the effective line width (FWHM) remains below 10 km s-1down to projected
distances of $\sim$4 au and then increases linearly to reach $\sim$20 km s-1
near the surface of the star. The values obtained for 13CO (right panel of
Figure 8) are less affected by absorption and are $\sim$5 km s-1 and $\sim$20
km s-1, respectively . Such line broadening is not explicitly accounted for in
the analysis of Homan et al. (2017); they use an rms turbulent velocity of
only 0.5 km s-1 and a modest thermal broadening (their Figure 12); including
an explicit line broadening in the model would probably produce lower rotation
velocities. To illustrate this point we show in Figure 9 the dependence on
position angle of the mean Doppler velocity, averaged over $R$ in successive
rings and integrated over $|V_{z}|$$<$20 km s-1. The results are summarized in
Table 2 and show a rotation velocity reaching up to some 8 km s-1 in the inner
ring, 30$<$$R$$<$60 mas, smaller than obtained by Homan et al. (2017) and
Kervella et al. (2016).

In summary, in spite of being qualitative, this analysis has shown reliably
that significant line broadening is observed at projected distances from the
star below $\sim$4 au and is absent above. Over this radial range, the
effective line width increases (FWHM) from $\sim$5 km s-1 to $\sim$20 km s-1.
Compared with R Dor and Mira Ceti, the extension of the line broadening region
is three times smaller for L2 Pup. We did not find in the analyses of the
infrared and visible observations presented by Kervella et al. (2014, 2015);
Lykou et al. (2015) and Ohnaka et al. (2015) any argument that might either
comfort or contradict this result.

Figure 8:  Left: scanning steps superimposed on the 29SiO moment 1 map.
Middle: dependence of $V_{z,20}$ on $|y|$ for the north (magenta) and south
(blue) scans of 29SiO(8-7) (middle-left) and 12CO(3-2) (middle-right)
emissions. Right: evolution of the 13CO line width (FWHM). In the three
rightmost panels the lines show linear fits.

Figure 9: Dependence on position angle of the mean Doppler velocity, averaged over $R$ in successive rings as indicated in the inserts (in arcsec) and integrated over $|V_{z}|$$<$20 km s-1. The lines show sine wave fits described in Table 2. Table 2: Sine wave fits of the form $<$$V_{z}$$>$$=$$A+B\sin(\omega-\omega_{0})$. Typical uncertainties are 0.2 km s-1 on A, 0.5 km s-1 on B and 4∘ on $\omega_{0}$. |  $A$ (km s-1) |  $B$ (km s-1) |  $\omega_{0}$ (degrees)
---|---|---|---
$R$ range (mas) |  12CO |  13CO |  29SiO |  12CO |  13CO |  29SiO |  12CO |  13CO |  29SiO
30-60 |  $-$0.2 |  $-$0.2 |  $-$0.5 |  $-$8.2 |  $-$7.0 |  $-$8.4 | 1 | 1 | 2
60-90 |  $-$0.1 | 0.2 |  $-$0.3 |  $-$6.5 |  $-$5.7 |  $-$7.2 |  $-$1 | 2 |  $-$1
90-120 | 0.0 |  $-$0.3 |  $-$0.3 |  $-$4.9 |  $-$4.3 |  $-$5.6 |  $-$1 | 7 |  $-$4
120-150 | 0.0 | 0.4 |  $-$0.3 |  $-$3.8 |  $-$4.3 |  $-$4.7 |  $-$3 |  $-$4 |  $-$13

##  5 The wind of L2 Pup

###  5.1 Searching for north/south bipolar outflows at short distance from the
star

All recent studies of the L2 Pup CSE (Kervella et al., 2014, 2015, 2016; Lykou
et al., 2015; Ohnaka et al., 2015; Homan et al., 2017) focus on the morpho-
kinematics of the gas and dust disc and the possible presence of a companion
but none of these addresses directly the question of the probable existence of
a wind escaping the gravity of the star. Kervella et al. (2015) note the
presence of features such as plumes and spirals at large angles from the disc
median plane and speculate (Kervella et al., 2015, 2016) about the existence
of broad bipolar outflows along the disc axis, but no direct observation of
such outflows has ever been made. Yet, from what we have seen in Sections 3
and 4 the presence of large velocities near the star suggests that L2 Pup,
like other oxygen-rich AGB stars, should give a primordial boost to the gas
near the surface of the star that would bring it to a region where dust grains
get accelerated and share with the gas some of their radial momentum. Part of
this wind would be absorbed by the disc, which covers a significant fraction
of the solid angle, but the other part should produce broad outflows of gas
and dust having their axes near the sky plane and pointing in the north and
south directions.

Chen et al. (2016) have performed a three-dimensional simulation of the CSE
that is meant to account for the most recent VLT and ALMA observations. They
do not model the launching of the wind but assume instead the ejection of a
pulse of dense wind (9.3$\times$10-6 M⊙yr-1) lasting 11.6 years and
superimposed on a steady wind of 39.3 km s-1 producing a mass loss rate of
1.67$\times$10-6 M⊙yr-1. These choices are meant to cope with the lack of
simulation of the launching mechanism while maintaining an expansion velocity
of 15 to 20 km s-1 in the region where the wind interacts with the companion.
The pulse of wind is meant to result from the ingestion of a planet by the AGB
star. The model predicts a gravitationally bound disc and wide polar outflows
along the disc axis with velocities reaching 20 km s-1.

However, beyond $R$$\sim$0.15 arcsec, such outflows cannot be detected using
the data analysed in the preceding sections, the uv coverage being inadequate.
This is illustrated in Figure 10, which compares the position angle
distributions of the 12CO(3-2) emission in different intervals of $R$ with
that produced by an isotropic wind. Beyond $R$$\sim$0.15 arcsec, the poor
$uv$-coverage at short baseline lengths causes an isotropic wind to appear as
a north-south emission as illustrated in Figure 10. Therefore, we cannot
distinguish the 12CO and 29SiO emission of Figure 3 in the interval [0.15,
0.4] arcsec from such artefacts.

Figure 10: Comparing the position angle distributions of the 12CO(3-2)
emission (black) and that of an isotropic wind (red) in successive intervals
of $R$. From left to right: 0.05$<$$R$$<$0.10 arcsec, 0.10$<$$R$$<$0.15
arcsec, 0.15$<$$R$$<$0.20 arcsec and 0.20$<$$R$$<$0.25 arcsec.

Staying within $R$$<$0.2 arcsec, we might hope to see evidence for a
north/south outflow close to the plane of the sky by confining the absolute
value of the Doppler velocity to very small values. Figure 11 displays
intensity maps integrated over |$V_{z}|$$<$1 km s-1 for each of the three
lines. The 12CO and 29SiO maps show emission that can be interpreted as a
northern outflow, the southern part being obscured by the tilt of the disc,
the cold outer surface of which is absorbing, particularly strongly in the
case of the SiO line. The 13CO map displays a north-south elongation that is
also compatible with an interpretation in terms of an optically thin north-
south outflow. However, these comments can only be taken as qualitative. Homan
et al. (2017) have given a detailed discussion of the mechanisms at stake in
this region in their Section 6.2.2. They underline their complexity, with
steep temperature gradients and hydrodynamical boundary instabilities at the
disc/outflow interface. In such a context it is difficult to ascertain that
the maps displayed in Figure 11, which also include emission from the upper
part of the disc, are indeed evidence for a north/south outflow and we refrain
from attempting from these an evaluation of the mass loss rate. Moreover, the
present observations of the CO(3-2) and 29SiO(8-7) emissions show that the
FWHM of the line profiles is $\sim$5 km s-1 beyond $\sim$4 au from the centre
of the star (Section 4), contrary to what could be expected from broad
outflows with velocities reaching 20 km s-1 as predicted by Chen et al.
(2016).

###  5.2 Overall wind kinematics within 200 au from the centre of the star

Having shown the difficulty to detect reliably north/south bipolar outflows
from the 12,13CO(3-2) and 29SiO(8-7) observations studied in the preceding
sections, we now analyse the second set of observations presented in Section
2. They are of the emissions of the 12CO(2-1) and 28SiO(5-4) lines, the
antenna configuration providing reliable imaging up to distances of $\sim$3
arcsec from the star. To our knowledge, there exists no published analysis of
these data. The channel maps are shown in the Appendix. At a distance of 64 pc
from the Earth, with a projected velocity of 10 km s-1 it takes $\sim$30 yr to
cover 1 arcsec; we can therefore assume that most of what is seen beyond
$R$$\sim$1 arcsec happened before the dimming event at the end of the past
century. Figure 12 compares the intensity maps, radial distributions and
Doppler velocity spectra of both line emissions. As commonly observed in
oxygen-rich AGB stars, the SiO emission is confined near the star, here within
$\sim$80 au, and displays therefore a slightly broader Doppler velocity
spectrum; this confinement is usually interpreted (Schöier et al., 2004) as
the result of the condensation of the gas molecules on dust grains; moreover,
the SiO emission is cut-off by photo-dissociation earlier than the CO
emission. These results suggest an overall standard behaviour of the wind.

Figure 11: Intensity maps integrated over |$V_{z}|$$<$1 km s-1. From left to
right: 12CO(3-2), 13CO(3-2) and 29SiO(8-7). The colour scales are in units of
Jy arcsec-2 km s-1.

In order to study its morpho-kinematics, we use the CO(2-1) emission, which is
expected to probe the CSE uniformly over large distances from the star. The
left panel of Figure 13 illustrates very clearly the transition away from the
rotation regime, dominated by the disc of gas and dust, when $R$ exceeds
$\sim$0.4 arcsec. However, the three rightmost panels of Figure 13 do not show
any evidence for enhanced outflow in the north/south direction. The left panel
of Figure 14 shows the map of the mean Doppler velocity of the 12CO(2-1)
emission. It displays a clear asymmetry consistent with earlier observations
at 11.7 and 17.9 $\mu$m by Jura et al. (2002) using the Keck I telescope
equipped with the Long Wavelength Spectrometer (LWS) with a PSF of $\sim$0.5
arcsec FWHM. It suggests the presence of a pair of back-to-back outflows in
the north-west/south-east direction, clearly different from the north/south
direction expected for an outflow collimated by the central gas-and-dust disc.
The central and right panels of Figure 14 display PV maps of the CO(2-1)
emission, both in $V_{z}$ vs $R$ and in $V_{z}$ vs $\omega$. The former shows
that Doppler velocities are confined within $\pm$ $\sim$2.5 km s-1,
independently from the value of $R$, suggesting that the terminal velocity has
already been reached shortly beyond 1 arcsec, where the escape velocity from a
0.66 solar mass star is $\sim$4.3 km s-1. The latter shows a clear sine wave
pattern, suggesting isotropically enhanced expansion in a plane inclined in
the north-west/south-east direction with respect to the plane of the sky,
explaining both the approximate isotropy of the intensity map (the rms
fluctuations of the dependence on position angle $\omega$ of the intensity
integrated over $|V_{z}|$$<$2.5 km s-1 are 17% for both rings 1$<$$R$$<$2 and
2$<$$R$$<$3 arcsec) and the asymmetry of the moment 1 map. It also shows the
presence of emission in phase opposition to the sine wave. Such wind
morphology is reminiscent of that observed in RS Cnc (Winters et al., 2021):
an equatorial enhancement together with broad outflows along its axis; it is
very different from the broad pair of back-to-back outflows oriented
north/south near the plane of the sky predicted by Kervella et al. (2015) and
Chen et al. (2016): these would appear as blobs of emission in the northern
and southern quadrants (near $\omega$ $=$0∘ and 180∘) but would not populate
the eastern and western quadrants: it deserves a detailed study.

Figure 15 illustrates the radial evolution of the 12CO(2-1) emission in
successive intervals of $R$, each 0.5 arcsec wide, starting from $R$$=$1
arcsec. Close inspection of the $V_{z}$ vs $\omega$ maps may suggest the
presence of two weak sine waves in the emission in phase opposition to the
dominant sine wave. In order to obtain a simple parameterization of these
features, we write the dominant sine wave as $V_{z}$ [km
s-1]$=$1.64sin($\omega$$-$57∘)and the weaker sine waves as
1.50sin($\omega$$-$230∘) and 2.43sin($\omega$$-$208∘), respectively. Each sine
wave is smeared with Gaussians having $\sigma$’s of 0.55 km s-1 in amplitude
and 15∘in phase. All these parameters have been estimated by eye to
approximately match the data. In each interval of $R$, the observed dependence
of the flux density on $V_{z}$ and $\omega$ is described as the sum of these
three smeared sine waves, multiplied by coefficients $a$, $b$ and $c$
respectively. The result of the best fits is listed in Table 4, which lists
also the mean values of the flux density in each interval of $R$ and the rms
deviations with respect to the mean. The contribution of the dominant sine
wave is constant over the whole $R$ range. Each of the weaker waves
contributes approximately one quarter of the dominant wave; the contribution
of one of them increases over the first half of the $R$ range, that of the
other decreases. While this provides a convenient parameterization of what is
observed, its precise form, in particular the description of the emission in
phase opposition to the dominant sine wave in terms of two weaker sine waves,
is somewhat arbitrary Figure 16 illustrates the dependence on $R$ of the $a$,
$b$ and $c$ coefficients. Both the intensity of the dominant sine wave ($b$)
and that of the flow in phase opposition ($a+c$) are approximately constant
over the whole $R$ range, the former being twice the latter. It seems
therefore reasonable to be satisfied with a global description of the emission
in phase opposition to the dominant sine wave, leaving the possible
identification of a finer structure for a future analysis including new
observations. What can be stated with confidence is the dominance of a sine
wave with amplitude 1.6$\pm$0.1 km s-1 and a phase of 54∘$\pm$6∘, as obtained
from a fit to the right panel of Figure 14, together with a flow of about half
the intensity in phase opposition.

Such a sine wave describes a disc, or equatorial enhancement, in radial
expansion. To describe its morpho-kinematics in some detail, as done by Homan
et al. (2017) for the central gas-and-dust disc or by Winters et al. (2021)
for RS Cnc, is well beyond what the present data can offer. We must content
ourselves with evaluations of the mean radial expansion velocity, $V_{exp}$,
and of the orientation of the disc axis. The position angle of the projection
of the disc axis on the plane of the sky is simply 54∘+90∘$=$144∘$\pm$6∘.
However, its inclination $i$ with respect to the lines of sight, equal to that
of the mid-plane of the disc with respect to the plane of the sky, is unknown.
Yet, the disc cannot be too close to edge on, otherwise it would produce a
spike at $-V_{exp}$ in the spectra of Figure 5; and it cannot be close to the
plane of the sky, otherwise the sine wave would not appear so clearly. To see
that better, we use the simple picture of a flared disc having a Gaussian
distribution of flaring angles with an rms value of $\sigma_{fl}$ and we
approximate the smearing in $V_{z}$ as a constant $\sigma_{Vz}$$=$0.55 km s-1,
independent from $\omega$. The amplitude of the sine wave, 1.6$\pm$0.1 km s-1,
is the product of $V_{exp}$ by the sine of $i$: $V_{exp}$$=$$1.6/\sin i$ km
s-1. The smearing in $V_{z}$ is dominated by flaring in the north-east/south-
west direction ($\omega$$=$54∘/234∘) where $V_{z}$$=$0:
$\sigma_{Vz}$$=$$V_{exp}\sin\sigma_{fl}\cos i$. In the north-west/south-east
direction ($\omega$$=$144∘/324∘), where $V_{z}$$=$$V_{exp}\sin i$, it is
instead dominated by the dispersion in the sine wave amplitude and flaring
does not contribute. Table 3 lists the values of $V_{exp}$$=$$1.6/\sin i$ and
of the rms flaring angle, $\sigma_{fl}$$=$$\sin^{-1}(0.55/[V_{exp}\cos i])$
for different values of $i$.

Table 3:  Disc parameters as a function of the angle $i$ between the disc mid-plane and the plane of the sky. $i$ (degree) | 20 | 30 | 40 | 50 | 60 | 70
---|---|---|---|---|---|---
$V_{exp}$ (km s-1) | 4.7 | 3.2 | 2.5 | 2.1 | 1.8 | 1.7
$\sigma_{fl}$ (degree) | 7 | 11 | 17 | 24 | 37 | 71

An approximate upper limit to $i$ is obtained by requiring that 90∘$-$$i$
exceed $\sigma_{fl}$, which means $i<\sim$60∘. Indeed, for such an
inclination, the disc projects on the plane of the sky as an ellipse having an
axis ratio of 2, incompatible with Figure 12. It is more difficult to obtain a
lower limit to $i$. When the median plane of the disc gets close to the plane
of the sky, the expansion velocity increases and the flaring decreases in
order to produce the observed sine wave. Strictly speaking, one cannot exclude
a very thin disc very close to the plane of the sky without making additional
assumptions. Yet, too thin a disc would be highly improbable in the CSE of an
AGB star and we retain as a reasonable range of acceptable values of $i$ the
interval [20∘,60∘], which we write as 40∘$\pm$20∘, it being understood that
this estimate rests on sensible but somewhat arbitrary arguments.

Figure 12: 12CO(2-1) and 28SiO(5-4) emissions. Left: radial distributions
averaged over position angle and integrated over $|V_{z}|$$<$5 km s-1. Middle:
intensity maps integrated over $|V_{z}|$$<$5 km s-1; the circle has a radius
of 1.5 arcsec. The colour scales are in units of Jy arcsec-2 km s-1. Right:
Doppler velocity spectra integrated over $R$$<$3 arcsec.

Figure 17 displays the spectra of the 12CO(2-1) and 28SiO(5-4) line emissions
inside a circle of 0.2 arcsec radius, namely well over the stellar disc, the
beam size preventing higher resolution inspection. Both spectra show the
slightly negative absorption peak that was interpreted as revealing the small
expansion of the gas and dust disc, estimated in Section 3 at the approximate
level of 0.8$\pm$0.5 km s-1. The peak is deeper in the SiO spectrum than in
the CO spectrum as expected from the shorter range of distances being probed.
In addition the spectra show hints of other absorption peaks, the CO spectrum
at $\sim$$-$3 km s-1 and the SiO spectrum at $\sim$$-$5 km s-1. If real, these
are probably unrelated to the disc wind.

Figure 13: 12CO(2-1) line emission close to the star. Left: map of the mean
Doppler velocity (moment 1) (km s-1) in the interval $|V_{z}|$$<$10 km s-1;
circles of 0.4, 0.8 and 1.2 arcsec radius are shown. Right: Dependence on
position angle $\omega$ of the intensity integrated over $|V_{z}|$$<$2.5 km
s-1 and, from left to right, 0.4$<$$R$$<$0.8 arcsec, 0.8$<$$R$$<$1.2 arcsec
and 1.2$<$$R$$<$1.6 arcsec.

Figure 14: 12CO(2-1) line emission away from the star. Left: map of the mean Doppler velocity (moment 1) (km s-1) in the interval $|V_{z}|$$<$2.5 km s-1. The circle has a radius of 1 arcsec. Middle: PV map ($V_{z}$ vs $R$) of the flux density (Jy) integrated over position angle. Right: PV map ($V_{z}$ vs $\omega$) of the flux density (Jy) integrated over 1$<$$R$$<$3.5 arcsec and 18∘ in omega. The lines show the sine waves described in the text. Table 4: Best fits of the 12CO(2-1) emission as the sum of three sine waves, smeared with 0.55 km s-1 in $V_{z}$ and 15∘ in $\omega$, of the form $V_{z}$ [km s-1]$=$1.50sin($\omega$$-$230∘), 1.64sin($\omega$$-$57∘) and 2.43sin($\omega$$-$208∘), respectively. The last two columns list the mean and rms values of the intensity integrated over $|V_{z}|$$<$2.5 km s-1.  $R$ range | $a$ | $b$ | $c$ | $a+c$ |  $<$$F$$>$ | Rms$F$
---|---|---|---|---|---|---
(arcsec) | (mJy) | (Jy arcsec-2 km s-1)
1.0 to 1.5 | 51 | 124 | 35 | 86 | 1.79 | 0.38
1.5 to 2.0 | 50 | 119 | 30 | 80 | 1.19 | 0.31
2.0 to 2.5 | 37 | 113 | 29 | 66 | 0.86 | 0.20
2.5 to 3.0 | 30 | 120 | 29 | 59 | 0.72 | 0.21
3.0 to 3.5 | 23 | 122 | 29 | 52 | 0.56 | 0.19

###  5.3 Mass loss rate

In order to obtain an estimate of the mass loss rate, we measure the flow of
12CO(2-1) emission across a sphere of 2 arcsec radius, where the terminal
velocity can be assumed to have been reached and the emission to have occurred
before the 1994 dimming episode. It has a value of 1.0 Jy arcsec-2 km s-1
(Figure 12 left). From Table 1, we see that this is 20 times the brightness
produced by a column density of 1 CO molecule cm-3 arcsec, at a temperature of
50 K. As a solar mass is 1.2$\times$1057 proton masses and 1
arcsec$=$0.96$\times$1015 cm, assuming an abundance ratio CO/H=10-4, the
measured brightness corresponds to a column density of
20$\times$0.963/1.2$\times$10-8$=$1.5$\times$10-7 M⊙arcsec-2. Taking the mean
sine wave amplitude as 1.7$\pm$0.5 km s-1 and the inclination angle as
40∘$\pm$20∘, namely an expansion velocity 2$\pm$1 times larger than the
absolute value of the Doppler velocity, we obtain a velocity projected on the
plane of the sky of 1.7$\pm$1.0 km s-1, namely 0.36$\pm$0.21 au yr-1, or
$\sim$6$\pm$4 mas yr-1. In one year, the wind covers therefore an area of
2$\pi$$R$$\times$0.006=0.08$\pm$0.05 arcsec2, meaning a mass loss rate of
0.08$\times$1.5$\times$10-7=(1.2$\pm$0.7)$\times$10-8 M⊙yr-1. This is
consistent with the values obtained indirectly from single dish observations,
1.4 to 2.0 10-8 M⊙ yr-1 (Danilovich et al., 2015; Olofsson et al., 2002).
While crude, the inclination angle of the wind mid-plane being unknown, it has
the value of being the first direct measurement of the gas flow escaping the
star gravity. It also shows that the wind described in the present article
accounts well for earlier estimates of the mass loss rate, strengthening the
case for the absence of a significant collimated north-south outflow near the
plane of the sky.

Figure 15: 12CO(2-1) line emission away from the star. Upper and middle rows:
PV maps ($V_{z}$ vs $\omega$) of the data (up) and of the model (middle). The
model sine waves are shown on the data maps. Lower panels: dependence on
position angle $\omega$ of the intensity integrated over $|V_{z}|$$<$2.5 km
s-1; the red arrows indicate the north-east and south-west directions.The
horizontal lines show the mean values. In all panels, from left to right,
1$<$$R$$<$1.5 arcsec, 1.5$<$$R$$<$2 arcsec, 2$<$$R$$<$2.5 arcsec,
2.5$<$$R$$<$3 arcsec and 3$<$$R$$<$3.5 arcsec. The colour scales are in units
of Jy. Figure 16: Dependence on $R$ of the best fit values of coefficients $a$
(red), $b$ (black), $c$ (blue) and $a+c$ (grey). Uncertainties are estimated
corresponding to a 3% increase of the best fit chi-square.

Figure 17: Emission of the 12CO(2-1) (left) and 28SiO(5-4) (middle) over the
stellar disc ($R$$<$0.2 arcsec). Spectra of 13CO(3-2), 12CO(3-2) and
29SiO(8-7) over the circle $R$$<$0.06 arcsec are shown for comparison in the
right panel.

###  5.4 A second search for north-south bipolar outflows at short distance
from the star

Having obtained a global view of the morpho-kinematics of the wind beyond
$\sim$1 arcsec from the centre of the star, we now have a second look at the
question of the expected presence of broad bipolar outflows oriented
north/south. We use again the CO(2-1) emission and explore the wedge defined
as $|\sin\omega|$$<$0.5, meaning $\pm$30∘ from the $y$ axis. The PV map,
$V_{z}$ vs $y$, of the flux density integrated within the wedge is shown in
Figure 18. It displays a number of remarkable features that can be easily
identified: the emission of the gas and dust disc, essentially unresolved, is
seen at very small values of $|y|$ and extends to very large Doppler
velocities in absolute value. The emission of the expanding wind discs is seen
at Doppler velocities confined to |$V_{z}|$$<$3 km s-1 and the three
components $a$, $b$ and $c$ listed in Table 4 are well separated: the dominant
wind $b$ is red-shifted in the south direction and blue-shifted in the north
direction and covers the whole y range; winds $a$ and $c$ are instead blue-
shifted in the south direction and red-shifted in the north direction, wind
$a$ covering shorter distances and wind $c$ larger distances from the star.
The emission of the pair of back-to back outflows expected by Kervella et al.
(2016) and Chen et al. (2016) would instead populate preferentially the
negative $y$ hemisphere for $V_{z}$$>$0, the gas-and-dust disc being inclined
toward us in this hemisphere; by how much depends on the velocity of the flow,
claimed by these authors to exceed $\sim$20 km s-1, meaning a mean
$|V_{z}|$$>$2-3 km s-1; however, the very large inclination angle of the disc,
82-84∘, would probably make the effect difficult to detect.

An unexpected feature is a blob of blue-shifted emission visible between
$\sim$$-$3 and $\sim$$-$5 km s-1 in the north direction, within less than 1
arcsec from the centre of the star. This is the region of Doppler velocity
where hints of absorption have been revealed in Figure 17. We show in Figure
19 the intensity maps of the 12CO(2-1) and 28SiO(5-4) emission integrated
between $-$3 and $-$5 km s-1. The emission is confined near the star and
elongated in the north direction. The expanding disc winds are not expected to
contribute such relatively large Doppler velocities in this region and it is
therefore probable that the blob is associated with the northern “loop”
identified by Kervella et al. (2014) in the NACO images at 3.74 and 4.05
$\mu$m. These authors suggest an interpretation in terms of a possible
interaction of a hidden companion with the dusty wind from the central star.
We note that the decrease with $R$ of the absorption band observed in the
$V_{z}$ vs $R$ map of the 29SiO(8-7) emission(lower-left panel of Figure 6) is
probably associated with the presence of this loop.

Figure 18: Searching for north-south outflows in the 12CO(2-1) emission. The
left panel shows a schematic view of the expanding dominant $b$ wind, inclined
in the north-west/south-east direction with respect to the plane of the sky,
and of the wedge, defined as $|\sin\omega|$$<$0.5, within which the PV map
shown in the right panel is integrated. The PV map is in the $V_{z}$ vs $y$
plane and indicates the various components that contribute to the emission.
The central gas and dust disc is indicated as G/D disc and the blob presumably
associated with the loop identified by Kervella et al. (2014) is indicated as
$X$. The colour scale is in unit of Jy arcsec-1.

Figure 19: Intensity maps of 12CO(2-1) (left) and 28SiO(5-4) (right) emissions
integrated between $-$5 and $-$3 km s-1. The colour scales are in units of Jy
arcsec-2 km s-1.

###  5.5 Interpretation

The disc morphology of the wind up to some 200 au from the centre of the star
revealed by the present analysis of the CO(2-1) emission is reminiscent of a
similar morphology observed in RS Cnc (Winters et al., 2021) and EP Aqr (Tuan-
Anh, 2019; Homan et al., 2020, and references therein), two oxygen-rich AGB
stars having mass loss rates at the 10-7 M⊙yr-1 scale. The formation of such
expanding discs, or equatorial enhancements, is not understood. In the case of
EP Aqr, Homan et al. (2020) invoked the possible presence of a companion. In
the present case of L2 Pup, the presence of another disc within some 20 au
from the centre of the star makes it even more difficult to propose a sensible
interpretation. The two discs have different orientations and expansion
velocities, the smaller disc being even possibly gravitationally bound to the
star. Invoking the role of companions in their formation requires therefore
the presence of two distinct companions. Moreover, the relation of the smaller
disc with the 1994 dimming episode is not understood and its configuration in
the period preceding it, during which the larger disc wind was blowing, is
unknown. As remarked by Homan et al. (2017) a latitude dependent mass loss is
unlikely to produce a disc that is as thin as observed for the dust disc. The
same comment applies to the wind observed at large distances. This brings up
an obvious question: how much of the disc morphology is already present at
launching stage, and how much of it is the result of subsequent interaction?
Major contributors to the former are expected to be pulsations and/or magnetic
fields, and to the latter interaction with a companion. Unfortunately, very
little is known of the role played by magnetic fields in the evolution of AGB
stars (Vlemmings, 2019).

Jura et al. (2002) and Bedding et al. (2005) have reviewed our present
understanding of the mechanisms governing the pulsations of semi-regular
variables. Both underline the peculiarity of L2 Pup, with a light curve
dominated by two completely different and independent mechanisms: gradual
dimming caused by circumstellar dust and seemingly random amplitude and phase
changes of pulsations. The former invoke non radial pulsations that can at
least in part account for the observed asymmetric mass loss, time variations
of the infrared fluxes, and time variations of the position angle of the
optical polarization. The latter prefer to blame these on stochastic
excitation, presumably from convection. Moreover, Jura et al. (2002) note that
there appears to be enough kinetic energy in the pulsations to drive the
outflow, which lends support to models where the main driving mechanism of the
circumstellar outflow is the stellar pulsation and where the dust plays only a
secondary role (Winters et al., 2000). Qualitatively at least, there is no
doubt that pulsations are major actors in the generation of the nascent wind
and their irregularity must somehow impact its further evolution. Yet, it
seems difficult to conceive a scenario where pulsations alone would produce
relatively thin discs as observed both in the wind at large distances and in
the gas and dust disc near the star.

Therefore most authors assume that the small central gas and dust disc was
formed by a companion funnelling part of the spherically symmetric wind of the
AGB star in its gravitational field and expelling it as a compact stream along
the orbital plane. Homan et al. (2017) note that the disc could be made of
both AGB wind material and evaporated planet material. If a similar mechanism
were to be invoked for the formation of the wind at large distances, it would
require the presence of at least another planetary companion funnelling part
of the AGB wind over the past century. To the extent that planets can be
expected to have orbital planes of similar inclinations, it would favour a
large inclination of the larger disc. However, it seems difficult to conceive
a simple scenario having the ability to generate, within a single century, at
least two different winds displaying different expansion velocities and
different inclinations with respect to the plane of the sky.

Our failure to detect bipolar outflows in the north/south direction deserves a
comment. At short distances from the star it can be blamed in part on the
inadequacy of the available observations: insufficient uv coverage for the
first set and insufficient angular resolution for the second set. At larger
distances from the star, however, the wind takes the form of expanding discs
that are completely unrelated to the morphology of the central gas and dust
disc expected to act as a collimator. This suggests that the gas and dust disc
did not exist in its present form before the 1994 dimming event.

##  6 Summary and conclusion

The recent literature (Kervella et al., 2014, 2015, 2016; Homan et al., 2017;
Lykou et al., 2015; Ohnaka et al., 2015; Bedding et al., 2005) focuses on the
morpho-kinematics of the gas and dust disc surrounding L2 Pup: its likely
relation with the dimming of the light curve that occurred at the end of the
past century and the possible presence of a planetary companion at a distance
of 2.4 au from the star. In contrast, the earlier literature underlines
peculiar features apparently displayed by the star: a very low mass loss rate,
at the level of 10-8 M⊙yr-1, and a very low gas expansion velocity, at the
level of 2 to 3 km s-1. These were pointed out in most publications (e.g.
Olofsson et al., 2002; González Delgado et al., 2003; Jura et al., 2002;
Winters et al., 2002) and the latter authors suggested that these peculiar
features might be understood in terms of a wind driven exclusively by
pulsations, with dust playing no dynamical role. Our analysis of the 12CO(2-1)
and 28SiO(5-4) emissions supports such a low value of the mass loss rate in
the pre-1994 period. The observed morpho-kinematics of the wind, in the form
of an inclined disc, or equatorial enhancement, expanding radially and
isotropically, also suggests the importance of pulsations in generating the
nascent wind but the observed confinement of the SiO emission supports the
condensation of SiO molecules onto dust grains over a distance of some 80 au
from the star, implying therefore that over this distance the dust transfers
some of its radial momentum to the gas. Moreover, one does not see how
pulsations alone could produce winds confined to relatively thin discs. It is
therefore natural to consider the possibility for the wind to have been shaped
by the gravity of a planetary companion, as generally accepted for the central
gas and dust disc. However, if such were the case, one would have to conceive
a scenario explaining how two different wind configurations can be present
within a short time period, at century scale.

In the post-1994 period, the recent VLT and ALMA observations have
considerably improved our knowledge of the morpho-kinematics of the CSE and
suggest that part of the L2 Pup wind flows along the disc axis near the plane
of the sky while the remaining part feeds the disc. However, the published
literature does not directly address the properties of the wind and, to our
knowledge, there exists no direct observation of gas escaping the gravity of
L2 Pup. In such a context, we have provided new information on the present
state of the star, in particular evidence for large velocities in its
vicinity, both from the shape of the absorption spectra measured over the
stellar disc and from the presence of large Doppler velocity wings in the line
profiles measured on line of sights crossing the star near its centre. This
suggests that the standard mechanism of wind formation at stake in most
oxygen-rich AGB stars also applies to L2 Pup in its present state. However,
the radial extension of the inner layer where shocks are expected to play a
role has been found to be small: it was estimated at the scale of only 4 au,
typically three times smaller than observed in stars such as Mira Ceti and R
Dor. Moreover, it has not been possible to reliably reveal the presence of a
gas outflow escaping the star gravity near the sky plane along the disc axis:
both the complexity of the mechanisms at stake and the insufficient $uv$
coverage at short spacing have prevented it.

In summary, the main contributions of the present study can be summarized as
follows:

Beyond $\sim$1 arcsec from the centre of the star, the wind of L2 Pup is
dominated by a disc, or equatorial enhancement, expanding isotropically with a
radial velocity not exceeding some 5 km s-1, inclined in the north-west/south-
east direction with respect to the sky plane by $\sim$40∘$\pm$20∘. In
addition, outflows of lower density are observed on both sides of the disc,
covering large solid angles about the disc axis, contributing about half the
flux of the disc. This is at strong variance with the expectation of a pair of
back-to-back outflows collimated by the central gas-and-dust disc. Such
outflows would not populate the eastern and western quadrants while our
analysis shows that these are populated in continuity with the northern and
southern quadrants. It raises new questions on the recent evolution of L2 Pup:
did the central gas-and-dust exist before the 1994 dimming event? if it did,
why did it not act as a collimator? what has been shaping the wind observed
before then? if it were a companion, it would have to be different from the
planetary companion associated with the shaping of the central gas-and-dust
disc. These new questions will require new observations in order to be
answered.

In addition to the dominant wind, which has its north-western half inclined
toward us, there are two additional winds inclined the other way.

Below $\sim$1 arcsec from the centre of the star, we failed to find any
evidence for the presence of collimated outflows oriented north/south.
However, difficulties inherent to the observations, uv coverage and angular
resolution, and the complexity of the dynamics at stake in this region prevent
us from ascertaining that there are no such outflows.

A blob of northern blue-shifted emission at Doppler velocities between $-$3
and $-$5 km s-1 has been identified and tentatively interpreted as the “loop”
observed in L band by Kervella et al. (2014).

Evidence for the apparent normality of the wind launching mechanism has been
obtained from the presence of large velocities within $\sim$4 au from the
centre of the star, the line width increasing from $\sim$5 km s-1 FWHM beyond
this distance to $\sim$20 km s-1 near the star. The effect of its explicit
inclusion in the models used by Homan et al. (2017) and Kervella et al. (2016)
would probably be to produce smaller rotation velocities. Moreover the
confinement of SiO emission within $\sim$80 au from the centre of the star
suggests that acceleration by dust grains plays a significant role.

The mass loss rate has been evaluated at the level of
(1.2$\pm$0.7)$\times$10-8 M⊙yr-1.

## Acknowledgements

We thank Dr Ward Homan for useful discussions; his detailed analysis of the
CO(3-2) data inspired the present work. We also thank Pr Albert Zijlstra for
having shared with us his understanding of the dynamics governing the CSE of
L2 Pup. We thank the anonymous referee for his/her very careful reading of the
manuscript and for the pertinence of his/her comments, which helped with
improving the quality of the presentation. This paper uses ALMA data
ADS/JAO.ALMA#2015.1.00141.S. ALMA is a partnership of ESO (representing its
member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST
and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the
Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and
NAOJ. We are deeply indebted to the ALMA partnership, whose open access policy
means invaluable support and encouragement for Vietnamese astrophysics.
Financial support from the World Laboratory, the Odon Vallet Foundation and
VNSC is gratefully acknowledged. This research is funded by the Vietnam
National Foundation for Science and Technology Development (NAFOSTED) under
grant number 103.99-2019.368.

## Data Availability

The raw data are available on the ALMA archive ADS/JAO.ALMA#2015.1.00141.S.
The calibrated and imaged data underlying this article will be shared on
reasonable request to the corresponding author.

## References

  * Bedding et al. (2002) Bedding, T.R., Zijlstra, A.A., Jones, A. et al., 2002, MNRAS, 337, 79
  * Bedding et al. (2005) Bedding, T.R., Kiss, L.L., Kjeldsen, H. et al., 2005, MNRAS, 361, 1375
  * Chen et al. (2016) Chen, Z., Nordhaus, J., Frank, A., Blackman, E.G. and Balick, B., 2016, MNRAS 460, 4182
  * Danilovich et al. (2015) Danilovich, T., Teyssier, D., Justtanont, K. et al., 2015, A&A, 581, A60
  * Dumm & Schild (1998) Dumm, T. & Schild, H., 1998, New Astronomy, 3/3, 137
  * Goldin & Makarov (2007) Goldin & Makarov, 2007, ApJS, 173, 137
  * González Delgado et al. (2003) González Delgado, D., Olofsson, H., Kerschbaum, F. et al., 2003, A&A, 411, 123
  * Haworth et al. (2018) Haworth, T.J., Booth, R.A., Homan, W. et al., 2018, MNRAS, 473, 317
  * Hoai et al. (2020) Hoai, D.T., Tuan-Anh, P., Nhung, P.T. et al., 2020, MNRAS, 495, 943
  * Höfner & Olofsson (2018) Höfner, S., & Olofsson, H., 2018, A&AR, 26, 1
  * Homan et al. (2017) Homan, W., Richards, A., Decin, L. et al., 2017, A&A, 601, A5
  * Homan et al. (2020) Homan, W., Cannon, E., Montargès, M. et al., 2020, A&A, 642, A93
  * Jorissen et al. (2009) Jorissen, A., Frankowski, A., Famaey, B. & van Eck, S., 2009, A&A, 498, 489
  * Jura et al. (2002) Jura, M., Chen, C., & Plavchan, P. 2002, ApJ, 569, 964
  * Kervella et al. (2014) Kervella, P., Montarges, M., Ridgway, S.T. et al., 2014, A&A, 564, A88
  * Kervella et al. (2015) Kervella, P., Montarges, M., Lagadec, E. et al., 2015, A&A, 578, A77
  * Kervella et al. (2016) Kervella, P., Homan, W., Richards, A.M.S. et al., 2016, A&A, 596, A92
  * Lebzelter & Hron (1999) Lebzelter, T. & Hron, J., 1999, A&A, 351, 533
  * Little et al. (1987) Little, S.J., Little-Marenin, I.R. & Bauer, W.H., 1987, AJ, 94, 981
  * Lykou et al. (2015) Lykou, F., Klotz, D., Paladini, C. et al., 2015, A&A, 576, A46, erratum A&A, 581, C2
  * McIntosh & Indermüehle (2013) McIntosh, G.C. & Indermüehle, B., 2013, ApJ, 774, 21
  * Nhung et al. (2021) Nhung, P.T., Hoai, D.T., Tuan-Anh, P. et al., 2021, MNRAS, 504, 2687
  * Ohnaka et al. (2015) Ohnaka, K., Schertl, D., Hofmann, K.-H. & Weigelt, G., 2015, A&A, 581, A127O
  * Olofsson et al. (2002) Olofsson, H., González Delgado, D., Kerschbaum, F., & Schöier, F. L., 2002, A&A, 391, 1053
  * Ramstedt et al. (2020) Ramstedt, S., Vlemmings, W.H.T., Doan L. et al., 2020, A&A, 640, A133
  * Schöier et al. (2004) Schöier, F.L., Olofsson, H., Wong, T. et al., 2004, A&A, 422, 651
  * Tuan-Anh (2019) Tuan-Anh, P., Hoai, D.T., Nhung, P.T. et al., 2019, MNRAS 487, 622
  * Vlemmings (2019) Vlemmings, W., 2019, in Proc. of the IAU Symp. on Why Galaxies Care About AGB Stars: A Continuing Challenge through Cosmic Time., Volume 343, pp. 19-26
  * Winters et al. (2000) Winters, J. M., Le Bertre, T., Jeong, K. S. et al., 2000, A&A, 361, 641
  * Winters et al. (2002) Winters, J.M., Le Bertre, T., Nyman, L.øA., Omont, A. and Jeong, K.S., 2002, A&A, 388, 609
  * Winters et al. (2021) Winters, J.M., Hoai, D.T., Wong, K.T. et al., 2021, A&A, submitted
  * Wong et al. (2016) Wong, K.T., Kamínski, T., Menten, K.M. & Wyrowski, F., 2016, A&A, 590, A127
  * van Leeuwen (2007) van Leeuwen F., 2007, A&A, 474, 653

## Appendix A

Figure 20: 12CO(2-1) (left) and 28SiO(5-4) (right) channel maps of the
brightness multiplied by $R$ (Jy beam-1 arcsec). The values of the Doppler
velocity (km s-1) associated with each channel are indicated in the upper-left
corner of each pannel. Circles of 1, 2 and 3 arcsec in radius are shown. Note
that the channel maps are shown only for $|V_{z}|$$<$2.5 km s-1.