Tiến Sĩ Nghiên cứu lớp vỏ của các sao khổng lồ đỏ ở bước sóng vô tuyến

Acknowledgements
This thesis was made under a joint supervision “cotutelle” agreement between Observatoire de Paris and
Institute of Physics in Hanoi. I spent four months each of three successive years in Paris working with
Pr. Thibaut Le Bertre and the rest of the time in Hanoi with Pr. Pierre Darriulat. I would like to thank
all people and organizations in Vietnam and in France who helped me with my thesis work and made it
possible for me to complete it under as good conditions as possible.
From the bottom of my heart, I would like to thank my supervisors, Pr. Thibaut Le Bertre and
Pr. Pierre Darriulat for their guidance, their continuous support and their encouragements. I would like
to thank Pr. Thibaut Le Bertre who taught me basic radio astronomy and introduced me to the physics
of evolved stars. I highly appreciate his kindness, carefulness and patience. I am very grateful for his
having introduced me to foreign colleagues and for having made it possible for me to attend schools and
conferences during my stays in Europe. I would like to thank Pr. Pierre Darriulat who encourages me
and protects me in all cases and is always ready to solve any problem I may meet in my research work.
I am very lucky to be a student of such wonderful professors.
I thank Pr. Dao Tien Khoa and Pr. Daniel Rouan for having accepted to chair the jury and Pr.
Stéphane Guilloteau and Dinh Van Trung for their referee work.
I particularly thank Dr. Pham Tuyet Nhung, who spent most of her time working with me during
these years and contributed a large part of the results obtained in my thesis. I am grateful for her sharing
her life with me, in particular during our stays in France. Her rigor, experience and good judgment
helped me a lot in improving the quality of the thesis work. I thank Dr. Jan Martin Winters for helping
me with the reduction of the IRAM data, spending time discussing about my studies and commenting
and correcting the manuscript. I thank Arancha Castro-Carrizo and her colleagues for having kindly
given me X Her and RX Boo data. The Red Rectangle data were observed, calibrated and cleaned by the
ALMA staff whom I am deeply grateful for. I thank Dr. Pham Tuan Anh for his efforts in answering my
questions on the technique and method of interferometry.
I am grateful to Dr. Pham Ngoc Diep and the members of the VATLY team who have been working
with me for many years, for having shared with me their stories, their complaints and for the happy and
enjoyable environment they create in the lab. I would like to thank our friends Nguyen Quang Rieu,
Michèle Gerbaldi, Eric Gérard, Lynn Matthews, Pierre Lesaffre and Alain Maestrini for their moral
support and help.
I am indebted to the Institute for Nuclear Science and Technology and the Vietnam Satellite Cen-
tre for their support. Financial support from the French Embassy in Hanoi, Campus France in Paris,
the Rencontres du Vietnam and the Odon Vallet foundation, the World Laboratory and NAFOSTED is
gratefully acknowledged.
Finally, I wish to thank my husband and my family who are always besides me, encouraging and
supporting me in my research work.ABBREVIATION
Asymptotic Giant Branch AGB
Atacama Large Milimeter/Sub-milimeter Array ALMA
CircumStellar Envelope CSE
Five-hundred-meter Aperture Spherical Telescope FAST
Hertzsprung-Russell diagram HR diagram
Infrared Astronomical Satellite IRAS
Institut de Radioastronomie Millimétrique IRAM
InterStellar Medium ISM
Jansky Very Large Array JVLA
Local Standard of Rest LSR
Low-Noise Amplifier LNA
Main Sequence MS
NOrth Extended Millimeter Array NOEMA
On-the-fly OTF
Planetary Nebula PN
Plateau de Bure interferometer PdBI
Point Spread Function PSF
Pulse-Driven Convective Zone PDCZ
Red Giant Branch RGB
Spectrum Energy Distribution SED
Thermal Pulse TP
Very Large Array VLA
White Dwarfs WDContents
1 INTRODUCTION 1
1.1 An introduction to AGB stars 1
1.1.1 An overview 1
1.1.2 Nucleosynthesis 4
1.1.3 Dust . 5
1.1.4 Gas molecules . 8
1.1.5 Variability 9
1.1.6 Mass-loss rate 10
1.2 Asymmetries in AGB and Post AGB stars . 14
1.2.1 Generalities on asymmetries 14
1.2.2 Binaries . 15
1.2.3 Magnetic fields . 16
1.2.4 Interaction with the ISM 17
1.3 Outline . 18
2 RADIO ASTRONOMY 21
2.1 Overview 21
2.2 Radio instruments 23
2.2.1 Antennas 23
2.2.2 Receivers 25
2.3 Interferometry . 26
2.4 The Nançay and Pico Veleta radio telescopes . 30
2.5 The Plateau de Bure and VLA interferometers . 31
2.6 The 21 cm line . 32
I2.7 Molecular lines: CO rotation lines . 33
2.8 Transfer of radiation 35
3 RS Cnc: CO OBSERVATIONS AND MODEL 41
3.1 Introduction . 41
3.2 Review of the 2004-2005 and earlier CO observations . 42
3.3 The new 2011 observations . 46
3.4 Modelling the wind . 49
3.4.1 Overview 49
3.4.2 Adequacy of the model . 52
3.4.3 Emission, absorption and dissociation . 53
3.4.4 Fitting the CO(1-0) and CO(2-1) data . 54
3.5 Central symmetry 56
3.5.1 Signatures of central symmetry 56
3.5.2 Central asymmetry in the CO(1-0) data 57
3.5.3 CO(1-0): mapping the asymmetric excess . 60
3.5.4 CO(2-1) asymmetry 63
3.6 Reprocessed data and global analysis 1 . 64
3.6.1 Description of CO(1-0) and CO(2-1) emissions using a centrally symmetric model 66
3.6.2 Deviation from central symmetry in CO(1-0) and CO(2-1) emission . 69
3.6.3 Conclusion . 72
4 CO EMISSION FROM EP Aqr
2
77
4.1 Introduction . 77
4.2 Observing a star along its symmetry axis 80
4.3 Comparison of the observations with a bipolar outflow model . 82
4.4 The CO(1-0) to CO(2-1) flux ratio . 85
4.5 Evaluation of the effective density in the star meridian plane . 88
4.6 The mean Doppler velocity of the narrow line component . 90
4.7 Discussion 91
1 The content of this section has been published (Nhung et al. 2015a)
2 The content of this chapter has been published (Nhung et al. 2015b)
II4.8 Conclusion . 96
5 CO EMISSION FROM THE RED RECTANGLE
3
97
5.1 Introduction . 97
5.2 Data . 98
5.3 Main features 99
5.4 Gas effective density 105
5.5 Temperature and density distributions . 107
5.6 Gas velocity . 109
5.7 Asymmetries 111
5.8 Continuum and dust . 112
5.9 Discussion 112
5.10 Summary and conclusions . 114
6 CO EMISSION OF OTHER STARS 117
6.1 X Her and RX Boo . 117
6.2 Results 118
6.2.1 X Her 118
6.2.2 RX Boo . 120
6.3 Summing up . 124
7 H i OBSERVATIONS OF THE WIND-ISM INTERACTION 127
7.1 H i observations . 127
7.2 H i model 129
7.2.1 Freely expanding wind (scenario 1) 130
7.2.2 Single detached shell (scenario 2) . 132
7.2.3 Villaver et al. model (scenario 3) 134
7.3 Discussion 136
7.3.1 Optically thin approximation 136
7.3.2 Spectral variations of the background . 137
7.3.3 Comparison with observations . 138
3 The content of this chapter has been published in Research in Astronomy and Astrophysics (Tuan Anh et al. 2015)
III7.4 Prospects 142
8 CONCLUSION AND PERSPECTIVES 145
8.1 CO observations . 145
8.2 H i observations . 149
8.3 Future prospects . 150
Appendix A 153
Appendix B 167
IVList of Figures
1.1 Sketch of the structure and environment of an AGB star (with the original idea from Le
Bertre 1997) . 2
1.2 Mass and radius scales for an AGB star of one solar mass (Habing & Olofsson 2004) 3
1.3 Evolution in the H-R diagram of a star having the metallicity of the Sun and twice its
mass (Herwig 2005).The number labels for each evolutionary phase indicates the log of
the approximate duration (in years) . 4
1.4 Details of the RGB and AGB evolution for a 1 solar mass star (Habing & Olofsson 2004). 5
1.5 Surface luminosity (solid line) decomposed as H burning luminosity (dashed line) and
He burning luminosity (dotted line) over a period covering two consecutive TPs for a 2
solar mass star (from Wood & Zarro 1981). Note the broken abscissa scale 6
1.6 Third dredge-up in a 2 solar mass AGB star following a TP. The red and blue lines mark
the boundaries of the H and He free core respectively. Convection zones are shown in
green (Herwig 2005) . 6
1.7 Formation of a dust shell around a carbon rich AGB star (Woitke & Niccolini 2005).
The white disks mark the star photosphere and black regions are not included in the
model. The star has C/O=2, T e f f =3600 K and L/L

=3000. The degree of condensation
is displayed in the left panel and the dust temperature in the right panel 8
1.8 Synthetic spectra of AGB stars with different C/O ratios (Gustafsson et al. 2003) . 10
1.9 Period-luminosity relation for optically visible red variables in a 0.5◦ × 0.5◦ region of the
LMC. The solid line shows the Hughes & Wood (1990) relation for Miras 11
1.10 Positions of selected mass shells in AGB atmospheres for two C/O values, 1.77 (left) and
1.49 (right) (Höfner & Dorfi 1997). Time is measured in piston periods P and radius in
units of stellar radius. Model parameters are (L
∗
, M
∗
, T
∗
and P): 10 4 L

, 1.0 M

, 2700
K and 650 days 12
1.11 Time dependence (starting from the first TP) of various quantities during the TP-AGB
phase of a star having a mass of 1.5 solar masses. The dotted line marks the end of the
AGB phase. M 6 is the mass-loss rate in units of 10ư 6 solar masses per year (Vassiliadis
& Wood 1993) 13
1.12 A HST gallery of Planetary Nebulae . 14
V1.13 Schematic evolution of close binaries (Jorissen 2004) . 16
1.14 The transient torus scenario (Frankowski & Jorissen 2007) . 17
1.15 Radio continuum map of post-AGB star IRAS 15445-5449 at 22.0 GHz (contours) over-
laid on the mid-infrared VLTI image . 18
2.1 The 30 m dish of the IRAM Pico Veleta radio telescope 22
2.2 Dependence on frequency of the atmospheric transmission at PdBI (2550 m). The dif-
ferent transmission curves are calculated for the amounts of water vapour (in mm) given
on the right 23
2.3 PSF pattern of a typical parabolic antenna response . 24
2.4 Plateau de Bure Interferometer: overall view (left) and a single dish (right) 26
2.5 Left: Principle schematics of the on-line treatment of the signals from a pair of antennas.
Right: Principle schematics of measurement of two visibility components . 28
2.6 The Nançay (France) radio telescope. The tilting plane mirror in the background sends an
image of the source to the fixed spherical mirror in the foreground. The mobile receiver
system is visible between the two mirrors 31
2.7 An antenna of the VLA (left) and an overview of the whole array (right) 32
2.8 Hyperfine splitting of the hydrogen ground state 32
2.9 The distribution of molecular clouds in the Milky Way as traced at 115 GHz by the CO(1-
0) transition (galactic coordinates with galactic centre in the centre of the figure) (Dame
et al. 2001) 34
2.10 Left: Energy levels of a molecule. Right: Rotation of a diatomic molecule 34
2.11 Dependence of the fractional population at different rotational levels of CO molecule on
kinetic temperature 36
2.12 The CO(1-0) (left) and CO(2-1) (right) fluxes of 400 spherical winds expanding with ve-
locity 8 km sư 1 without absorption effect (black) and with the effect at different values of
mass loss rates: 10ư 7 M

yrư 1 (red), 10ư 6 M

yrư 1 ( × 0.1, green) and 10ư 5 M

yrư 1 ( × 0.01,
blue). Distance of the source is d=122 pc 37
2.13 The comparison between the red-shifted parts (red) and the blue-shifted parts (blue) of
the CO(1-0) (left) and CO(2-1) (right) fluxes shown in Figure 2.11. The black line shows
the flux without the absorption effect 38
2.14 Observed absorption spectra caused by a background and optical depth of the source
having Gaussian distributions (Levinson & Brown 1980) 38
3.1 Spitzer 70 µm map (Geise 2011) (left) and IRAS/LRS infrared SED (right) of RS Cnc 42
VI3.2 Radio maps (Hoai et al. 2014; Libert et al. 2010b). Left, bipolar structure in CO(1-0);
blue lines are integrated between ư 2 and 3 km sư 1 and red lines between 9.5 and 16
km sư 1 , the background image being at 6.6 km sư 1 ; Right, H i total intensity map. Note
the very different scales . 42
3.3 Variability data (Percy et al. 2001; Adelman & Dennis 2005) . 43
3.4 Top: mass-loss rate (left) and gas expansion velocity (right) distributions for S-type stars
(solid green line, 40 stars), M-type stars (dashed-dotted blue line) and carbon AGB stars
(dashed, red line). Bottom: mass-loss rate vs gas expansion velocity (left) and versus
periods (middle); gas expansion velocities vs periods (right). Green dots are for S stars,
blue squares for M stars and red triangles for carbon stars. In all panels, RS Cnc is shown
in black 44
3.5 30 m dish spectra centred on RS Cnc. The fit of a two-wind model is shown in red. The
abscissas are in km sư 1 and the spectral resolution is smoothed to 0.2 km sư 1 45
3.6 CO(1-0) (left) and CO(2-1) (right) emission of RS Cnc integrated over the width of the
line ( ư 2 to 17 km sư 1 ) 46
3.7 CO(1-0) (left) and CO(2-1) (right) brightness distributions in the central velocity channel
at 7 km sư 1 (of width 0.8 km sư 1 ). Arrows show widths at half maximum, ∼ 2.800 and
∼ 1.700 respectively 46
3.8 Position-velocity diagrams for CO(1-0), left, and CO(2-1), right 47
3.9 Bipolar structure in CO(1-0). Blue lines: emission integrated between
ư 2 km sư 1 and 3 km sư 1 . Red dotted lines: emission integrated between 9.5 km sư 1 and
16 km sư 1 . The background image shows the 6.6 km sư 1 channel 47
3.10 Wind model of Libert et al. (2010b). The jet axes are nearly (PA=10◦) in the north-
south plane, tilted by 45◦ with respect to the line of sight, the jet moving toward us
aiming north. The half aperture of the jet cones is ε = 20◦. The disk is normal to the jets
with a half aperture ϕ = 45◦ . 48
3.11 The 6.6 km sư 1 CO(1-0) map (2011, left panel) compared with the 7.4 km sư 1
CO(2-1) map (2004-2005, right panel) 48
3.12 Continuum map at 115 GHz of RS Cnc (A+B configuration data obtained in 2011). The
cross corresponds to the 2000.0 position of the star. The contour levels are separated by
steps of 0.90 mJy/beam (20σ) 49
3.13 Meridian plane configuration of the molecular outflow for the model allowing for non-
radial velocities. The curves are equally spaced in γ (steps of 0.1). The abscissa is the
star axis, the ordinate on a radius along the equator, both in arcseconds. The right panel
is a zoom of the left panel for r<100 . 54
3.14 Dependences on a of the value of χ
2 (square symbols, left hand scales) and of the product
aρ normalized to its zero-gap value (Rρ , dotted symbols, right hand scales) for the disk
(left panel) and the jet (right panel) respectively 54
VII3.15 Dependence of log(T[K]) on log(r[cm]) (r is the distance to the central star) used in
this work (full straight line, α=0.7) compared with the results obtained by Schöier &
Olofsson (2001) for three different mass-loss rates. Remember that 1000=2.14 10 16 cm 55
3.16 Values of ζ (upper curves, left scale) and r 1/2 (lower curves, right scale) as a function
of ˙M. The short-dashed curves correspond to V=7.5 km sư 1 , the others to 15 and 30
km sư 1 (Mamon et al. 1988) . 55
3.17 Spectral map of the CO(1-0) data (black) and best fit (red) . 57
3.18 Spectral map of the CO(2-1) data (black) and best fit (red) . 58
3.19 Best fit results of CO(1-0) (red) and CO(2-1) (blue): Dependences on sine of the latitude,
γ, of the flux of matter (up-left), of the velocity at 100 (up-right) and of the density at
100 (down-left); and r-dependence of the velocity (down-right) at equator (lower curves)
and poles (upper curves) . 59
3.20 Velocity distributions summed over the northern half of the velocity spectra (24 cells)
of the CO(1-0) data. Left: Δ dir (red) and P
dir (black), central symmetry would require
P
dir ( ư V x ) = P
dir (V x ) and Δ dir ( ư V x ) = ư Δ dir (V x ). Centre: Δ mir (red) and P
mir (black),
central symmetry would require Δ mir =0. Right: Schematic two-component interpretation
of the CO(1-0) lack of central symmetry . 60
3.21 Distributions of R asym summed over the 21 (3 × 7) northern (left) and 21 southern (right)
spectra of the CO(1-0) data (black line). The standard model predictions are shown for
zero offset (blue) and for an offset of 0.1500 West and 0.3700 South (red) 60
3.22 Mapping the northern excess of the CO(1-0) data (left panel) and of the prediction of the
standard wind model modified to include a static cool sphere of gas in the northern sky
(right panel, see text) . 61
3.23 Distributions of R asym summed over the 21 northern (left) and 21 southern (right) spectra
of the CO(1-0) data (black line). The prediction (red) is shown for a modified standard
model including a sphere of cool gas (see text) . 62
3.24 CO(2-1) channel maps (black) compared with the form [a+b(y
2
+z
2 )+cz]CO(1-0) (red)
where a, b and c take the best fit values of 8.3, ư 0.20 and ư 0.37 respectively . 64
3.25 Same as Figure 3.20 for the CO(2-1) data, using a star velocity of 7.1 km sư 1 as pivot
to define mirror quantities. Left: Δ dir (red) and P
dir (black). Right: Δ mir (red) and P
mir
(black) 65
3.26 Mapping the excess in the CO(2-1) data (left panel) and standard model (right panel) . 65
VIII3.27 Velocity distribution (log scale) of the excess observed in the CO(2-1) data (black curve)
when using 7.1 km sư 1 as pivot for the mirror spectra. The red line shows the model
prediction when using offsets in right ascension and declination twice as small as for the
CO(1-0) data. The blue curve shows the model prediction when the offsets are set to zero,
in which case absorption is the only source of central asymmetry. The excess is summed
over the 48 central spectra (the central spectrum being excluded) and normalized to the
total flux over the associated area 66
3.28 R yz distributions of <CO(1-0)> (left panel) and <CO(2-1)> (middle panel) as observed
(black symbols) and obtained from the standard model in its present version (red curves)
or in the version used in Hoai et al. (2014) (cyan curves). Right panel: R yz dependence
of the <CO(2-1)>/<CO(1-0)> ratio as observed (black symbols) and obtained from the
model (red and blue curves). The best fit results of the standard model (shown here) are
essentially identical to those of its modified asymmetric version. The error bars show
root mean square deviations with respect to the mean (not defined at r = 0 where a single
cell contributes) . 67
3.29 Dependence on r of the gas temperature (upper panel) and of the detected flux density
obtained from the model (Jy per bin of 0.2 arcsec, lower panel), in log-log scales. Tem-
peratures are displayed for the present version of the standard model (red), the version
used in Hoai et al. (2014), (cyan line) and the radiative transfer calculations of Schöier
& Olofsson (2001), (black dotted line). The flux densities are shown for CO(1-0) (or-
ange) and CO(2-1) (magenta, divided by 10) separately. The restriction of the study to
the 49 central cells implies an effective progressive truncation of the r distribution from
∼ 500 onward 69
3.30 Dependence on the sine of the star latitude, γ, of the flux of matter (up-left), of the wind
velocity at r = 100 (up-right) and of the gas density at r = 100 (down-left). Down-right: r-
dependence of the equatorial (lower curves) and polar (upper curves) velocities. The best
fit results of the symmetric model are shown in red and those of its modified asymmetric
version in blue. The dashed curve is for γ = 1 (north) and the dotted curve for γ = ư 1
(south) 71
3.31 Velocity distributions of P
dir , Δ dir , P
mir , Δ mir , evaluated over the 24 pairs of diametrically
opposite spectra of the CO(1-0) (left) and CO(2-1) (right) spectral maps. The upper pan-
els are for mirror quantities and the lower panels for direct quantities. In each case, the
data are shown in black, the best fit results of the standard model in red and of its modi-
fied asymmetric version in blue. The reference velocity is 7.25 km sư 1 , the CO(1-0) data
of Libert et al. (2010b) and Hoai et al. (2014) having been corrected by +0.5 km sư 1 . 72
3.32 Spectral map centred on the star of the CO(1-0) observations (black) and best fit results
of the modified asymmetric version of the standard model (blue). Steps in right ascension
and declination are 1.400. The synthesized beams are Gaussian with a full width at half
maximum of 1.200 . 74
IX3.33 Spectral map centred on the star of the CO(2-1) observations (black) and best fit results
of the modified asymmetric version of the standard model (blue). Steps in right ascension
and declination are 1.400. The synthesized beams are Gaussian with a full width at half
maximum of 1.200 . 75
4.1 PACS image of EP Aqr at 70 µm (left) and 160 µm (right) (Cox et al. 2012) . 77
4.2 Channel maps in the 12 CO(J=1-0) line (smoothed to a width of 1 km sư 1 ). Contours are
plotted at 5, 10, 20, 30, 40 σ (1 σ = 14 mJy/beam). The synthesized beam is indicated in
the lower left . 79
4.3 Channel maps in the 12 CO(J=2-1) line (smoothed to a width of 1 km sư 1 ). First contour is
plotted at 10 σ, the following contours start at 20 σ and are plotted in 20 σ steps (1 σ =
16 mJy/beam). The synthesized beam is indicated in the lower left . 80
4.4 Definition of coordinates. The (ξ, η) coordinates are obtained from (y, z) coordinates
by rotation of angle ω in the sky plane about the x axis (line of sight and star axis, cf.
Sect. 4.2). In the sky plane, y is towards East, and z towards North . 81
4.5 Relation between the Doppler velocity V x and the star latitude α (cf. Eq. (4.2), upper
panel), the ratio r/R = 1/cosα (middle panel) for the simple star model described in the
text. Lower panel: velocity spectra obtained for the same model at R=1, 2, 3, 4 and 5
(running downward) . 82
4.6 Spectral maps centered on the star of the CO observations (black) and the best-fit model
(blue). The CO(1-0) map is shown in the upper panel, CO(2-1) in the lower panel. Steps
in right ascension and declination are 100 . 84
4.7 CO(1-0) to CO(2-1) flux ratio (black) where each of the CO(1-0) and CO(2-1) fluxes has
been averaged over 5 successive velocity bins and over the concentric rings defined in
the text. The lower right panel is for all pixels having R < 500. The result of the best fit
of the model described in Sect. 4.3 is shown in red and that of its modification described
in Sect. 4.4 is shown in blue. The horizontal lines indicate the level (0.063) above which
the data must be under the hypothesis of local thermal equilibrium . 86
4.8 Distribution of the gas temperature. Left: as a function of α at distances from the star
r = 100 to 800 (from top to bottom) in steps of 100; right: as a function of r at latitudes
α = 0◦ (red), 30◦ (black), 60◦ (green) and 90◦ (blue) 87
4.9 Reconstructed maps of the effective density, multiplied by r
2 , in the star meridian plane
under the assumption of a wind velocity having the form obtained from the best fit of
the model of Sect. 4.3. The colour codes are such that the ratio between maximum and
minimum values of ρr
2 are the same for CO(1-0) (left) and CO(2-1) (right). Units are
Jy beamư 1 km sư 1 arcsec. The rectangles show the regions selected for displaying the ω
distributions shown in Figure 4.11 (for CO(1-0), abscissa between 000 and 300, ordinate
between 500 and 900; for CO(2-1), abscissa between 2.000 and 5.400, ordinate between 1.800
and 5.200) . 89
X4.10 Distributions of the average effective density, multiplied by r
2 , reconstructed in the
meridian plane of the star for a wind velocity having the form obtained from the best
fit of the model of Sect. 4.3. Note that the µ-correction has not been applied. left: radial
dependence of r
2
ρeff , averaged over α and ω; middle: latitude dependence of r
2
ρeff , aver-
aged over r and ω; right: longitude dependence of r
2
ρeff , averaged over r and α. In each
panel, CO(1-0) results are shown in red and CO(2-1) results in blue. The dashed curves
show the results of the model, ignoring absorption . 90
4.11 Distributions of the effective density, multiplied by r
2 , as a function of star longitude ω
for the annular regions delineated by the rectangles shown in Figure 4.9. CO(1-0) data
are shown in red, CO(2-1) data in blue 91
4.12 Sky maps of R f for CO(1-0) (upper panels) and CO(2-1) (lower panels) observations.
Units are Jy beamư 1 km sư 1 arcsec. From left to right: all velocities, | V x | < 2 km sư 1
and | V x | > 2 km sư 1 . The circles at R = 3.500 correspond to the enhancement seen by
Winters et al. (2007) in CO(2-1) data restricted to the narrow velocity component. The
projection of the star axis on the sky plane (making an angle of 13◦ with the line of sight)
and the axis from which the star longitude ω is measured (positive clockwise) are shown
as black arrows 92
4.13 Illustration of the procedure used to evaluate the mean Doppler velocity Δ3 of the narrow
component. The velocity spectra summed over the 1369 pixels of the map are shown in
black for CO(1-0) (upper panel) and CO(2-1) (lower panel). The quadratic fit over the
two control regions is shown in red and its interpolation below the narrow component in
blue. The vertical blue lines show the mean Doppler velocities of the narrow component
from which the interpolated broad component has been subtracted. They are used as
reference for evaluating Δ3 in each pixel separately . 93
4.14 Left: distributions of the mean Doppler velocity Δ3 (km sư 1 ) measured with respect to
its value averaged over the whole map (shown as "reference" in Figure 4.13). The black
curve shows a two-Gaussian common fit to the two distributions. Right: dependence of
the projection of the mean Doppler velocity Δ3 (km sư 1 ), averaged over pixels included in
the bands shown in Figure 4.15, on coordinate ξ measured from south-east to north-west.
The black curve shows a polynomial common fit to the two distributions. In both panels
the CO(1-0) data are shown in red and the CO(2-1) data in blue 94
4.15 Sky maps of the mean Doppler velocity Δ3 (km sư 1 ) measured with respect to its value
averaged over the whole map (shown as "reference" in Figure 4.13) for CO(1-0) (left)
and CO(2-1) (right). The black lines limit the bands in which pixels are retained to
evaluate the ξ dependence of Δ3 (Figure 4.14 right) . 94
4.16 Results of the model introduced in Sect. 4.3 for the distributions displayed in Figure 4.14.
The smooth curves are the results of the fits (respectively Gaussian and polynomial) made
to the observations in Figure 4.14 95
4.17 Results of the model introduced in Sect. 4.3 for the maps displayed in Figure 4.15. The
red arrows indicate the projection of the star axis on the sky plane . 95
XI5.1 Left: HST wide field planetary camera 2 image of the Red Rectangle from Cohen et al.
(2004). Right: Keck telescope near-infrared speckle image from Tuthill et al. (2002).
North is up and East is left 98
5.2 CO(3-2) (left) and CO(6-5) (right) images (400 × 400) rotated by 13◦ clockwise integrated
over Doppler velocities from ư 7.2 kmsư 1 to 7.2 kmsư 1 (present work). Unit of color bars
is Jy beamư 1 km sư 1 . 98
5.3 Projections on y (left) and z (middle) of the continuum emission (Jy/beam). Right: Empty
sky contribution at low values of the line flux density distributions (Jy arcsecư 2 ). The
upper panels are for CO(3-2) and the lower panels for CO(6-5). Gaussian fits are shown
on the peaks . 100
5.4 Left: the upper panel displays (in blue) the map of retained pixels and the lower panel
that of A T , the CO(6-5) to CO(3-2) flux ratio. Sky maps of Aη (middle) and A z (right) are
shown for CO(3-2) and CO(6-5) in the upper and lower panels respectively 101
5.5 Sketch of sky regions having velocity spectra in Figure 5.6 101
5.6 Velocity spectra integrated over sky regions defined in Figure 5.5. Dotted lines are for
CO(6-5), solid lines for CO(3-2). P and E stand for polar and equatorial sectors respec-
tively, followed by a digit labelling the radial rings from centre outward. Different colors
correspond to different regions as defined in Figure 5.5 . 102
5.7 Measured flux densities (blue) averaged over (R,α) intervals of sizes (0.300,11.25◦) are
compared with the result (red) of integrating over the line of sight the effective densities
obtained by solving the integral equation. The upper panels display α distributions in
eight successive R intervals, the lower panels display R distributions in eight successive
α intervals. In each case, the upper row is for CO(3-2) and the lower row for CO(6-5).
Panels are labelled with the corresponding interval, in arcseconds for R and degrees for α. 103
5.8 Distribution of the effective densities multiplied by r
2 in the (ξ,z) meridian half-plane
of the Red Rectangle for CO(3-2) (left panel), CO(6-5) (middle panel) and the ratio
CO(6-5)/CO(3-2) (right panel). The upper panels are for the solutions of the integral
equation and the lower panels for the model described in the text. Parabolas correspond-
ing to β=1 and β=2 are shown in the lower panels 104
5.9 Dependence on q = 1 ư exp( ư β ln 2/β0 ) of the parameterized effective densities multiplied
by r
2 for r=0.500, 1.000, 1.500, 2.000 and 2.500 for CO(3-2) (upper panel) and CO(6-5) (lower
panel) . 105
5.10 Dependence on r of the parameterized effective densities multiplied by r
2 for q values of
0 and 0.25 (equator, red), 0.5 (bicone, black) and 0.75 and 1 (poles, blue) for CO(3-2)
(upper panel) and CO(6-5) (lower panel) 105
XII5.11 Left: Map of temperatures in the half-meridian plane of the star obtained from the effec-
tive densities using Relation 4. The parabolas are for β=0.3, 0.8, 2.5 and 3.5 and define
the sectors illustrated in the central panel. Middle: r-distribution of the gas temperature
averaged over the three angular sectors delineated in the left panel: the red points are for
the equatorial region (inside the β = 0.3 parabola), the black points are on the bicone
(between the β = 0.8 and β = 2.5 parabolas) and the blue points are for the polar region
(outside the β = 3.5 parabola). Error bars show the dispersion within each r bin. Right:
CO density (in molecules per cm 3 ) multiplied by r
2 (in arcsec 2 ) 108
5.12 Left: In the polar region (β > β0 ) the gas velocity V out is confined to meridian planes
(ξ,z) and tangent to parabolas of equation z
2
= βξ. Right: In the equatorial region (β <
β0 ) the gas velocity is confined to planes parallel to the equatorial plane and tangent
to hyperbolic spirals with a constant radial component V rad and a rotation velocity V rot
proportional to rư k 109
5.13 CO(3-2) (left) and CO(6-5) (right) velocity spectra for data (blue) and model (red) aver-
aged over groups of 49 pixels, each group covering 0.700 × 0.700, the whole map covering
4.200 × 4.200 110
5.14 Sky maps of the deviation from full symmetry (see text) multiplied by R of the measured
fluxes for CO(3-2) (left panel) and CO(6-5) (right panel). Units are Jy km sư 1 arcsecư 2 .
The south-eastern excess reaches ∼ 70% of the symmetric value at maximum . 111
6.1 Angular distance distributions from the star centre of <CO(1-0)>, <CO(2-1)> and <
CO(2-1)
CO(1-0)
>
as observed (black) and obtained from the model (red) . 119
6.2 X Her. Dependence on the sine of the star latitude, γ, of the flux of matter (up-left), of the
wind velocity at r = 100 (up-right) and of the gas density at r = 100 (down-left). Down-
right: r-dependence of the equatorial (lower curves) and polar (upper curves) velocities.
The results of the standard model are in red and its modified model in blue 121
6.3 X Her. Spectral map centred on the star of the CO(1-0) observations (black), the best-
fit standard model (red) and the modified model (blue). Steps in right ascension and
declination are 200 . 122
6.4 RX Boo. Spectral maps for CO(1-0) (left) and CO(2-1) (right) observations of RX Boo
as observed (black) and described by the model (red) 123
6.5 RX Boo. Dependence on R yz of the averaged integrated fluxes in CO(1-0) (left), CO(2-1) (mid-
dle) and their ratio (right). The data are shown in black, the model predictions in red for
the separated fits and in blue for the combined fit 123
6.6 RX Boo. Integrated missing flux of the spherical model over the red-shifted velocity
range (6 to 8 km sư 1 ) (left) and over the blue-shifted velocity range ( ư 6 to ư 4 km sư 1 )
(right) . 124
6.7 The best fit parameters of CO(1-0) with bipolar structure 125
XIII7.1 VLA images of AGB stars. The arrow shows the space motion direction of the star
(adapted from Matthews et al. 2008, 2011, 2013) . 128
7.2 Density and temperature profiles for an outflow in uniform expansion (scenario 1, V exp =
10 km sư 1 , ˙M = 10ư 5 M

yrư 1 ) 131
7.3 H i line profiles of shells in free expansion for various mass-loss rates with no back-
ground. The profiles for 10ư 7 , 10ư 6 , 10ư 5 M

yrư 1 are scaled by factors 1000, 100, and 10,
respectively. The distance is set at 200 pc 132
7.4 H i line profiles of a shell in free expansion for ˙M=10ư 5 M

yrư 1 , and for various back-
ground levels (T BG = 0, 3, 5, 7, 10 K) 133
7.5 H i line profiles of single detached shells for various circumstellar masses (A: 0.05 M

,
B: 0.1 M

, C: 0.2 M

, D: 0.4 M

,), in the absence of background . 134
7.6 H i line profiles of a single detached shell (scenario 2, case D) for various background
levels (T BG = 0, 10, 30, 50 K) 135
7.7 Density, velocity and temperature profiles for a detached shell model (scenario 2, case D). 136
7.8 Y CVn integrated spectrum (Libert et al. 2007) and best fit result using scenario 2 (d =
321 pc, ˙M = 1.3 × 10ư 7 M

yrư 1 , age = 7 × 10 5 yr) 137
7.9 H i spectral maps of Y CVn from VLA data (black) and from the detached shell model
(blue) . 138
7.10 Density, velocity and temperature profiles for the Villaver et al. (2002) model at three
different epochs [5.0 × 10 5 yr (left), 6.5 × 10 5 yr (centre), 8.0 × 10 5 yr (right)] 139
7.11 H i line profiles of a circumstellar shell model around a 1.5 M

star during the evolution
on the TP-AGB phase (5.0, 6.5, 8.0 × 10 5 yr; Villaver et al. (2002), in the absence
of background. The distance is set at 1000 pc. The first two profiles, scaled by up
by factors of 37.7 and 3.87 respectively, in order to help the comparison, are virtually
indistinguishable . 139
7.12 Ratio between the estimated and real values of the mass of atomic hydrogen for sce-
nario 1 (freely expanding wind) with mass-loss rates ranging from 10ư 7 M

yrư 1 to 10ư 4
M

yrư 1 (see Section 7.3.1) and different cases of temperature dependence (see text).
Upper panel: no background. Lower panel: with a 5 K background 140
7.13 Effect of a background intensity varying linearly from 10 K to 5 K across the line profile
for scenario 1 with ˙M = 10ư 5 M

yrư 1 . The curves labelled “T BG =5 K”, and “T BG =10
K”, are taken from Figure 7.4 141
XIVList of Tables
1.1 Typical AGB star parameters 1
1.2 Most abundant atoms and molecules under LTE 9
3.1 Two-wind description of the CO(1-0) and CO(2-0) lines of RS Cnc (Libert et al. 2010b). 45
3.2 Best fit parameters obtained for the CO(1-0) and CO(2-1) data . 56
3.3 Best fit model parameters with and without explicit asymmetries. The optimisation uses
uncertainties combining a 9% [8%] error with a 14 mJy [116 mJy] noise for CO(1-0) [CO(2-1)]
respectively, adjusted to have for each set of observations a value close to the number of
degrees of freedom. Values in parentheses display the last digits corresponding to an
increase of χ
2 of 1% when the parameter is varied with the others kept constant. The
distance to the star is taken to be 143 pc (van Leeuwen 2007) . 70
4.1 The line profile features of EP Aqr . 78
4.2 Best fit parameters obtained for the CO(1-0) and CO(2-1) data. A distance of 114 pc is
adopted 85
4.3 Best fit parameters of the CO(2-1) to CO(1-0) ratio . 87
5.1 Best fit parameters to the CO(3-2) and CO(6-5) effective densities multiplied by r
2 107
5.2 Best fit parameters P of the joint fit to the CO(3-2) and CO(6-5) spectral maps. Also
listed are the values of Δ + and Δư measuring the sensitivity of the value of χ
2 to small
deviations of the parameter from its best fit value (see text) . 109
6.1 The properties of stars: EP Aqr, X Her and RX Boo 118
6.2 Best fit values of the parameters of the standard model and the modified model 120
6.3 Best fit values of spherical model for RX Boo . 121
6.4 Best fit results to the CO(1-0) emission of RX Boo with a bipolar outflow . 124
7.1 Model parameters (scenario 2), d =200 pc, V exp = 8 km sư 1 and ˙M = 10ư 7 M

yrư 1 133
7.2 Model parameters of Y CVn 134