% --- \chapter{Introduction} ---

\chapter{Setting a background}
\pagenumbering{arabic}

\section{AGB-stars}
\subsection{The interest in AGB-stars}

A number of reasons make the study of Asymptotic Giant Branch (AGB)
stars very fascinating.  The vast majority of stars in the Universe,
including our sun, will eventually become AGB-stars in their way to
the final stages of evolution.  Stars on the AGB track participate in the
enrichment of galaxies, replenishing the interstellar medium (ISM)
with nuclear-processed material (Busso et. al 1999).  They are very
likely the main producers of interstellar dust particles, thereby
playing an important role in the birth of the next generation of
stars.  AGB-stars are among the most luminous stars and therefore they
contribute to the integrated starlight of many galaxies.  Seen as
stellar populations, they can also be used to study the structure and
dynamical state of galaxies (Dejonghe \& Caelenberg 1999).

Furthermore, stars on the AGB track provide intricate systems (see
Fig~\ref{schematicview}) where interplays between physical and
chemical processes certainly issue a challenge for understanding
the mechanisms that govern this stage of evolution.  They are also
excellent laboratories for theories about astrophysical processes of
wider significance than just the objects themselves: mass loss, maser
excitation and radiative transfer, formation of solid state particles,
molecular chemistry, radiation driven hydrodynamics,\ldots


\subsection{Their state of evolution}

Single stars of low and intermediate mass evolve through the
Asymptotic Giant Branch (AGB) as they experience the last substantial
nuclear burning phase.  After completion of central hydrogen and
helium burning, stars with masses in the range 0.8-8 \msun~reach the
AGB stage with a core composed of an electron-degenerate C/O mixture,
an overlying He-shell and a H-mantle which extends to regions cool
enough ($\leq$ 3500 K) for the formation of molecules to take place. 

During the early evolution along the AGB track (E-AGB), He-burning
at the base of the He-shell provides the energy that counteracts
gravitation.  For stars with M $\geq$ 4 \msun~the outer convection can
penetrate the H-exhausted layers leading to a second dredge-up of
CNO cycled material to the surface.  Eventually, H-burning takes over
and He-burning becomes recurrently unstable [every 10$^4$-10$^5$ yr,
depending on the core-mass] during short periods [$<$10$^3$ yr], giving
rise to run-away situations: the so-called thermal pulses.  This
defines the thermally pulsing AGB phase (TP-AGB) [$\approx$ 5-20 \% of
the E-AGB time scale].  During a thermal pulse the luminosity
increases effectively up to $\approx$ 10$^4$\lsun. A pulse-driven 
convection zone develops in the intershell region due to the huge amount of 
energy produced. At the same time the H-shell is pushed outwards and 
H-burning is quenched. In later pulses the convective envelope, in 
response to the cooling of the outer layers, can penetrate the 
intershell region [now enriched in $^{12}$C]. This leads to the third 
dredge-up of material to the surface, a process that may change the 
elemental abundance in the atmosphere [and account for the formation 
of C-rich stars, see Sect.~\ref{properties}].


\subsection{Basic properties of AGB-stars}
\label{properties}
\subsubsection{Identification}

The use of stellar luminosity as a criteria to identify AGB-stars is
certainly not accurate.  In the limit of highest AGB luminosities,
contamination with supergiants is plausible.  For the barely variable
low-luminosity AGB-stars a clear separation from the more common Red
Giant Branch (RGB) stars can be elaborate.  There are alternative ways
of discriminating among these different groups, e.g. based on
comparison of near-infrared CO and H$_{2}$O absorption bands (Jones
et al. 1982) or CO radio line and 60\micron~fluxes (Josselin et. 
al. 1998), but none of them can avoid misclassifications.  Maser
diagnostics can be used for the identification of stars departuring
from the AGB towards the Proto Planetary Nebula (PPN) phase (Engels
2001).  To pinpoint extrinsic AGB-stars, i.e. stars showing
AGB-characteristics due to mass transfer from a companion, is more of
a problem but this can be achieved, e.g, by searching for spectral lines of 
Technitium (van Eck \& Jorissen 2000).

\subsubsection{Masses, luminosities and effective temperatures}

The occurance of AGB-stars in globular clusters sets a lower limit of
$\approx$0.85 \msun~to the initial mass of the AGB-progenitors.  An
upper value of $\approx$6-8 \msun~is imposed by the development of an
electron-degenerate core after central He exhaustion.  The absolute
luminosities of stars in the Magellanic Clouds (MC) can be derived
since the distances are well known.  Wood et al.  (1983) have
determined the luminosities of known Long Period Variables (LPVs)
stars in the MC [most of them identified as AGB-star] to be in the
range from that of globular cluster Miras (\mbol $\approx$ -3.8) to
the AGB limit luminosity (\mbol $\approx$ -7.1).  Using pulsation
theory, the assigned current masses to the stars fall in the expected
range $<$1-8 \msun. Interferometer measurements of stellar radii have
provided determinations of effective temperatures for AGB-stars in the
range $\approx$ 2200-3300 K (e.g., van Belle et al. 1996).


\subsubsection{Surface abundances: O- and C-rich stars}

During the third dredge-up that occurs on the AGB stage, the surface
elemental abundances of the stars change as freshly processed material
in the previously burning He-shell is injected in the convective
H-mantle.  Of special interest is the abundance of carbon with
respect to oxygen, which is originally given by that of the ISM from
which the star was formed (i.e., C/O$<$1).  After several
pulses the surface abundance of carbon can exceed for the first time
that of oxygen.  This has little effect on the evolution of the star. 
However, it has a profound effect in the stellar spectrum.

Traditionally, AGB-stars are divided into two main groups on the
basis of their C/O-ratio.  Thus, stars where the abundance of oxygen
is higher than that of carbon are labelled O-rich or M- stars [e.g.,
those in {\bf Papers III} and {\bf IV}] and their optical spectra are
dominated by TiO bands.  On the contrary, if the abundance of carbon
is higher than that of oxygen the star is said to be C-rich, or
simply, a C-star [e.g., those in {\bf Papers I} and {\bf II}].  In
these stars C$_{2}$ and CN bands dominate the optical spectra.

It is generally accepted that the occurrence of the third dredge-up is
a necessary condition for the formation of C-stars.  However, it is
not sufficient.  A process called Hot Bottom Burning (HBB), which
operates in the more massive AGB-stars ($\geq$ 4-5 \msun), is known to
prevent the stars from becoming C-rich by CNO-cycling of envelope
material through the outer parts of the H-burning shell (e.g.,
Lattanzio \& Forestini 1999).  The effect seen in HBB models is the
destruction of $^{12}$C and the building up of $^{13}$C and $^{14}$N.
This mechanism accounts for the deficit of C-stars brighter than
\mbol$\approx$ -6.

\begin{figure*} \centering \vspace{9.6 cm}
\special{psfile=cse.ps hoffset=0 voffset=-30 hscale=78 vscale=78 angle=0}
\caption{A schematic picture of the structure of an AGB-star} 
  \label{schematicview}
\end{figure*}

\subsubsection{Galactic distribution}

The radial distributions of M- and C-stars found in the Galaxy are
quite different.  The M-stars follow an exponential disk with a scale
height of $\approx$ 4 kpc (Blommaert et al. 1993).  The surface density
of infrared C-stars is relatively constant out to the galactocentric
distance of the Sun, after which it follows an exponential decline with
a scale length of 2.5 kpc (Guglielmo et al. 1998). Therefore, the
M/C-ratio shows a strong dependence with galactocentric distance, very
likely due to the effects of metallicity.



\section{Variability}

AGB-stars commonly are pulsating variables.  For instance, the large
majority ($\geq$ 90\%) of stars on the TP-AGB observed in a 0.5
$\times$ 0.5 degree region of the Large Magellanic Cloud (LMC) bar are
variable at the level of a few percent or more (Wood et al. 1999).
The most likely mechanism responsible for the observed variability is
the pulsation of the star's outer layers due to departures from
hydrostatical equilibrium.  Furthermore, helium shell flashes can lead
to long-term variability which can interact with the short-term
pulsation.  Furthermore, brightness variations of much shorter time
scale (2 hours to 6 days) have been seen in $\approx$40 LPVs from
Hipparcos photometric observations (de Laverny et al. 1998).  In some
cases, there is also evidence for variations caused by episodic
ejection of dust shells or orbiting gas clouds.

The red giant variable stars in the General Catalogue of Variable
Stars (GCVS) are divided into three main groups: Mira, semiregular
(SRVs) and irregular variables (IRVs).  The Mira Ceti-type stars are
long period variables with visible amplitude variation $\geq$ 2.5$^m$
in V, well-expressed periodicity, good regularity and periods from 80
to 2000 days.  They occupy the tip of the AGB. The large amplitude of
variation in the shorter wavelength regions very likely being the
result of changing absorption in the atmosphere due to TiO molecules.
The SRVs are further divided into four classes [a-d].  Only the SRa
and SRb groups contain mostly late-type giants.  The SRa usually show
smaller light amplitudes than the Miras ($\leq$ 2.5$^m$ in V).  The
light curves show persistent periodicity and shapes that generally
vary.  The SRb have poorly defined periodicity.  Some show
simultaneous presence of two or more periods.  The SRas are very
likely not a distinct class of variables but a mixture of Miras and
SRbs (Kerschbaum \& Hron 1992).  Finally, the IRVs show little
periodicity, although this is often due to poorly studied light curves
rather than lack of intrinsic periodicity. The sample studied in {\bf
Paper~III} contains semiregular and irregular O-rich variables. In
{\bf Paper~IV} stars of the three types of variability are studied.

An important class of AGB-variables not found in the GCVS consists of
the dust-enshrouded, infrared variables.  The O-rich versions have
been found by their 1612 MHz OH maser emission (OH/IR stars) and/or by
infrared surveys.  The C-rich counterparts are only found through
infrared surveys.  In both cases, the stars generally pulsate with
larger amplitudes (up to 3$^m$ in K) and longer periods ($\geq$ 600
days) than the optical Mira variables.

One of the hottest topics of research on AGB-stars concerns the mode
in which the different types of variables pulsate.  From MACHO
observations of AGB-stars in the LMC, Wood (2000) obtained parallel
K-log P relations for the Miras and SRVs.  A comparison of linear
pulsational models with these observations shows that a fundamental
mode pulsation in Miras is able to reproduce the observed
period-luminosity (P-L) relations and the period ratios between
different modes.  On the other hand, the majority of SRVs are 1st,
2nd or 3rd overtone pulsators.  However, the situation where the
measurement of Miras radii suggest pulsation in the first overtone
still exists.  The problem is partially due to observational
difficulties since the radius of an AGB star is not well defined. It
varies as much as a factor of 2 with wavelength and it is affected,
e.g., by scattering in the upper layers of the atmosphere.  But very
likely the modelling of the convective energy transport used in
non-linear calculations is introducing the largest uncertainties.


\section{Mass loss during the AGB stage}

The ejection of material plays a major role in the life cycle of
stars.  On the AGB stage the stars are known to experience intense mass
loss in the form of a cool, slow and essentially spherically symmetric
wind.  During this phase of evolution they lose copious amounts of
matter at a rate significantly higher than that of the Sun.
Eventually, the mass loss will remove practically the entire hydrogen
envelope of the stars, and thus puts an end to their evolution as AGB
stars.  Therefore, mass loss rather than nuclear burning determines
the evolutionary time scale of these stars.  This severely limits the
lifetime and the maximum luminosity reached on the AGB. It also puts a
high lower mass limit for supernova precursors.  The mass loss process
is so effective during this stage that stars as massive as about 8
\msun~will leave the AGB with a core mass well below the Chandrasekhar
limit of 1.4 \msun.

Through mass loss the ISM is replenished with nuclear-processed 
material and dust particles. Stars on the AGB appear to be the main
contributors to the replenishment of the ISM, possibly $\approx$ 70\%
in the solar neighbourhood (Sedlmayr 1994). As the
material returned to the ISM has been enriched in elements processed
in the stellar interiors, AGB-stars play a major role in the chemical
enrichment of galaxies.

The mass loss mechanism seems to operate irrespective of the chemistry
(O-rich or C-rich) or the variability pattern (irregular, semi-regular
or regular) of the star. However, when it comes to the details the
situation becomes more uncertain. The mass loss dependence on stellar
parameters, its evolution with time for individual sources and the
geometry are important aspects that need to be understood for the
study of AGB-stars in a broader context.

\subsection{Dependence on stellar parameters}

Different studies suggest that stars with higher main sequence mass
have higher maximum mass loss rates. The mass loss rate increases with
the pulsation period presumably because stars with higher main
sequence mass also have longer periods. However, the existence of a
period-luminosity relation means that the higher the mass the higher
the luminosity. Therefore, it is not clear whether it is the
regularity of the pulsation or the luminosity that causes the increase
with period.

For low mass loss rate AGB-stars the temperature in the stellar
atmosphere probably plays no role. Only C-rich Miras seem to follow a
weak trend with mass loss rate decreasing with increasing effective
temperature. In a sample of C-rich AGB-stars [close to complete within
500 pc] Sch\"oier \& Olofsson (2001) found no correlation
between the mass loss rate and the C/O-ratio, which is surprising
considering that the dust-to-gas mass ratio in a C-rich CSE should be
sensitively dependent on this.

Groenewegen et al. (1995) studied three stars in the Galaxy, LMC and
SMC with similar pulsational periods and luminosities and derived CSE
dust optical depths ratios of $\approx$15:10:1. They showed that the
dust-to-gas mass ratio varies significantly with the metallicity. This
does not necessarily mean that the mass loss rate varies significantly
with the metallicity. In fact, the evidence is that it does, but the
effect is not very strong.


\subsection{Dependence on time}

It is not known when the onset of mass loss occurs. It is likely that
the information lies among the low mass loss rate objects (Kerschbaum
\& Olofsson, 1999). At the other end, it appears that
the mass loss ceases abruptly as the AGB evolution is terminated.

The temporal variation of the mass loss rates is to a large extent
unknown. For the long term behaviour (10$^5$--10$^6$ yr) we are
restricted to statistical studies since we lack suitable observational
probes. From these studies it appears that on average the mass loss
rate increases with time. At the end of AGB evolution there is a
substantial increase in the mass loss, a so called superwind
phase. This is supported by the ratio between the CO J=2$\rightarrow$1
and J=1$\rightarrow$0 lines on a number of highly evolved OH/IR-stars
which give much higher values than the theoretical limit of two for a
steady mass loss rate (Heske et al. 1990). A reasonable explanation
is a relatively recent increase in the mass loss rate, which has
affected the J=2$\rightarrow$1 emission which comes from a smaller
region than the J=1$\rightarrow$0.

For the short time variations (10--10$^2$ yr) we are limited by the
spatial resolution of the observations. However, density modulations
in the wind of a M-Mira (IK Tau) corresponding to a time scale of
$\approx$10 yr have been reported (Hale et al. 1997).

On the intermediate time scales (10$^3$--10$^4$ yr) there is also
growing evidence for substantial variations in the mass loss
rate. Detached CO and dust shells have been detected around a number
of AGB and post-AGB stars (Olofsson et al. 1996; Lindqvist et
al. 1999; Waters et al. 1994; Izumiura et al. 1996, 1997; Hashimoto et
al. 1998; Speck et al. 2000) and multiple-shell structures have been
seen in scattered light towards IRC+10216 and a number of post-AGB
objects (Harpaz et al. 1997; Kwok et al. 1998; Sahai et al. 1998;
Mauron \& Huggins 2000; Murakawa et al. 2002; Fong et al. in
press). The detached shells of gas and/or dust presented in {\bf
Papers~I} and {\bf~II} represent a new evidence for mass loss
variations on intermediate time scales.

\subsection{Geometry}

The conclusion drawn from observations of sufficiently high
sensitivity and spatial resolution is that the AGB mass loss is
essentially isotropic, e.g., from OH maser imaging (Bowers \& Johnson
1990). However, there are examples among the low mass loss rate
sources where bipolar outflows have been found (Kahane \& Jura
1996). This picture of over-all spherical symmetry contrasts with the
appearance of post-AGB objects where clear axi-symmetry is the role. A
current acceptable picture is one of isotropic mass loss on the AGB,
except perhaps at the final stages. During post-AGB evolution a high
velocity wind, maybe inherently bipolar or channelled by a weak
equatorial density enhancement in the AGB envelope, will effectively
lead to an axi-symmetric CSE.

\subsection{Driving mechanism}

The mechanism behind the mass loss process has not been completely
resolved yet. The most invoked scenarios involve thermal winds
driven by the gradient of gas pressure, radiation-driven winds
receiving their momentum directly from the radiation field of the
stars and wave-driven winds (acoustic waves, shock waves,
magneto-hydrodynamic waves,...). (REFERENCES TO EACH MECHANISM)

The existing models of a dust-driven mass loss mechanism originating
from pulsating AGB stars predict mass loss rates and wind velocities
in qualitative agreement with observations, indicating that this is a
likely mass loss scenario. It is a two-stage process in which the
pulsation of the star pumps up the atmosphere to the extent that at
least a moderate mass loss is the result. High mass loss rates are
probably only attained when dust grains form in the extended
atmosphere. The grains are accelerated by the radiation pressure and
the gas is dragged along.



\section{The circumstellar medium around AGB-stars}

The primary observational consequence of the mass loss is the
formation of a circumstellar envelope (CSE) of escaping gas and dust
particles.  In many cases these envelopes are so thick that they
completely obscure the central star, thereby totally dominating the
emission. The first detection of such a CSE was done by Deutsch
(1956) who observed the existence of a common
circumstellar envelope in the binary system of $\alpha$ Her, an M-type
supergiant.

\subsection{Structure}

The gas is to a large extent molecular with a composition which
reflects the chemistry of the star. The molecules are located in
envelopes of different sizes (by far the largest ones being those of
CO and H$_2$), or shells of different radii and widths, depending on
their resistance to interstellar UV photons and the formation
routes. There are presently about 60 different molecular species
detected in AGB-CSEs.

The dust grains exist way beyond the molecular envelopes. The gross
features of the spectral energy distributions can be well modelled
using dirty amorphous silicates for O-rich CSEs and amorphous carbon
(featureless) and SiC (11.3$\mu$m) for C-rich CSEs. (REFERENCES)


\subsection{Kinematics}

The kinematical properties of CSEs can be estimated directly from the
line profiles. From extensive studies of CSEs around different types
of AGB-stars (Galactic Centre OH survey, CO surveys of bright C-stars
and M-type irregular and semiregular), the terminal wind velocities
are found to stretch about an order of magnitude, from $\approx$3 to
30 km/s. For AGB-CSEs the data support a scenario where the terminal
expansion velocity is reached within $\approx$10 stellar radii.

There is a tendency for the terminal velocity to increase with
increasing main sequence mass, probably an effect of its dependence on
luminosity. This tendency is also indicated by the correlation between
the expansion velocity and the pulsation period, which is very likely
positively correlated with the stellar mass. There is also some
evidence that the expansion velocity depends on the metallicity. For
instance, AGB OH/IR-stars detected in the LMC have expansion
velocities lower than similar Galactic stars. Galactic centre stars
have higher expansion velocities than similar stars in the Bulge and
the solar neighbourhood, which presumably have lower
metallicities. The results also indicate that given the mass loss rate
and pulsational behaviour, a C-CSE will have a higher expansion
velocity than an O-CSE.




\section{Motivation for this thesis work}

The study of CSEs around AGB-stars is of fundamental astrophysical
importance for several reasons: the emission of CSEs is a measure of
the rate at which these stars lose matter, it is also a measure of the
rate at which these stars replenish the ISM with matter (metals and
dust grains), and they are very likely progenitor of PNe.


\subsection{{\bf Papers I \& II}: The observability of circumstellar
envelopes$^1$}\addtocounter{footnote}{1}\footnotetext{The
word {\it envelope} is used in this thesis to designate the
circumstellar medium around a star.  If not specified, it can
be attached-to or detached-from the star.  On the contrary, the word
{\it shell} is employed for circumstellar material of detached nature
and therefore is equivalent to a detached envelope.}

There is a substantial number of observational probes of mass loss
rate for the study of CSEs around AGB-stars: measurement of emission
lines of rotational transitions of various molecules (particularly
\co~which emits the strongest lines in rotational transitions in the
ground vibrational state), measurement of the infrared continuum
emission produced by dust particles, study of maser emission lines,
absorption lines in the optical and infrared, scattering and emission
from resonance lines of KI and Na\,D, scattering of optical and near
infrared light from circumstellar dust,... The first two probes are by
far the most commonly used.

The interpretation of the CO emission is hampered by the fact that it
depends on the excitation as well as on the chemistry (particularly
the photodissociation by the interstellar radiation field) of the CO
molecules. Hence, the relationship between the density distribution
(and consequently the mass loss history) and the CO brightness
distribution is uncertain. Infrared emission from dust is the only
probe of CSEs that is not destroyed by the interstellar radiation
field and therefore these observations trace the long-term history of
mass loss. However, the data are often of very poor spatial
resolution. Hence, alternative ways of observing
the CSEs are necessary.

The observation of optical stellar light scattered in the CSEs has
some advantages.  Typically, the achieved spatial resolutions are high
even under poor conditions.  The feasibility of optically observing
CSEs was first shown spectroscopically by Bernat \& Lambert
(1975).  They used a method whereby normalized on-star
spectra are subtracted from off-star spectra, to reveal the faint
circumstellar emission.  However, the number of such observations made
over the last years has remained small and only very bright stars have
been studied.  The smallness of this number may have different causes:
the measurements are difficult to make, the quantitative
interpretation is awkward and the possibility that, e.g. the resonance
scattering agents such as atoms of Na and K, are depleted onto dust
particles or simply ionized making the derivation of basic quantities,
such as the mass loss rate, difficult.

In {\bf Paper~I} we presented the first optical images of stellar
scattered light from large detached gas/dust shells around two C-rich
stars.  They confirmed results obtained in CO radio line observations,
but also revealed new and interesting structures. 

The presence of a dusty medium in the detached shells, which scatters
the light from the central source, and the fact that these shells can
be spatially resolved by the advent of modern imaging techniques make
them ideal targets for polarimetric studies.  Furthermore, imaging
polarimetry can be used as a strong tool to pinpoint the dust grains
as the scattering agent.  Following this spirit, we presented in {\bf
Paper~II} polarimetric observations of the detached shells previously
detected through direct imaging.


\subsection{{\bf Papers III \& IV}: The derivation of mass loss rates \& SiO abundances}

Several methods have been proposed and used to determine the mass loss
rates from red giants. They all rely on modelling of the circumstellar
emission by dust in the infrared or by molecules in the radio, and on
an estimate of the object's distance. Therefore, these methods can
only be applied to well studied sources. Relations between the mass
loss rate and some near infrared colors are also used. As the colours
are distance independent, these relations can be applied in principle
to large samples of stars for which little information is
available. However, these colour estimators only provide an order of
magnitude values.

Detailed modelling of CO line emission is expected to give mass loss
rates that are accurate to within a factor of a few provided that the
assumption of a standard CSE is correct.  In {\bf Paper~III}, we have
made use of a Montecarlo code to model circumstellar CO radio line
emission from a sample of M-type AGB stars.  Through a detailed
radiative transfer analysis combined with an energy balance equation
for the gas, we have determined the mass loss rates of the stars in
the sample.

SiO is expected to be a major component of grain nucleation and growth
in O-rich stars. These processes are, however, difficult to study in
detail since they do not proceed at thermal equilibrium.  Using the
mass loss rates obtained from the analysis of the CO data, we have
used the Montecarlo code in {\bf Paper~IV} to derive the SiO
abundances in the CSEs in an attempt to study the gas depletion onto
dust grains.
