\chapter{Stellar light scattered in the circumstellar medium of AGB stars}
\section{The targets}
\markboth{CHAPTER 3. SCATTERED STELLAR LIGHT}{3.1. THE TARGETS}
A survey of circumstellar CO emission on a sample of bright carbon
stars (Olofsson et al. 1993) revealed the existence of a
few sources with detached gas shells.  The large shell distances from
the stars make them ideal candidates for direct/polarimetric imaging
in the optical.  Therefore, the backbone of this project is centred on
the study of the circumstellar material around these stars seen in
scattered stellar light.  Some other sources with detected dust shells
were incorporated to this work at a later point.

\subsection{The carbon stars with detached CO shells}
\paragraph{R~Scl.}
R~Scl is a carbon star (C/O$\approx$) in the southern sky with a 370
days semiregular variability period.  Its visual magnitude is 5.8. 
The distance derived from the period-luminosity relation for carbon
stars (Groenewegen \& Whitelock 1996) is 360 pc.

The CO brightness maps of R~Scl (Olofsson et al. 1996) show a
marginally resolved detached shell which appears to have detached
fairly recently ($\leq$10$^3$ yr).  This shell radius is $\approx$
10\arcsec, or 5.2$\times$10$^{16}$ cm at the adopted distance.  The CO
shell is expanding with a velocity of 15.9 km/s.  Detections from
other molecules, such as HCN, CN and CS, point to a dense shell where
these molecules are still relatively abundant and excited. This source
also shows an excess at 60\micron.

Additional information on the circumstellar medium of R~Scl is
obtained from the spectroscopic observations by Gustafsson et
al. (1997). They show that there exist KI resonance line scattered
emission out to at least 12\arcsec from the star, and that its
brightness decreases as the third power of the angular distance from
the star, i.e., they see no hint of a detached shell. These
observations motivated the search for scattered stellar light using
resonance line filters, despite the disadvantages explained in Sect.
2.1.3.

\paragraph{U~Ant.}
U~Ant is a carbon star (C/O$\approx$) in the southern sky with
irregular variability.  Its visual magnitude is 5.5.  The distance
derived from the Hipparcos parallax is 260 pc.

In the case of U~Ant the CO data clearly reveal a detached shell
(Olofsson et al. 1996).  The shell radius of $\approx$41\arcsec, or
1.6$\times$10$^{16}$cm at the Hipparcos distance, is relatively well
determined, but the width is unresolved at $\approx$15\arcsec resolution.
The CO shell expansion velocity is 18.1 km/s. The CO data also contain
evidence that this star has a central spatially unresolved envelope
that expands with a much lower velocity.

Deconvolved IRAS 60 and 100\micron~observations of U Ant have shown
the existence of two extended dust shells (Izumiura et al. 1997).  The
(uncertain) size of the inner shell, apparent as a brightness
distribution broader than the PSF, is consistent with that of the CO
shell.  The outer shell has an inner radius of 3' and no CO
counterpart.

\paragraph{S~Sct.}
S~Sct is a carbon star (C/O$\approx$1.07) visible in both hemispheres. 
It is a semiregular pulsator with a period of 148 days.  Its visual
magnitude is 6.8.  It is located close to the galactic plane (b=-3.4),
i.e, in a crowded field which certainly complicates the imaging of its
circumstellar environment.  The distance estimated assuming the star
has an absolute K-magnitude of -8.1 (Frogel et al. 1980)
is 540 pc.

The CO radio line maps of the circumstellar medium around this star
reveal the presence of CO emission from a detached shell with a radius
of 66\arcsec, which corresponds to 5.4$\times$10$^{17}$cm at the adopted
distance.  The existence of the present mass loss is also inferred from
these CO maps.  This stars fall in the region of the IRAS two-colour
diagram which shows 60\micron -excess sources.  Models of the observed
spectral energy distribution (SED) based on the spatial information
from the CO maps explain the measured IRAS fluxes at 60 and
100\micron~in terms of thermal emission from a dust shell (Groenewegen
et al. 1994).

\paragraph{TT~Cyg.}
TT~Cyg is a northern sky carbon star (C/O$\approx$) that pulsates
semiregularly with a period of 118 days. Its visual magnitude is 7.6. 
It is located close to galactic plane (b=4.9) and the distance derived 
from the (uncertain) Hipparcos parallax is 510 pc.

TT~Cyg provides a splendid example of an AGB star with highly episodic
mass loss.  Interferometric CO radio line observations (Olofsson et
al. 2000) show that this star is surrounded by a gas
shell with a radius of 35\arcsec, or 2.7$\times$10$^{17}$cm (see
Fig.~\ref{ttcygshell}).  The shell is geometrically thin ($\approx$
2.5\arcsec) and has a remarkable overall spherical symmetry but its
centre is displaced with respect to the star.  It expands with a
velocity of 12.6 km/s.  TT~Cyg is presently losing mass at a modest
rate and with a low expansion velocity.

\begin{figure*} \centering \vspace{9.6 cm}
\special{psfile=ttcyg.ps hoffset=50 voffset=-10 hscale=60 vscale=60 angle=0}
\caption{CO (J=1$\rightarrow$0) brightness map towards the C-star TT~Cyg showing a geometrically thin detached shell at 2.7$\times$10$^{17}$ cm from the star (Olofsson et al. 2000)} 
  \label{ttcygshell}
\end{figure*}

\paragraph{U~Cam.}
U~Cam is a carbon star (C/O$\approx$) visible in the northern sky. It 
is a semiregular variable  with a period of ??? days. Its magnitude 
is 7.4 in the visual. The distance derived assuming the star
has an absolute K-magnitude of -8.1 (Frogel et al. 1980)
is 500 pc.

Radio interferometry observations towards this star in CO rotational
lines (Lindqvist et al. 1999) show a geometrically thin
($\approx$2\arcsec) shell of gas at a distance of 8\arcsec~from the
star, or 6$\times$10$^{16}$cm at the adopted distance.  The expansion
velocity of this shell is relatively high, 23 km/s.  The shell has also
been detected in HCN and CN lines (Lindqvist et al. 1996).


\subsection{Other sources}

\paragraph{U~Hya.} 
U~Hya is a southern sky carbon star.  It pulsates semiregularly with a
period of 450 days.  Its visual magnitude is 4.9 and the distance
derived from the Hipparcos parallax is 160 pc.  

High resolution image reconstruction techniques applied to the IRAS 60
and 100\micron~data reveal the presence of a detached ring around
U~Hya (Waters et. al 1994).  The ring radius is 1\amin.75 and
its width is not resolved.

\paragraph{R~Hya.}
R~Hya is a late M-type Mira variable visible in the southern sky.  The
period of variability is 390 days.  It is a 6.4 magnitude star in the
visible and the distance is about 110 pc.

An extended emission component around R Hya is clearly found in the
reconstructed IRAS 60 and 100 \micron~images which firmly indicates
the existence of an extended circumstellar dust envelope around this
star (Hashimoto et al. 1998). The IRAS data further suggest the dust
envelope being detached from the central star.  Its radius being
3'-4'.  It is, so far, the only O-rich source with a detected detached
dust shell.

\paragraph{X~TrA.}
X~TrA is carbon star in the southern sky with irregular variability. 
Its visual magnitude is 5.6 and the distance estimated assuming a 
luminosity of 4000 \lsun~is 460 pc.

A detached shell centred on the stellar position is seen in
reconstructed IRAS 60 \micron~images of X~Tra (Izumiura et
al. 1995). The radius of the shell is 2\amin.3.

\paragraph{VX~Sgr.}
VX~Sgr is an M-type supergiant visible in the southern sky.  It is a
long-period (732 days) semiregular variable.  Its magnitude is 10 in
the visual and it is located in the galactic plane (b=-1) towards the
centre of the Galaxy.  The distance to VX~Sgr is 1.7Kpc but it can be
lower by a factor of 4.

Interferometric observations at millimeter and mid-infrared
wavelengths (Greenhill et al.1993) show that SiO maser
emission arises from a region around VX~Sgr which is about 2.6 stellar
radii across.  The distribution of the emission is asymmetric.  The
structure of the 11 microns dust emission from the circumstellar shell
has also been resolved.  The effective radius at which dust condenses
is about 4.6 stellar radii.

\section{Tools for the data analysis}
\subsection{A simple analytical approach}
Provided that an estimate of the ratio of circumstellar-to-stellar
fluxes (CS/S-ratio), [i.e, the amount of stellar light scattered in
the circumstellar medium relative to the direct stellar light], can be
given for a certain object, a number of analytical formulae can be
used for a simple analysis of the observations.  Thus, they can be
analysed in terms of line or dust scattering of central stellar light
in a geometrically thin, spherical shell.  Such study, however, has to
be restricted to the optically thin regime.

For example, the maximum CS/S-ratio in a given filter cannot exceed

\begin{equation}
    \frac{F_{sc}}{F_{\ast}} \leq 
     \frac{\alpha_{eff} \delta \lambda_{sc}}{\Delta 
    \lambda} ,
\end{equation}
%     
where $\alpha_{eff}$ is the ratio of the average stellar flux
in the scattering wavelength range, $\delta \lambda_{sc}$, and
the average stellar flux in the filter passband, $\Delta \lambda$. 
This estimate yields different values depending on the scattering
mechanism and therefore, when compared to the observed CS/S-ratios,
can be used to hint the scattering agent.  A more strict limit is
provided by the fact that the observed surface brightness in a filter
cannot exceed the source function for scattering at the position of
the shell. 

In the case of atoms or single-sized grains uniformly distributed over
the shell, the optical depth is given by the ratio of the 
total scattering surface and the geometrical surface, i.e.,

\begin{equation}
    \tau=\frac{N_{sc} \sigma_{sc}}{4\pi R_{sh}^2}\,.
\end{equation}

Under the assumption of optically thin scattering in a shell with no 
velocity gradient, the expected CS/S-ratio is given by,

\begin{equation}
    \frac{F_{sc}}{F_{\ast}}=\frac{F_{{sc},\lambda} \delta
    \lambda_{sc}}{F_{\ast,\lambda} \Delta \lambda_{f}} = \frac{\delta
    \lambda_{sc}}{\Delta \lambda_{f}}\, \frac{1}{4\pi R_{sh}^2} N_{sc}
    \sigma_{sc}\alpha_{eff},
\end{equation}
%
where $N_{sc}$ is the number of scattering atoms, $\sigma_{sc}$ is the
scattering cross section, and $R_{sh}$ is the shell radius. Again, 
the derived values differ between resonance line and dust scattering.

In the case of resonance line scattering and assuming a Boltzmann 
distribution of the level populations,

     \begin{equation}
	N_{sc}=\frac{\eta_{n} f_{X} M_{sh}}{\mu m_{H}} \frac{g_{l}
	e^{-\frac{E_l}{kT}}}{\cal{Z}}\,,\,\,\,\,\,\,\,\,\,\,\,\,
	\sigma_{sc}=\frac{1}{\Delta\lambda_{sc}}\frac{1}{4
	\epsilon_{0}} \frac{q^2\lambda^2f}{m_{e}c^2}\,,
     \end{equation}
%     
where $M_{sh}$ is the shell mass, $\mu$ is the mean molecular
weight, $\cal{Z}$ is the partition function, $g_l$ is the statistical
weight of the lower level, $E_l$ is the excitation energy of the lower
level, $f_{X}$ is the number abundance of species X with
respect to H, $\eta_{n}$ is the fraction of X that remains in
neutral form, and $f$ is the oscillator strength of the line.

In the case of dust scattering, and assuming single-sized, spherical 
grains, 

     \begin{equation}	 
	N_{sc}=\frac{3 f_{dg} M_{sh}}{4\pi \rho_{g}
	a^3}\,,\,\,\,\,\,\,\,\,\,\,\,\, \sigma_{sc} = \frac{128 \pi^5
	a^6} {3\lambda^4} \, {\rm Re} \left[ \left (\frac{\tilde
	n^2-1}{\tilde n^2+2}\right)^2 \right]\,,
     \end{equation}
%  
where $f_{dg}$ is the dust-to-gas mass ratio, $\rho_{g}$ is the
density of a dust grain, $a$ is the grain radius, and $\tilde n$ is
the complex index of refraction of the dust particle relative to the
surrounding medium.  In the above derivation it is assumed that the
condition for Rayleigh scattering is fulfilled (i.e.,
$a/\lambda$$\ll$0.16).



\subsection{A Montecarlo scattering code}

In order to gain a deeper insight a more sophisticated tool is
required, especially when it comes to the analysis of the polarimetric
data. A Montecarlo scattering code can be used to compute model 
brightness distributions to be compared with the observations. We have 
made use of a modified version of the scattering code by M\'enard 
(1989). 

The code only treats the scattering of stellar photons by dust grains. 
Consequently, we assume in this analysis that the dust grains are the
scattering agent responsible for the bulk of the detected polarised
light.  In principle, the polarisation due to line scattering has the
same angular behaviour as in the case of Rayleigh scattering by dust
grains.  There are processes that may decrease the polarisation of
line scattering, e.g., the presence of a weak magnetic field (Hanle
effect), non-coherent scattering due to collisions, and/or
interference of atomic sublevels, but none of them is expected to have
any sizeable effect in our case.  Therefore, our assumption can only
rest on optical depth effects that would make the polarisation
introduced by either scattering agent more or less effective.

A number of photons, emitted by the star, are followed through the
dusty CSE, and the new photon paths and Stokes intensities are
recalculated after each scattering event.  Two-dimensional scattered
light images are obtained from the number of photons that escape the
CSE.

The outer radii of the envelopes ($r_{out}$) are constrained by the
observations.  A set of four parameters are allowed to vary between
models: the envelopes inner radii ($r_{in}$), the grains number
densities at the inner radii ($n_{in}$), the density variations in the
envelopes and the grain size distributions.  We have used an assumed
density law [given by a constant mass loss and a uniform expansion
with a smooth decrease (r$^{-\alpha}$) inwards the inner radii] and
grain size distribution [a power law of exponent $\beta$ in the range
between a$_{min}$=0.05 \micron and a$_{max}$=2 \micron].  The inner
radii are determined by fitting the peak radius of the polarised
intensity profiles and the value of $\alpha$ is derived from fitting
its width.  The number densities at the inner radii are well constrained
by the CS/S-ratios.  Finally, the value of $\beta$ is obtained from a
comparison of the model and observed total intensity profiles since this
parameter is very sensitive to the amount of forward-scattering.

The inner radii [along with the outer radii determined from the
observations] provide a direct estimate of the envelopes widths.  The
dust masses contained in the envelopes can be derived from

     \begin{equation}	 
	M_{d}=\frac{16}{3} \left ( \frac{\beta -1}{\beta - 4} \right )
	\pi^2 \rho_{gr} n_{in} r_{in}^2 a_{min}^3 a_{max}^3 \left (
	\frac{a_{max}^{\beta - 4} - a_{min}^{\beta -
	4}}{a_{max}^{\beta - 1} - a_{min}^{\beta - 1}} \right ) \left
	( r_{out} - \frac{\alpha + 2}{\alpha + 3} r_{in} \right ) \,,
     \end{equation}
%
where $\rho_{\rm gr}$ is the density of an amorphous carbon grain.

Under the assumption that the scattering by dust grains is the only
means of introducing significant polarisation in the scattered stellar
light, a comparison between the model and observed total intensity
profiles provides with an estimate of the amount of scattered stellar
light that is due to other scattering agents, e.g., resonance line
scattering.

\section{The information carried by the scattered stellar light}

Scattered stellar light was only detected in two of the targets: R~Scl
and U~Ant. For the other sources a combination of observational
limitations and/or unfavourable conditions for the detection of
scattered stellar light (shells located or with peak densities close
to the star, very extended shells, presence of crowded stellar fields)
hampered the imaging of the scattered emission. For TT~Cyg and S~Sct
we made tentative detections using a crude instrumental setup. Recent
data on S~Sct confirm the tentative detection with a much higher
S/N-ratio (see Appendix). 

In the case of U~Cam radio interferometry observations in CO
rotational lines show a geometrically thin shell of gas at a distance
of about 8\arcsec.  This small shell radius certainly lies at the
limit of observability in scattered stellar light using the direct and
polarimetric imaging techniques presented in this thesis work.  To
that, it can be added the fact that the observations towards this
northern star were done with the inadequate alt-az NOT (see
Sect.~2.1).  We cannot then exclude the existence of stellar light
scattered in the circumstellar regions of this star.

\subsection{R~Scl}
The direct images of R~Scl in the F77 and F59 filters presented in
{\bf Paper~I} revealed brightness distributions in the form of disks
of 21\arcsec~radius (1.1$\times$10$^{17}$cm).  The intensity in the
disks was essentially uniform but the quality of the data was such that
we could not exclude small-scale structure inside the disks.  

The observed CS/S-ratios in both filters were about three times higher
than the maximum allowed CS/S-ratio for resonance line scattering.
However, they lay well below 1, which is the maximum value for dust
scattering.  A simple analytical approach indicated that dust
scattering alone could not explain the detected scattered light.  The
main problem being that the observed circumstellar scattered fluxes
were weakly dependent on wavelength.  This required dust grains of
radius $>$0.1\micron~which could not reproduce the observed
CS/S-ratios.  A more plausible scenario consisted in a major
contribution by optically thin dust scattering together with resonance
line scattering, shown by our calculations to be optically thick in
both filters.  Finally, a possibility that resonance line scattering
was fully responsible for the observed scattered stellar light could
not be ruled out from the analysis of the direct images.  The
inaccurate data calibration was such that a factor of a few in the
observed CS/S-ratios could be accommodated.

In {\bf Paper~II} we presented the polarimetry imaging results obtained
towards this star.  The images showing the Stokes parameters and the
polarised intensities in the F77 and F59 filters reveal ring-like
brightness distributions in scattered light, which are clearly
detached from the star.  The images showing the total intensities
reproduce fairly well, in both filters, the disk-like brightness
distributions observed in the direct images.  The polarisation degree
reaches a maximum value of 35-40\% in both filters at a distance that
agrees well with the outer radius of the total intensities.

The results obtained from the Monte Carlo scattering modelling of the
polarimetric data fit the observations very nicely.  They suggest the
presence of a geometrically thin dust shell at the position of
the observed total intensity outer radius.  The disk-like appearance
of the total brightness distributions, which are in principle
inconsistent with isotropic scattering in a geometrically thin shell in
the optically thin regime, results naturally if forward scattering
[inherent to the dust properties] is allowed for.  As much as 70\% of
the observed total intensities are reproduced by the scattering models. 
Therefore, there appears to be also room for some resonance line
scattering.


\subsection{U~Ant}
 The direct images of U~Ant in the F77 and F59 filters presented in
 {\bf Paper~I} provide very interesting results.  In the F77 filter
 image a geometrically thin, almost circular, ring with a diameter of
 $\approx$85\arcsec~is centred on the star.  This is very likely the
 result of limb brightening in a geometrically thin, essentially
 spherical shell.  The observations performed in the F59 filter show a
 quite different morphology of the circumstellar medium seen in
 scattered stellar light.  The appearance suggests a multiple-shell
 structure.  Three different shell components are discernible with the
 two outer ones not being concentric.  The shell radii are: {\it shell1} at
 25\arcsec (1.0$\times$10$^{17}$cm), {\it shell2} at 37\arcsec
 (1.4$\times$10$^{17}$cm) and {\it shell3} at 43\arcsec
 (1.7$\times$10$^{17}$cm).  A much weaker component, shell4, is seen in
 the F77, F59 and Str\"omgren b filters as a small bump in the radial
 brightness profile at $\approx$50\arcsec offset from the star.

 A simple analytical study indicates that the observed CS/S-ratios of
 the three main components ({\it shell1-shell3}) can be explained if
 resonance line scattering by circumstellar atoms of KI and NaI
 provides the bulk of scattered stellar light in the images.  It also
 suggests that the Na~D lines can produce optically thick scattering,
 while KI line scattering may be at least partly optically thin, and
 this would explain the different appearances seen in both filters. 
 Finally, it points to optically thin Rayleigh scattering by
 small-sized dust particles as responsible for the weaker {\it shell4}
 component.
 
 The polarimetry imaging results are presented in {\bf Paper~II}.  The
 images showing the Stokes parameters and the polarised intensities in
 the F77 and F59 filters reveal ring-like brightness distributions in
 scattered light, which are clearly detached from the star.  The
 images showing the total intensities reproduce fairly well, in both
 filters, the brightness distributions observed in the direct images.
 Of particular interest is the mismatch in position between the peaks
 of polarised intensity (which lie in {\it shell4}) and the size of
 the total intensity distribution (which falls off steeply outside
 {\it shell3}).  This suggests that the {\it shell4} component is only
 due to optically thin dust scattering, thus confirming the
 interpretation of the direct images.  The polarisation degree reaches
 a maximum value of $\approx$~50\% in both filters but this value is
 somewhat uncertain in view of the low S/N-ratio of the images.
 
 The Monte Carlo scattering code results also support the scenario
 suggested from the simple analytical approach to explain the direct
 imaging results.  The observed polarised intensity profiles are
 relatively well fitted by a geometrically thin dust shell at the
 position of the observed {\it shell4} component.  The model total
 intensities are about 30\% the observed ones, suggesting that the
 bulk of stellar light is scattered by KI and NaI atoms.  The model
 results also indicate that if the stellar light is scattered by the
 dust in the inner shell components, then it should show clear
 evidence of polarisation in these components as well, contrary to
 what is observed.



\section{The origin of the detached shells}

Unpuzzling the scenario under which the various detached gas shells
around AGB stars (detected in scattered stellar light and CO radio
line emission) have formed, is beyond the scope of this thesis work. A
brief description of the state-of-the-art is given below.

It is somewhat surprising that the only AGB-stars with detected
detached gas shells are low mass loss rate C-stars. However, it might
be possible that the high mass loss rate objects also have detached
shells, but their contrast against the normal envelope (e.g., in CO
emission) is much lower. Schr\"oder et al. (1998) suggested that
the shells are more prominent in low mass objects, since these can
drive (by radiation pressure on dust) substantial mass loss only
during a He-shell flash. The absence of detached gas shells around
M-stars could then be due to the different compositions of their dust
grains. However, Knapp et al. (1998) suggested that the presence of
multi-component CO radio line profiles towards a number of C and
M-stars may be related to episodic mass loss.

Two extreme scenarios for the origin of the detached shells could be
pictured: all the material in the shells being ejected at a very high
rate during a short period and evolving during the expansion, or the
ejected material interacting with a previous slow stellar wind and
leading to narrow shells of mainly swept-up gas. Both scenarios have
their pros and cons. The isotropy of the velocity and mass ejection
evidenced by, e.g.,the interferometric CO maps towards TT~Cyg, points
in the direction of a coordination of the ejection, i.e., something
that can be provided by a He-shell flash. However, the shells are
expected to broaden as they expand, due to thermal/turbulent
motions. Putting limits to the present random motion by using the CO
line shapes suggests highly episodic mass loss at rates that are
considerably higher than what can be driven by radiation pressure on
dust. It is most likely that the stars were losing mass at some rate,
and probably at a lower velocity, before the mass ejection and some
interaction could therefore be expected.

Of particular interest is the multi-component circumstellar medium
around U~Ant. The morphology resembles to a large extent the
multiple-shell structures (in the form of arcs, i.e., incomplete
shells centered on the star) seen towards the extreme carbon star
IRC+10216 (time interval 200--800 yr; Mauron \& Huggins 1999, 2000),
and the post-AGB objects IRAS 17150--3224 (200--300 yr; Kwok et
al. 1998), and CRL2688 (150--450 yr; Sahai et al. 1998), and similar
structures towards the M supergiant $\mu$~Cep where shells are seen in
KI emission (Mauron 1997).  In these cases the shells represent
density enhancements on a general $r^{-2}$ density law.  Suggestions
for mechanisms for the formation of these shell structures range from
modulated mass loss due to a companion (Harpaz et al. 1997), shock
waves in the CSE due to a close binary (Mastrodemos \& Morris 1999),
mass loss variations due to surface effects related to a magnetic
activity cycle strengthened by a binary companion (Soker 2000), and
pulsation induced effects internal to the star (Icke et al.  1992).
It is not clear whether the multiple-shell structure seen towards
U~Ant is of the same type.  An attractive alternative explanation is
that there exist only two gas shell components ({\it shell1} being
then a by-product of the PSF-subtraction), of which the outer one is
the shock formed by a fast, short-term wind running into a slower,
long-term wind, and the inner shell is the reverse shock set up by
this interaction.

\section{Achievements in Paper~I \& Paper~II}

\subsection{Feasibility of this type of observations}

One of the great accomplishments in this thesis is the fact that it
shows the feasibility of imaging stellar light scattered by the
circumstellar medium around AGB-stars. The techniques are far from
standard.  Thus, it required the experience gained in previous runs
before being able to achieve an optimal instrumental setup that
maximises the possibility of detecting the scattered stellar light. 
The success of this type of observations rests, however, on the fact
that they should only be performed [if only medium-sized telescopes
are available] towards bright stars with dense circumstellar material at
sufficiently large distances from the central star.

The reduction of the data has also been a crucial part of the project.
By far, the most difficult task has been to subtract the stellar PSF
present in the total intensity images.  Numerous ways of performing an
optimised PSF-subtraction have been tried out.  The results point
towards the fact that the quality of a subtraction is strongly
dependent on various factors, e.g. the S/N-ratio of the images, the
positioning of the stars behind the coronographic mask and the seeing
conditions.  Therefore, it is not possible to standardise the
reduction process.

\subsection{The circumstellar medium around R~Scl}

The work on R~Scl presented in {\bf Paper~I} and {\bf Paper~II} has
revealed that the structure of the circumstellar medium around this
star is more complex than previously known. The existing observations 
indicate the presence of shells of different composition.

An inner attached envelope extending out to 10\arcsec
(5.5$\times$10$^{16}$ cm) has been seen in emission radio lines of
HCN, CN and CS. These molecules require high densities and
temperatures in order to be excited so it is likely that their
emission originates close to the star in a present mass loss wind. 
Spectroscopic observations have shown a clear detection of KI
resonance line scattered light of circumstellar origin, which declines
as the third power of the angular distance from the star out to a
distance of about 10$\arcsec$.  This is also consistent with a steady
mass loss rate wind, estimated to carry about
10$^{-6}$\,M$_{\odot}$\,yr$^{-1}$.

The CO radio line observations towards this star cannot be easily
interpreted since the emission may emanate from both a present mass
loss envelope and a detached shell.  We have used a Monte Carlo code
to model the CO line emission considering a present mass loss
envelope.  The line intensities can be reproduced using a mass loss
rate of 1.1$\times$10$^{-5}$\,M$_{\odot}$\,yr$^{-1}$ but this is
inconsistent with the star being optically bright.  Furthermore, the
observed double-peaked CO(3-2) line profile is not well reproduced.
Thus, the emission must have a significant contribution from a
detached shell.  A crude estimate assuming that all of the CO radio
line emission comes from a detached shell suggested a lower limit
shell radius of about 9\arcsec (5.5$\times$10$^{16}$ cm) and an upper
limit shell width of 12\arcsec~(6.6$\times$10$^{16}$ cm), therefore,
lying approximately outside the present mass loss envelope.  The
scattered light images cannot exclude the presence of KI and NaI atoms
in this shell component.  Partly optically thick resonance line
scattering of stellar light stemming from this shell could be
contributing to the observed scattered light.  The fact that no
polarised scattered light is detected in this shell component suggests
that it contains very little dust.

The polarimetry imaging of the light scattered around R~Scl is
consistent with the existence of another shell component.  A thin
(2$\arcsec$, or 1.1$\times$10$^{16}$ cm) shell with a radius of
20$\arcsec$ (1.1$\times$10$^{17}$ cm) can be inferred.  The dust mass
is estimated to be a few$\times$10$^{-6}$\,M$_{\odot}$.  The
scattering modelling is able to explain the measured thermal dust
emission at far-IR wavelengths.  They also suggest that as much as
70\% of the total scattered stellar flux seen in the optical can be
due to scattering by dust grains.  However, there appears to be room
also for scattering due to KI and NaI atoms, which have strong
resonance lines inside the used filters.  Modelling of the CO line
emission has shown that a dust envelope of the size and mass estimated
from the scattering data would under normal circumstances (e.g., a
normal dust-to-gas mass ratio) be easily detected in CO radio line
emission.  However, it would produce highly double-peaked line
profiles in both the CO(2--1) and CO(3--2) transitions, and there is
no apparent evidence of this.  Therefore, this shell component must
contain little CO gas, and by inference very little gas.
Nevertheless, the separation between the gas and dust shell is
uncertain.

In conclusion, the data suggest the existence of three different
circumstellar components, an inner one due to the present mass loss
epoch of the star, a middle one producing the bulk of the CO radio
line emission, and an outer one mainly composed of dust.


\subsection{The circumstellar medium around U~Ant}

The results of {\bf Paper~I} and {\bf Paper~II} have shown the
existence of a number of enhanced density distributions in the form of
multiple detached shells around U~Ant seen in scattered stellar light.
This adds new interesting aspects of the circumstellar medium around
this star.

The direct and polarimetric images show the existence of four
different shell components.  The innermost component ({\it shell1}) is
uncertain because it lies in regions close to the star, where the
reduction process is less accurate.  The second component ({\it shell2}) is
markedly not centred on the star.  The third component ({\it shell3}) is the
brightest shell in scattered stellar light.  It clearly shows the
effects of limb brightening in an optically thin shell in the F77
filter.  Only the outermost component ({\it shell4}), weak in total
scattered light, is detected in polarised scattered light.  Modelling
of the polarised intensities shows that dust scattering is able to
explain all of the emission from this outer component.  The dust mass
is estimated to be a few$\times$10$^{-6}$\,M$_{\odot}$.  However, only
less than 30\% of the total scattered stellar light observed towards
U~Ant can be accounted for in this way.  Either a very different grain
composition, without polarising properties, or e.g. resonance line
scattering by K and Na atoms likely provides the bulk of the observed
scattered stellar light.  The former appears unlikely since the dust
component in {\it shell4} accounts also for the measured IRAS fluxes.
The latter is certainly possible.  In particular, the different
morphological appearances in the F77 and F59 filters can be attributed
to different optical depths in the KI and Na\,D resonance lines.  In
favour of this interpretation is also that only the {\it shell4}
component was (marginally) detected through direct imaging with a
Str\"omgen~b filter, which contains no resonance lines ({\bf
Paper~I}).

CO radio line maps of U~Ant reveal a detached CO gas shell
which coincides spatially with {\it shell3}.  The angular resolution of
the CO observations is rather poor ($\approx$15$\arcsec$), and the
dynamic range is limited.  Therefore, it cannot be excluded that there
exists also CO emission from, at least, {\it shell2} and {\it shell4},
but it must be considerably weaker than that of {\it shell3}.  The
detailed spatial structure of the CO gas can only be resolved by
interferometer observations.

In summary, there is evidence for a CO gas shell that coincides
relatively well with one of the shell components seen in resonance
line scattering of stellar light by atoms of K and Na.  Inside this
detached shell there is another component (maybe two) seen in
resonance line scattered stellar light but not in CO maps [likely due
to observational limitations].  Finally an external component
attributed to dust scattering has been detected in polarised scattered
stellar light. There is a good evidence in the case of U~Ant that the
dust and the gas have separated.  The reason for such a separation is
not clear.  It may be explained by a gas-grain drift scenario or by
the result of hydrodynamical effects.  In the former case, the drift
velocity is estimated to be about 3 km/s. 



\section{Outlook}

Well-calibrated, higher S/N-ratio images of the stellar light
scattered in the circumstellar medium of these stars would be
desirable.  Also, observations similar to those presented in this
thesis but done in high quality filters that contain no strong
resonance lines are an appropriate tool to discriminate between dust
and resonance line scattering.  Observations done in these filters are
especially interesting towards R~Scl where the existence of a detached
dust/gas shell is possible.  In particular, observations in filters
centred on the wavelength range between the F77 and F59 filters are of
great interest.  In such filters (e.g., H$\alpha$), the stellar flux
and the scattering efficiency lie in between their values at the
central wavelengths of the F77 and F59 filters in which we have
detected scattered stellar light of circumstellar origin.

Imaging polarimetry towards U~Ant in the F59 filter and in some
continuum filters and towards S~Sct in the F77 filter has been
recently performed (see Appendix).  The data awaits reduction and
analysis.  The images are of significantly improved quality.  In the
case of U~Ant they support the results presented in this thesis.  The
new observations of S~Sct provide a clear detection of polarised
scattered stellar light, thus confirming the tentative detection
suggested in the thesis.

Spectroscopic observations of the KI and NaD lines would also provide
an additional way to disentangle the contributions from dust and gas
scattering.  In high resolution such observations will also make it
possible to observe regions close to the star.  Therefore, they might
provide the only means to detect in scattered stellar light apparent
small shells like the one around U~Cam.  Spectropolarimetric
observations would provide simultaneously the information
obtained with polarimetric and spectroscopic techniques, but the
instrumental setup might become too elaborate to make this type of
observations feasible.

R~Scl and U~Ant are both obvious targets once radio interferometers
become available for southern sky objects.  Coronographic imaging
performed with STIS on board the Hubble Space Telescope are very
interesting in order to probe the structure of the scattered stellar
light at a higher spatial resolution.

Finally, a novel technique can be of great use for stars in the
presence of a crowded field of view.  This is the case of S~Sct,
TT~Cyg and VX~Sgr which lie in the vicinity of the galactic plane. 
The main idea is to obtain optical absorption spectra towards background
stars lying behind the envelopes.  The wide number of field stars and
the small distances to our targets would certainly provide a
reasonable number of candidates.  This type of observations has
already been done to probe the circumstellar envelope of IRC+10216
(Kendall et al. 2002) and they report successful
detections of the CSE around this star in the KI and Na~D resonance
lines.



