2 Observations

   
2.1 Observational methods

The polarimetric observations of R Scl and U Ant were done in November 2000 and March 2001, respectively, with the EFOSC2 focal reducer camera on the ESO 3.6 m telescope. A summary of the observations is given in Table 1.

In all cases the observations were done through 5 nm FWHM filters centred on the resonance lines of NaI (589.0 nm and 589.6 nm; the D lines) [hereafter F59] and KI (769.9 nm) [hereafter F77]. These resonance lines, under the conditions commonly present in the CSEs around AGB stars, only cover a small fraction of the filter bandwidths. Therefore, observations taken in these filters contain information on the scattering by both the gas and the dust particles in the CSEs. These filters were chosen initially because spectroscopic observations showed the presence of extended circumstellar KI resonance line scattered light towards R Scl (Gustafsson et al. 1997). The subsequent observations reported in Paper I indicated a more complex situation where also dust scattering may contribute. Attempts to obtain images in standard filters, covering no strong spectral lines in AGB-CSEs, at the 3.6 m ESO telescope have proven to be difficult for our large dynamic range observations. Only in the Strömgren b filter was an acceptable image obtained (see Paper I). Therefore, we have continued to use our high-quality filters despite the difficulty to properly separate different scattering agents.

The energy flux of the stellar light scattered in the circumstellar medium is very low when compared to that of the central star. The images presented in Paper I show that they typically differ by (at least) a factor of 10³. In addition, the weak scattered light is spread over a sizeable area, substantially larger than the dominating part of the stellar point spread function (PSF), and long exposure times are required. Therefore, the use of a coronograph is essential for separating the light scattered in the circumstellar medium from the direct strong stellar light which is scattered in the Earth's atmosphere and the telescope, and for allowing long exposure times, which would otherwise lead to a saturation in the CCD images. An important factor is the size of the coronographic mask to be used. The ideal occulting mask is small enough to allow detection of light scattered in regions close to the star, but large enough that the direct stellar flux does not dominate the detected light or saturate the detector in too short exposure times. Following several tests, we selected a coronographic mask of $\approx$8 $\hbox{$^{\prime\prime}$ }$ in radius for all observations. A Lyot stop was used to avoid the diffraction pattern of the telescope spiders.

Even the use of a coronograph cannot eliminate the wings of the stellar PSF in the images, since the direct stellar light is scattered outside the coronographic mask by the Earth's atmosphere and the telescope. The presence of such a remaining stellar component in the images introduces difficulties when estimating the intensity distribution of the scattered light and it needs to be removed. Images of stars of about the same spectral type and magnitude as our targets, but not showing scattered light of circumstellar origin, were observed regularly during the night to trace the time variations of the stellar PSFs due to changes in the atmospheric seeing and the telescope focus. The template stars are given in Table 1. In this way, the subtraction of any remnant of the stellar PSF in the image can be performed in a rather accurate fashion. The detailed procedure for removing the stellar PSF is described in Paper I. Note, however, that the images showing the polarimetric information of the scattered light do not contain any stellar component after reduction. They are obtained from the subtraction of observations taken at orthogonal polarisation angles, and therefore any remaining (unpolarised) stellar light is essentially cancelled out (see Sect. 3).

   
2.2 The instrumental setup for EFOSC2

The imaging polarimetry with EFOSC2 was done using a rotating half-wave plate and a fixed polaroid. By rotating the half-wave plate in steps of 22.5 $\hbox{$^\circ$ }$ we obtained images in linear polarisation with position angles in steps of 45 $\hbox{$^\circ$ }$.

The observations of R Scl were done with a needle/spot coronograph, which turned out to produce images less neat than expected due to diffraction along the supporting needle. For this reason, this coronograph was replaced in the observations of U Ant by a small, black, metal disk supported by 7 $\mu$m-wide kevlar spiders.

The pixel plate scale of the images was set to 0 $\hbox{$.\!\!^{\prime\prime}$ }$32/pixel by binning the images by a factor of two.

   
2.3 Data calibration

In a quantitative analysis of the scattered light, the calibration of the data is of course essential. A calibration in physical units requires observations of spectrophotometric standards. Although this was our goal, the weather conditions during the runs did not allow us to observe calibration standards. However, to study the nature of the detected light, it is often enough to estimate the total flux of the light scattered in the circumstellar medium relative to the stellar total flux (in CCD counts). This requires images of the target stars without the coronographic mask so that the stellar total fluxes can be derived. Due to different degrees of cloud cover during the runs we were not able to obtain such data.

Instead we used an indirect method for deriving the fluxes. The stellar flux densities were calculated based on published magnitudes. The variability of our targets ($\approx$0.5 mag at visual wavelengths) introduces some uncertainty in the calculation, but the obtained values should be within a factor of two of the actual fluxes.

The scattered light fluxes were converted from CCD units to physical units in the following way. The counts/s were transformed to fluxes above the atmosphere by correcting for atmospheric absorption, telescope aperture with a central obstruction, telescope reflectivity, instrument transmission, filter bandpasses and transmission, and the quantum efficiencies and gains of the CCDs. This is the same approach as used in Paper I. A 20% uncertainty in the reflectivity, transmissions, efficiencies and gains, and a 50% uncertainty in the atmospheric absorption translate into scattered light fluxes that are accurate to within a factor of three. In all, we estimate that the ratios of the scattered flux (in the circumstellar medium) to the stellar flux given here are accurate to within a factor of five. It is important to emphasize that the ratios of polarised scattered flux to total scattered flux, i.e., the polarisation degrees, given here are relatively accurate, since they are estimated from the same images and hence are independent of the absolute calibration. An uncertainty in these ratios are introduced by the subtraction of the stellar PSF (see below), and we estimate that they are accurate to within 20%.

Furthermore, observations of spectropolarimetric standards are needed in imaging polarimetry in order to determine the polarisation introduced by the telescope and the instrument. Once again, such observations could not be done. Therefore, we were forced to neglect any instrumental polarisation. Finally, for an accurate calibration of the data one needs to observe regions close to the target stars in order to measure the sky polarisation, e.g., due to the presence of moonlight. We estimate that such polarisation has a negligible effect on our final results. Below we give some reasons which justify these assumptions, including the results from the observations of the template stars.