4 Imaging of circumstellar polarised light

   
4.1 Results towards R Scl

The images in the F77 (Fig. 1) and F59 (Fig. 2) filters of the circumstellar scattered light around R Scl display the measured Stokes parameters ($q_{\rm m}$, $u_{\rm m}$), the polarisation degree ($p_{\rm m}$), as well as the distribution of the total intensity ( $I_{\rm sh}$). The $q_{\rm m}$, $u_{\rm m}$, and $p_{\rm m}$ data, in both filters, reveal geometrically thin distributions of scattered polarised light, which are clearly detached from the central star (which lies behind the central mask). On the other hand, the $I_{\rm sh}$ images show disk-like distributions very similar to those obtained in the direct imaging observations presented in Paper I (the quality of the data is such that we cannot exclude small-scale structure inside the disks). These results are consistent with the presence of a hollow (meaning depleted of gas and/or dust inside a certain radius), spherically symmetric, detached shell around R Scl. Photons scattered along any line-of-sight passing inside the shell outer radius contributes to the observed total intensity, which is therefore detected as a disk-like structure. On the contrary, only those photons which are scattered nearly perpendicularly towards us produce polarised light. This 90 $\hbox{$^\circ$ }$ scattering takes place most effectively in the 2D-cut of the spherical shell which is contained in the plane of the sky through the star, and hence, ring-like structures, such as those exhibited by the Stokes and polarisation degree images, result. Thus, the imaging polarimetry observations effectively reveal the spatial structure of the scattering medium. They allow a determination of the shell inner radius (see Sect. 5.3), which is not measurable in observations of scattered light using direct imaging techniques.

Some quantitative results obtained from these images are also shown in Figs. 1 and 2. The vector maps show the polarised intensities ( $P_{\rm sh}$) and polarisation angles ( $\theta _{\rm sh}$) at different positions around the star. In both filters there is a centre-symmetric polarisation pattern, typical of isotropic illumination from a central point source.

The azimuthally averaged radial profiles (AARPs) of the $I_{\rm sh}$ images are relatively constant in both filters, i.e., at both wavelengths the scattered light shows a uniform-intensity brightness distribution. The AARP of $I_{\rm sh}$ in the F77 filter image extends to an outer radius of 20 $\hbox{$.\!\!^{\prime\prime}$ }$8 (corresponding to $1.1\times10^{17}$ cm at the adopted stellar distance of 360 pc). The outer radius is defined as the half power radius of a step function (convolved with the seeing Gaussian) fitted to the observed radial profile (this smoothed function was introduced in Paper I to provide a size estimate, as well as to show that the gradual brightness decline is not an effect of the seeing). The decrease in the total intensity inwards of 15 $\hbox{$^{\prime\prime}$ }$ is very likely not tracing the scattered light, but is probably a by-product of the PSF subtraction procedure, which is less accurate closer to the star. The AARP of $I_{\rm sh}$ in the F59 image is constant out to a radius of 20 $\hbox{$.\!\!^{\prime\prime}$ }$5. The errors introduced during the reduction of the images (locations of the stars, PSF subtraction, ...) can account for the small differences in the shell outer radii ($\lesssim$1 $\hbox{$^{\prime\prime}$ }$) as derived from the observations in both filters here and from the direct images in Paper I. CO radio line maps towards this star marginally resolve a tentative detached shell (Olofsson et al. 1996), with a peak intensity radius that is a factor of two smaller ($\approx$9 $^{\prime\prime}$) than the shell observed in the scattered light. The radial distribution of the CO( $J=3\rightarrow 2$) intensity, obtained with a spatial resolution of about 10 $\hbox{$^{\prime\prime}$ }$, is shown in arbitrary units for comparison.

Figure 3: Images showing the polarimetric information in the F77 filter of the light scattered in the circumstellar medium around U Ant. Upper left panel: measured normalized Stokes $q_{\rm m}$. Upper middle panel: measured normalized Stokes $u_{\rm m}$. Lower left panel: measured polarisation degree $p_{\rm m}$. Lower middle panel: brightness distribution of the scattered light $I_{\rm sh}$. The dashed circle marks the mean position of the maximum reached by the polarised flux. Upper right panel: vector map showing the polarised intensity ( $P_{\rm sh}$) and polarisation angle ( $\theta _{\rm sh}$) averaged over square-boxes of 3 $\hbox{$.\!\!^{\prime\prime}$ }$8 (the total intensity image is shown as a shadow). Lower right panel: AARP of the polarised intensity ( $P_{\rm sh}$; dash-dot-dot line), total intensity ( $I_{\rm sh}$; solid line) and polarisation degree ( $p_{\rm sh}$; asterisks) of the light scattered in the envelope. Fits of shell brightness distributions, convolved with the seeing Gaussian, to the total intensity have been added (dotted line; see text for details). The AARP of the CO( $J=2\rightarrow 1$) radio emission seen towards this star (Olofsson et al. 1996) is included for comparison (triangles). The CO peak value has been normalized to the most prominent peak of the fit to the total scattered intensity.

The total fluxes of the circumstellar scattered light are given in Table 2. They are, in both filters, derived from a step-function fit to the AARPs. These values are 0.8 and 0.7 times the total fluxes found in the F77 and F59 filter observations presented in Paper I, respectively. The uncertainties in the indirect calibration of our data in this paper and in Paper I are such that these differences are well accounted for. We estimate the values presented here to be accurate, on an absolute scale, to within a factor of three (see Sect. 2.3).

The AARPs of $P_{\rm sh}$ show that the scattered polarised flux increases outwards, peaking at positions which coincide with the outer radii derived from the AARPs of $I_{\rm sh}$. The rise is followed by a steep decline, which reproduces relatively well, in both filters, the decrease in total intensity outside the shell. The polarised fluxes are given in Table 2, and they are uncertain by a factor of about three.

The R Scl data are of limited S/N-ratio and this produces problems when producing images of the intrinsic circumstellar polarisation degree ( $p_{\rm sh}$), since this involves division of frames. To overcome this problem, we obtained the AARPs of the polarisation degree by direct division of the AARPs of $P_{\rm sh}$ and $I_{\rm sh}$. This provides values for the polarisation degree which are independent of the inaccurate data calibration. We have excluded the outermost points where the spread in the data results in highly uncertain values. The polarisation degree in the F77 filter reaches a maximum of about 33% at a distance of 20 $\hbox{$.\!\!^{\prime\prime}$ }$2 from the star. In the F59 filter the polarisation degree rises to 40% at 18 $\hbox{$.\!\!^{\prime\prime}$ }$6. The polarisation degree maxima agree well in radius with the outer radii of the total scattered intensities. There is only a weak dependence of the polarisation on wavelength. Since the detached shell lies at $\approx$20 $\hbox{$^{\prime\prime}$ }$ from R Scl, we estimate that there are no substantial effects on the values of $p_{\rm sh}$ due to the inaccuracy of the PSF subtraction. In any case, a lower limit to the shell polarisation degree is given by the measured polarisation degree ($p_{\rm m}$) which peaks at a value of $\approx$20% in both filters.

   
4.2 Results towards U Ant

Figure 4: Same as Fig. 3 in the F59 filter.

The polarimetric images of U Ant showing $q_{\rm m}$, $u_{\rm m}$, and $p_{\rm m}$ in the F77 filter (Fig. 3) and in the F59 filter (Fig. 4) reveal ring-like brightness distributions in scattered light, which are clearly detached from the star. The image showing $I_{\rm sh}$ in the F77 filter exhibits a fairly uniform disk which is somewhat limb-brightened. In the F59 filter, the presence of multiple shells can be discerned. These latter images reproduce fairly well, in both filters, the brightness distributions observed in the direct images of U Ant presented in Paper I. Of particular interest is the mismatch in position between the peaks of polarised intensity (marked as dashed circles on the total intensity images) and the size of the total intensity distribution. The clearly detached nature of the scattered light (both polarised and total) at a large distance from the star exclude the image reduction process (and in particular the PSF subtraction) as a possible reason for the mismatch.

Some quantitative results from these images are also shown in Figs. 3 and 4. In both filters the pattern followed by the vector lines is centre-symmetric, typical of a spherically symmetric distribution of material which is illuminated by a central source.

The AARPs towards U Ant appear more complicated than those obtained towards R Scl. In Paper I we tentatively introduced four circumstellar shells around U Ant. The bulk of the scattered light comes from shell3, of size $\approx$43 $\hbox{$^{\prime\prime}$ }$, which coincides with the detached shell seen in the CO radio lines (Olofsson et al. 1996). Substantially weaker emission comes from shell4, which lies outside shell3 and appears to be somewhat broader. In addition, two tentative shells (shell1 and shell2) inside shell3 were introduced to explain the inner peaks in the total intensity distribution (seen primarily in the F59 filter). These components are more uncertain since the images may still contain stellar light close to the star despite the subtraction of the stellar PSF. The best fits to the $I_{\rm sh}$ AARPs use the four shell brightness distributions (convolved with the seeing Gaussian) which were employed in Paper I: shell1 to shell3 are fitted using brightness distributions which correspond to optically thin, isotropic scattering in geometrically thin shells, while the fainter (and more extended) shell4 component is fitted using a Gaussian (see more details in Paper I).

 

 

Table 2: Observational results for R Scl and U Ant. The total and polarised scattered fluxes have an uncertainty of about a factor of three, but their ratio is considerably more accurate since the fluxes are obtained from the same images. The ratios of total scattered flux to stellar flux are estimated to be correct to within a factor of five (see text for details).

	Filter	Comp.	R	$\Delta R$	Total scattered flux	Polarised scattered flux	CS/S 1
			[ $\hbox{$^{\prime\prime}$ }$]	[ $\hbox{$^{\prime\prime}$ }$]	[erg s-1 cm-2]	[erg s-1 cm-2]
R Scl	F77		20.8		$2.2\times10^{-12}$	$5.2\times10^{-13}$	$6.7\times10^{-4}$
	F59		20.5		$1.1\times10^{-12}$	$2.9\times10^{-13}$	$7.8\times10^{-4}$
U Ant	F77	shell3	43.2	3.2	$1.4\times10^{-12}$
		shell4	46.1	10	$3.3\times10^{-13}$
		all shells			$3.0\times10^{-12}$	$3.4\times10^{-13}$	$7.1\times10^{-4}$
	F59	shell3	43.4	3.5	$7.3\times10^{-13}$
		shell4	46.1	10	$2.2\times10^{-13}$
		all shells			$2.0\times10^{-12}$	$1.3\times10^{-13}$	$1.1\times10^{-3}$

¹ The ratio of total scattered flux and stellar flux.

We will not make a quantitative study of the two inner shells due to the low S/N-ratios of the images. The two outer components lie at mean radii (of the results in the two filters) of $\approx$43 $\hbox{$^{\prime\prime}$ }$ and $\approx$46 $\hbox{$^{\prime\prime}$ }$, corresponding to $1.7\times10^{17}$ cm and $1.8\times10^{17}$ cm, respectively, at the Hipparcos distance of 260 pc. The fits also allow a rough determination of the shell widths. For shell3 we derive a value of $\approx$3 $\hbox{$^{\prime\prime}$ }$ ( $1.2\times10^{16}$ cm). In the case of shell4 the inferred value of $\approx$10 $\hbox{$^{\prime\prime}$ }$ represents the FWHM of the Gaussian fit. Some disagreements between the adopted brightness distributions and the observed AARPs are evident, in particular the widths of the multiple shells. This can be an indication of optical thickness in the scattering process since this would have a tendency to broaden the observed profiles. The total fluxes of the light scattered in the two outermost components are given in Table 2. The values are 2.5 and 2 times the total fluxes found in the direct F77 and F59 filter images presented in Paper I, respectively (which were calibrated using photometric standards). Thus, they are in agreement with the factor of about three in uncertainty which we estimate for the crude calibration method used here (see Sect. 2.3). The CO( $J=2\rightarrow 1$) radial intensity distribution (in arbitrary units) obtained with an angular resolution of about 15 $\hbox{$^{\prime\prime}$ }$ is shown for comparison. It coincides well with the bulk of the scattered emission, and an analysis of the data gives a CO shell radius of $\approx$41 $\hbox{$^{\prime\prime}$ }$ (Olofsson et al. 1996).

In both filters the $P_{\rm sh}$ AARPs reach a peak at a distance of about 47 $\hbox{$^{\prime\prime}$ }$ (1.9$\times$10¹⁷ cm) from the star, i.e., at the position of shell4. This is clearly outside the bulk of the scattered light which is shown in the $I_{\rm sh}$ images. We have indicated this by the dotted circles added to these images. Table 2 gives the derived polarised fluxes. The $p_{\rm sh}$ AARPs were obtained from direct divisions of the AARPs of $P_{\rm sh}$ and $I_{\rm sh}$. The low S/N-ratio of the U Ant data limits the reliability of the AARPs. They reach $\approx$50% at $\approx$50 $\hbox{$^{\prime\prime}$ }$ in both filters. This suggests at most a weak dependence on wavelength, the same result as for the scattering around R Scl. In Fig. 3 we have omitted the outermost points in the $p_{\rm sh}$ AARPs due to their large variations. The measured polarisation degree $p_{\rm m}$ sets a lower limit to the polarisation of the scattered light at a value of $\approx$10% in both filters.

The fact that the disk-like brightness distributions of the total scattered light lie, in both filters, inside the peak of the ring-like brightness distributions seen in the polarised intensity images is quite remarkable. In Paper I, we suggested the existence of a component (shell4) much fainter than, and outside, the main shell (shell3). Light scattered in this outer component was also detected in a continuum filter (Strömgren b; Paper I) at a level comparable to those in the F77 and F59 filters. This led us to suggest that the shell4 component is only due to dust scattering. The results obtained here from the imaging polarimetry observations confirm our suggestion.