We have carried out observations of R Dor in the near infrared (1.25m) and the red (855nm) using aperture-masking. This technique involves modifying the telescope pupil with a mask, the rationale for which has been discussed elsewhere [Haniff & Buscher 1992, Buscher & Haniff 1993, Bedding et al. 1995, Haniff 1994]. In brief, an aperture mask with a small number of non-redundantly spaced holes provides more accurately calibrated measurements at the full diffraction limit. This comes at the expense of lower sensitivity and poorer spatial-frequency coverage, and a good compromise in the photon-rich infrared regime is to use an annular mask [Haniff & Buscher 1992]. This has full spatial frequency coverage while being minimally redundant: roughly speaking, each baseline is measured twice. Furthermore, a thin annulus whose width is comparable to the atmospheric coherence length (r(0)) largely retains the advantages of accurate calibration and enhanced resolution. To date, however, results from annular masks have only been published for binary stars [Haniff et al. 1989].
In the visible regime, where photon noise generally dominates over atmospheric noise, an annular mask is not a good choice. Instead, improved sensitivity and spatial-frequency coverage is best achieved by using a long slit [Buscher & Haniff 1993].
Observations with the 3.5-m New Technology Telescope (NTT) were made with the SHARP infrared camera [Hofmann et al. 1992]. Details of the experimental setup are given in Bedding et al.1993 and Bedding et al.1995. We observed R Dor on 1993 August 7 using an aperture mask with seven holes arranged in a non-redundant two-dimensional configuration. Each hole had an effective diameter (as projected onto the primary mirror) of 25cm and lay on a circle of diameter 3.05m. The wavelength was 1.25m, selected using a standard J filter. For both R Dor and a calibrator star ( Ret), we obtained 500 short (0.1s) exposures.
Fringe visibilities were extracted from the averaged power spectrum and were calibrated for atmospheric and instrumental effects by dividing by visibilities from the calibrator star. The upper panel of Fig 1. shows these calibrated visibilities as a function of baseline length. It is clear that R Doradus is resolved, despite the fact that the visibility at this wavelength does not fall below 50%, even on the longest baselines. There is a scatter in the visibility measurements at fixed baselines whose cause is unclear, although it may be due to a mismatch in seeing conditions for observations of R Dor and its calibrator star. Fitting a uniform-disk model to these data gives a diameter of 57+/-5 mas (milliarcsec).
Note that we expect the calibrator star Ret (HR 1264; V=4.5; M4 III) to be slightly resolved. This star has no measured angular diameter, but Ochsenbein & Halbwachs 1982 estimate a diameter of 11mas based on its spectral type. Using the V-K calibration of Di Benedetto1993 gives 7.5mas. Correcting the visibility curve of R Dor for the non-zero size of the calibrator star leads to a slight upwards revision in the diameter by 0.5-1mas, depending on the actual diameter of Ret.
We also observed R Dor on 1993 August 6 using the J filter, this time with an annular mask that had an effective outer diameter of 3.3m and a width of 20cm (lower panel of Fig. 1). Further observations using the same setup were obtained almost two years later, on 1995 July 19 (Fig 2). The former data set gave a uniform-disk diameter of mas and the latter gave mas, both in good agreement with the results from the 7-hole mask. The anomalous feature seen at short baselines in fig.vis-NTT1995 is due to miscalibration caused by slight differences in seeing between observations of the object and its calibrator star [Haniff & Buscher 1992]. The effect is seen to lesser degrees in all of the plots presented here, and the affected data were excluded from the fits to the visibility function.
We observed W Hya with the annular mask on 1993 August 8. These observations used a variable filter (CVF) with a resolving power of about 50, set to a wavelength of 1.45 micron. Two calibrator stars were used: HR 5192 and HR 5287. The result, shown in Fig 3, is a uniform-disk diameter of 44+/-4 mas.
On 1995 January 13 we observed R Dor and Ori at 855nm with a slit mask using the 3.9-m Anglo-Australian Telescope (AAT). We used the MAPPIT facility (Masked APerture-Plane Interference Telescope; Bedding et al. 1994), which consists of optical elements mounted on fixed rails at the coudé\ focus. The system differed in two important respects from that described by Bedding et al. Firstly, the wavelength-dispersed system was not used. Instead, the prism and cylindrical lens were replaced by an interference filter (nm, nm). Secondly, the detector was a CCD with on-chip binning, similar to the system used by Buscher et al. 1990.
For each observation we obtained 10000 short (13ms) exposures of the target followed by an identical number of the calibrator star. The calibrator for R Dor was again Ret, while for Ori we used Ori. The aperture mask was a narrow slit whose effective width was 8cm. The slit was aligned diametrically so that the maximum baseline corresponded to the full 3.89m aperture of the AAT. The central 1.51m was obscured by the secondary mirror, which results in a gap in spatial-frequency coverage: baselines having lengths between 1.19m and 1.51m are not sampled.
For R Dor we obtained two observations with the slit oriented at position angle 65 on the sky and a further observation at 145. Fig 4 shows calibrated visiblities for these three observations, as well as for a single observation of Ori obtained at position angle 115. The visibilities of R Dor have been corrected for the non-zero angular size of the calibrator star, assumed to be 10mas. This correction is only a few percent, even at the longest baselines. Note that fringe visibilities from alpha Ori are likely to be affected by the presence of surface features [Buscher et al. 1990, Wilson et al.1992]. However, our aim here is to establish that R Dor exceeds alpha Ori in angular size, which is demonstrated by our observations, at least at this wavelength. We should note that our measured angular diameters will be affected by limb darkening and the presence of hotspots and non-circularity, which may be different for the two stars. By calculating the bispectrum of each observation, we find that R Dor shows non-zero closure phases (Fig 5). These imply an asymmetrical brightness distribution similar to that previously found for the supergiant alpha Ori and Mira variables such as o Cet [Wilson et al.1992, Haniff et al. 1992, Tuthill et al. 1994a]. R Dor is the first non-Mira giant from which non-zero closure phases have been detected. Note that Di Benedetto & Bonneau 1990 found anomalously high visibilities on long baselines for the star beta And (M0 III) which may indicate surface structure, but those measurements did not provide phase information.
The limited position-angle coverage of our data prevents image reconstruction and R Dor is clearly a good candidate for more detailed observations, particularly in view of its large angular size.