On 1992 November 22, 8.4 GHz VLBI observations of Centaurus A were obtained and three days later on 1992 November 25, 4.8 GHz VLBI observations were obtained with the SHEVE array. Both observations utilised similar arrays of telescopes. For the 8.4 GHz observations the participating telescopes were: Tidbinbilla (70 m), Parkes, Hobart, Narrabri, Mopra, Perth (15 m), and Hartebeesthoek. For the 4.8 GHz observations the participating telescopes were: Parkes, Hobart, Narrabri, Mopra, Perth (27 m), and Hartebeesthoek. The data were obtained and processed as described in chapter 2.
Figure 5.1: VLBI image of Centaurus A at 8.4 GHz from 1992 Nov. 22. Map peak, 1.5 Jy/beam. Contours, -1, 1, 2, 4, 8, 16, 32, 64% of peak. Beam FWHM, 1.9 
1.5 mas @ 6.7 
.
Figure 5.2: VLBI image of Centaurus A at 4.8 GHz from 1992 Nov. 25. Map peak, 0.7 Jy/beam. Contours, -1, 1, 2, 4, 8, 16, 32, 64% of peak. Beam FWHM, 3.1 2.6 mas @ -24.4 .
Several trial images were made of each data set, for instance including or excluding the data on baselines to Hartebeesthoek. Eventually the best images (Figures 5.1 and 5.2) were produced without the sparse Hartebeesthoek data.
The image at 8.4 GHz (Figure 5.1) is dominated by a bright component at the south-west end of the source, with components extending to the north-east. The structure is aligned along a position angle of 51 and has an angular length of approximately 35 mas. The bright south-west component is also the most compact, no more than 0.8 mas in extent.
The image at 4.8 GHz (Figure 5.2) is of a lower resolution than the 8.4 GHz image. The brightest component now lies midway along the source, with a further discrete component to the south-west and extensions toward both the north-east and the south-west.
The registration adopted for the images at 4.8 and 8.4 GHz is shown in Figure 5.3. The two images have been plotted on the same flux density scale after being convolved with a circular Gaussian beam of 3 mas FWHM (corresponding to the major axis length of the formal restoring beam from the 4.8 GHz image), rotated by 39 and aligned horizontally. The registration is based on two considerations. First, the relative positions and the morphologies of the components C1 and C2 are the same at 4.8 and 8.4 GHz. In particular, the component C1 is elongated and noticeably curved in both images and C1 is separated from C2 by a sharp pinching in both images. Second, the overall extent of the source at 4.8 and 8.4 GHz is the same. The bright and compact south-west component in the 8.4 GHz image is therefore aligned with the extension at the south-west end of the source in the 4.8 GHz image.
Figure 5.3: Montage peak, 2.7 Jy/beam. Contours, 5, 10, 15, 20, 25, 35, 45, 55, 65, 75, 85, 95% of peak. Beam FWHM, 3.0 mas.
The registration adopted is consistent with the previously suggested model for the sub-pc-scale structure of Centaurus A. Meier et al [1989] concluded that a self-absorbed core component was seen at 8.4 GHz but missed at 2.3 GHz at the south-west end of the source, and that a strong jet component was seen at both frequencies. The registration for the current data shows a component with a highly inverted spectrum at the south-west end of the VLBI source, with the north-east components possessing flat to steep spectra. The inverted spectrum component is taken to be the core of the radio source which is absent from images at 2.3 GHz, but can be seen weakly at 4.8 GHz and is the brightest feature at 8.4 GHz. The remaining components comprise the sub-pc-scale jet which originates at the core and is aligned at the same position angle as the inner part of the kpc-scale jet.
From Figure 5.3, the spectral index of the core component is 
( 
) between 4.8 and 8.4 GHz, allowing for the 10% error in the flux density scales (see chapter 2). Jones et al. [1996], from simultaneous VLBA observations, also find that the core has a highly inverted spectrum between 2.3 and 8.4 GHz, 
. The spectral index of the component C2 is 
and the spectral index for C1 is 
. Here the surface brightnesses of the images have been used to estimate spectral indices since the core does not appear as a distinct component at 4.8 GHz and therefore cannot be easily de-convolved from the restoring beam.
The spectral index of the core component is too highly inverted to be explained simply by synchrotron self-absorption, which can achieve a limiting spectral index of 
[Rybicki & Lightman 1979]. It is possible that an additional source of absorption is causing the 
spectral index, namely thermal bremsstrahlung (free-free) absorption. If we assume that the intrinsic spectrum of the core component is , at the limit for synchrotron radiation, then it can be argued that the additional steepening of the spectrum may be caused by a free-free absorbing structure which lies between us and the radio source. The expression for free-free absorption (e.g. Rybicki & Lightman 1979) can be used to estimate the amount of absorption, given assumptions about the electron density in the structure, its temperature, chemical composition, and the path length through the structure. Following Rybicki & Lightman [1979],
where
With an 
pc path length through ionised but overall electrically neutral Hydrogen (Z=1) of electron density 
and temperature 
K, the observed spectral index between 4.8 and 8.4 GHz of 
corresponds to an intrinsic spectral index, before free-free absorption, of 
(using the appropriate Gaunt factors; Karzas & Latter 1961).
There is no need to assume that C1 and C2 are free-free absorbed since their spectral indices are each less than 2.5. However, if the free-free absorption region extends beyond the core component to obscure components C1 and C2 with the same optical depth of material as is obscuring the core, unreasonably steep (in the sense of decreasing flux density with increasing frequency) intrinsic spectra are found.
If assumptions are made for the intrinsic spectra of components C1 and C2, some information can be derived concerning the form of the free-free absorbing structure. An assumption which can be made is that the emission from C1 and C2 is optically thin synchrotron radiation, 
, which suffers from no self-absorption, but only extrinsic free-free absorption.
Using this assumption and retaining the temperature, density and composition of the free-free absorbing structure constant, only a reduction in the path length ( 
) need occur so that the observed spectra for these two components correspond to the assumed intrinsic spectral index of . The path length required for component C2 is approximately 0.9 pc and for component C1 is approximately 0.5 pc. The path length through the free-free absorbing structure drops by a factor of two within approximately 0.4 pc of the core.
Under these assumptions the free-free absorbing structure could take the form of a torus of circular (diameter 
1 pc) cross section which lies perpendicular to the jet direction. To make the intrinsic spectral index of the core significantly less than the limiting value for synchrotron self-absorption ( ) the path length through the torus, in the direction of the core, would have to be increased. In this case the torus would assume a form more resembling a thick disk. A similar situation has been noted in 3C 84 [Vermeulen, Readhead, & Backer 1994] for which a pc-scale free-free absorbing disk or torus with 
pc, 
K, and 
may be plausible. Also, from HI observations of Cygnus A, some evidence has been found supporting the existence of a free-free absorbing torus on the scale of approximately 15 pc [Conway & Blanco 1995].
In any case, a significantly inverted intrinsic radio spectrum for the Centaurus A core appears likely. Botti & Abraham [1993] have shown that the spectrum of the nuclear radio source in Centaurus A remains inverted between 22 and 43 GHz and is variable on time-scales of a few months, evidence that flux outbursts brighten first at higher frequencies. This may partly explain the extreme spectral index of the core, as observed with VLBI.
The form and extent of the possible free-free absorbing structure in Centaurus A is uncertain since, as calculated above, it relies heavily on fairly arbitrary assumptions about the intrinsic spectra of the components in the sub-pc-scale jet and the core. However, the effect of free-free absorption at some level is almost unavoidable due to the extreme spectral index observed for the core in both the near simultaneous imaging presented here and the simultaneous images of Jones et al. [1996]. This calculation is therefore a reasonable one to consider.