The core component appears strongly in each of the models. The component C2 can also be identified at each epoch. The component C1 can be identified at seven of the nine epochs. At two epochs, 1991 November 24 and 1993 October 20, it is not clear which, if any, of the model components corresponds to C1. In the last four epochs, an additional component can be identified between the core and C2, and is designated C3. Lastly, at eight of the nine epochs one or more of the components in the models have been identified as possible or definite jet-like components. These components are often required by the model to take an extended (elongated along the jet) and diffuse appearance, in contrast to the discrete components. Such a component was first noted by Meier et al. [1989] in their modelling of the first 8.4 GHz VLBI observations of Centaurus A. This component probably represents the underlying, smooth emission from the jet.
The main aim of the model-fitting analysis was to quantify the evolution of the components in the source. To achieve this aim further analyses of the models were undertaken to estimate the errors on the best-fit parameters at each epoch. The model-fitting errors are required so as to determine whether or not the differences between the different models are significant.
To estimate errors, the best-fit model at a given epoch and its corresponding dataset were taken back into the MODELFIT program. The best-fit value for a single parameter of a given component in the model was then altered by a certain amount and fixed at the new value. MODELFIT was then allowed to re-converge the model with all parameters varying, except for the parameter which had been fixed and the position of the core. First the gradient search method was employed and then the brute force method immediately afterwards. When the model had re-converged to its new goodness-of-fit (worse than for the best fit model), its fit to the visibility amplitudes and closure phases was compared to the fit of the best-fit model. The Caltech VLBI task VPLOT was used to plot the data against the model predictions and a visual comparison of the two fits was made. If no significant difference could be found between the fit of the two models then the process was repeated, after the parameter in question had been fixed again at a new, larger displacement from its best-fit value.
When a displacement was reached at which the fit of the re-converged model to the data was significantly worse than for the best-fit model, the displacement defined the error bar in one direction. Displacements in the opposite sense were used to define the error bar in the opposite direction.
The comparison of model fits was necessarily a subjective one. However, several ground rules were established for the purposes of deciding whether a difference between fits was significant or not. First, none of the fits were perfect, there were differences between model and data on some baselines and closure triangles in every data set. The baselines and closure triangles which were very well fit by the best-fit model were most closely monitored in the error determination process. The fit was deemed to be significantly worse than the best-fit if the model prediction was outside the scatter in the visibilities for periods longer than 2 hours on 2 or more baselines and/or closure triangles which were well fit by the best-fit model, and if further steps away from the best-fit solution caused even greater divergence from the data. Otherwise any differences in the fits were deemed not significant.
This method can be applied to any of the parameters in the models. However, the analysis was successful only in its application to the core-component separations for the discrete components in the source, namely C1, C2, and C3. For example, from an analysis of the errors on the flux densities of individual components it became clear that the various components in a given model were easily able to ``trade'' flux density in a way which satisfied the MODELFIT program over a large range in displacement from best-fit values, giving no useful estimate of the errors. The core-component separations for the discrete components were the best constrained parameters, probably because the closure phase information maintained a strong influence.
Even for the core-component separations it would appear that this method is near the limit of its usefulness for this source. It was noted that the core-component separation could be systematically compensated by the core-component position angle to retain a good fit to the data over a (sometimes) wide range in displacement.
Figure 5.13 presents the results of the model-fitting error analysis for the core-component separations of C1, C2, and C3 and shows that components C1 and C2 have significantly changed their positions relative to the core over the 4.3 years of the monitoring. A least-squares fit to the series of core-C2 separations gives an angular motion for C2 relative to the core of 
mas/yr corresponding to an apparent speed of 
=v/c= 
, with small residuals at most epochs. Extrapolating the motion back in time gives a core-C2 zero separation time of approximately 1989.5.
Figure 5.13: Evolution of major model components
A least squares fit to the core-C1 separations gives an angular motion for C1 relative to the core of 2.6 mas/yr, corresponding to =v/c=0.16. However, the residuals on this fit are large at most epochs and it appears that a single, constant expansion speed may not be the best description for the evolution of this component. From the visibility data, the images, and the models, it is apparent that C1 undergoes strong internal evolution.
Over the period of the first three epochs (1991 March 6 to 1992 March 26) C1 changed its structure appreciably, from being a discrete component at 1991 March 6 (see images and model) to being possibly absent from the source model at 1991 November 24, and returning as a bright and discrete component some time during the following 4 months to 1992 March 26 [Meier et al. 1993; Tingay et al. 1994]. The evolution between 1991 November 24 and 1992 March 26 could be characterised by the appearance of a component within C1 approximately 0.3 ly (4.5 mas) in projected extent (from a comparison of the models) over the 0.34 year period (Figure 5.14). Also between the epochs of 1992 November 22 and 1993 October 20, C1 altered its appearance considerably. C1 appears to have increased its separation from the core by approximately 0.4 ly (6 mas) over the 0.9 year period, remaining close to that separation until the end of the series of observations. This change in position is significant, as can be seen in Figure 5.13.
Figure 5.14: Comparison of 1991 Nov. 24 and 1992 March 26 models
From the two episodes of evolution in C1, and assuming that the changes seen are the result of component motions, lower limits on the speed of 0.85c and 0.45c can be inferred respectively. These speeds are much greater than inferred from the long term monitoring. The behaviour of C1 appears to be accounted for by a slow, linear motion combined with internal changes on much shorter time-scales, < 4 months.
The component C3 was only detected in the last four epochs of observation and the error bars do not indicate any significant motion, but it might be expected that with further observations C3 will be shown to have a motion with respect to the core similar to C2.