3. The mas structure of 3C 273
The images obtained for each epoch at 22 GHz and 43 GHz are shown in Figs. 1-8. The quality of the images is variable since the data quality from each station, the calibration accuracy, the (u,v ) coverage change between sessions.
3.1. The overall structure
With the observations at 22 GHz and 43 GHz we were able to track the jet up to a distance of 8 mas (12 pc) from the core. We identify the core with the easternmost component and we furthermore assume this to be stationary. The jet consists of a bright region of emission, which extends up to 2 mas and a region of much weaker emission which extends from 2 to 8 mas. The resolution achieved was not enough to resolve the jet in a direction transverse to the major axis. The images confirm that the jet is not collinear and has a wiggling structure.
The image from the best available data set at 22 GHz (project bj5b; 21Dec92) has a beam of 1 0.5 mas and shows that the jet can be tracked as far as 15 mas from the core (see Fig. 9). The ridge line of emission clearly oscillates around the main orientation. We will discuss this subject in more detail in Sect. 3.5.
The jet major axis has a Position Angle (PA) of . It is interesting to compare that PA with those available in the literature for interferometric observations made at different resolutions. As shown in Table 2, the PA changes from for the arcsecond jet, which is aligned to an accuracy of with the optical jet (Bachall et al. 1995) to for the 1 mas jet.
Table 2. The position angle of the jet major axis in 3C 273.
3.2. The first 2 mas of the jet
To be able to describe the structure of the source and check for any structural variations, we have model-fitted with gaussian components the final self-calibrated visibilities of each data set. The criteria adopted to model the source are that the model should be as simple as possible and fit the visibilities with a good agreement factor. As one can see from the images in Figs. 1-8, the source is dominated by the central 2 mas-jet. The weak components which lie along the jet, at a radial distance from the core larger than 2 mas, only marginally affect the best fit between model and data. In other words, these components are not well constrained by the data. Therefore those components are mainly missing from the tables. Table 3 lists the models for the 22 GHz data sets, Table 4 lists the models for the 43 GHz data sets and Table 5 lists the models for the 22 GHz data sets for baselines shorter than 450 M. The formal errors associated with the positions of each component as derived from the modelfitting procedure are rather small.
Table 3. Modelfitting 22 GHz data sets
Table 4. Modelfitting 43 GHz data sets
Table 5. Modelfitting of the 22 GHz data sets using baseline length
A more realistic estimate of the errors comes from independent attempts to model the source. This gave a distribution of positions for each component from which errors have been estimated. For components which are compact compared to the beam size, the errors associated with their positions are estimated to be 10% of the beam. For more extended components, the associated errors are 10% of the full width, half maximum of the gaussian derived from the modelfitting.
The inner part of the jet of 3C 273 at 43 GHz can be modelled with five compact components. The modelfitting was performed using DIFMAP. The reduced chi-squared, which measures the goodness of the fit, gives values close to 1 (see Pearson 1994). In order to verify the goodness of the models, the following checks were done: (1) to verify that the source structure was actually changing with epochs, each model was used to fit the visibilities of an other data set; in each case, a poor fit was always obtained; (2) each model was used to make a restored map which was compared by eye with the related hybrid image; (3) the ratio between the total flux density from the hybrid images and the flux density obtained adding up the flux density from the individual components in the related model was always close to 1. This last result also suggests that the error estimate associated with the flux density of each component is 10%.
Each components position in polar coordinates has been projected along two orthogonal directions and plotted in Fig. 10. The components have been shifted in such a way that the easternmost components, assumed to be the `core', do overlap. It is clear that the components are not collinear and that the PA of the line joining the core with each of the components position changes dramatically, oscillating around a line in PA .
In order to prove if such a structure is real, we have model-fitted the 22 GHz data sets using the visibilities from baselines in the range M to match the resolution to that of the 43 GHz observations in the east-west direction. (At 43 GHz, the resolution was poorer in the east-west direction than at 22 GHz but better in the north-south direction.) As a result, a more sparse coverage of the uv -plane was achieved at 22 GHz. The image is plotted in Fig. 11. The bends along the jet are less evident because of the poorer resolution in north-south of these observations, however, the curved structure is confirmed. The variation in the positions in y -direction between 22 GHz and 43 GHz for each component might be caused by opacity effects. However, we are comparing observations made in the steep part of the spectrum so the displacement could be caused by the relatively sparse coverage of the uv -plane at 22 GHz. The variation of component position as a function of opacity at 22 GHz and 43 GHz in 4C 39.25 was been examined by Alberdi et al. (1997); they find no evidence for any displacement.
3.3. Structural variation with time
To look for any short term structural variation of 3C 273, we have plotted the separation from the core with time of the components along the x and y directions (East-West and North-South directions respectively) projecting the polar vectors of the 43 GHz models. The core is labelled component 1, the next component 2, than 3, etc... The results are shown in Fig 12 and Fig 13 respectively. Error bars, 10% of the HPBW are also plotted. In the plot for the x -direction the error bars are of the same size of the symbols used. A line, which represents the best fit, has also been drawn and its correlation coefficient is reported in Table 6. A value of 1 means the maximum for the best fit. In the x -direction, components 4 and 5 change their separation from the core at the same apparent speed, with values in agreement with previous measurements obtained with observations which had a much larger time sampling. Component 3 has a lower speed, while component 2 shows a separation from the core which decreases with time. The probability given from the reduced chi-square analysis to obtain a similar fit by random is . Such a reverse speed, if real, has not been observed in a superluminal source before.
Table 6. Apparent speed for modelfitting components in 3C 273 at 43 GHz
In the y -direction, where the positional accuracy is lower, we have sufficient resolution to be able to measure the apparent speed of the components. Component 2 seems to be stationary with respect to the core. Components 3 and 4 are moving north with different speeds, while component 5 is moving in a direction opposite to component 4.
In Table 6 the projected velocities, obtained by combining the two velocity components, are given (Columns 6 and 7 respectively). The direction of the radial velocity vectors are not parallel to the jet axis, of course, in agreement with the view that the components in 3C 273 are moving along a wiggling path.
3.4. Spectral index of individual components
The observations at 22 GHz and 43 GHz were quasi-simultaneous during the full series of sessions. In order to estimate the spectral indices of the components, we have used the flux densities obtained from model-fitting the source structure. At 22 GHz, the adopted flux densities come from data sets with comparable uv ranges to the 43 GHz observations (i.e.M). The spectral index of each component for each session is shown in Fig. 14. Among the five components, only component 1, believed to be the core of emission, has an inverted spectrum. During the last session, the flux density of the core at 43 GHz is much higher than at 22 GHz and the spectrum more inverted. This might suggest that a new component is emerging from the core itself. All of the components along the jet do show a steep spectrum, which steepens progressivle with distance from the core. The spectral indices (), are in the following ranges: component 1 between 0.2 and -1.5; component 2 between 0.2 and 1.9; component 3 between 0.7 and 1.2; component 4 between 1.1 and 3.0; component 5 between 1.3 and 2.2. These spectral indices are quite steep. This may be because some flux density was lost at 43 GHz because of the better resolution in the north-south direction.
3.5. The jet structure in the region 2-8 mas from the core
It is difficult to model the weak components in the region from 2 to 8 mas from the core. To visualize the outer part of the jet, the position of the peak of the emission for each blob has been derived from the hybrid maps of Figs. 1-8. As a reference point we have taken the strongest component in the images; this corresponds to component 3 in the model-fitting.
From this we find that, to within the positional accuracy, the components are co-moving with the reference component, i.e. we do not detect any change in separation with time between the reference point and any blob in the outer part of jet during the period of our observations. The position of the peak of emission derived for each component from both the 22 GHz and 43 GHz images is plotted in Fig. 15 together with the estimated errors, weighted by the signal-to-noise ratio of those components. The linear-correlation coefficient obtained by fitting the points with a straight line gives -0.27 which is rather poor. The straight line drawn in Fig. 15 represents the major axis PA of the jet. Obviously, the points lie both above and below that straight line. The second line represents a polynomial, which fits the distribution of the series of data and has a multiple-correlation coefficient very close to 1. The points at 22 GHz and 43 GHz are fully mixed. Independent polynomial fits to the two series of data give almost identical results. We do not see any effects of opacity on the component positions within the accuracy of our measurements. The jet path is not collinear with the major axis and the wiggles, are now clearly tracked. From Fig. 15 we can derive the wavelength of the oscillation, which is 6 mas (or 11 pc).
© European Southern Observatory (ESO) 1999
Online publication: May 21, 1999