Astron. Astrophys. 329, 504-510 (1998)

3. Results

In order to calibrate the VLBI scans on Cygnus X-3, the quasar 2005+405 was observed with sufficient sampling to allow a model reconstruction of its structure. A two-component model yielded a good fit to the data of 2005+403 at the four epochs; details will be presented elsewhere. The analysis shows that in contrast to Cygnus X-3, the radio source 2005+405 did not display significant variability during the observations or image broadening due to interstellar scattering on scales larger than 5 mas, so that the data could be used for calibrating the visibility amplitudes of Cygnus X-3.

Fig. 2 shows the visibility amplitudes for the observations of Cygnus X-3 obtained between January 24 and January 27. Observations were made with all available telescopes. Unfortunately, there are large gaps in the data due to the difficulty of scheduling telescopes with very short leadtimes. Table 1 lists the dates and telescopes for which observations were made. Fig. 1 shows that the radio flaring event is characterized by multiple outbursts. The flaring event is preceded by an initial flare of order 3 Jy detected on 1991 January 10 (c. Waltman et al., 1994). A flare with maximum flux density of 14.8 Jy at 3.6 cm occurs on January 21.5 (denoted Max 1 in Fig. 1) and is followed by secondary maxima of almost equal amplitude on January 24.8 (7.0 Jy, Max 2) and January 27.8 (7.1 Jy, Max 3), and at least six distinct peaks 4 Jy during the 30 following days. (see Fig. 1b). The profile of the lightcurve may be described by one peak and three consecutive plateaus of average (maximum) flux densities of order 7 Jy, 3.5 Jy, and 1.5 Jy in the time intervals 7 - 12, 12 - 22, and 22 - 34 days after the onset of the flaring event on January 18.

Fig. 1a-c. The lightcurves at 13.3 cm (2.25 GHz) (a) and 3.6 cm (8.3 GHz) (b) of Cygnus X-3 during the outburst of January 1991 measured by the NRL - Green Bank Interferometer, along with the spectral indices (c). All epochs are referred to the onset of the outburst (at 3.6 cm wavelength) on 1991 January 18 (JD 2448275), as discussed in the text.

Fig. 2. Visibility amplitudes of Cygnus X-3 on 1991 January 24 - 27. Note that the visibilities are all plotted on the same scale. The visibilities on the shortest baseline, Effelsberg - Westerbork, do not reach unity, indicating that the source displays significant spatial structure on scales exceeding the 6 cm scattering size of 16 mas.

The occurrence of multiple flares is reflected in the spectral index distribution (): after the steep rise during the first maximum drops to -0.4 at the first minimum (c. Fig. 1c). The average spectral index, not including the time of the outburst, is -0.4 indicating a mixture of steep ( 0.7) and inverted () component spectra as expected by the blending of consecutive flares. The presence of two components in the total spectrum may also explain that the flares Max 2 and Max 3 occurr simultaneously at 3.6 and 13.3 cm (c. Fig. 1a,b), whereas the large flare Max 1 displays a timelag: the peak at the shorter wavelength preceeds the one at the longer wavelength by 0.4 days.

The spectral index is inverted prior to the large outburst on January 18 (). An analysis of the flaring events from the Green Bank Interferometer longterm monitoring has to show if the occurence of an inverted spectral index of the quiescent component prior to the large flares is significant and may serve as pre-indicator of these events.

The four VLBI observations separated by one day each have been performed between Max 1 and Max 3 . In addition to the total flux densities at the VLBI epochs the values of the three peaks Max 1, Max 2 and Max 3 and the onset of the outburst (ZERO) are shown in Table 2.

Comparison of Fig. 1 with Fig. 2 shows that the source is heavily resolved even on the shortest baseline (B-W), with maxima of (also M-N at epoch I), and of the total flux densities at 6 cm for the others (see Table 2). A similar characteristic has been independently found during the October 1985 outburst at the two epochs with data for the Effelsberg to Westerbork and Effelsberg to Medicina baselines (Schalinski et al. 1995), with different levels of the total flux density (10 and 2 Jy at 6 cm wavelength, respectively).

Table 2. Total flux densities at 3.6 cm and 13.3 cm wavelength (cols. 3,4) of Cygnus X-3 at selected epochs (cols. 1,2) obtained with the NRL-Green Bank Interferometer, along with the corresponding flux densities at 6 cm wavelength (col. 6), interpolated from the spectral index (col. 5). Notes: Cols. 7-9 list the maximum correlated flux densities on the baselines B-W, B-M and M-N during the four VLBI - observations (labelled I-IV in Col. 1) at 6 cm wavelength (in % of the total flux density) a:  , b:  , and c:  . All epochs are referred to the onset of the outburst (at 3.6 cm wavelength) on 1991 January 18 (JD 244 8275).

The large reduction of visibility amplitudes can in principle be fitted by two classes of models:
(1) many compact components with sizes on the order of the interferometer beam or less of similar flux density and spatially blended together, or
(2) component sizes larger than the fringe spacing on the longest baseline and with flux densities adding up to the total source flux density.

However, a source representation on the basis of incomplete uv-data is ambiguous, because a mixture of these two types of models is likely, and the occurrence of different flaring events blending with each other will result in a superposition of component flux densities. Another complication for these observations is that Schalinski et al. (1995) have shown that individual components will have scattering sizes of order 16 mas at 6 cm wavelength. The interferometer for these observations is not very sensitive to structures on these size scales with the exception of the Bonn - Westerbork baseline. If there were a single large flare, the interferometer would be easily capable of measuring the evolution of this flare. However given multiple flares, this interferometer can only give evidence of multiple events and give a general description of the geometry of the radio emission associated with them. Given the flux density variability at the four VLBI epochs a possible influence on the source structure has to be considered. Since the variations of the visibility amplitudes appear not to be correlated with the variations of the overall intensity we estimate any effects on the source structure to be negligible for the study presented here.

To derive structural information and determine a preferred position angle from the current VLBI observations many possible image representations were investigated through simulations (varying source component parameters and generating continuous tracks with four stations) and subsequent modelfitting using the CalTech-Package (Pearson & Readhead, 1988). The simplest model adopted for the start of the simulations was three components of scattering size 16 mas, a total flux density of 6.6 Jy, angular separations exceeding 30 mas, along position angles . The results may be summarized as follows:

1) The visibility amplitudes show multiple (at least six) maxima and minima below a correlated flux density of 1 Jy except for the shortest baseline (Effelsberg to Westerbork, 270 km). The maximum flux density obtained from the model fits rises up to 4 Jy (80% of the total flux density) on the Bonn to Medicina baseline, and is less on the other baselines due to the limited visibility.

2) In case of similar component sizes and intensities, the minima are close to zero (here at the detection limit of VLBI data). The location of the minima defines, unaffected by residual amplitude calibration errors, a preferential position angle of the structure. A p.a. change of changes the location of minima significantly and also reduces the amplitude of the main maximum significantly - from 4 Jy to 0.6 Jy for the tested data sets.

3) On longer baselines (Effelsberg to Noto), or adopting larger component sizes and separations, the contrast between main maximum and secondary minima is enhanced. Thus only minimal component sizes can be derived.

In order to constrain a preferred position angle of the structure, we plotted the correlated flux densities of the January 25 data as a function of projected baseline, and varied the position angle of the projection. Even for complex data the minima of different baselines will appear at the same uv-locations, if the baseline p.a. equals the position angle of the structure. A significant match of visibility amplitude minima in the data set of January 25 could be only found in the small range of position angles of .

Using the above additional constraints on any representation of the source on January 25, we performed multiple modelfits to this data set. A five component model (with parameters listed in Table 3) appears to be the minimum requirement but non-unique solution to fit the visibility amplitudes, with evidence for more complex structure. Since the minima are well defined on the baselines, we only assume the position angles of component orientations with respect to a central component to be reliable for interpretation: starting from these values tend to vary up to . With the value obtained from the projected baseline plots we thus determine the p.a. to be in the range of . Multiple modelfits for the other epochs, especially for the Medicina to Noto baseline of January 24 and 25 also indicate, that more than three components are required to fit the visibility amplitudes.

Table 3. Typical modelfit to the Cygnus X-3 6 cm VLBI data of 1991 January 25. Notes: S: flux density, R: separation from central component, with corresponding position angle ; MAX: major axis, MIN: minor axis of elliptical components; : position angle of major axis. Due to the visibility fine structure and the poor uv-coverage the solution is not unique, and only gives a representative fit with least complexity (at least five components). Error analysis of VLBI modelfits of Cygnus X-3 see Schalinski et al. (1995).

© European Southern Observatory (ESO) 1998

Online publication: December 8, 1997
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