3 Results

In Fig. 3 we show a plot of the amplitude visibility as a function of baseline length on the first epoch 21 October 2000. The decaying trend of the amplitude is the unmistakable signature of a resolved source. Cygnus X-3 was still a very bright radio source ($\sim$0.45 Jy) during the first epoch of observation. With such a high flux density, it is feasible to carry out reliable model fits in the uv plane every few minutes in order to look for fast structure variations. The AIPS task UVFIT was used for this purpose with an elliptical Gaussian model assumed. The results of the fit, shown in Fig. 4, were fairly stable and clearly indicate an extended elongated radio source. The fact that Cygnus X-3 becomes resolved at the VLA resolution in the weeks following strong radio outbursts is also well evident in Fig. 5. This figure displays the VLA contour map for the third epoch of observation. In this image, the elongated radio source present during the first epoch has produced a remarkable bipolar asymmetric radio jet. For the first time, the jet and counterjet in Cygnus X-3 are clearly detected with no subtraction procedure being necessary to reveal them. The progressive development of radio jets in Cygnus X-3, at arcsecond scales, is better illustrated in Fig. 6. The vertical separation of the different maps in this figure is proportional to the elapsed time between the observing epochs and the direction of the jets has been rotated $90^{\circ }$ counterclockwise.

Figure 3: Plot of the Cygnus X-3 visibility amplitude as a function of the projected baseline on 21 October 2000. The amplitude decay for the longest baselines of the VLA is the clear signature of a resolved source. This plot contains only averaged visibility data at 6 cm from blocks 1 and 2 of the first epoch.

Figure 4: Best elliptical Gaussian fit to the Cygnus X-3 radio structure on 21 October 2000. The fit was carried out directly in the uv plane using the AIPS task UVFIT at regular intervals of 5 min.

Assuming that the arcsecond jets were created when the GBI saw the triggering outburst event (JD 2451802.5), the corresponding age of the ejecta is 36.1, 51.0 and 66.0 days for the first, second and third epochs, respectively. For quantitative proper motion estimates, the position of the jet components in the third epoch has been measured by direct model fitting in the uv plane. Two point sources for the jet components plus one elliptical Gaussian for the central core were fitted with UVFIT. In the second epoch, only the northern jet component was fitted since it is the only one visible in the maps. A summary of the fit results for both the core and the jet components is given in Tables 2 and 3. In all fits, the core position was kept fixed at the phase origin since we are dealing with self calibrated data. It is important to mention that model fitting in the uv plane did not differ significantly from fitting in the image plane using the alternative AIPS task IMFIT. For a bright radio source, such as Cygnus X-3, the UVFIT results are nevertheless preferred since they avoid the intermediate step of CLEAN deconvolution.

 

 

Table 2: Results of an elliptical Gaussian fit in the uv plane for the central core.

Epoch	Angular Size	Position Angle	Flux Density
	(mas2)	($^{\circ}$)	(mJy)
1st	$145.3 \times 45.7$	$4.0\pm0.1$	$452.36 \pm 0.07$
	$\pm 0.2$   $\pm 0.3$
2nd	$85.7 \times 35.3$	$7.1\pm0.3$	$241.85 \pm 0.04$
	$\pm 0.3$   $\pm 0.5$
3rd	$66.6 \times 30.0$	$6.5\pm0.5$	$107.52 \pm 0.28$
	$\pm 2.4$   $\pm 1.3$

 

 

Table 3: Results of a point source fit in the uv plane for the jet components.

Epoch	Jet	$\Delta \alpha \cos{\delta}$	$\Delta \delta$	Flux Density
	Comp.	(mas)	(mas)	(mJy)
2nd	North	$+7\pm4$	$435\pm4$	$1.70\pm0.03$
	South	-	-	-
3rd	North	$+7\pm3$	$+611\pm20$	$1.45\pm0.02$
	South	$-31\pm7$	$-460\pm10$	$0.89\pm0.02$

If equipartition of the energy between the relativistic particles and the magnetic field is assumed, we can derive some of the physical parameters in a radio source. We have carried out these calculations for central core of Cygnus X-3 based on the observed values in Table 2. The formulation by Pacholczyk (1970) has been used, together with a synchrotron optically thin spectral index of -0.6 (between 0.1-100 GHz) and a 10 kpc distance. The corresponding results for the radio luminosity, brightness temperature, minimum energy content and magnetic field are given in Table 4. It is remarkable that the magnetic field estimates are practically the same in all three epochs in spite of the variations in radio luminosity.

 

 

Table 4: Physical parameters of the Cygnus X-3 core derived assuming equipartition.

Epoch	Radio	Brightness	Minimum	Magnetic
	Luminosity	Temperature	Energy	Field
	(erg s-1)	(K)	(erg)	(G)
1st	$2.1 \times 10^{33}$	$5.1 \times 10^6$	$3.6 \times 10^{43}$	$2.0 \times 10^{-2}$
2nd	$1.1 \times 10^{33}$	$6.0 \times 10^6$	$1.5 \times 10^{43}$	$2.3 \times 10^{-2}$
3rd	$0.5 \times 10^{33}$	$4.0 \times 10^6$	$0.7 \times 10^{43}$	$2.2 \times 10^{-2}$

Figure 5: Self-calibrated VLA map of Cygnus X-3 at the 6 cm wavelength obtained on 19/20 November 2000. Only visibilities in the interval not affected by variability have been used. The bipolar radio jets of Cygnus X-3 extending over one arcsecond are clearly developed at the third epoch of observation. Contours are -3, 3, 4, 6, 8, 10, 12, 15, 20, 25, 30, 35, 40, 60, 100, 200, 300, 500, 1000, 2000 and 3000 times 0.034 mJy beam-1, the rms noise. The ellipse at the bottom left corner represents the synthesized beam of $337 \times 285$ mas2, with position angle of $-34^{\circ }$.

Figure 6: Sequence of development of arcsecond radio jets in Cygnus X-3. The vertical offset between the different maps is proportional to the elapsed time. The maps have been rotated $90^{\circ }$ counterclockwise for easier display. In all maps, the clean components have been restored using an averaged circular beam of 361 mas diameter shown at the bottom left corner. Contours are 4, 6, 8, 10, 15, 20, 25, 30, 35, 40, 50, 100, 200, 300, 500, 1000, 1500, 2000, 2500, 3000 times the rms noise of the map. The rms noise is 0.12, 0.072 and 0.034 mJy beam-1 for the top, middle and bottom panel, respectively.