5 Discussion

The VLA maps in this paper clearly indicate that relativistic expansion in Cygnus X-3 creates a two-sided radio jet extending over $\sim$1 $^{\prime\prime}$ or $\sim$0.05 pc at the distance of this microquasar. Such a bipolar structure is completely different from the one-sided radio jet interpretation based on the VLBA maps by Mioduszewski et al. (2001). These authors imaged Cygnus X-3 several times with an angular resolution of a few mas in the days following the 1997 outburst event. The VLBA structures are interpreted by them as a curved one-sided radio jet, with strong Doppler boosting effect, extending over $\sim$100 mas or $\sim$10^-3 pc. Their estimated jet velocity is $\geq$0.81c based on the non-detection of the counterjet. The inclination angle with the line of sight of the approaching jet is consequently limited to $\leq$36$^{\circ}$, a value further constrained to $\leq$14$^{\circ}$ by their precessing jet models. In contrast, our observations point to radio jets being ejected with a large inclination angle and a velocity roughly half the speed of light. Incidentally, the velocity that we infer is similar to that recently reported for the lobes of the Sco X-1 (Fomalont et al. 2001). At this point, the obvious question is: how the VLA and VLBA structures can be reconciled? The scope of this problem is not limited to Cygnus X-3 only, as it may seem. In fact, some other microquasars occasionally appear as one-sided or two-sided when observed with the VLBA or the VLA. The superluminal systems GRS 1915+105 (Mirabel & Rodríguez 1994; Dhawan et al. 2000) and GRO J1655-40 (Hjellming & Rupen 1995; Tingay et al. 1995) are good examples of this statement.

5.1 A one-sided versus a two-sided jet

The Mioduszewski et al. (2001) results proposed a major change in our picture of the Cygnus X-3 ejecta. The previous two decades of interferometric observations suggested symmetric double or triple radio source structures, always with moderate relativistic velocities ($\sim$0.3c). The works by Geldzahler et al. (1983), Spencer et al. (1986) and Schalinski et al. (1995) are good examples of such a statement. It is true that these historical interpretations were sometimes based on model fitting analysis using a limited number of baselines in the array. However, evidence for nearly symmetrical arcsecond structures around Cygnus X-3 is also present in good synthesis maps by independent observers such as Strom et al. (1989) and Martí et al. (2000). On the other hand, all observations by different authors are consistent with any radio jet structure in Cygnus X-3 (either one or two-sided) always being elongated approximately in the North-South direction. This fact immediately suggests that any precession of the jets is not of wide angle. Considering all the observed facts, the apparent contradiction may be due to several reasons:

1.

The one-sided jet appearance at VLBA angular scales could be due to the over-resolving power of the array;

2.

The ejection and physical jet parameters may vary substantially from outburst to outburst. However, a strongly precessing jet does not seem likely as mentioned above. On the other hand, the two sided arcsecond radio jet reported by Martí et al. (2000) was seen in the months following the same 1997 event observed by Mioduszewski et al. (2001);

3.

It could also be possible that the identification by Mioduszewski et al. (2001) of the Cygnus X-3 core is not correct and, consequently, the jet is not actually one-sided. The objections against this possibility are that the proposed core remained stationary in position within 3 mas and that its VLBA flux density behaved just like the total of flux the source;

4.

The motion of the ejecta could not be perfectly ballistic and deceleration may take place as the jets travel away and interact with the surrounding medium. If strong deceleration occurs, the one-sided jet appearance very close to the core, as seen with the VLBA, could be significantly different from what the VLA sees at significantly larger scales. The interaction of microquasar ejecta with the environment has been already observed in the case of XTE J1748-288, where jets were seen to collide with external material and decelerate (Hjellming et al. 1998);

5.

Alternatively, we could be dealing with jet obscuration by an absorbing medium instead of a Doppler boosting effect. This possibility was already tentatively suggested by Fender et al. (1999) for Cygnus X-3 and discarded by Mioduszewski et al. (2001) when considering the problems of having opaque material at 15 GHz out to a least $\sim$1000 AU away from the core.

None of the different possibilities considered above can be strictly ruled out with the available information. However, among them we believe that the absorption hypothesis is probably the most plausible one provided that we have a non-spherical and highly flattened wind. This suggestion is based on the recent estimate of the wind mass loss from the Woft Rayet companion in Cygnus X-3, that appears to be much higher than suspected. An enhanced mass loss would naturally imply that absorption effects are relevant in this case contrary to previous expectations. It is relevant to mention here that the absence of counter-jet in some VLBA images of GRS 1915+195, within few hundred AU of the core, has been also interpreted as possibly due to thermal free-free absorption (Dhawan et al. 2000).

5.2 Is the northern milli-arcsecond radio jet absorbed by a flattened disc-like wind?

The Cygnus X-3 observations with the Infrared Space Observatory (IS0) by Ogley et al. (2001) provide a wind mass loss of $\dot{M}_{\rm w} \sim10^{-4}$ $M_{\odot}$ yr^-1 assuming spherical symmetry and an outflow velocity at infinity of $v_\infty \sim 1500$ kms^-1. If the wind geometry is not spherically symmetric but flattened in the plane of the binary orbit, the corresponding mass loss is different and depends on the solid angle covered by the wind. The infrared spectroscopic observations of Fender et al. (1999) clearly show a double peaked emission line of HeI with day to day variability. This fact strongly supports a significantly flattened disc-like wind, common for Wolf-Rayet stars, that is aligned with the orbital plane and extends far beyond the orbital size of a few solar radii. The inclination angle of the disk with the line of sight is unknown, but probably values of a few tens of degrees could be consistent with the small optical depth to X-rays.

According to Ogley et al. (2001), when their ISO observations are interpreted in the context of such a disc-like wind model, the corresponding mass loss may be as high as $1\times 10^{-3}$ $M_{\odot}$ yr^-1sterad^-1 for a solid angle 10% of $4\pi$. The total mass loss is then $1.3 \times 10^{-3}$ $M_{\odot}$ yr^-1. Such a high value exceeds current estimates of powerful winds in massive Of/WN stars by one order of magnitude (Lang et al. 2001). In order to be cautious, we will adopt an intermediate mass loss of $5 \times 10^{-4}$ $M_{\odot}$ yr^-1 for qualitative discussion in a flattened wind scenario. With a $\dot{M}_{\rm w}$ value of this order, the interpretation of absorption by the wind at 15 GHz does not look so unreasonable. The situation would be somewhat analog to the obscured radio jet in the Seyfert 2 galaxy NGC 4258. In this extragalactic object, the brightness asymmetry between jet and counterjet is related to thermal free-free absorption instead of Doppler boosting (Herrnstein et al. 1997).

In order to better check this possibility, it is instructive to estimate the optical depth of a line of sight through the wind disc. The geometric parameters involved are illustrated in Fig. 7. For simplicity, we will consider an unaccelerated, isothermal and fully ionized wind. A wind velocity of $v_\infty=10^8$ cms^-1, an electron temperature of $T_{\rm e}=10^4$ K, a disc opening angle such that $\sin{\vartheta}=0.1$ and a disc inclination of $i=30^{\circ}$ will be also assumed as plausible values. The wind electron density $n_{\rm e}$ at a distance r from the binary can be then expressed as:

$$n_{\rm e} = {\dot{M}_{\rm w} \over 4 \pi r^2 v_{\infty} m_{\rm H} \sin{\vartheta}},$$ (6)

where $m_{\rm H}$ is the proton rest mass. To be consistent with the VLBA images, the northern jet needs to be absorbed up to an angular distance of at least 50-100 mas. At 10 kpc, this corresponds to a linear size of l=(0.75- $1.5) \times 10^{16}$ cm (500-1000 AU) projected on the plane of the sky. A visual at this projected distance would cross the disc at a radius of $r=l/\sin{i}=(1.5$- $3.0) \times 10^{16}$ cm, where electron densities of (6.7- $4.4) \times 10^5$ cm^-3 are expected.

Figure 7: Diagram showing the parameters involved in the obscuration interpretation of the apparent one-sided radio jet of Cygnus X-3 close to the binary system. The obscured jet is the one directed towards the observer, which later appears brighter than the counterjet when observed with the VLA due to relativistic aberration. In this interpretation, the jet flow velocity v is not exactly perpendicular to the disc plane of the wind. However, the misalignment is a few tens of degrees at most.

Assuming only free-free absorption by the ionized plasma, the absorption coefficient at radio wavelengths can be expressed as (Pacholczyk 1970):

$$\kappa_\nu^{\it ff} = 0.206~n_{\rm e}^2 T_{\rm e}^{-1.38} \nu^{-2.08}.$$ (7)

Based in Fig. 7, the path length of the line of sight through the disc can be approximated by $s \simeq 2 l \tan{\vartheta} / \sin^2{i} = (0.6{-}1.2) \times 10^{16}$ cm. The corresponding optical depth is then:

$$\tau_{\nu}^{\it ff} \simeq \kappa_\nu^{\it ff} s,$$ (8)

where we approximate the absorption coefficient trough the line of sight by its value at the middle point in the path s (see Fig. 7). From Eq. (8) at $\nu=15$ GHz, we finally obtain $\tau^{\it ff} \simeq 1.15$-0.14 and the result would be even higher for lines of sight with smaller l. These calculations are not very sensitive to moderate variations in the parameters.

The proximity of the $\tau^{\it ff}$ values to unity makes difficult to completely reject that absorption may play a relevant role in the appearance of the Cygnus X-3 radio jets at the VLBA angular scales. Together with a flattened disc-like wind, the key of this interpretation is the recent and significantly higher wind mass loss estimates from ISO. Then, the wind would absorb the radio emission from the northern and brighter jet as suggested in Fig. 7. Although this interpretation is consistent with a large value of the jet angle with the line of sight, as derived above, the simple sketch in Fig. 7 suggests a relativistic jet flow not exactly perpendicular to the orbital and disc plane. Nevertheless, the perpendicularity could be still be preserved by assuming a warped disc with a geometry similar to the obscuring molecular disk in NGC 4258. In addition we could also have a narrow angle precession of the jet.

On the other hand, the proposed disc would be permanently emitting thermal free-free radio emission. It is then important to check that the expected level of thermal emission is consistent with the weakest flux densities ever observed for Cygnus X-3. Using the formulae of Panagia & Felli (1975), we find that a thermal contribution of about 6 mJy is expected at 15 GHz for a spherical mass loss of $5 \times 10^{-4}$ $M_{\odot}$ yr^-1. Of course our wind is not spherical, but we are only interested in an order of magnitude estimate. The thermal emission will be even lower at lower frequencies for the spectral index of a thermal wind ( $S_\nu \propto \nu^{+0.6}$). The expected emission is well consistent with the normal quiescent levels of Cygnus X-3 ($\leq$100 mJy at cm wavelengths). Moreover, it is also very close to the quenched states of very low flux density ($\leq$5 mJy at 15 GHz) prior to strong radio outbursts (Waltman et al. 1996).