3 Discussion

   
3.1 Morphology

Figure 3: Top: EVN uniform weighted map of LS I +61$^{\circ }$303 at 5 GHz frequency obtained on 1994 June 7 (this paper). The contours are at -3, 3, 4, 6, 8, 11, 16, 22, 30, 45, 60 and 75 times the rms noise of 0.28 mJy beam-1. The filled ellipse in the bottom-left corner represents the FWHM of the synthesized beam, which is 5.9  ${\rm mas} \times 3.8$ mas at a PA of 74.2$^{\circ }$. Bottom: VLBI map (at 5 GHz) by Massi et al. (1993), obtained on 1990 June 6, with a resolution of 0.6  ${\rm mas} \times 0.5$ mas.

In view of the models that can fit the data, the source in Fig. 3 can be explained as a central core (point source of Model 2 in Table 1) and a one-sided jet (elliptical Gaussian in the same model). If we assume that the Gaussian component is the result of an expanding source that originated at the onset of the major outburst, that is about 13 days before our observations, and that the expansion velocity of the jet is constant, the derived velocity, taking into account the size of the Gaussian and the offset to the point source, is $\sim$0.3 mas$\:$d^-1. This corresponds, at a 2.0 kpc distance, to a projected expansion velocity of $\sim$0.003 c.

The most interesting aspect of the EVN map is that, for the first time, we detected asymmetric emission in the southeast direction. The morphology is quite similar to that observed by Stirling et al. (2000, Fig. 4) in Cygnus X-1 at 15 GHz: a central source with a small but clear elongation. Is this morphological analogy enough to interpret the structure in the EVN map as a one-sided jet? In the case of Cygnus X-1 the interpretation of the small jet-like elongation has proved to be correct: a later observation of this source at 8 GHz shows the elongation developed into an extended jet.

LS I +61$^{\circ }$303 has been observed several times with mas resolution. In Table 2 we report previous VLBI observations focusing on two special items: the position angle (PA) of any extended feature present and its expansion velocity.

 

 

Table 2: Summary of published VLBI observations of LS I +61$^{\circ }$303 at 5 GHz. Phase is computed according to P=26.4917 d and $T_0={\rm JD}~2\,443\,366.775$.

Epoch	Array	Phase	State	Flux Density	Size	PA	Expansion
				(mJy)	(mas)	($^{\circ }$)	Velocity/c
1987 Sep. 25a		0.59	quiescent	40-54	$3.2\pm0.9$
	EVN						$\leq$0.002
1987 Oct. 1a		0.81	burst, decaying	260-200	$1.6\pm1.2$
1990 Jun. 6b	EVN + VLA	0.74	burst, decaying	244-205	$\sim$2	$\sim$135, $\sim$30	$\sim$0.0021
1992 Jun. 8c	Global VLBI	0.42	quiescent, minioutburst	35	0.5-2	$\sim$160	0.06
1993 Sep. 9d		0.69	burst, variable	76-131	2-3
	Global VLBI						0.007
1993 Sep. 13d		0.84	quiescent	60	$\sim$7	$\sim$120
1994 Jun. 7e	EVN	0.92	quiescent	34	$\sim$6	$\sim$120	0.003
1999 Sep. 16-17f	HALCA +	0.69	burst, variable	140	$\sim$4		$\sim$0.0022
	Global VLBI

^a Taylor et al. (1992); ^b Massi et al. (1993); ^c Peracaula et al. (1998); ^d Paredes et al. (1998); ^e This paper; ^f Taylor et al. (2000).
¹ Recalculated according to new outburst peak ephemerides (Gregory et al. 1999), for the extended structure at ${\rm PA}=135^{\circ}$.
² There is not enough resolution at ${\rm PA} \sim 140$ to know if there was expansion in that direction.

As can be seen, an extended feature with PA from 120$^{\circ }$ to 160$^{\circ }$ seems to be present in other maps. While the identification is perhaps ambiguous in Paredes et al. (1998) because the extension is coincident with the direction of the major axis of the beam, the observations by Peracaula et al. (1998), report on one extended feature with comparable PA with that of the feature in our map. The reason why in the past this extended structure was never clearly associated with a jet is because an internal structure at another PA ($\simeq$30$^{\circ }$) makes the morphology confusing. To better understand this point we show at the bottom of Fig. 3 the map by Massi et al. (1993). The VLBI map resolves two components (at ${\rm PA} \simeq 30 ^{\circ}$) inside the extended structure (at ${\rm PA} \simeq 135 ^{\circ}$). The extended structure is asymmetric as well as that in our map, but towards the northwest direction. This is probably a projection effect corresponding to a different ejection angle due to precession (Sect. 3.3). In Paredes et al. (1998) the double internal source is not resolved, but the authors propose the presence of an unresolved component stable and not participating in the flaring process, inside an extended structure at ${\rm PA} \simeq120^{\circ}$. These two components are again resolved in the recent VLBI observation using HALCA (Taylor et al. 2000). While in the past this double internal source was supposed to be the jet, in light of the EVN map we propose that:

1.

the double source at PA of $\simeq$30$^{\circ }$ is not the jet. Instead, it is almost orthogonal to the jet. It has a size of 2 AU and therefore is comparable with the orbital size (1.4 AU);

2.

the jet is identified with the structure with PA in the range 120$^{\circ }$-160$^{\circ }$ seen in at least three VLBI observations, and best defined in our EVN map where it has a size of $\sim$8 AU.

An emitting region perpendicular to the jet has been observed indeed also in SS 433 by Paragi et al. (1999) and perhaps in Cygnus X-1 by Stirling et al. (2000) and preliminary interpreted as shocked gas in the orbital/accretion plane. If this interpretation holds true also for LS I +61$^{\circ }$303 the strong wind opacity close to the periastron, discussed in the introduction, certainly severely affects the morphology of such emission. For the jet, however, wind opacity effects are negligible. The jet is generated by outbursts occurring at quite a displaced orbital phase with respect to the periastron. Moreover, the size of the jet is much greater than the orbital size.

   
3.2 One-sided jet and Doppler boosting

It is well known that while some extragalactic radio sources have two jets, for some others only one jet is observed. The unification model for AGN (see a review in Urry & Padovani 1995) assumes that all of them represent the same class of objects (all having two jets) and their different appearance depends on different observing angles. Let us assume a symmetric ejection of two jets at velocity $\beta$ (i.e. expressed as fraction of c). The two jets, approaching and receding, move at an apparent velocity $\beta_{\rm a,r}$related to the intrinsic $\beta$ by (Rees 1966; Mirabel & Rodríguez 1994)

$$\beta_{\rm a,r}={\beta \sin\theta\over 1\mp \beta\cos\theta},$$ (1)

where $\theta$ is the angle between the direction of motion of the ejecta and the line of sight.

Following the method of Mirabel & Rodríguez (1994) one can determine the quantity $\beta \cos \theta$ by means of the ratio of flux densities from the approaching and receding jets,

$${S_{\rm a}\over{S_{\rm r}}}=\left({1+\beta\cos\theta\over1-\beta\cos\theta} \right)^{k-\alpha},$$ (2)

where $\alpha$ is the spectral index of the emission ( $S\propto \nu^{\alpha}$) and k is 2 for a continuous jet and 3 for discrete condensations.

In our case we deal with one jet only. However, we can determine the lower limit

$$\beta\cos\theta> {\big({S_{\rm a}^{\rm peak}/3\sigma}\big)^{1... ...er \big({S_{\rm a}^{\rm peak}/3\sigma}\big)^{1/(k-\alpha)}+1},$$ (3)

using the noise level ($\sigma$) of the map and the peak value of the approaching component ( $S_{\rm a}^{\rm peak}$). The spectral index a few days after the outburst is $\alpha=-0.5$ (Strickman et al. 1998). To be consistent with the lowest limit we select k=3.

For our EVN map, with $\sigma=0.28$ mJy beam^-1 and $S_{\rm a}^{\rm peak}=21.6$ mJy beam^-1, we have $\beta\cos\theta>0.43$.

Using Eq. (1) we obtain

$$\beta=\sqrt{{(\beta\cos\theta)}^2+{\beta_{\rm a}}^2{(1-\beta\cos\theta)}^2},$$ (4)

which for $\beta_{\rm a}=0.003$ (Sect. 3.1) and $\beta\cos\theta>0.43$ gives an intrinsic velocity of $\beta>0.43$ and an ejection angle $\theta\simeq0\hbox{$^\circ$ }$. If we consider a typical size of $\sim$10^-2 pc for the jets in other known microquasars, the $\sim$8 AU size of the LS I +61$^{\circ }$303 jet would result in an angle of $\theta\simeq0\hbox{$.\!\!^\circ$ }2$, compatible with our estimation.

As reviewed by Mirabel & Rodríguez (1999), the expansion velocities for microquasars range from $\sim$0.1 c to $\sim$0.9 c(SS 433, Cygnus X-3, GRS 1915+105, GRO J1655-40). The above determined lower limit of 0.4 c for LS I +61$^{\circ }$303 is therefore well within that range. Finally, we note that the combination of the values estimated for $\theta$ and $\beta$gives a Lorentz factor $\gamma=1.1$, and a Doppler factor $\delta_{\rm a,r}={1\over \gamma (1 \mp \beta\cos\theta)}$, $\delta_{\rm a}=1.59$ for the approaching jet and $\delta_{\rm r}=0.63$ for the receding one.

   
3.3 Precession of the accretion disk

The measured expansion velocities shown in Table 2 span a range of 0.002-0.007 c and reach a value of 0.06 c at epoch 1992 June 8. On the basis of our discussion in Sects. 3.1 and 3.2, we interpret the observed expansion velocities as apparent transverse velocities, $\beta_{\rm a}$, defined by Eq. (1). A possible explanation for the large range of observed velocities is a variable intrinsic velocity $\beta$ and a constant $\theta$. However, this is not supported by the observations available up to now; moreover, for example, SS 433 has shown a quite constant velocity of $\beta=0.26$ for years. The alternative explanation is precession of the jet, with the angle $\theta$ between the direction of the jet and the line of sight being a function of time. Evidence for precession has been found at least for SS 433 and Cygnus X-1 (Brocksopp et al. 1999). Moreover, for LS I +61$^{\circ }$303, precession of the jet has already been suggested to explain the 4 yr modulation of the peak of the radio outbursts (Gregory et al. 1989).

If the latter assumption is correct, we would expect an anticorrelation between the flux density of the radio outburst peak, and $\theta$ or $\beta_{\rm a}$. In other words, when the jet is pointing directly towards us ($\theta$ small), $\beta_{\rm a}$ is also small, and the flux density of the outburst peak is the highest possible due to the Doppler boosting effect. On the contrary, when the jet is not pointing directly towards us, $\theta$ and $\beta_{\rm a}$ increase, and the flux density decreases. In Fig. 4 we show the flux density of the radio outburst peak versus $\log\beta_{\rm a}$,

Figure 4: Flux density of the radio outburst peak versus $\log\beta_{\rm a}$ (see text). Each data point in this diagram is the result of the corresponding VLBI observation identified with letters a to f (see Table 2). For observations a, b, e and f the flux density of the radio outburst peak was known from the same VLBI observations or from the GBI monitoring program. Point d is a lower limit of the outburst peak, while c is taken from the average outburst peak flux modulation of Gregory et al. (1999).

for the VLBI observations listed in Table 2, taking $\beta_{\rm a}$ as the observed expansion velocity. We can see from Fig. 4 that the available data are consistent with the anticorrelation of the flux density of the radio outburst peak and $\beta_{\rm a}$ predicted by our model, and thus with the precession of the jet of LS I +61$^{\circ }$303.

Assuming that the the intrinsic velocity of the jet remains constant ( $\beta\simeq0.4$) for all the observations listed in Table 2, we can derive that the maximum value of the ejection angle $\theta$, corresponding to the maximum value of $\beta_{\rm a}=0.06$, is $\theta\simeq4\hbox{$.\!\!^\circ$ }5$. This maximum angle is consistent with a moderate precession of the jet, and could be the result of the precession of the accretion disk.

The range of values obtained for $\theta$ imply that the orbital plane of the system would be close to the plane of the sky, i.e., the inclination of the orbit, i, should be small. The other available information about i comes from spectroscopic optical and UV observations carried out by Hutchings & Crampton (1981). Although their observations reveal shell absorption, this fact alone does not give information on the angle of inclination, because the shell can cover the whole star and not be just an equatorial bulge (Kogure 1969; Geuverink 1970). We note that the observations by Waters et al. (1988) establish that, together with a dense and slow disk-like wind around the equator, there exists a high velocity, low density wind at higher latitudes up to the polar regions. On the other hand, Hutchings & Crampton (1981) obtain $v\sin~i=360\pm25$ km s^-1, where v is the equatorial rotational velocity of the Be star. As the maximum rotational velocity of a Be star (Hutchings et al. 1979) is v=630 km s^-1, this would result in a value of $i\sim 35^{\circ}$. However, Hutchings & Crampton (1981) comment that the velocity data are "extensive and unwieldy" and indeed the value of $v\sin~i$ given above seems large if compared with the statistical study of Be stars by Slettebak (1982). New observations would be very useful to clarify this issue.