Astron. Astrophys. 319, 607-616 (1997)

5. Discussion

In the analysis of the SiO line wings two possibilities could be considered : a) the region where SiO line wings are formed coincides with the zone where the terminal velocity of the circumstellar envelope has been reached and, b) the SiO line wings are formed in the innermost regions of the envelope where the radial velocity associated to the expansion of the envelope is still small, but where the kinematics of gas allows velocities larger than . In both cases different kinematical processes could contribute to the production of SiO line wings such as : (i) turbulent motions; (ii) rotation ; (iii) gas infall and outflow; and (iv) asymmetric mass outflow. We will analyze now the possibility to produce weak SiO maser emission at velocities similar or larger than for these different cases.

5.1. Turbulent motions

The simplest models for circumstellar envelopes suggest a spherical envelope expanding with a constant radial velocity, , for distances larger than a few stellar radii. Between the stellar photosphere and the outer circumstellar layers the gas is accelerated, and its velocity increases monotonically until it reaches (see, e.g., Kwok 1975; Goldreich and Scoville 1976). In order to study qualitatively the conditions for which SiO v=1 J =2 1 line wings may form under the assumption of monotically increasing radial velocity fields, we have modelled the SiO emission by means of a non-local radiative transfer code that has been described in detail by González-Alfonso (1995) and González-Alfonso & Cernicharo, (1996, in preparation).

Our calculations indicate that a combination of high mass loss rate, low terminal velocity and large turbulent motions can produce weak blue wings reaching the terminal velocity of the envelope. However, our models fail to produce redshifted wings. Turbulence would apply to some stars showing blue wings, narrow linewidths, and high mass loss rates. If the regions where the line wings arise are very close to the star, the shadowing of the gas behind the central object could be important. In this case, our models predict mainly blue wings. However, only S Per and R Crt show a blue wing without red counterpart. Our observations (see Table 1) indicate that in most cases the SiO wings appear in the red. Hence, the standard kinematical models even in the presence of high turbulence seem insufficient to explain the full behaviour of the SiO maser wing emission.

5.2. Rotation

Rotation has been invoked by van Blerkom and Auer (1976), van Blerkom (1978), and Zhou Zhen-pu and Kaifu (1984) to explain the SiO J =1 0 v =1, 2 line profile in VY CMa.

Rotational velocities in a kleperian disk can be large near the central star and can play a role in the formation of the of the SiO line wings. However, the dependence of the angular velocity versus radius as reduces considerably the effect of rotation on the SiO line wing profile for longer distances. For instance, for a star with a mass of 1 and a radius, , of 5 10¹³ cm, the keplerian rotational velocity, , is 16 km s^-1 at r=2 , but reduces to 8 km s^-1 at r=8 . If strong amplification occurs near the star as VLBI and lunar occultation data seem to indicate, and if is similar or smaller than at r=2-3 , the effect of rotation in the formation of line wings exceding the terminal velocity must be considered for envelopes with moderate or low expansion velocities, 15 km s^-1.

As mentioned above, all stars showing high values of R have moderate terminal velocities, 10-12 km s^-1. The question that now arises is whether maser amplification near the star can take place under this geometry and kinematics. To elucitade this question and in order to evaluate qualitatively the effect of rotation in the formation of line wings we have modelled the SiO maser emission in a kleperian rotating non-expanding ring, using a non-local radiative transfer code (González-Alfonso 1995; González-Alfonso & Cernicharo, in preparation). The results show that the v =1 J =2-1 line is inverted (by the stellar radiation) only in the innermost part of the ring, where the rotation velocity is the highest (11 km s^-1). In other regions the inversion disappears beacuse the opacity in the axial direction becomes smaller than that in the radial direction. The emergent profiles consist then of two pronunced peaks at the extreme (rotation) velocities,  11 km s^-1. The predicted two peaked structure is not seen in the profiles, but note that the real kinematics in the inner envelope must be much more complex than the simple model used here. We conclude that rotation can not be eliminated as possible candidate for the origin of (some of) the line wings we have detected in SiO.

5.3. Pulsation: gas infall

For Mira and semi-regular variable stars, pulsation models indicate a complex velocity field near the star with successive gas infall and outflow. The gas also reaches the terminal velocity but, in the innermost part of the envelope the gas velocity can be larger than (Bowen 1988). The presence of infalling and outflowing gas layers due to the stellar pulsation could produce red and blue features from the gas lying in front of and/or behind the star. The later part could contribute to the emission provided that shadowing by the star is not important. If shadowing is important, however, red wings may still arise from the infalling gas in front of the star. In this context, the broad SiO line wings could be related to the optical or infrared absorption lines observed in the same kind of objects (e.g. Barbier et al. 1988; Hinkle 1978). However, the lack of general trend between R and the stellar phase for all observed stars indicates that more complex processes must be invoked to explain the data.

5.4. Asymmetric mass loss

Asymmetric mass loss processes could also constitute a natural explanation for the observed SiO line profiles. The only high angular resolution observations of the weak and broad SiO wings available in the literature are the lunar occultation data for R Leo reported by Cernicharo et al. (1994). These observations show that the line wings are detected far from the star ( 4-5 ), and are probably produced by an asymmetric mass loss process. High resolution studies from VLA observations of OH and H₂ O (see Bowers, Johnston and Vegt 1989 and Gómez et al 1994) also indicate that outflows from evolved stars are not isotropic but axisymmetric. In U Ori, Bowers & Johnston (1988) propose a model for the maser region in which OH is distributed in axisymmetric, biconical density concentrations embedded in an approximately spherical shell. Bowers, Johnston and de Vegt (1989) also propose for NML Tau, U Her, R Aql, RR Aql, and S Per similar axisymmetric structures in the expanding shells, with the shell of RR Aql being highly asymmetric. For their data they exclude radial acceleration, rotation or random velocity fields as origin of the distribution of OH and H₂ O masers and propose outflow of gas in a radially expanding ellipsoidal configuration with gas density being a function of radial distance and latitude from the equatorial plane of the star. In particular, they found that U Her and U Ori show blue and red features separated into opposite quadrants on the sky, a result similar to that found by Cernicharo et al (1994) for the SiO line wings emission in R Leo. All the objects quoted above also present red or blue SiO wings in our data.

The relatively large number of stars showing SiO broad wings (this work) and H₂ O velocity anomalies (Gómez et al, 1994), could also be related to the presence of binary systems (Morris 1987, 1990). The complex kinematic effects related to binary- or multiple-star systems may mean that asymmetric or axisymmetric mass loss processes are common in evolved O-rich stars. In this context, o Cet, a known binary sistem with a slow bipolar outflow, shows in our 1995 observations a broad pedestal in SiO emission which practically covers, at least in the red part of the spectrum, the outflow velocities as traced by the emission of CO. The case of o Cet suggests that bipolar mass loss processes could also play a role in the formation of SiO line wings.

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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