## 4. Discussion and interpretation
CFTWO concluded that IRAS 20126+4104 consists of a disk-outflow system
originating from a young early type massive (proto)star. Is this
scenario confirmed by the present observations? And, if so, do they
improve the understanding of the jet/outflow and disk structure? In
the following we shall give an answer to these questions. In
particular, in Sect. 4.1 we show how the new SiO measurements are
fundamental to understand the geometry and kinematics of the
outflow/jet, while in Sect. 4.2 we make use of the
CH ## 4.1. The outflow/jet systemAs already noted in Sect. 3.1.1 and discussed in CFTWO, the morphology of the outflow in IRAS 20126+4104 is very intriguing: the blue-shifted lobe of the flow corresponding to the inner blue wing lies to the SE, whereas the same lobe lies to the NW in the maps of the outer wings; a similar statement holds for the red-shifted lobe (see Fig. 3, left). The tentative explanation proposed by CFTWO and supported by models such as that by Cabrit & Bertout (1986) is that the axis of the outflow lies very close to the plane of the sky. As we shall see, such an interpretation is confirmed by the SiO observations. In order to better illustrate the kinematics and morphology of the
outflow/jet system, we show in Fig. 12 the position-velocity plots
along the flow axis for the HCO
A possible explanation for these characteristics is that the
relatively wide outflow seen in HCO In order to confirm the previous scenario, one should elaborate a detailed physical model describing the line emission in an expanding flow with given density and excitation temperature gradients. Such a model goes beyond the purpose of this work; however, it is possible to fit the S-shaped pattern of the SiO position-velocity plot using a simple-minded approach. Our assumption is that the jet traced by SiO is conical in shape and that the gas in it is uniformly accelerated up to a maximum distance from the centre, where its velocity drops abruptly to zero. The latter hypothesis is justified by the clear existence of a bow shock at the end of the SiO jet (see Figs. 3 and 4). This simple model allows to easily reproduce the maximum extent of the emission pattern in Fig. 12 bottom, namely the shape of the faintest contour level. Note that the assumption of velocity proportional to the distance from the centre ("Hubble" law) is consistent with what observed in other outflows such as that in HH 211 (see Guilloteau et al. 1997). The details of the model are given in Appendix A; however, it is easy to understand that the emitting region in the position-velocity plot is included between two straight lines (corresponding to the expansion velocity along the surface of the cone) and an ellipse (corresponding to the maximum velocity reached by the expanding gas). The inclination of the straight lines and the size and eccentricity of the ellipse depend on the free parameters of the model, namely the semi-aperture angle of the cone, its inclination with respect to the plane of the sky, the maximum velocity of the gas, and the angular distance from the centre at which this velocity is reached. In Appendix A we demonstrate that these parameters can be reasonably determined from the observational data and we present the best fit obtained in Fig. 13.
The most important result of the model is the accuracy of the determination of crucial quantities such as the inclination angle of the jet axis. This is due to the sensitive dependence of the fit on the input parameters. Clearly the inclination angle is very small, thus confirming the hypothesis of CFTWO that the flow axis lies close to the plane of the sky. Incidentally, we note that the faint emission seen in Fig. 13 along
the line of sight through the centre at
-70,
50, and 90 km s Finally, we note that the previous treatment cannot be applied to
HCO ## 4.1.1. Time scale and physical parameters of the jetAs done by CFTWO for the HCO
We note that all the quantities in Table 6 computed from the observed velocity (i.e. energy, momentum, and luminosity) must be corrected for the inclination of the flow axis: this can be obtained by dividing the momentum by and the energy and luminosity by , where is the angle between the flow axis and the plane of the sky. In Appendix A we show that a reasonable guess is and hence the correction factor amounts to 6.4 for the momentum and momentum rate, and 41 for the energy and mechanical luminosity. ## 4.2. The rotating diskAs shown in Sect. 3.1.2, the CH ## 4.2.1. Temperature gradientIf a temperature gradient does exist, this should affect the
distribution of lines with different excitation energies. In order to
investigate this effect, we plot in Fig. 14 three quantities measured
for each
Looking at Fig. 14, one sees that is clearly decreasing with increasing excitation energy of the transition. This demonstrates two facts: that higher energy lines arise from smaller regions; and that the excitation temperature increases towards the centre of the core. We stress that the trend shown in Fig. 14 bottom, cannot be due to optical depth effects: in fact, in this case the size measured in the high energy lines should be greater or equal to that measured in an optically thin tracer such as CCN(12-11), whereas Fig. 14 shows that is marginally greater in the latter (filled circles above 400 K) than in the former (empty circles) lines. Also, the ratio between in the highest and that in the lowest energy lines is 0.4, whereas it is possible to demonstrate that in a spherical homogeneous core the ratio between in the optically thick and thin limit cannot be less than . ## 4.2.2. Velocity field: rotationThe fact that higher excitation lines trace inner regions of the core (and hence of the disk) can be used to study the velocity field in it. The trend of and in Fig. 14 reflects a variation of these quantities as a function of distance from the centre. In particular, if we are dealing with a rotating disk whose mass is not much larger than that of the embedded star, the rotation velocity should increase towards the centre. Such an effect cannot be seen in Fig. 5c because the core is only barely resolved; however, just for this reason the whole disk falls into the beam and hence one should see an increase of the line width in the higher energy transitions, which arise closer to the centre of rotation. This is exactly what the middle panel of Fig. 14 shows. In order to clarify this issue, in the top panel of Fig. 15 we plot versus on a logarithmic scale. A linear fit to the data gives the following relation: The dependence on is very close to that expected for Keplerian rotation: in this case the line width is equal to twice the velocity at an angular distance /2 from the centre and is given by the expression where
We caution that the result obtained above needs further
confirmation because the spectral resolution of our observations is
much larger than the formal errors reported in Fig. 15. However, a
couple of facts support this interpretation. First of all, Fig. 5c
shows a maximum dispersion along the velocity axis towards the centre
of the core (indicated by the dashed vertical line): this is just what
one expects for Keplerian rotation. Secondly, the trend shown by the
CH If we are indeed observing a Keplerian disk, then its mass must be
less than that of the star. An estimate of the disk mass on the scale
traced by CH ## 4.2.3. Velocity field: collapseSo far, we have presented an explanation for the trends in the bottom and middle panels of Fig 14, namely for the dependence of and on the excitation energy of the transition. However, the rotating disk model cannot explain the trend of , shown in the top panel of the same figure. As already discussed for , also for an increase with excitation energy implies an increase with decreasing distance from the centre: such a red-shift of the line is not expected if the disk is purely rotating, but might be explained if the inner regions of it are collapsing towards the centre. In this scenario, the line profile arising from the outer regions is quite symmetric because the collapse is less enhanced than close to the centre and because both the front (blue-shifted) and the rear (red-shifted) parts of the disk contribute to it; on the contrary, a line tracing the part of the disk closer to the centre must be fainter in the blue, if the rear emission is partly suppressed by the continuum absorption due to the dust in the core. In order to check this effect one needs high spectral resolution in
a high excitation line: the
Incidentally, we note that self-absorption can be probably excluded
because it should be more evident in the low energy transitions (i.e.
low The explanation proposed above requires that a suitable region
close to the centre of the core is optically thick in the continuum at
1.3 mm. Is this realistic? Following Wilking et al. (1989), one
can express the dust optical depth as
, where we have assumed a dust
absorption coefficient proportional to
. A mean value of the column density
over the core can be computed using the mass estimate of Sect. 4.2.2
(1.7 ) and the diameter as
derived from Fig. 5b (0:004 or 0.0033 pc): one obtains
= cm ## 4.2.4. The nature of the YSOIn Sect. 4.2.2 and 4.2.3 we have illustrated the evidence in favour of IRAS 20126+4104 being a YSO of 24 surrounded by a collapsing and rotating Keplerian disk. Now, we use this result to investigate the nature of such a YSO.
where =24 is the mass of the protostar and the mass accretion rate on its surface. An estimate of can be obtained from the equation with and We conclude that the previous results favour the hypothesis that
IRAS 20126+4104 is a massive © European Southern Observatory (ESO) 1999 Online publication: April 28, 1999 |