Astron. Astrophys. 337, 832-846 (1998)

4. Results

With the code described above we determined SEDs, continuum isophotal maps and line profiles for the forbidden lines [NII ] 6584, [OII ] 3726 and [OIII ] 5007 as well as the H-line for the models introduced in Sect. 3.1. Their relevant physical parameters are listed in Table 2.

4.1. Continuum emission

4.1.1. Spectral energy distributions

Fig. 6 shows the SEDs of model G2 presented in Paper II for different viewing angles . The spectra can be divided into three regimes dominated by different physical processes:

1. In the frequency range from to Hz the SED is dominated by the thermal free-free radiation in the ionized region around the dust torus.

2. The IR -excess from to Hz is due to the optically thick dusty torus itself, which has a mean surface temperature of about 250 K.

3. Beyond Hz the SED depends strongly on the viewing angle: if the star is obscured by the dusty torus then the free-free radiation of the HII -region again dominates the spectrum, otherwise the stellar atmosphere shows up. Due to the uncertainties in the stellar spectra and the neglect of scattering by dust in Eq. (16), which becomes more and more important with increasing frequency, a discussion of the SED beyond  Hz and comparison with observations are not useful.

Fig. 6. Spectral Energy Distribution for model G2 and different .

According to the analysis of Panagia & Felli (1975), who calculated analytically the free-free emission of an isothermal, spherical, ionized wind, the flux density should obey a -law:

Schmid-Burgk (1982) showed that this holds, modified by a geometry dependent factor of order unity, even for non-symmetrical point-source winds as long as drops as . Additionally he postulated that the flux density should hardly be dependent on the angle at which the object is viewed. In Fig. 6 we include for comparison the flux distribution given by Eq. 25 for the photoevaporation rate (see Paper II),  K and derived from the line profiles in Sect. 4.2. The slope of the SED in regime 1 is slightly steeper in our results, because our volume of integration is finite; Panagia & Felli (1975) derived their analytical results by assuming an infinite integration volume. The flux is almost independent of , which is in good agreement with Schmid-Burgk (1982). The deviations between and Hz are due to the break in the -law caused by the neutral dust torus.

Fig. 6 also includes the SED of a blackbody at  K. The flux in the far IR between Hz and Hz is slightly steeper than the comparison blackbody spectrum, because the dust torus is not quite optically thick. With increasing the maximum shifts towards lower frequencies, because the warm dust on the inside of the torus is being concealed by the torus itself.

We obtain qualitatively the same results for a number of models presented in Paper II.

4.1.2. Isophotal maps

We also calculated isophotal maps over the projected grid of the sky for models C and G4 (Figs. 7,8). The maps were convolved with a Gaussian point spread function (FWHM 03 for cm, 01 for cm and m) in order to compare the numerical models with observations of limited resolution. The values (in percent) of the contour lines relative to the maximum flux per beam are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90 for cm, and 2, 5, 15, 25, 35, 45, 55, 65, 75, 85, 95 for cm and m.

Fig. 7. Isophotal maps of model C for different viewing angles and wavelengths as indicated. Assumed distance 300 pc. The circle in the lower right corner marks the FWHM of the point spread function. Values for contours see text.

Fig. 8. Isophotal maps of model G4 for different viewing angles and wavelengths as indicated. Assumed distance 300 pc. The circle in the lower right corner marks the FWHM of the point spread function. Values for contours see text.

The difference in these two models is revealed most strikingly in the maps for cm and cm. The mass outflow of model C is more evenly distributed over its whole opening angle, whereas in model G4 most of the mass is transported outward in a cone between and . This leads to the X-shape of the corresponding radio maps for viewing angles . The high density in the region between star and disk for this model results in an optically thick torus in this region at cm. Thus the contours for and are not symmetric to the equatorial plane at .

In the maps corresponding to m there appears a peculiar horseshoe-like feature. It is generated by the hottest region of the dust torus, which is the innermost boundary with the smallest distance to the star. It can be seen as a ring in the maps for . For the part of the ring next to the observer is obscured by the dust torus, whereas the other parts are still visible. The beam width chosen by us allows the resolution of the ring and thus leads to the horseshoe-like feature. For only the most distant part of this hot ring is visible, leading to a maximum in the flux with a smaller spatial extent than for .

4.2. Line profiles

Line profiles can provide useful information on the velocity structure in HII regions. Because the thermal doppler broadening decreases with increasing atomic weight as , ions such as NII and OIII are better suited for velocity diagnostics than . This can be seen in the line profiles we obtained (Figs. 9 - 12). They show the flux integrated over the whole area of the object including the disk, the evaporated flow and the cone of the stellar wind. In all cases the line broadening of several ten km s^-1 is dominated by the velocity distribution of the escaping gas. For comparison, the rotational velocity of the dust torus  km s^-1 for the inner parts, and the thermal Doppler broadening from Eq. (8) at  K is  km s^-1 for H and  km s^-1 for OIII .

Fig. 9. Lines [NII ] 6584 and H for models G2, G3 and G4, and different "viewing angles" . The models differ only in wind velocity .

Fig. 10. Lines [NII ] 6584 and H for models A and C, and different "viewing angles" . In model A scattering of UV photons by dust was neglected, in model C included. Note the different scales on the abscissae.

Fig. 11. Lines [OII ] 3726 and [OIII ] 5007 for models G2, G3 and G4, and different "viewing angles" . The models differ only in wind velocity .

Fig. 12. Lines [OII ] 3726 and [OIII ] 5007 for models A and C, and different "viewing angles" . In model A scattering of UV photons by dust was neglected, in model C included. Note the different scales on the abscissae.

Figs. 10 and 12 show the line profiles for the models A (no scattering of H-ionizing photons) and C (calculated assuming non-negligible UV scattering during the hydrodynamical evolution) from Paper II. UV scattering leads to stronger illumination of the neutral torus by ionizing radiation and thus to a higher photoevaporation rate in model C (by a factor of ) compared to model A. Due to the higher density in the regions filled with photoevaporated gas, the lines for model C are generally more intense. In the case of the line [OII ] 3726 one notices that the difference between the fluxes for different angles is the smallest of all transitions. Not only is the density of the outflowing ionized gas higher for case C, but the charge exchange reactions discussed in Sect. 2.2.1lead to the establishment of a non-negligible OII -abundance even in the "shadow" regions not accessible to direct stellar illumination. These regions dominate the line spectra for all angles.

Figs. 9 and 11 show the calculated line profiles for the models G2, G3 and G4, which only differ by the assumed stellar wind velocity , increasing from 400 km s^-1 (G2) to 1 000 km s^-1 (G4). Comparing the results we find two features:

1. The intensity and overall structure of the line profiles considered are almost independent of the stellar wind velocity .

2. No high-velocity component appears in the lines due to the stellar wind.

Both features can be explained by the fact that the density of material contained in the stellar wind is much lower than the density in the photoionized outflow. Remembering that in a steady-state outflow and that the line emissivity , we can understand why the low expansion velocities of about 20 km s^-1 (i.e. material close to the torus) dominate the spectra. The overall evaporation rates as well as the expansion velocities are almost equal for all three models, leading to very similar line profiles. It would be necessary to consider transitions which predominate in hot winds in order to detect this high velocity component and to find significant differences between these models.

In spite of our assumption of optically thin line transfer, the profiles for are not symmetric. This is due to the dust extinction within the HII -region. The receding material is on average further away from the observer than the approaching. The longer light paths result in stronger extinction of the redshifted components.

We are aware of the fact that the neglection of scattering by dust in Eq. (16) may lead to serious errors in the calculated line profiles. We expect non-negligible contributions especially in the red-shifted parts of the lines due to light scattered by the dense, dusty surface of the neutral torus. This light was originally emitted by gas receding from the torus. The resulting redshift "seen" by the torus remains unchanged during the scattering process and will thus lead to enhancement of the red-shifted wings of the lines.

Nevertheless, we expect our qualitative results still to hold since the arguments mentioned above referring to the geometry of the underlying models are still applicable.

© European Southern Observatory (ESO) 1998

Online publication: August 27, 1998
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