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Astron. Astrophys. 340, 508-520 (1998)

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5. Spectral appearance

We calculate spectral energy distributions (SEDs), intensity maps, and line profiles of the models using a three-dimensional ray-tracing code. The basic concept of this code can be found in Yorke (1986). Here a version especially adapted to photoevaporating disks is used, which is described in Kessel et al. (1998, Paper III of this series).

5.1. Continuum

For the continuum radiation transfer we consider free-free emission, dust emission and the direct radiation of the star embedded in the center of the disk over the wavelength range 1 µm - 2 m. Many proplyds observed in the Trapezium of M42 are elongated objects with tails pointing away from [FORMULA] Ori C (O`Dell & Wen 1994, McCullough et al. 1995). Therefore we chose for the analysis of continuum radiation the massive disk with the weak tail shown in Fig. 5 (henceforth referred to as the tail model) and the low mass model with the extended wings shown in Fig. 7 (henceforth the wing model).

In Fig. 11 the SEDs of these models are shown at various viewing angles. The viewing angle is defined as the angle between the rotation axis of the disk and the line of sight. A viewing angle of [FORMULA] means we observe the disk pole-on from the direction of the ionizing star. At a viewing angle of [FORMULA] the disk is observed edge-on. The SEDs of the tail model are clearly dominated by the emission of the dust. The free-free continuum is only prominent in the radio region for wavelengths longer than [FORMULA] cm and in the near infrared at viewing angles where the stellar radiation is obscured by the disk. By contrast the dust emission of the wing model is significantly reduced compared to the free-free continuum. Still, in the wavelength range 10µm - 1 mm dust emission is the dominant process. In both models the variation with viewing angle is reflected in the strength of dust emission: both the wavelength of maximum [FORMULA] and the integrated dust emission increase with decreasing viewing angle as warmer parts of the disk become visible. The very flat radio spectra are consistent with radio observations of the Orion proplyds (Garay et al. 1987, Felli et al. 1993b).

[FIGURE] Fig. 11. Spectra of the model shown in Fig. 5 (left, "tail" model) and Fig. 7 (right, "wing" model) for various viewing angles.

In Fig. 12 we show intensity maps for the tail model (left) and the wing model (right) for a viewing angle of [FORMULA] at three different wavelengths from top to bottom. At 6.1 cm the free-free emission of the ionized gas above the disk is visible in both cases. There are only very faint emission tails along the ionization front in the map of the tail model, whereas the wings of the wing model are well recognizable. The appearance of emission "rings" in the wings is a result of the limited resolution of the numerical grid. The wings extend into coarser grids where a continuous variation of free-free emission along the ionization front is difficult to model. At 2.3 mm the warm inner regions of the disks become visible. Still, the free-free emission dominates at 2.3 mm in the wing model. The 100 µm maps emphasize the neutral denser parts of the models. The collimated tail and the wings are clearly recognizable.

[FIGURE] Fig. 12. Intensity maps at three different wavelengths as indicated. The left column refers to the model displayed in Fig. 5 ("tail" model) and the right column to the model in Fig. 7 ("wing" model). The maps are shown for a viewing angle of [FORMULA] between the rotation axis of the disk and the line of sight.


For the line transfer calculations we used the final models of case B, C, and D (displayed in Fig. 9) to get information about the variation of line profiles with the distance from the ionizing star. Distributions of the H[FORMULA] emission coefficient [FORMULA] for these three models are displayed in Fig. 13. The emission coefficient [FORMULA] is calculated from


where [FORMULA] is the effective recombination coefficient, [FORMULA] the electron number density and [FORMULA] the energy of the transition. In order to obtain H[FORMULA] surface brightness maps (Fig. 15) from the [FORMULA] distributions, line of sight integrations (including dust absorption) were performed for selected viewing angles. Most of the line emission originates from the regions close to the ionization front in front of the disk ([FORMULA]).

[FIGURE] Fig. 13. Distribution of the H[FORMULA] emission coefficient for the three final models of case B , C and D displayed in Fig. 9.

Fig. 14 shows the H[FORMULA] line profiles for the selected models of case B, C and D from left to right. Here we also calculate the line profiles for angles greater than [FORMULA]. The disk is optically thick for H[FORMULA], so that mayor changes in the line profiles for angles greater than [FORMULA] are to be expected. With decreasing source distance the ionizing flux increases and differences (with viewing angle) in the structure of the lines become more apparent. Viewing the disk at an angle of [FORMULA] most of the radiation is blue shifted; there is a net shift of the line towards negative velocities. With increasing viewing angle a greater fraction of the radiation is red shifted and at an angle of [FORMULA] the line velocity centroid is positive. The total H[FORMULA] emission is roughly the same for angles [FORMULA] and decreases for larger angles due to disk shadowing effects.

[FIGURE] Fig. 14. H[FORMULA] line profiles for the three final models of case B , C and D displayed in Fig. 9 for various viewing angles.

The corresponding H[FORMULA] surface brightness maps are shown in Fig. 15. The columns from left to right refer to the models of case B, C and D. From top to bottom the maps are drawn for different viewing angles, illustrating the three-dimensional structure of the H[FORMULA] emission. The [FORMULA] and [FORMULA] frames show the bright upper sides of the disks and the effects of increasing source brightness with decreasing distance. For viewing angles [FORMULA] the ionization front is most clearly visible; the disks appear as "silhouettes" against the H[FORMULA] background.

[FIGURE] Fig. 15. H[FORMULA]-maps for the three final models of case B , C and D displayed in Fig. 9 for various viewing angles.

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© European Southern Observatory (ESO) 1998

Online publication: November 9, 1998