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

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6. Discussion

Proplyds do not appear to be a species with well defined characteristics but rather a family of species. O'Dell & Wen (1994) classify them according to their form: Some appear as bright cusps with elongated tails. There are cusps and round heads without tails, teardrop shapes and irregular forms. Many of them are probably associated with supersonic jets (O'Dell 1995, O'Dell 1998).

The models presented here can reproduce some general characteristics of the more regular proplyds. The interaction of the ionizing radiation with protostellar disks tends to destroy the outer parts of the disks producing extensions which appear as elongated tails (see Fig. 12). Round heads without tails could be explained as disks observed nearly face-on (see Fig. 15).

Applying our model to radio observations requires evaporations rates [FORMULA] (Churchwell et al. 1987), in agreement with our results. Since the radii of our disk models are about a factor of 2-3 larger than that inferred from observations, our calculated [FORMULA] are somewhat higher. Johnstone et al. (1997, 1998) derive an analytical formula for the evaporation rate of a spherical clump due to Lyman continuum photons. In a dust free medium the incident EUV photon flux is approximately equal to the number of recombinations

[EQUATION]

where [FORMULA] is the recombination coefficient, [FORMULA] the particle density distribution above the ionization front and r the distance from the clump's center. For a freely expanding wind with [FORMULA] the integration of Eq. 8 yields the particle density [FORMULA] at the position of the ionization front [FORMULA]

[EQUATION]

The photoevaporation rate is obtained by integrating the particle flux [FORMULA] over the ionization front surface which is [FORMULA]. Hence

[EQUATION]

where [FORMULA] is the velocity of the evaporating flow. We used the [FORMULA] dependence to scale [FORMULA] of case B and C to the same disk radius of case D. The results are shown in Fig. 10; our power law exponent ([FORMULA]) is somewhat steeper than expected from Eq. 10. The deviation can be attributed to several effects. The ionized envelope of the disk is not a sphere and considerable mass loss arises from the edge of the disk. Thus the scaling with [FORMULA] is not entirely valid. The diffuse flux determines the evaporating flow on the shadow side of the disk. A comparison between both components of the diffuse photon density on the shadow side of the disk, shows that for case B the density of scattered photons [FORMULA] and the density of ground state recombination photons [FORMULA] are nearly equal. By comparison, [FORMULA] is more than an order of magnitude greater for case D, whereas [FORMULA] has increased only [FORMULA]%. A relatively minor contribution to the deviation results from the dependence of [FORMULA] on d.

However, the results of these simulations fail to match other important qualitative features. Recent molecular hydrogen observations (Chen et al. 1998) confirm the existence of molecular circumstellar disks embedded in the proplyds, but they also demonstrate that the ionization front stands off at a distance from the surface of the disk - most clearly visible in the case of the investigated teardrop shaped proplyd HST 10. Johnstone et al. (1997, 1998) attribute this to the fact that the molecular hydrogen at the disk surface is dissociated by FUV radiation penetrating the ionization front. The FUV radiation field is able to heat the atomic gas between the ionization front and the disk surface to temperatures of order [FORMULA]K (e.g. Tielens & Hollenbach 1985), producing a neutral outflow within the ionization front. In order to simulate this effect with our radiation hydrodynamic code we are currently implementing a FUV radiation transfer module with appropriate heating and cooling contributions. We expect that the results of future simulations will help us determine the influence of FUV radiation on the evolution and appearance of the proplyds. Nevertheless, the final models of case B, C and D are presumably useful models for the proplyds close to the ionizing star. For short distances mass loss is instigated predominately by EUV radiation and the warm transition layer arising from FUV radiation is relatively thin (Johnstone et al. 1998).

The ionizing stars of the Trapezium Cluster have ages in the range [FORMULA]-[FORMULA] yr (Prosser et al. 1994). By contrast, the disks of cases B, C and D already lose their appendages after several [FORMULA] yr. Why are there still proplyds with elongated tails? Our axially symmetrical illumination of the disk apparently could not reproduce long-lived ([FORMULA]) tails. We suspect that an off-axis illumination, presumably in conjunction with disk warping and precession, can continuously produce outflow "tails" in a direction pointing away from the source of illumination. Since parts of the disk surface will repeatedly enter shadow regions and regions of direct illumination, the varying strength of the shock front associated with the D type I-front should enhance the removal of disk material. Because the axis of the tail will not be identical to the disk's rotational axis, there would be less of a centrifugal barrier. Also, the fact that we used a dynamically stable disk originating from the collapse of an isolated molecular cloud as a starting model could have prevented the disk from continuously losing material via dynamic interaction. Neutral disk winds due to effects other than the FUV heating of surface layers could also contribute to an ionization front "stand-off" and long-lived disk tails. Finally, we have not considered the effects of external stellar winds. These additional effects should be considered in future numerical investigations. Although the tail and wing model are too young for direct comparison with the Orion proplyds they should be applicable to disks in the vicinity of young hot stars where the FUV /EUV photon ratio is small.

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© European Southern Observatory (ESO) 1998

Online publication: November 9, 1998
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