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Astron. Astrophys. 351, 192-194 (1999)

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3. Discussion

A rough approximation of the emission measure of a region in which [FORMULA] can be obtained if [FORMULA] in Eq. (4) and [FORMULA] in Eq. (5) are equated, giving

[EQUATION]

While we do not necessarily attribute the origin of the MWC 349 recombination line maser region at a distance of [FORMULA] (Cohen et al. 1985) to ionisation by ambipolar diffusion, we note that the emission measure of that region is probably around [FORMULA] - [FORMULA] (Thum & Greve 1997). In fact, the emission measure of a region ionised by ambipolar diffusion in the corona of a disk is likely to be reduced from the value given in (6) as the lengthscale over which the magnetic force varies is likely to grow beyond the density scaleheight as the magnetic flux moves into the corona. The rigorous calculation of such a reduction factor would be very difficult, but one might expect the reduction factor to be of the same order as the number of density scaleheights above the disk the flux must travel (to reach a region where ambipolar diffusion can induce a high fractional ionisation) divided by the ratio of the density scaleheight at that location to the mean density scaleheight up to that location. Given that the density scaleheight will increase significantly in the region where the fractional ionisation due to ambipolar diffusion becomes high, due to a significant temperature increase, the reduction factor may be closer to unity than 0.1. Note that the growth of the lengthscale over which the magnetic force varies does not necessarily imply a great weakening of the field strength, as the corona is likely to be filled with neighbouring flux tubes responding to the forces they exert on one another; indeed, we assume that the corona of a protostellar disk resembles the corona of our Galaxy in that the magnetic field strength in it at a height many times the disk thickness is only modestly less than that in the disk.

Some constraints on the detectability of Paschen recombination line radiation can be inferred from the fact that the weakest lines detected towards NGC 7027 in an integration in that spectral range had strengths of about 1.5 - [FORMULA] that of [FORMULA][FORMULA] from that source (Baluteau et al. 1995). From that fact and the known properties of NGC 7027 (e.g. Osterbrock 1974), we can conclude that Paschen recombination lines from a source that fills the beam can be detected in a source with an emission measure down to roughly [FORMULA]

We will assume that observations can be made at a diffraction limited resolution of [FORMULA]. Thus, so that the central star is not in the field of view the disk of a star at [FORMULA] must be observed at 15 and more A.U. from it. As the product of the density and the square of any relevant speed near the midplane of the disk is likely to be about two orders of magnitude less at such a distance than it was where much of the meteoritic material (examined in field strength estimates) cooled, the value of [FORMULA] used in (6) probably should be reduced by a couple of orders of magnitude. A region [FORMULA] across with an emission measure of [FORMULA] would be detectable in Paschen recombination emission if no other source of emission interfered with the observations, and, of course, a number of regions ionised by ambipolar diffusion might together cover a substantial fraction of a disk making detection of such radiation rather easier.

The winds of T-Tauri stars are sources of recombination radiation which may affect the observability of the regions ionised by ambipolar diffusion. The emission measures associated with the winds are of order [FORMULA] as one can infer from Table 5 of Edwards et al. (1987), and a wind will fill a beam. However, much of a wind's emission originates at much higher velocities than those of the ambipolar diffusion regions. Given the proximity of the Taurus cloud, recombination line emission from regions ionised by ambipolar diffusion around protostellar disks may be detectable with instruments to become available in the near future, if the disks are not embedded in material having high extinctions.

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© European Southern Observatory (ESO) 1999

Online publication: November 2, 1999
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