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6.3. Collapse models

6.3.1. Simple collapse models

Earlier reviews of the theoretical status of our knowledge on protostellar disk magnetic fields, with some applications to observations, are summarized below.

Galli (1995) used a theoretical size for a protostellar disk as characterized by a radius defined as the radius inside which infalling gas lands on its equatorial plane:

Equation 14

A radius of 600 AU corresponds to 0.003 pc. Many protostellar disks with gas density 106 to 107 cm-3 may have a magnetic field strength around 1 to 10 milliGauss.

Pudritz (1986) thus envisioned the magnetic fields in starforming cloudlets to be oriented parallel to the direction of the twin bipolar outflows (be it molecular or ionized), and suggested a picture where magnetic fields could dominate all aspects of cloud dynamics. Rotating outflows, corotating with an underlying object, is probable evidence for a hydromagnetic wind mechanism. Only a strong magnetic field can force accelerating gas at large distances to corotate out to 20 disk radii.

Königl & Ruden (1993) thus discuss the possibility that a significant magnetic flux is carried by the inflowing matter onto a protodisk, removing some of the angular momentum of the accreted matter. They pointed to meteoritic evidence for a ~ 1 Gauss magnetic field at a distance of 3 AU from the center of the early protosolar nebula. The young protostellar object itself could then develop a stronger magnetic field by dynamo action when it becomes convective. Magnetic braking of the stellar rotation could ensue, as well as disruption of the circumstellar disk out to a few stellar radii. Magnetic driving is proposed as the mechanism for launching the high-momentum neutral winds that give rise to the bipolar molecular lobes outside the disk.

Shu et al. (1987) discussed, among other things, the relative importance of turbulence versus magnetic field pressure in starforming cloudlets. The observed well ordered alignment of magnetic fields over the dimensions of cloudlets demonstrates that turbulence cannot be totally dominant over magnetic fields. Otherwise, a more tangled field configuration would result. Thus the observed turbulent motions are more probably wavelike than eddylike, and the magnetic field still has a well-defined mean direction. Their model favors a decoupling of the magnetic field from the gas density by ambipolar diffusion for gas density n > 1011 cm-3 (e.g., their Equation 17). Recent observational data shows that significant magnetic flux loss is not seen at n < 1012 cm-3 (e.g., Fig. 2 in Vallée 1995a).

6.3.2. Complex Collapse Models

Embedded disks are often needed by theories. Protostellar disks around protostars have dust, molecules, and magnetic fields inside, and protostars often (but not always) have a twin outflow (or twin jet) going away perpendicular to the protostellar disks (on both sides). These twin outflows/jets may be turned on or off by a 'magnetic switch', depending if gravitational forces dominate or not over magnetic forces in the hot tenuous corona close to the dense thin protostellar disk, i.e., if Bcorona is above or below [4pigas density]0.5Vescape, (e.g., Meier et al. 1997). Embedded disks are also observed. In L1551-IRS5, a large diffuse elongated envelope or protostellar disk (~ 20000 AU, ~ 0.1 parsec) has been seen around a small dense protostellar disk (~ 1400 AU, ~ 0.01 parsec) at its center, both with the same orientations, with a twin outflow going away perpendicular to these disks (e.g., Tamura et al. 1995). In HL Tau, a diffuse protostellar disk (~ 4000 AU, ~ 0.02 parsec) has been seen around a very small dense protostellar disk (~ 100 AU, ~ 0.0004 parsec) at its center, both with the same orientations, with a twin outflow going away perpendicular to these disks (e.g., Tamura et al. 1995). The tidal interaction between a protostellar disk and a nearby massive companion has been modelled (without magnetic fields), predicting gaps in the protostellar disk and tidal truncation (e.g., Lin & Papaloizou 1993; Shu et al. 1993).

What is the spatial orientation of twin outflows with respect to the galactic plane? Some pre main sequence stars with outflows seem to have their outflow axis roughly perpendicular to the galactic plane (Cohen et al. 1984). Some post main sequence stars with outflows seem to have their outflow axis roughly parallel to the galactic plane (Phillips 1997). Various mechanisms have been suggested to explain this situation, including the influence of the galactic magnetic field. None of these seem entirely plausible (the galactic magnetic field energy density is 10-4 times that of the kinetic energy density of twin outflows). Since we are dealing with relatively few well-defined outflows, then we may have to wait for bigger statistical studies in these areas.

Molecular disks around protostars are threaded by magnetic fields. In most models, the interstellar magnetic field lines frozen in the large parent cloud are advected inward, either (i) early on during the gravitational collapse of the cloud core/center, or (ii) later on during the subsequent accretion to the disk around the core/center (Königl, 1995). Magnetic waves are expected inside molecular cloudlets. Carlberg and Pudritz (1990) thus predicted excited hydromagnetic waves, with large velocity differences between resolved clumps (clump size < 2000 AU) as material oscillates between vibrating magnetic field lines, and a velocity coherence with density as material accumulates at the wave nodes. Thi spredicted velocity coherence is not seen with HPBW from 0.2 pc out to 100 pc (e.g., Heyer et al. 1996), indicating that the magnetic field is not dominant.

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