Next Contents Previous

6.4. Magnetic Disk Classes

There are various theories on magnetic field in dusty molecular disks around protostars, with different predictions for the direction and strength of the magnetic field. I group them here into a simple classification of 'magnetic disk classes' - a simple classification scheme using (a) magnetic field shape, (b) the disk's thickness, and (c) nearby companion(s). Such a simple classification can be complexified later, i.e., by combining two classes along or across the line of sight, and by adding different shapes above and below the disk.

6.4.1. Magnetic Class I: B shape parallel to disk, thick disk, no companion

Figure 10 shows a sketch of this magnetic class.

Figure 10

Figure 10. Magnetized molecular disk, with parallel B shape, thick disk (disk height/outer radius ~ 0.1). B lines are drawn into the disk by differential rotation. Adapted from Uchida & Shibata (1985).

The 'magnetic twist' model of Uchida and Shibata (1985) predicts a large scale poloidal magnetic field direction, that can be twisted by disk rotation to give a small scale toroidal magnetic field parallel to the disk major axis (their Fig. 2) to within 30 degrees. The theory of Uchida and Shibata (1985) also predicts a warm disk heated by magnetic field slippage (Joule heating), by adiabatic compression, and by stellar radiation, giving a disk temperature Tdisk = Tcorona / 400, which covers a wide range of hundreds of degrees K (after their Equ. 32 and their Fig. 6), with a minimum field strength B = 10 mG for a gas density n ~ 107 cm-3 and a maximum B = 100 G for a gas density 1013 cm-3 (after their Equ. 4).

A similar model uses a radial contraction of a rotating disk to twist the B field lines in the disk plane, with or without differential rotation in the disk (e.g., Fig. 6 in Kaifu et al. 1984). The 'dynamo' theory is another model (Stepinski & Levy 1990; Vishniac et al. 1990; Stepinski 1995) employing a B field direction parallel to the disk elongation, with substantial differential rotation in the disk. Here magnetic field amplitudes of 100 to 1000 Gauss are needed at the near edge of the disk, very much higher than expected from the submillimeter continuum observations and from the B vs nk relation with k = 0.5.

The 'cored-apple' model or 'circulation' model of Henriksen & Valls-Gabaud (1994) uses a toroidal magnetic field in a disk, an empty outflow cavity with a poloidal magnetic field, and a tangled magnetic field elsewhere within a large sphere. With a large telescope beam, the net polarization would come from the toroidal magnetic field in the disk.

Inside the disk: what happens to the magnetic field lines (inside the width of the disk) ? Variations of the geometry of the magnetic field in the disk can be thought. Thus in the 'twist' model, while the magnetic field turns around the disk center, the magnetic field lines are undulating, going slightly below the middle plane of the disk and than going slightly above the middle plane of the disk, as discussed further in Hildebrand (1996).

Main model advantages: the submm radio power from the dusty protostellar disk should be large in this class; differential rotation in the disk is normally included, with its effect on the magnetic field; twin jets out of the disk center can be accommodated; model can be followed theoretically. Main model disadvantage: many protostellar disks have one or more nearby companions, possibly affecting the primary disk in some way (gravitational and magnetic).

6.4.2. Magnetic Class II : B shape parallel to the disk, thin disk, no companion

Figure 11 shows a sketch of this magnetic class.

Figure 11

Figure 11. Magnetized molecular disk, with parallel B shape, thin disk (disk height/outer radius ~ 0.01). Adapted from Shu et al. (1988).

The theory of Shu et al. (1988) employs a magnetic field parallel to a very thin and long accretion disk (their Fig. 1), but the dust is not thick enough to emit much continuum radiation. Above the disk, the magnetic field lines are drawn outward by a centrifugally driven magnetic wind. In the disk, the magnetic field lines follow spirals aligned by differential rotation.

The thin disk model of Shu et al. (1997) could explain X-ray emission, notably during flares, due to interaction between an accretion disk and the magnetosphere of a central star, in the part of the disk closest to the star. Here in their modeled protostars, the gas density ~ 1010 cm-3, the magnetic field ~ 1000 Gauss, X-ray flares have a magnetic loop size ~ 107 km from the protostar, and these flares can heat the chondrules in the protodisk as well as release cosmic rays to bombard primitive rocks in the protodisk and induce short-lived radioactivities.

Main model advantages: differential rotation in the disk is normally included, with its effect on the magnetic field; model can be followed theoretically; twin jets out of the disk center can easily be accomodated by the central wind; can explain some characteristics of chondrules. Main model disadvantages: the submm radio power from the dusty protostellar disk should be small in this class; many protostellar disks have one or more nearby companions, possibly affecting the primary disk in some way (gravitational and magnetic).

6.4.3. Magnetic Class III : B shape perpendicular to the disk, thick disk, no companion

Figure 12 shows a sketch of this magnetic class.

Figure 12

Figure 12. Magnetized molecular disk, with perpendicular B shape, thick disk (disk height/outer radius ~ 0.4). Adapted from Pudritz (1985) and Pudritz & Norman (1983).

The 'disk-wind' model of Pudritz and Norman (1983) predicts a B field direction in the disk's surroundings and in the disk to be perpendicular to the disk major axis (their Fig. 1) to within 30 degrees. The theory of Pudritz and Norman (1983) also predicts, among other things, a cool disk temperature covering a range in the tens of degrees K (their Equ. 4), with a B strength of about 1 milliGauss (after their Equ. 69).

A similar model uses a spherical disk collapsing in 1-dimension along the regional B lines to give a disk (e.g., Fig. 1 in Pudritz 1985; Fig. 1 in Pudritz and Silk 1987). The ambient/regional B field direction outside the disk is nearly parallel to the B field in the disk. Such a B structure is partially supported by polarimetric observations at 0.8mm wavelength by Minchin & Murray (1994).

The 'cloud-collapse' model of Holland et al. (1996, their Fig. 7) for high-mass sources predicts a poloidal magnetic field in two cases (original; slighly compressed field), and a toroidal magnetic field in one case (highly compressed field). There is no mention of an outflow in this model (but it is assumed to lie along the external magnetic field lines).

Off the disk: what happens to the magnetic field lines outside the disk ? Variations of the geometry of the magnetic field outside of the disk can be thought. Thus in the 'hourglass' model the magnetic field lines start by stretching out radially away from the disk center, then go vertically away perpendicular to the disk. In the 'bulge' model the magnetic field lines start by concentrating towards the outflow axis, then go vertically away perpendicular to the disk. And in the 'torus' model, the magnetic field lines always go vertically away perpendicular from the disk. These models are discussed further in Hildebrand (1996).

Main model advantages: The submm radio power from the dusty protostellar disk should be large in this class; twin outflows out of the disk center can be accommodated; can be followed theoretically; can be adapted off the disk to the hourglass model. Main model disadvantages: differential rotation in the disk is not easily included, with its effect on the magnetic field; many protostellar disks have one or more nearby companions, possibly affecting the primary disk.

6.4.4. Magnetic Class IV: B shape perpendicular to the disk, thin disk, no companion

Figure 13 shows a sketch of this class.

Figure 13

Figure 13. Magnetized molecular disk, with perpendicular B shape, thin disk (disk height/outer radius < 0.1). Here the distance scale is in arbitrary units. Adapted from Newman et al. (1992) and Lovelace et al. (1991).

The 'magnetic-pinch' models of Lovelace et al. (1991), Wang et al. (1990), and Newman et al. (1992) use a B field direction perpendicular to a thin accretion disk, with twisting of the B lines above and below the disk to drive a bipolar outflow. The bipolar flow and the disk are both very close to the star at the center, so it is unlikely that dust grains will survive in large quantity. The initial poloidal magnetic field could arise from dynamo processes in the protodisk. Differential rotation is included here. Super-Kleperian rotation of the gas at large radii is predicted for a strong magnetic field.

Warp stability has been studied by Lovelace & Zweibel (1997) in a cold, magnetically-supported (approx 50 µGauss), thin (minor/major axis approx 0.1), non-rotating, disk of size approx 0.1 parsec and mass ~ 1 solar mass, without a central protostar (preceding star formation). Differential rotation is not included here. They found the disks to be stable against thermal or dissipative instabilities, for magnetic fields strong enough to control the environment (gas density ~ 103 cm-3).

Main model advantages: twin outflows out of the disk center can be easily accommodated; can be followed theoretically. Main model disadvantages: the submm radio power from the dusty protostellar disk should be small in this class; strong magnetic control required; many protostellar disks have one or more nearby companions, possibly affecting the primary disk.

6.4.5. Magnetic Class V: B shape perpendicular to the disk, thick main disk, with companion(s)

Figure 14 shows a sketch of this magnetic class.

Figure 14

Figure 14. Magnetized molecular disk, with predominently perpendicular B shape, thick main disk (disk height/outer radius ~ 0.2), with one secondary disk companion. Some tidal interaction has caused precession of the main rotating disk.

To get a magnetic field direction perpendicular to a disk elongation, a binary origin of the major object (disk) and minor object (companion) must be envisioned in the plane of the larger thin cocoon. With the common onset of gravitational collapse, the disk and cocoon have initially parallel axes of elongation. If the gas in the cocoon collapses along the ambient magnetic field lines, the magnetic field in the main disk is initially perpendicular to the main disk elongation. The companion object may or may not have fragmented later on from the main disk object.

Later interaction between the two objects (main disk and companion) could cause gravitational torques, changing the direction of the main disk elongation, and causing a precession of the main disk. Here, the magnetic field direction (perpendicular to the main disk elongation) may no longer be aligned with the ambient magnetic field direction (outside the cocoon). A fragmentation theory - without magnetic fields - by Bonnell & Bastien (1991; 1992a; 1992b) employs two companions (each with its own disk) embedded in a larger disk/cocoon. Each companion disk can be at an arbitrary angle with respect to the larger cocoon elongation. One needs to observe each disk to get the whole picture. The magnetic field does not have to dominate the interaction, which could be entirely gravitational in character, leaving the magnetic field to be a tracer of what goes on.

Main model advantages: the submm radio power from the dusty protostellar disk should be large in this class; there should be a dust companion nearby; twin outflows should be easily accommodated; differential rotation in the primary disk is normally included, with its effect on the magnetic field. Main model disadvantage: more difficult to follow theoretically and to make suitable predictions; need to observe both primary and secondary components to deduce the interaction history.

Figure 15 shows a simple model case for 2 clumps in a cloudlet. Here the two small propostellar disks are placed side by side within a common envelope, all the components having the same elongation perpendicular to the magnetic field lines.

Figure 15

Figure 15. Magnetic field model for 2 clumps in a cloudlet. Arrows show the directions of the model magnetic field lines, roughly parallel to the minor axis of the gas elongation.

Figure 16 shows a more complex model case for 5 clumps in a cloudlet. In this cloudlet, a central concentration of gas and dust along a ridge has formed, with gas peaks or dust cores located where future star(s) may form inside the ridge.

Figure 16

Figure 16. Model magnetic field as predicted for 5 clumps in a dusty molecular cloudlet. Note the dust cores/peaks along the cloudlet ridge.

Next Contents Previous