2.2.5. Magnetic field shapes in Dusty Elongated Molecular Clouds
On the theoretical side, there has been many detailed models published for the behavior of gas density, temperature, turbulence, velocity, pressure, and of magnetic field in isolated or colliding molecular clouds, often involving ambipolar diffusion and energy equilibrium between some of these physical parameters (e.g., McLaughlin & Pudritz 1996; Ciolek and Mouschovias 1994; Morton et al. 1994; Crutcher et al. 1994; Just et al. 1994; Porro and Silvestro 1993; Elmegreen & Fiebig 1993; Ciolek & Mouschovias 1993; Elmegreen & Combes 1992; Elmegreen 1988; Mouschovias et al. 1985; etc).
While current limited observations cannot test many of the detailed physical parameters mentioned above, at least the distributions of thermal gas density and magnetic fields are amenable to observations, within the beamwidth limitations of the telescopes used. Various magnetic field theories have been published in the literature, predicting the magnetic field direction and amplitude in and near a molecular cloud. In this research area, there is a plethora of theories on magnetic field direction, yet few observations.
2.2.5.1 SUPERPOSITION OF CLOUDS A possible classification of observed magnetic fields in five 'spatial pattern types' has been suggested by Myers & Goodman (1991), involving chiefly a superposition of clouds or sub-clouds. The five 'spatial pattern types' found in typical clouds are as follows. (a) One cloud, with similar polarization PA values over its entire length (e.g., L1755, B216, etc). (b) One cloud, with randomly distributed polarization PA values over its entire length (e.g., L1689, N1333). A cloud with 2 distinct sub-clouds, each having a distinct polarization PA over its entire region, is classified as follow: (c) the 2 sub-clouds are seen across the line-of-sight (e.g., Lupus 3; L203; etc); or (d) the 2 sub-clouds are seen along the same line of sight (e.g., Perseus complex). (e) One cloud, with 2 distinct sub-clouds, one region with a distinct polarization PA and a small dispersion in polarization PA values, and another region across the line of sight with nearly random polarization PA values and a large dispersion in polarization PA values (e.g., Lupus 2; Ophiucus complex; etc).
The Myers and Goodman (1991) classification (a) - (e) uses two parameters, namely the number N of correlation lengths of the magnetic field in a cloud (i.e., the number of independent regions in a cloud), and the amount of the dispersion in polarization PA values. They concluded that N is small, perhaps 1 to 4, for a typical cloud size ~ 1 pc, from the spatial patterns of observed optical polarization vectors of background stars seen through a nearby cloud. Their classification, involving correlation lengths and angular dispersions between sub-clouds, has been used by Kobulnicky et al. (1994) and Jones et al. (1992).
2.2.5.2 MAGNETIC FIELD CLASSES A new classification has been proposed by Vallée & Bastien (1996, hereafter V&B) based on 11 'magnetic field classes', involving only one cloud (no superposition of sub-clouds). This classification has several bonuses. (i) It is physically simple, compared to the combinations of Myers &Goodman (1991). (ii) It can be later complexified by a simple superposition of any 2 of the 11 magnetic field classes here; thus one cloud in V&B class F seen along the same line of sight of one cloud in V&B class G can give the spatial pattern type d of Myers and Goodman (1991). (iii) These 11 magnetic field classes, when combined two by two along or across the line of sight, could of course allow more combinations than the five spatial pattern types of Myers and Goodman (1991) known so far.
The simple classification scheme of V&B uses 2 parameters: the magnetic field's shape and the magnetic field's distance scale. It has been used by V&B to compare with actual JCMT polarimetric observations in the extreme infrared.
Figure 2a-k shows several cartoon-style drawings with the main features for each magnetic class, as described further below.
 |
 |
 |
|
Figure 2. Cartoon-style drawings showing the main features of each 'magnetic class', described further in the text. Class A. Magnetized molecular clouds of varied shapes, with a spiral galactic magnetic field shape on 10 kpc scale. The B field shows a clockwise direction outside a 6 kpc radius from the galactic center, even inside molecular clouds (as shown). In this model, B-vectors are parallel to the galactic plane, and the magnetic field lines shown are going clockwise. In addition, a B reversal in the radial range 5.5 kpc < rg < 7.5 kpc is known (magnetic field lines going counterclockwise), but not shown here. Class B. Magnetized molecular cloud, with a halo-disk magnetic field shape on 1 kpc scale. B-vectors follow a U-shaped bowl, coming from the galactic halo and being parallel to the galactic plane at the bottom of the bowl. Class C. Magnetized molecular cloud, with cloud-cloud magnetic field shape on 1 kpc scale. B-vectors follow the cloud elongation in a cloud, except near the edges of a cloud where B-vectors enter and leave in a Y-shape fashion (taken here at up to +40 or -40 degrees from the cloud elongation). Class D. Magnetized molecular cloud, with cloud magnetic field perpendicular to the regional magnetic field shape on 100 pc scale. Class E. Magnetized molecular cloud, with cloud magnetic field parallel to the regional magnetic field shape on 100 pc scale. B-vectors in a cloud are parallel to the regional magnetic field outside the cloud (~ 100 pc). Class F. Magnetized molecular cloud, with pinched magnetic field shape on 1 pc scale, and a local magnetic field on 10 pc scale. B-vectors in a clump show pinching effects of magnetic field lines in clump edges (X-shaped). Class G. Magnetized molecular cloud on 1 pc scale, with 1-dimensional collapse along localised magnetic field shape on 10 pc scale. B-vectors are perpendicular to the cloud elongation at each point, whatever the curvature of the cloud. Class H. Magnetized molecular cloud, with orthogonal-field in clumps and aligned-field in filament shape, 0.2 to 10 pc scale. B-vectors in clumps are perpendicular to cloud elongation, and B-vectors in-between clumps are aligned along cloud elongation. Class I. Magnetized molecular cloud, with aligned-field in clumps and orthogonal-field in cloud shape, 0.2 to 10 pc scale. B-vectors in clumps are parallel to cloud elongation, and B-vectors in-between clumps are aligned perpendicular cloud elongation. Class J. Magnetized molecular cloud, with helically-wrapped field shape, 1 pc scale. Here B-vectors are skewed -20 degrees from the direction of cloud elongation. Class K. Magnetized molecular cloud, with magnetized independent-clump shape, 0.1 pc scale. B-vectors are randomly oriented in clumps. See Vallée & Bastien (1996) for more details. |
|
Class A. The spiral-galactic magnetic field, with a galactic magnetic field on a scale of 10 kpc. In this first class of theoretical models, the B-vectors are parallel to the galactic plane, following the spiral arms, even in molecular clouds. A model in this class is supported by OH maser Zeeman observations (Reid and Silverstein, 1990), suggesting that the magnetic field direction is largely preserved during cloud contraction from low interstellar densities through the medium densities in giant molecular clouds up to the higher densities in star forming sites (e.g., Fig. 3 in Elitzur 1992).
Class B. The halo-disk magnetic field, with a galactic magnetic field on a scale of 1 kpc. In this second class of theoretical models, the B-vectors follow a U-shaped bowl, first coming from the galactic halo (perpendicular to b = 0°), then being parallel to the galactic plane at the bottom of the bowl (where the cloud sits). A model in this class employs cosmic-rays generated near the galactic plane to inflate magnetic arches between clouds, causing the magnetic field to expand upward at greater galactic latitudes (e.g., Fig. 3 in Parker 1976) and to drive the galactic dynamo (e.g., Parker 1992).
Class C. The linked cloud-cloud magnetic field, with a galactic magnetic field scale around 1 kpc. In this third class of models, the B-vectors are parallel to the cloud elongation, except near the two edges of the elongated cloud where the B-vectors enter and leave (as in a Y-shaped funnel). A model in this class employs galactic magnetic field lines connecting together several elongated molecular clouds (e.g., Fig. 4 in Beck et al. 1991). Here magnetic field lines are anchored in the clouds and influence cloud motions and cloud collisions (e.g., Clifford and Elmegreen 1983).
Class D. The cloud's magnetic field is perpendicular to the regional magnetic field, with a regional magnetic field on a scale of 100 pc, and a cloud magnetic field on a scale of 10 pc. In this fourth class of models, the B-vectors in the clumps are perpendicular to the magnetic field in the region on a scale of 100 pc surrounding the cloud and clumps. This 100 pc scale is the scale of the perturbation of the galactic magnetic field by interstellar magnetic superbubbles (100-125 pc in radius (e.g., Vallée 1993d). A model in that class was employed to explain the polarization around the stars HL Tau and Star #4 in L1551 by Vrba et al (1976), and to explain the arched filaments of the Galactic Center Arc by Morris et al. (1992), as well as to explain the polarization of the Taurus cloud by Nakajima & Hanawa (1996).
Class E. The cloud's magnetic field is parallel to the region's magnetic field, with a regional magnetic field on a scale of 100 pc, and a cloud magnetic field on a scale of 10 pc. In this fifth class of models, the B-vectors in clumps are parallel to the magnetic field in the region over a scale of 100 pc surrounding the cloud and clumps. This 100 pc scale is similar to that of the sizes of interstellar magnetic bubbles (100-125 pc in radius). Models in that class were employed by McDavid (1984) and Pudritz and Silk (1987), in which cloud fragmentation gives rise to cloudlets with B-vectors in cloudlets, and in between cloudlets, that are parallel to the original B-vector direction in the original cloud and in the 100-pc region.
Class F. The pinched galactic magnetic field in clumps, with a local magnetic field on a scale of 10 pc, and a collapsing core magnetic field on a scale of 1 pc. In this sixth class of models, the B-vectors in clumps and in-between clumps are parallel to the cloud elongation, with pinching effects of the magnetic field lines in clump edges (X-shaped). A model in this class was invoked for the clump W3-IRS5 (Greaves et al., 1992), and can be explained via a sudden collapse of gas to form a high-mass star, with pinching of the magnetic field lines at the stellar position.
Class G. The 1-dimensional collapse along localized magnetic field lines, with a local magnetic field on a scale of 10 pc, and a cloud magnetic field on a scale of 1 pc. In this seventh class of models, the B-vectors are roughly perpendicular to the cloud elongation, whatever the wavyness of the cloud. A model in this class employs a cloud originally spherical that collapses along the magnetic field lines in one dimension, becoming highly flattened in the process (e.g., Mestel 1965; Langer 1978). Another model in this class invokes the evolution of an elongated cloud by magnetic field control (50 µGauss) to minimise the disturbances which act on a cloud (McCutcheon et al., 1986). Whittet et al. (1994) showed evidence in Chamaeleon for such a magnetic class.
Class H. The orthogonal magnetic field in clumps plus aligned magnetic field in filament, with a cloud magnetic field on a scale of 0.2 pc to 10 pc. In this eighth class of models, the B-vectors in the clumps (within an elongated cloud) are perpendicular to the cloud elongation, whereas the B-vectors in-between clumps are parallel to the cloud elongation. A model in this class is employed to explain two dust filaments in the Ophiuchus cloud (optical data in Vrba et al., 1976; radio HI data in Heiles, 1987) and to explain a filament in R Coronae Australis (Vrba et al., 1981). McGregor et al. (1994) showed evidence in Chamaeleon for such a magnetic class.
Class I. The aligned magnetic field in clumps plus orthogonal magnetic field in cloud, with a cloud magnetic field on a scale of around 0.2 pc to 10 pc. In this ninth class, the B-vectors in clumps (within an elongated cloud) are parallel to the cloud elongation, whereas the B-vectors in-between clumps are perpendicular to the cloud elongation. A model in this class was employed to explain 3 elongated dense condensations in Taurus (DG Tau; Haro 6-13; Star no.1 in Fig. 1 of Moneti et al., 1984), and one in Serpens (Warren-Smith et al., 1987).
Class J. The helicoidally-wrapped magnetic field in a cloud, with a cloud magnetic field on a scale of 0.5 to 5 pc. In this tenth class of models, the B-vectors are helicoidally wrapped around the cloud elongation, but the magnetic field lines are skewed by about 20° from the cloud elongation. A model in this class is employed when there is a claim for a close connection between the cloud kinematics (the local-standard-of-rest velocities change gradually along the cloud elongation) and the magnetic fields (the polarization changes gradually along the cloud elongation), as in Bally (1989). A theoretical example is worked out in Hanawa et al. (1993) and in Shibata and Matsumoto (1991).
Class K. The magnetized independent, random clumps, with a clump magnetic field on a scale of 0.1 pc. In this eleventh class of models, the B-vectors are randomly oriented in clumps. A model in this class is that of pressure-confined clumps in magnetized molecular clouds (e.g., Bertoldi and McKee 1992). Turbulent support inside a clump is provided by magnetic fields with an amplitude of about 10 to 40 µGauss for clump densities of 103 cm-3 and increasing as the square root of the clump density. In another model, it is postulated that the magnetic field lines thread both the clump and the interclump medium in a cloud (e.g., Blitz 1991, his Section 9). Because of thermal equilibrium between atomic gas in-between clumps and molecular gas in clumps, the deduced magnetic field amplitude is about 10µGauss in gas densities of 103 cm-3 (e.g., Blitz 1991).
2.2.5.3 COMPARISON The above classification system of
V&B has been successfully compared with recent
observations of the M17-SW molecular cloud at Extreme-Infrared
wavelengths (
800
µm) with
the JCMT. Six positions of peak intensity (clumps) in the ridge
of dust were observed with the
Aberdeen-QMW polarimeter, and the observed linear polarization PA
were converted to
magnetic field PA (V&B, their Table 4). Also, the magnetic field
PA predicted from each
'magnetic class' A to K was computed (V&B, their Table 5), and a
comparison of observed
minus predicted magnetic field PA was made (V&B, their Table 6)
showing that 9 of the 11
'magnetic classes' could not explain M17-SW. Magnetic Class E and
Class G could explain the
magnetic field observed in M17-SW, and to separate them would
require new observations to
be made in the interclump medium, located between clumps (peak
intensity positions) in the molecular cloud.
Figure 3 shows the proposed magnetic field map
over the cloud M17-SW, with
magnetic field lines going from bottom-left to the right (upper-right
and lower-right). The
dense dust and gas peaks/clumps were observed at the JCMT at
800 µm
(Vallée and Bastien,
1996),
while the light dust and gas areas/halo data come from the
KAO polarimeter at 100
µm
(Dotson, 1996a;
Dotson, 1996b).
Some problems inherent to Far Infrared Polarimetry
near 100
µm are discussed further in
Hildebrand (1996).
 |
Figure 3. Observed magnetic field in the
molecular cloud M17-SW. The ridge line
(dots) links the 6 main dust peaks (P1 to P6) in the cloud core.
The magnetic field vectors
are shown by the bars. In the higher gas density core, the thick
bars show the magnetic field derived from the JCMT
|
A few other magnetic field maps of dusty molecular clouds
observed at Extreme-Infrared
(800 µm;
450 µm)
wavelengths have now
been made for smaller clouds, mainly with the JCMT, i.e., W75N-IRS1
(Vallée and Bastien,
1995),
Sagittarius B2
(Greaves et al., 1995a),
MonR2 core
(Greaves et al., 1995b),
and Orion A
(Schleuning et al.,
1996).
Preliminary results indicate that the medium-scale magnetic field lines do
bend a little in MonR2 core in
a similar way that they do in M17-SW, suggesting that there is
some evolution of the
magnetic field inside a molecular cloud, but without any
excessive tangling of the magnetic field lines.