7.4. Polarization Position angles and Physical Parameters
The Extreme IR polarization data for these dusty objects can reveal the magnetic field direction (from polarization position angle), and the degree of polarization (from polarization amplitude and total continuum), and can permit testing physical models. The total continuum emission allows the derivations of the 'optical' depth and thermal density upon reasonable physical assumptions (e.g. McCutcheon 1992).
In the following I describe briefly the physical correlations obtained so far in the submillimeter / Extreme IR, involving the position angle of polarization. More observations would certainly improve and extend these correlations, and then a proper testing of these correlations against the theoretical model predictions could be done better.
7.4.1. Angle Correlation 1 (B shape and companionship)
An interaction effect among companion disks is possible. In Table 1, the presence or absence of a cold gas companion nearby (within two source radii) seems to be correlated with the angular difference between the magnetic field direction and the source elongation. Most sources in this Table 1 having 'a poloidal magnetic field direction' also have 'a nearby companion within two source radii', and those having 'a toroidal magnetic field direction' are more likely to be isolated. A similar correlation for 3 low-mass sources has been noted by Holland et al. (1996): two sources with companions have a poloidal magnetic field, one source without companion has a toroidal magnetic field. More data are badly needed.
|Object||B||Source|||PA(B) -||Total||Source||Gas||Cold gas||Note|
|(i) B toroidal|
|s.d. of mean:||03||99||0.1||07||0.1|
|(ii) B poloidal|
|Mon R2-IRS2||170||045||55||(b)||0.02||0.7||29||SW ext.||(f)|
|s.d. of mean:||04||690||0.1||07||0.1|
| (a): Cold gas companion located nearby, no more than
two source radii away.
(b): Aitken et al. (1993), and references therein. Mid IR polarization data.
(c): Sato et al. (1985), and references therein. Near IR polarization data. These data may be due to a magnetic field or to multiple scattering. They are kept for statistical purposes.
(d): Vallée & Bastien (1998). Extreme IR polarization data.
(e): Mundy et al. (1992), their Fig. 1.
(f): Wolf et al. (1990), their Fig. 4.
(g): Vogel et al. (1984), their Fig. 3.
(h): Hayashi et al. (1985), their Fig. 4.
(i): Vallée & Bastien (1995). Extreme IR polar. data.
(j): Minchin & Murray (1994).
(k): Tamura et al. (1995)
(l): Minchin et al. (1995)
(m): Holland et al. (1994).
(n): Minchin et al. (1991).
(o): Leach et al. (1991)
(p): Akeson et al. (1996)
(q): Kane et al. (1993)
7.4.2. Angle Correlation 2 (B shape and viewing angle)
A viewing angle effect is claimed by Minchin et al. (1996), whereas poloidal magnetic field lines parallel to the minor axis of a cloudlet (or disk) can be well detected, but toroidal magnetic field lines parallel to the major axis of a cloudlet (or disk) will be subject to wide misinterpretations. Greaves et al. (1977) found with 7 sources that a small viewing angle (outflow direction close to the line-of-sight to Earth) yields a poloidal magnetic field, while a large viewing angle (outflow direction orthogonal to the l-o-s to Earth) yields a toroidal magnetic field. More observational work would help.
7.4.3. Angle Correlation 3 (B shape and beam size)
A beam size effect is claimed by Holland et al. (1996), i.e. for nearby sources the telescope beamwidth can detect well the toroidal magnetic field lines (parallel to the major axis of the cloudlet), but for distant sources the telescope beamwidth includes both the toroidal magnetic field in the denser part of the cloudlet (or disk) and the poloidal magnetic field in the huge thin envelope/outflow (above and below the elongated cloudlet/disk) thus leading to a net poloidal magnetic field. More data are needed. Figure 18 shows the possible misunderstanding due to the beam size effect. The inner circle represents a telescope beamwidth englobing a nearby cloudlet/disk (square) with a toroidal magnetic field inside (horizontal arrows) - leaving out the outer diffuse gas in the envelope/outflow above and below the disk, thus yielding a toroidal magnetic field answer. The outer circle represents a telescope beamwidth englobing a distant cloudlet/disk and its envelope/outflow (twin cones, above and below the disk) having a poloidal magnetic field (vertical arrows), thus yielding a poloidal magnetic field answer (diffuse gas over a large volume wins over dense gas over a minuscule volume).
Figure 18. Illustration of the "beam size effect", in which a small telescope beam (inner circle) sees mostly the magnetic field in the core/cloudlet/protostellar disk (rectangle), while a large telescope beam (outer circle) sees both the magnetic fields in the twin outflow/envelope (twin cones) and in the core (rectangle). For a fixed telescope beam (in angle), the cores of nearby sources are mostly seen, while the full extent of distant sources are mostly seen in the beam. Adapted from Holland et al. (1996).
7.4.4. Angle Correlation 4 (B shape and time evolution)
A time evolution may be at play. At a young age, the protostellar disk and its surroundings may both have a poloidal/vertical magnetic field. At a later age, differential rotation sets in the protostellar disk, so a toroidal magnetic field would be seen in the protostellar disk while a poloidal magnetic field would still be seen in the surroundings. More observations would help.