7.2. Magnetic Field Strengths

What is the statistical B strength inferred from dust emission? In the dust thermal emission method, the magnetic field strength B is not measured directly but it can be deduced to first order by various mechanisms. (1) Deduced by scaling the theoretical polarization amplitude (predicted by model equations) to match the observed polarization amplitude. (2) Deduced by using the turbulent scatter in the polarization position angle from a mean in a map of a dusty object, such as with the equation

(e.g., Hildebrand 1989; Heiles et al. 1991; Chrysostomou et al. 1994). (3) Deduced by using the gas density n through the appropriate B ~ n^k law, such as with the equation (e.g., Vallée 1995a):

How about real Zeeman detections ? Zeeman detections of B > 100 µGauss are now being made. Using the Zeeman method at the VLA interferometer near the HI line at 21 cm, an hourglass-shaped magnetic field has been observed in the cloudlet W3 Core, consisting of the components W3a (-47 µGauss) and W3b (+103 µGauss) separated by 0.6 parsec (e.g., Fig. 1 and 6 in Roberts et al. 1993). Using the VLA at HI 21 cm, several localized hot spots are seen by the Zeeman method within the large 30" (= 0.3 pc) DR21 region, with hot spot magnetic field ~ 400 µGauss aligned along the edges of a conical V-shaped cavity caused by an outflow from a young star (Roberts et al. 1997).

Can weak magnetism be typical? Using the Zeeman method with the IRAM 30m telescope at the CN gas 3mm line, only upper limits of 200 µGauss were placed in cloudlets which were expected by strong virial equilibrium arguments to be around 600 µGauss (e.g., Crutcher et al. 1996). This shows that one cannot assume a strong magnetic energy, in equilibrium with gravitational and kinetic energies. We may still assume the simple virial equilibrium (grav. energy kinetic energy), both being much larger than the magnetic energy. This would entail rejecting strong magnetic field models.

Using the Zeeman method with the Hat Creek 26m single-dish telescope at the HI 21 cm line, Goodman and Heiles (1994) claim the detection of B ~ 10 µGauss in the Ophiuchus Dark Cloud Complex. The HI profile are comprised of multiple (~ 4) components, which are tentatively identified as arising from different régimes along the line of sight; their telescope beamwidth is ~ 36 arc minutes, and could thus convolve multiple components across the line of sight as well as along the line of sight. Their deconvolution requires multiple input assumptions, and yields low magnetic field values obtained using single-dish telescopes.

Caveat: measurements by the Zeeman splitting method are difficult. Claimed Zeeman detections in nearby dust cores and cloudlets must always come with proper corrections for instrumental sidelobe effects and self-correction for source brightness gradient effects; these effects are specially large for the Zeeman detections of low magnetic field values (< 100 µGauss) using single-dish telescopes. For the OH line ( = 1.665 GHz), the split is 0.02 km/s for a B strength of 100 µGauss, far smaller than the full OH line width. Exemple: after pointing single dishes at the HI 21 cm line toward cloudlets H0928+02, MBM12, and MBM40, all of sizes ~ 1 parsec, uncorrected HI Zeeman claims of B ~ 5 µGauss become after corrections ~ 0.2 µGauss (e.g., Table 5 in Verschuur 1995). This amounts to a sizable reduction of ~ 625 in observed magnetic energies (~ B²).

Future trends: the advent of the detection of Zeeman effects with the VLA and other interferometers at the HI 21 cm line (with a synthesized beamwidth of ~ 25 arc seconds in the C and D configurations) should help to establish reliable magnetic field strengths, free of the large instrumental and angular limitations of single-dish data.