7. OBSERVED MAGNETIC FIELDS IN PROTOSTELLAR DISKS (OUT TO ~ 200 AU OR SO; ~ 10^-2 PC) AND DENSE INTERSTELLAR STARFORMING CLOUDLETS (0.1 TO 1 PC)

7.1. Excess line width for small objects (sizes < 1 parsec)

One of the most important signatures of small scale turbulence is the presence of a spectral line width W_observed having an excess of (i) the thermal width (expected from the gas temperature) and of (ii) the line broadening due to large scale motions such as expansion or contraction. The large scale motion is generally subtracted out linearly first. The thermal line width is given by the relation

where T_k is the kinetic temperature in kelvins and m_a / m_H is the atomic mass (in units of the hydrogen atom mass). The excess line width W_excess (often called the non-thermal line width) is given by the quadratic subtraction thus:

where <V_turb> is the equivalent turbulent rms speed; here <V_turb> = 0.74 W_excess . All line widths W are measured or expressed as full widths between half-intensity points (FWHP).

A relation between the excess line width (= W_excess) and the object size (= R), of the form W_excess = R^q, has been known since the late 1970s, in both radio molecular studies and in optical HII region studies (e.g., Larson 1979). Objects in this category encompass molecular/dust cores with stars inside (W_excess = 0.25 km/s, R = 0.1 pc), large low-brightness molecular/dust cloudlets (0.38 km/s, 0.1 pc), Ori cloudlets (0.38 km/s, 0.3 pc), some globules (0.6 km/s, 0.3 pc), high galactic latitude molecular/dust cloudlets (2.4 km/s, 0.7 pc), ionized carbon interfaces between molecular clouds and HII regions (4.2 km/s, 1.0 pc), etc.

A well-known separation occurs for object sizes R = 1 pc, in the log W_excess - log R plane. At small sizes, taking all types of objects with R < 1 pc, one finds the relation W_excess ~ R^0.7. Splitting these objects by mass, it seems that q = 0.7 (Fuller & Myers 1992) or 0.5 (Caselli & Myers 1995) for low-mass cores ~ 1 M (using density ~ 10⁴ cm^-3, radius = 0.1 pc) , while q = 0.2 (Caselli & Myers 1995) for high mass cores ~ 100 M (using density ~ 10⁵ cm^-3, radius = 0.2 pc). More data are needed on small objects with R 0.1 pc to 0.01 pc, and future improvements are expected there. W_excess could be due physically to cascading/macroscopic turbulences, to energetic stellar outflows, to collisions of cores, or else to magnetic turbulences. This small scale behaviour differs from the behaviour at larger scale. For all types of objects with R > 1 pc, one typically finds W_excess ~ R^0.5 (e.g., Vallée 1994) in objects like small molecular clouds (~ 10³ M), cloud complexes (~ 10⁴ M) and others, indicative of gravitational and other equilibrium supports.