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 Wobserved 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 Tk is the kinetic temperature in kelvins and ma / mH is the atomic mass (in units of the hydrogen atom mass). The excess line width Wexcess (often called the non-thermal line width) is given by the quadratic subtraction thus:
where <Vturb> is the equivalent turbulent rms speed; here <Vturb> = 0.74 Wexcess . All line widths W are measured or expressed as full widths between half-intensity points (FWHP).
A relation between the excess line width (= Wexcess) and the object size (= R), of the form Wexcess = Rq, 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 (Wexcess = 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 Wexcess - log R plane. At small sizes, taking all types of objects with R < 1 pc, one finds the relation Wexcess ~ R0.7. 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. Wexcess 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 Wexcess ~ R0.5 (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.