STATISTICAL-ANALYSIS OF TURBULENCE IN MOLECULAR CLOUDS

We present an investigation of the statistical properties of fluctuati ng gas motions in five nearby molecular clouds using the two-point aut ocorrelation and structure functions and the power spectra of their ra dial velocity structure as traced by emission-line centroid velocities . Our analysis includes observations made with the AT&T Bell Laborator ies 7 m Crawford Hill antenna (1.7' beamwidth) of (CO)-C-13 J = 1 --> 0 emission in Orion B, Mon R2, L1228, and L1551 and also (CO)-C-13 J = 2 --> 1 observations of the molecular gas surrounding the Herbig-Haro object HH 83 lying just west of L1641 in the Orion A cloud that were obtained with a higher spatial resolution (0.22') using the IRAM-30 m telescope on Pico Veleta, Spain. The effects of beam smoothing and the interpolation of a set of observations onto a regular spatial grid ar e studied using model spectral line data cubes, and we find that the b ehavior of the statistical functions presented here and those presente d elsewhere by other authors are heavily influenced by these effects a t scales comparable to and somewhat larger than the beamwidth. At larg er lags real correlations are detected, and we use the e-folding lengt h of the autocorrelation function (i.e., the correlation length) to in vestigate the characteristic scales of the underlying turbulent flow. We find that this measure is dependent on the range of scales sampled by the observations themselves both for our data and for previously ex isting observations presented by other authors, and we interpret this result and the observed similarity between the functional forms of the statistical functions derived for different data sets as evidence for a self-similar turbulent hierarchy of gas motions extending over a wi de range of scales in the interstellar medium. Power-law fits to the o bserved structure functions yield a mean index describing the hierarch y of 0.86 +/- 0.3, which translates into a velocity dispersion-region size relationship of the type first introduced by Larson (1981), DELTA V is-proportional-to l(gamma), with gamma = 0.43 +/- 0.15. This result is consistent with that found by Larson in his original analysis, gam ma almost-equal-to 0.38, and with the range found in more recent studi es, 0.35 < gamma < 0.7. We also discuss the observed scaling laws in r elation to the predictions of phenomenological theories of forced, iso tropic turbulence. The mean turbulent stress and maximum energy transp ort rate as a function of scale are obtained from the velocity power s pectra following the procedure of Kleiner & Dickman, and the results a re discussed in the context of scale-dependent star formation and the generation of turbulence in molecular clouds.