Mathematics – Logic
Scientific paper
Jul 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994apj...429..645m&link_type=abstract
The Astrophysical Journal, vol. 429, no. 2, pt. 1, p. 645-671
Mathematics
Logic
142
Astronomical Models, Carbon Monoxide, Carbon 13, Gas Flow, Molecular Clouds, Power Spectra, Scaling Laws, Turbulent Flow, Variations, Velocity Distribution, Antennas, Autocorrelation, Energy Dissipation, Errors, Estimates, Pressure, Radio Telescopes, Statistical Analysis
Scientific paper
We present an investigation of the statistical properties of fluctuating gas motions in five nearby molecular clouds using the two-point autocorrelation and structure functions and the power spectra of their radial velocity structure as traced by emission-line centroid velocities. Our analysis includes observations made with the AT&T Bell Laboratories 7 m Crawford Hill antenna (1'.7 beamwidth) of (13)CO J = 1 right arrow 0 emission in Orion B, Mon R2, L1228, and L1551 and also (13)CO J = 2 right arrow 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 min .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 are studied using model spectral line data cubes, and we find that the behavior of the statistical functions presented here and those presented elsewhere by other authors are heavily influenced by these effects at scales comparable to and somewhat larger than the beamwidth. At larger lags real correlations are detected, and we use the e-folding length of the autocorrelation function (i.e., the correlation length) to investigate 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 existing 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 wide range of scales in the interstellar medium. Power-law fits to the observed structure functions yield a mean index describing the hierarchy of 0.86 +/- 0.3, which translates into a velocity dispersion-region size relationship of the type first introduced by Larson (1981), Delta V varies as lgamma, with gamma = 0.43 +/- 0.15. This result is consistent with that found by Larson in his original analysis, gamma approximately equals 0.38, and with the range found in more recent studies, 0.35 less than gamma less than 0.7. We also discuss the observed scaling laws in relation to the predictions of phenomenological theories of forced, isotropic turbulence. The mean turbulent stress and maximum energy transport rate as a function of scale are obtained from the velocity power spectra following the procedure of Kleiner & Dickman, and the results are discussed in the context of scale-dependent star formation and the generation of turbulence in molecular clouds.
Bally John
Miesch Mark S.
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