Statistical analysis of turbulence in molecular clouds
M. S. Miesch, J. Bally;
ApJ, 1994, 429, 645
ABSTRACT: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 l(sup gamma), 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.
KEYWORDS: 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
PERSOKEY:turbulence, ,
CODE: miesch94