The relation between the true and observed fractal dimensions of turbulent clouds
Date
2019
Authors
Beattie, James
Federrath, Christoph
Klessen, Ralf S.
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Volume Title
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Oxford University Press (OUP)
Abstract
Observations of interstellar gas clouds are typically limited to two-dimensional (2D) projections
of the intrinsically three-dimensional (3D) structure of the clouds. In this study,
we present a novel method for relating the 2D projected fractal dimension (Dp) to the
3D fractal dimension (D3D) of turbulent clouds. We do this by computing the fractal
dimension of clouds over two orders of magnitude in turbulent Mach number (M = 1–100),
corresponding to seven orders of magnitude in spatial scales within the clouds. This
provides us with the data to create a new empirical relation between Dp and D3D. The
proposed relation is D3D(Dp) = 1 erfc(ξ1 erfc−1
[(Dp − Dp,min)/2] + ξ2) + D3D,min, where
the minimum 3D fractal dimension, D3D,min = 2.06 ± 0.35, the minimum projected fractal
dimension, Dp,min = 1.55 ± 0.13, 1 = 0.47 ± 0.18, 2 = 0.22 ± 0.07, ξ 1 = 0.80 ± 0.18,
and ξ 2 = 0.26 ± 0.19. The minimum 3D fractal dimension, D3D,min = 2.06 ± 0.35, indicates
that in the high M limit the 3D clouds are dominated by planar shocks. The relation between
Dp and D3D of molecular clouds may be a useful tool for those who are seeking to understand
the 3D structures of molecular clouds, purely based upon 2D projected data and shows promise
for relating the physics of the turbulent clouds to the fractal dimension.
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Monthly Notices of the Royal Astronomical Society
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Journal article
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Open Access
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