FRACTAL DIMENSIONS OF INTERSTELLAR MEDIUM: II. THE MOLECULAR CLOUDS ASSOCIATED WITH THE H_II REGION SH 156

Abstract

We have estimated the fractal dimension of the molecular clouds associated with the H ii region Sh 156 in the Outer Galaxy. We selected the 12 CO cube data from the FCRAO CO Survey of the Outer Galaxy. Using a developed code within IRAF, we identified slice-clouds (2-dimensional clouds in velocity-channel maps) with two threshold temperatures to estimate the fractal dimension. With the threshold temperatures of 1.8 K, and 3 K, we identified 317 slice-clouds and 217 slice-clouds, respectively. There seems to be a turn-over location in fractional dimension slope around NP (area; number of pixel) = 40. The fractal dimensions was estimated to be D = 1.5 ∼ 1.53 for NP ≥ 40, where P ∝ A D/2 (P is perimeter and A is area), which is slightly larger than other results. The sampling rate (spatial resolution) of observed data must be an important parameter when estimating fractal dimension. Fractal dimension is apparently invariant when varying the threshold temperatures applied to slice-clouds identification.

The FRACTAL DIMENSION OF THE Ρ OPHIUCUS MOLECULAR CLOUD COMPLEX

“…The slopes (equal to D/2 by definition; see below) for two threshold temperatures are found to be almost the same; D = 1.52 ∼ 1.54. In the meanwhile, we also estimated fractal dimension using 12 CO (1-0) integrated intensity map, and obtained a similar result of D = 1.5, as mentioned in our previous studies (Lee 2004;Lee et al 2008). Results using 13 CO (1-0) are not shown since they show almost the same trend.…”

“…The number of pixels of the largest slice-clouds are 52 820 for 3σ, and 39 723 for 5σ. These numbers are the largest among similar studies of molecular clouds (Falgarone et al 1991;Lee et al 2008;Walch et al 2011). Figures 4 and 5 show good correlation between two parameters for both cases, though there is some dispersion from an arbitrary fit line.…”

“…The relatively low percentage of emission sum above threshold temperatures may be due to spurious noise near the boundary of the mapped area. For comparison, Lee et al (2008) reported that the emission sum of Sh 156 above 3σ of the rms noise level was 82.0% of the total emission of the selected region, and 65.1% above 5σ.…”

“…log(P ) = 1.52(±0.06)/2 log(N P ) + 0.25(±0.02) (1) log(P ) = 1.54(±0.06)/2 log(N P ) + 0.24(±0.02) (2) We estimate fractal dimension of clouds having more than 100 pixels since clouds with small number do not give reliable estimates. In fact, Lee et al (2008) used smaller number of pixels (NP = 40) as the limit. The largest number of pixels of their slice-cloud was less than 2000, while that of our target slice-cloud in this study is more than 39 000.…”

“…Instead, we can construct arbitrary three dimensional database with spectroscopic observation, in the form of (l, b, v) or (v, l, b) when observing in Galactic coordinates. A new way of estimating fractal dimension had been reported by Lee et al (2008) using slice-clouds instead of projected clouds. In the following, we will describe their method.…”