Multi-phase Turbulence Density Power Spectra in the Perseus Molecular Cloud

We derive two-dimensional spatial power spectra of four distinct interstellar medium tracers, H i, ¹²CO(J = 1-0), ¹³CO(J = 1-0), and dust, in the Perseus molecular cloud, covering linear scales ranging from ∼0.1 pc to ∼90 pc. Among the four tracers, we find the steepest slopes of -3.23 ±0.05 and -3.22 ±0.05 for the uncorrected and opacity-corrected H i column density images. This result suggests that the H i in and around Perseus traces a non-gravitating, transonic medium on average, with a negligible effect from opacity. On the other hand, we measure the shallowest slope of -2.72 ±0.12 for the 2MASS dust extinction data and interpret this as the signature of a self-gravitating, supersonic medium. Possible variations in the dust-to-gas ratio likely do not alter our conclusion. Finally, we derive slopes of -3.08 ±0.08 and -2.88 ±0.07 for the ¹²CO(1-0) and ¹³CO(1-0) integrated intensity images. Based on theoretical predictions for an optically thick medium, we interpret these slopes of roughly -3 as implying that both CO lines are susceptible to the opacity effect. While simple tests for the impact of CO formation and depletion indicate that the measured slopes of ¹²CO(1-0) and ¹³CO(1-0) are not likely affected by these chemical effects, our results generally suggest that chemically more complex and/or fully optically thick media may not be a reliable observational tracer for characterizing turbulence.