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

We derive two-dimensional spatial power spectra of four distinct interstellar medium tracers, HI, $^{12}$CO($J$=1--0), $^{13}$CO($J$=1--0), and dust, in the Perseus molecular cloud, covering linear scales ranging from $\sim$0.1 pc to $\sim$90 pc. Among the four tracers, we find the steepest slopes of $-3.23\pm0.05$ and $-3.22\pm0.05$ for the uncorrected and opacity-corrected HI column density images. This result suggests that the HI 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 $-2.72\pm0.12$ 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 change our conclusion. Finally, we derive slopes of $-3.08\pm0.08$ and $-2.88\pm0.07$ for the ${}^{12}$CO(1--0) and ${}^{13}$CO(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 ${}^{12}$CO(1--0) and ${}^{13}$CO(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.