The Column Density Probability Density Function of Cygnus-X

TL;DR

Cygnus-X N-PDF analysis demonstrates how turbulence and gravity shape the cloud's density distribution and how the N-PDF evolves with star formation. The study uses a Herschel-based H2 column density map plus HI and YSO data to fit log-normal + power-law models, deriving $N_{TP}$, $s$, $N_{peak}$, and $\\sigma_{\\eta}$, and interprets these in terms of physical conditions such as $A_V$ and turbulence forcing. The global N-PDF is described by a log-normal with $\\sigma_{\\eta}=0.48$ and $N_{\\rm peak}=4.37\\times10^{21}$ cm$^{-2}$, transitioning at $N_{\\rm TP}=1.62\\times10^{22}$ cm$^{-2}$ to a tail with $s=2.33$ (implying $\\alpha\\approx1.86$) and a corresponding $A_V\\approx17.2$ mag, with $b\\approx0.08$ and $M_s\\approx34.3$ suggesting predominantly solenoidal forcing. The N-PDF parameters broadly agree with prior work after LOS corrections, supporting a turbulence+gravity interpretation, and regional analysis reveals variations in $\\sigma_{\\eta}$, $N_{TP}$, and the presence of a potential second power-law or feedback-driven features in specific sub-regions, highlighting the N-PDF as a diagnostic for evolutionary state and star-formation thresholds.

Abstract

The density distribution within molecular clouds offers critical insights into their underlying physical processes, which are essential for understanding star formation. As a statistical measure of column density on the cloud scale, the shape and evolution of the column density probability density function (N-PDF) serve as important tools for understanding the dynamics between turbulence and gravity. Here we investigate the N-PDFs of Cygnus-X using the column density map obtained from Herschel, supplemented by HI and Young Stellar Objects (YSO) data. We find that the N-PDFs of Cygnus-X and four sub-regions display log-normal + power-law shapes, indicating the combined effects of turbulence and gravity in sculpting the density structure. We find evidence that the power-law segment of the N-PDFs flattens over time, and the transitional column density can be seen as a unique and stable star formation threshold specific to each molecular cloud. These results not only clarify the physical state of Cygnus-X but also emphasize the utility of the N-PDF as a statistical diagnostic tool, as it is an accessible indicator of evolutionary stages and star formation thresholds in molecular clouds.

Figures (5)

• Figure 1: The column density map of Cygnus-X in [$\rm cm^{-2}$]. Red rectangles show the five sub-regions we selected. White contour outlines pixels with column density larger than $2.64\times10^{21}\,\rm{cm}^{-2}$, which are used in the N-PDF fitting. Black polygons show the three areas used for subtracting LOS contamination, their mean column density is $2.36\times 10^{21}\,\rm cm^{-2}$. White circles show the developed HII regions from Anderson2014. The orange contour outlines structures with column density larger than $1.62\times10^{22}\,\rm{cm}^{-2}$, which are called dense structures in Section \ref{['sec:TPclump']}. The yellow contour outlines structures with column density larger than $1.23\times10^{23}\,\rm{cm}^{-2}$.
• Figure 2: Histogram of the H$_2$ N-PDF of Cygnus-X. The solid vertical line marks $2.64\times10^{21}\,\mathrm{cm}^{-2}$, above which the N-PDF is fitted with a log-normal + power-law function. The green dashed line shows best-fit result to the N-PDF, the transition point between log-normal and power-law is shown in the dotted vertical line. The error bars on the histogram are derived from Poisson statistics and are small due to the large number of pixels used in the N-PDF. The standardized residuals of the fit, calculated in the logarithmic scale, are displayed in the lower panel.
• Figure 3: The HI column density map of Cygnus-X in $N_{\rm HI}$ [$\rm cm^{-2}$]. White and orange contours are from the dust continuum map and make the column densities of $2.64\times10^{21}\,\rm{cm}^{-2}$ and $1.62\times10^{22}\,\rm{cm}^{-2}$, respectively.
• Figure 4: HI and H$_2$ N-PDFs of Cygnus-X. The orange line shows the HI N-PDF. The grey region represents the H$_2$ N-PDF analyzed throughout this work. The blue line shows the same H$_2$ N-PDF after convolution to the HI angular resolution and with no LOS contamination correction applied. The vertical orange line marks $N\rm_H = 4\times10^{21}\, cm^{-2}$, below which the HI data are visibly affected by HISA. To make fair comparison of the N-PDFs, the $x$ axis is in $N_{\rm H}/2$.
• Figure 5: Similar to Figure \ref{['fig:npdf']} but for N-PDFs of the five sub-regions in Cygnus-X. For the first four panels, the green curves show log-normal + power-law fitting to the N-PDFs, and the vertical dashed lines mark the transition points. While for region "Northwest", the N-PDF is fitted with a log-normal + double power-law function, with vertical dashed lines showing the two transition points between the three parts.