Predicting dust temperature from molecular line data using machine learning

TL;DR

This work demonstrates that dust temperatures in the Orion A cloud can be accurately inferred from CO isotopologue line data using a supervised learning approach with an Extra Trees Regressor. Training on as little as 0.5–5% of pixels—provided the training set spans the full dust-temperature range and matches the overall distribution—yields robust predictions, with the $^{12}$CO/$^{13}$CO ratio often the most informative feature, linking to PDR physics. Importantly, the method does not require assumptions about gas-dust thermal coupling and can capture broader observational correlations beyond conventional astrophysical concepts. The approach enables dust-temperature mapping in regions lacking multi-band continuum coverage, offering practical utility for large-scale cloud studies and archival datasets.

Abstract

We conducted experiments with machine learning techniques to construct dust temperature maps from the CO isotopologue molecular line data in the Orion A molecular cloud. In the classical astrophysical methodology, multi-band continuum data are required to derive the dust temperature. The present study aims to investigate the capability and limitations of machine learning techniques to derive dust temperatures in regions without multi-band dust continuum data. We investigated how the number of pixels used for training influences prediction accuracy, and how the dust temperatures sampled in the training area influence prediction accuracy. We found that $\sim$5\% of the total number of pixels in the observational region is sufficient for training to obtain accurate predictions. Furthermore, a dust temperature sample within the training area should cover the whole temperature range and have a similar sample distribution to that of the entire observing region for an accurate prediction. The $^{12}$CO / $^{13}$CO ratio is often found to be the most important feature in predicting the dust temperature. As the $^{12}$CO / $^{13}$CO ratio is a tracer of PDR, the machine learning technique could connect the dust temperatures to the PDRs. We also found that the condition of thermal gas-dust coupling is not required for accurate prediction of the dust temperature from the molecular line data, and that machine learning is capable of capturing information more than classical astrophysical concepts.

Figures (16)

• Figure 1: (a--c) $^{12}$CO (1--0), $^{13}$CO (1--0), and C$^{18}$O (1--0) integrated intensity (moment 0) maps, (d--f) $^{12}$CO, $^{13}$CO, and C$^{18}$O peak intensity maps, (g--h) maps of the integrated intensity ratio of $^{12}$CO to $^{13}$CO and of $^{13}$CO to C$^{18}$O, (i) excitation temperature map as derived from the $^{12}$CO peak, and (j) HGBS dust temperature map toward the Orion A molecular cloud. The angular resolution of all maps is 36$\arcsec$. Black box indicates the training area for Regressor-Region-A.
• Figure 2: Plots of (a) recursive feature elimination with cross-validation (RFECV), (b) training and cross-validation scores as a function of the number of the training pixels, i.e., learning curves, (c) training and validation curves as a function of the maximum depth of the tree, and (d) feature importance, for Regressor-Region-A. In panels (b) and (c), the blue and orange curves show the training and cross-validation scores, respectively, with the range of the standard deviation. Panel (a) shows only the cross-validation scores, along with their standard deviations. The scores refer to R2.
• Figure 3: Maps of (a) the dust temperature in the Orion A region produced from the HGBS data, (b) the dust temperature predicted from Regressor-Region-A, (c) the fidelity between the observation and prediction, and (d) the histogram of the fidelity. The black boxes in panels (a), (b), and (c) show the area used for training the regressor.
• Figure 4: (a) Pixel-to-pixel correlation between the predicted and observed dust temperatures. Red points denote data points from the training area, while blue points outside the training area. Opacity of the colors indicates the density of the data points. The black line shows the identical predicted and observed dust temperatures, and the yellow line shows the relationship $T_{\rm dust, pre}$ = (1.016 $\pm$ 0.001) $\times$$T_{\rm dust, obs}$ obtained through the least-square fitting. (b) Pixel-to-pixel histograms of the predicted (color) and observed (gray) dust temperature in the whole Orion A region, (c) those within the area of Regressor-Region-A (i.e., inside the black box in Fig. \ref{['fig2']}(a)), and (d) those outside Regressor-Region-A.
• Figure 5: Relationships (a) between the fraction of the training pixels and the average predicted dust temperature and (b) between the fraction of the training pixels and R2. The predicted map is generated using a regressor trained on a randomly selected subset of pixels, covering a specific percentage of the total pixels. The red line in panel (a) indicates the average observed dust temperature. The dotted lines in panels (a) and (b) indicate the fraction of the training pixels of 5% of the entire pixels, which is regarded as a sufficient level of pixel number for accurate prediction. At this point, the R2 value is 0.7409 (red line in panel b).