Torsionally excited methanol in massive young stellar objects: The role of the mid-IR radiation field

Observing the earliest stages of high-mass star formation in the mid-infrared (mid-IR) is challenging because the extinction is high and the resolution limited. Millimeter vibrationally and torsionally excited transitions of several molecules have been proposed as indirect probes of local mid-IR radiation fields around young stellar objects (YSOs). We investigate the excitation and spatial distribution of torsionally excited methanol ($\mathrm{C}{\mathrm{H}}_3\mathrm{O}\mathrm{H}$) in 12 high-mass star-forming clumps in different evolutionary stages, assessing their potential as tracers of the mid-IR luminosity of embedded protostars. We analyzed rotational transitions of methanol within the same torsionally excited states $v_{\mathrm{t}}$$\ge$1 in the Atacama Large Millimeter/submillimeter Array (ALMA) 890 $\mu \mathrm{m}$ observations and compared them with Spitzer 24 $\mu \mathrm{m}$ data by plotting line luminosities normalized by methanol abundance against mid-IR luminosities. The torsionally excited methanol emission is generally compact and systematically coincident with ALMA dust continuum peaks and 24 $\mu \mathrm{m}$ emission, even in faint sources. The only clump without an IR counterpart also shows no $v_{\mathrm{t}}$$\ge$1 emission, supporting radiative pumping as the dominant excitation mechanism. We found a promising power-law trend between $v_{\mathrm{t}}$$\ge$1 methanol lines and 24 $\mu \mathrm{m}$ luminosities, largely independent of the methanol abundance. $\mathrm{C}{\mathrm{H}}_3\mathrm{O}\mathrm{H}$ $v_{\mathrm{t}}$$\ge$1 transitions appear to be promising tracers of local mid-IR radiation fields of embedded protostars, providing core-scale information even in highly extincted regions. As a pilot study, our results suggest that extending our study to a larger statistical sample is crucial for testing and improving this method.