2023MNRAS.523..233B

We construct Convolutional Neural Networks (CNNs) trained on exponentiated fractional Brownian motion (xfBm) images, and use these CNNs to analyse Hi-GAL images of surface density in the Galactic Plane. The CNNs estimate the Hurst parameter, ${\cal H}$ (a measure of the power spectrum), and the scaling exponent, ${\cal S}$ (a measure of the range of surface densities), for a square patch comprising $[{\cal N}\times {\cal N}]=$ [128 × 128], [64 × 64], or [32 × 32] pixels. The resulting estimates of ${\cal H}$ are more accurate than those obtained using Δ-variance. We stress that statistical measures of structure are inevitably strongly dependent on the range of scales they actually capture, and difficult to interpret when applied to fields that conflate very different lines of sight. The CNNs developed here mitigate this issue by operating effectively on small fields (small ${\cal N}$), and we exploit this property to develop a procedure for constructing detailed maps of ${\cal H}$ and ${\cal S}$. This procedure is then applied to Hi-GAL maps generated with the PPMAP procedure. There appears to be a bimodality between sightlines with higher surface density ($\gtrsim 32\, {\rm M}_{_\odot }\, {\rm pc^{-2}}$), which tend to have higher ${\cal H}\, (\gtrsim 0.8)$ and ${\cal S}\, (\gtrsim 1)$; and sightlines intercepting regions of lower surface density ($\lesssim 32\, {\rm M}_{_\odot }\, {\rm pc^{-2}}$), which tend to have lower ${\cal H}\, (\lesssim 0.8)$ and ${\cal S}\, (\lesssim 1)$; unsurprisingly the former sightlines are concentrated towards the Galactic Midplane and the Inner Galaxy. The surface density PDF takes the form dP/dΣ ∝ Σ^–3 for $\Sigma \gtrsim 32\, {\rm M}_{_\odot }\, {\rm pc^{-2}}$, and on most sightlines this power-law tail is dominated by dust cooler than $\, \sim 20\, \rm {K}$, which is the median dust temperature in the Galactic Plane.