Quantitative Morphology of Galactic Cirrus in Deep Optical Imaging

TL;DR

This study develops a multi-faceted, quantitative framework to characterize the morphology of optical Galactic cirrus and compare it to dust tracers from FIR, MIR, Planck radiance, and HI maps. By combining local PDF statistics, Fourier-based measures (power spectrum and Δ-variance), cross-correlations, and wavelet scattering transforms, the authors show that optical cirrus shares a near-universal power-law structure with γ ≈ -2.9 across tracers and exhibits filamentary, scale-coherent morphology. The WST analysis provides a non-Gaussian, scale-coupled morphospace, enabling mock-cirrus synthesis and showing promise for distinguishing cirrus from extragalactic light such as tidal features in single-band data. These morphometric insights offer practical tools for ISM studies and improved foreground separation in deep wide-field surveys, with implications for upcoming Euclid and Roman datasets.

Abstract

Imaging of optical Galactic cirrus, the spatially resolved form of diffuse Galactic light, provides important insights into the properties of the diffuse interstellar medium (ISM) in the Milky Way. While previous investigations have focused mainly on the intensity characteristics of optical cirrus, their morphological properties remain largely unexplored. In this study, we employ several complementary statistical approaches -- local intensity statistics, angular power spectrum / $Δ$-variance analysis, and wavelet scattering transform analysis -- to characterize the morphology of cirrus in deep optical imaging data. We place our investigation of optical cirrus into a multi-wavelength context by comparing the morphology of cirrus seen with the Dragonfly Telephoto Array to that seen with space-based facilities working at longer wavelengths (Herschel 250 $μm$, WISE 12 $μm$, and Planck radiance), as well as with structures seen in the DHIGLS HI column density map. Our statistical methods quantify the similarities and the differences of cirrus morphology in all these datasets. The morphology of cirrus at visible wavelengths resembles that of far-infrared cirrus more closely than that of mid-infrared cirrus; on small scales, anisotropies in the cosmic infrared background and systematics may lead to differences. Across all dust tracers, cirrus morphology can be well described by a power spectrum with a common power-law index $γ\sim-2.9$. We demonstrate quantitatively that optical cirrus exhibits filamentary, coherent structures across a broad range of angular scales. Our results offer promising avenues for linking the analysis of coherent structures in optical cirrus to the underlying physical processes in the ISM that shape them. Furthermore, we demonstrate that these morphological signatures can be leveraged to distinguish and disentangle cirrus from extragalactic light.

Figures (28)

• Figure 1: Dragonfly RGB mosaic image of the Spider field at the top left and multi-wavelength images from different dust tracers used in this work. Top middle: Dragonfly combination of $g$ and $r$ after source removal, approximating diffuse radiation in the V band. Top right: Herschel 250 $\mu m$. Bottom left: WISE 12 $\mu m$. Bottom middle: Planck radiance. Bottom right: DHIGLS HI LVC column density. See text for details. The images are displayed on a linear scale with the same contrast between 0 and the 99.99% quantile.
• Figure 2: Illustration of the extraction of local PDFs and PDF statistics. (a) Local PDF extracted from the intensity map within a circular region moving across the field. This example shows an extraction with radius of $r=3\arcmin$ at the same position on the optical (left), FIR (middle), and MIR (right) map. The lower right panel shows the KDE-smoothed PDFs of the logarithm of the normalized intensity in the circular regions (${z = \log} \,\tilde{I}_{\nu}$). The PDFs are used for computing statistics and distance metrics. $D_{\rm H}$ indicates the distance between the PDF of the FIR/MIR data and that of the optical data within the particular subregion. (b) Skewness, kurtosis, and Gini coefficient of the local PDFs at the same position measured on the optical, FIR, and MIR cirrus data with varying kernel radius $r$. The rightmost panel shows the PDF distance of the FIR and MIR data relative to the optical as a function of kernel radius.
• Figure 3: Illustration of wavelet scattering transform applied to cirrus images, adapted from Figure 4 of 2021arXiv211201288C. The input field is "scattered" through convolution with a bank of Morlet wavelets at different scales $j$ and orientations $\theta$ (not displayed for clarity), followed by a non-linear operation (modulus). The output fields are shown up to $j_2=3$. The scattering coefficient $S_n$ is computed by taking the spatial average of the output field. Only $j_2>j_1$ coefficients are used.
• Figure 4: Spatial distributions of local skewness, kurtosis, and $Gini$ extracted from the Dragonfly optical (left column), Herschel FIR (middle column), and WISE MIR (right column) data, using a moving circular kernel with a kernel width of $d_k=10\arcmin$. These maps trace where cirrus morphology changes.
• Figure 5: Left column: Histograms of skewness, kurtosis, and $Gini$ measured from the local PDFs in optical, FIR, and MIR data. Fainter histograms represent smaller kernel scales used for PDF extraction. Middle column: Histograms showing the distributions of differences of the statistics between FIR or MIR and optical data. The difference is calculated by [optical-$\sf X$], where $\sf X$ stands for the band. Right column: Mean absolute difference of statistics between FIR or MIR and optical as a function of kernel scale.