The Hidden Geometry of Astrophysical Spectra: Path-Signatures of Line Profiles

2026-06-25

AI Summary

Traditional spectral line profile summaries—such as intensity, central velocity, and width—struggle to distinguish morphologically distinct yet statistically similar complex features (e.g., double-peaked, shoulder-like, or emission–absorption composite profiles). This work introduces rough path theory into astrophysical spectral analysis for the first time, treating line profiles as paths in velocity–flux space to construct an interpretable geometric representation. Low-order path signatures—including signed area and blue–red asymmetry—are extracted to capture ordered morphological characteristics. The method successfully disentangles profiles with nearly identical FWHM and W80 but different shapes in synthetic data. Applied to MaNGA observations, it yields spatially coherent clustering, and stacked spectra recover large-scale structures consistent with reference velocity fields, significantly enhancing the resolution and classification of complex line morphologies.

Abstract

The morphology of a spectral-line profile contains information beyond scalar summaries of line strength, centroid, width, global asymmetry, or diagnostic line ratios. Broad wings, shoulders, double peaks, secondary components, and composite emission--absorption structures encode how flux is ordered across wavelength but can remain indistinguishable under conventional summaries. We introduce an interpretable geometric representation of line profiles inspired by rough path theory. Each wavelength-sampled profile is mapped to a common systemic rest-frame velocity grid and treated as a trajectory in velocity--flux space, traversed from blue to red. From this path, we define a compact set of low-order descriptors measuring signed velocity--flux area, blue--red imbalance localization, higher-order shape complexity, and emission--absorption ordering. Using synthetic profiles, we show that these descriptors separate morphologies with similar full width at half maximum (FWHM), non-parametric velocity width ($W_{80}$), and low-order moment summaries. We then apply the method to MaNGA integral-field spectroscopy by computing H$α$ descriptors in individual spaxels and clustering them in a low-dimensional feature space. The resulting classes form spatially coherent regions of similar ordered line morphology. Although no external velocity field is supplied to the clustering, stacked spectra within these regions recover coherent large-scale centroid-velocity patterns broadly consistent with the MaNGA reference velocity fields. We release a minimalist MIT-licensed package ${\it spectropath}$, available at \href{https://rafaelsdesouza.com.br/spectropath/}{the project website}.

Problem

• spectral-line profiles
• morphology
• astrophysical spectra
• line shape complexity
• emission-absorption structures

Innovation

• path signatures
• spectral line profiles
• rough path theory
• geometric representation
• integral-field spectroscopy