Mapping the Galaxy Color─Star Formation Rate Relation with Manifold Learning and Infrared Image Stacking
February 2026 • 2026ApJ...998...87L
Abstract • Modern surveys present us with billions of faint galaxies for which we only have broadband images in ∼6─8 optical-to-near-infrared (NIR) filters. Galaxy star formation rates (SFRs) are difficult to estimate accurately without spectroscopic diagnostics or far-infrared (FIR) photometry, both of which are prohibitively expensive to obtain for large numbers of faint, high-redshift galaxies. Here we present the empirical relation between SFR and broadband optical-to-NIR colors learned from Spitzer MIPS and Herschel PACS/SPIRE imaging using an innovative stacking analysis that bins galaxies with similar optical-to-NIR spectral energy distributions using a self-organizing map (SOM). Stacking based on optical-to-NIR colors ensures that our FIR stacks are built from galaxies with similar intrinsic physical properties as opposed to stacking simply by stellar mass. We train a 40 × 40 SOM using 230,638 galaxies selected from the Cosmic Evolution Survey (COSMOS) field, and stack the mid-IR to FIR images from 24─500 μm. We are able to measure the median FIR luminosities from half of the SOM cells to calibrate the SFR. In addition to investigating the common structures of optical-to-NIR properties and FIR detections labeled on the SOM, we provide calibrated SFRs for nearly half of the galaxies in the COSMOS fields down to i-band magnitude ≤25.5, and present the evolution of the galaxy main sequence for low-mass galaxies to redshift z ∼ 2.5.
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