Mapping the Galaxy Color-Star Formation Rate Relation with Manifold Learning and Infrared Image Stacking

TL;DR

The paper tackles the problem of estimating star formation rates for billions of faint galaxies with limited broadband photometry. It introduces a color-based Self-Organizing Map (SOM) to cluster galaxies on optical–NIR SEDs and stacks Spitzer and Herschel FIR images per SOM cell to calibrate FIR luminosities and SFRs, with redshifts fixed from $z_{photo}$. By predicting individual galaxy FIR photometry from the scaled cell stacks, and validating against direct measurements, the study derives the $\text{SFR}-M_*$ relation up to $z\sim2.5$ and demonstrates a scalable pathway to extend SFR studies to future surveys. The approach enables FIR-based SFR calibrations for low-mass, high-redshift galaxies and offers a practical framework for analyzing LSST, Euclid, and Roman data without requiring per-object FIR data.

Abstract

Modern surveys present us with billions of faint galaxies for which we only have broadband images in $\sim$6-8 optical-to-near-infrared (NIR) filters. Galaxy star formation rates (SFRs) are difficult to estimate accurately without spectroscopic diagnostics or far-infrared (FIR) photometry, both of which are prohibitively expensive to obtain for large numbers of faint, high-redshift galaxies. Here we present the empirical relation between SFR and broadband optical-to-NIR colors learned from Spitzer MIPS and Herschel PACS/SPIRE imaging using an innovative stacking analysis that bins galaxies with similar optical-to-NIR spectral energy distributions using a Self-Organizing Map (SOM). Stacking based on optical-to-NIR colors ensures that our FIR stacks are built from galaxies with similar intrinsic physical properties as opposed to stacking simply by stellar mass. We train a 40$\times$40 SOM using 230,638 galaxies selected from the COSMOS field, and stack the mid-to-far infrared images from 24 micron to 500 micron. We are able to measure the median FIR luminosities from half of the SOM cells to calibrate the star formation rate. In addition to investigating the common structures of optical-to-NIR properties and FIR detections labeled on the SOM, we provide calibrated star formation rates for nearly half of the galaxies in the COSMOS fields down to $i-$band magnitude $\leq 25.5$, and present the evolution of the galaxy main sequence for low-mass galaxies to redshift $z\sim2.5$.

Figures (16)

• Figure 1: The median absolute dispersion of the adjacent photometric colors. The red lines mark the median, and the upper and lower limits of the bars and the boxes are (95, 5) percentile and (75, 25) percentile, respectively.
• Figure 2: The color SEDs of galaxies within the bin of $10.5<\log(M_*/{\rm M_\odot})<11.0$ and $0.9<z<1.2$. The gray lines are the SEDs of 800 galaxies randomly selected from this mass-redshift bin. The red and blue lines are the SEDs of 100 galaxies from the same mass-redshift bin, but assigned to different cells on the SOM.
• Figure 3: The 40$\times$40 cell SOM of COSMOS galaxies labeled with the occupation numbers per cell, the adjacent optical-to-NIR photometric colors used to train the map, and the $i-H$ color.
• Figure 4: The 40$\times$40 SOM of COSMOS galaxies labeled with (a) the median of photometric redshifts, (b) the redshift dispersions, (c) the assigned galaxies' median of $i-$band magnitudes, (d) the dispersions of the $i-$band magnitudes, (e) the median of Log($M_*$), (f) the Log($M_*$) dispersions, (g) the median of Log(SFR),(h) the median of Log(sSFR)of the galaxies in each cell. The $z_{photo}$, $M_*$, SFR and sSFR are adopted from the COSMOS2020 classic catalog Weaver_2022.
• Figure 5: Example of the stacking process at 250$\mu$m. Top: Results of stacking 7, 24, 76, 241 images from the cell 1246. Bottom: The SNR increase with the number of stacks, and roughly follows the trend of $\sqrt{N}$ for N numbers of images in stack (orange dashed line).