MIYU — Stellar Mass Fraction in Galaxy Clusters

MIYU (Multi-layer Iterative Yielding Unprojection) is a mathematical framework that recovers the radial stellar mass fraction profile in 3D from projected observables, using caustic mass profiles and iterative deprojection. We apply it to HeCS-omnibus clusters, include the ICL component, and compare with TNG simulations for calibration and cluster baryon budget studies.

We only observe projected surface density Σ(R); recovering the true 3D stellar mass profile M_*(r) is an inverse problem. MIYU assumes spherical symmetry and a vanishing outer boundary, then links 2D projected annuli to 3D spherical shells via a linear system of geometric intersection volumes, so that any projected stellar mass profile can be deprojected analytically. The aim is to apply this to stacked cluster samples and compare with cosmological simulations to study baryon content and galaxy formation efficiency.

We use TNG-Cluster for validation (mock projections, R ≤ R₂₀₀ cut to limit projection effects) and MACH survey data for observations. Results show that simulations have a 3–4× excess in the central stellar mass and a deficit in the outskirts compared to observations at similar M₂₀₀, with discussion of ICL/BCG separation, centering, stellar mass errors, and baryon fraction f_*(r).