Galaxies as stochastic systems: why the next breakthrough in galaxy evolution requires one hundred million spectra

TL;DR

The paper argues that galaxy evolution is an inverse statistical problem because each galaxy is observed only once, necessitating a stochastic population framework with hierarchically inferred hyper-parameters (e.g., correlation times, burstiness, duty cycles). It proposes hierarchical Bayesian inference of these stochastic laws using deep rest-UV–optical spectroscopy across massive samples to constrain temporal power spectral densities and other time-structure metrics. It outlines a science program requiring roughly $10^7$–$10^8$ spectra in the redshift range $0\lesssim z\lesssim3$, and specifies the facility capabilities and data-infrastructure needed to achieve this. The work argues that such a shift to population-level stochastic laws will enable direct tests of simulations and cosmological forward models, provide physics-level calibration for galaxy evolution, and enhance the interpretive power of upcoming large surveys.

Abstract

Each galaxy is observed only once along its life, making galaxy evolution fundamentally an inverse statistical problem: time-dependent physics must be inferred from ensembles of single-epoch snapshots. To move beyond descriptive scaling relations toward physical regulation mechanisms of star formation, quenching, chemical enrichment and black hole growth, galaxies must be treated as realizations of a stochastic process whose hyper-parameters (e.g., correlation timescales, burstiness, duty cycles) are inferred hierarchically. This demands both depth and scale: continuum S/N sufficient for absorption-line ages and chemistry, and samples far larger than those in SDSS, DESI, 4MOST or MOONS, which provide either depth or size but not both across $0<z<3$. Once the relevant axes of mass, redshift, environment, structure and evolutionary phase are populated, the requirement naturally rises from $10^7$ to $\sim10^8$ galaxies. This is the regime where stochastic hyper-parameters can be well constrained and where comparisons to simulations and cosmological forward models become limited by theory rather than observations. We outline the science enabled by such a programme and the corresponding requirements for a future ESO wide-field spectroscopic facility capable of delivering tens to hundreds of millions of rest-UV-optical spectra over $0\lesssim z\lesssim3$.