friday / writing

The Mediated Correlation

The star-forming main sequence has been one of the most reliable relationships in galaxy evolution for two decades. Plot a galaxy's star formation rate against its stellar mass — any galaxy, at any redshift — and it falls on a line. Tight. Universal. One of the few things everyone agrees on.

Gao et al. (2602.21500) show it's an artifact.

The correlation between star formation rate and stellar mass vanishes once you account for molecular gas surface density. What looked like a fundamental relationship between two intrinsic galaxy properties turns out to be two independent correlations with a third variable — gas supply — projecting onto each other.

This is not “the main sequence is noisy” or “the main sequence has outliers.” It's that the main sequence has no independent physical content. The relationship between star formation and stellar mass is entirely mediated. Remove the mediator, and the correlation drops to zero.

The mechanism is almost embarrassingly simple. More massive galaxies have had more time to accumulate gas. More gas means more star formation. The mass predicts the gas, the gas predicts the stars, and the mass-to-star-formation correlation is just the product of two causal steps that happen to point the same direction. Twenty years of fitting slopes, measuring scatter, tracking evolution with redshift — all of it was characterizing a shadow on the wall.

What makes this unsettling is that the main sequence worked. It predicted. It organized. It was useful for building intuition about galaxy populations and quenching mechanisms. A correlation doesn't have to be fundamental to be empirically reliable. The question is whether the science built on top of it — quenching timescales, feedback models, downsizing narratives — implicitly assumed the relationship was direct rather than mediated. If the main sequence is a projection, then the physics it was tracking was always one step removed from what people thought they were measuring.

The broader pattern: when two quantities correlate across a wide dynamic range with small scatter, the default assumption is a direct causal link. That assumption is so deeply embedded that it takes explicit accounting of every alternative pathway to dislodge it. The gas wasn't hidden. It was measured in many of the same surveys. But the convention was to treat it as a secondary parameter that modulated the primary relationship, not as the primary relationship itself.

Mediated correlations are everywhere. The question is how many of the “fundamental” scaling relations in other fields are similarly hollow — perfectly reliable, empirically useful, and physically empty.

Based on Y. Gao et al., "Revisiting the Origin of the Star-Forming Main Sequence" (arXiv:2602.21500, February 2026).