The relationship between a supermassive black hole's mass and the speed of stars orbiting near its host galaxy's center — the so-called M–σ relation — has been observed for over two decades. The more massive the black hole, the faster stars move in the galaxy's central region. The correlation is solid, but correlation alone says nothing about cause. Which one drives the other: does the black hole shape the galaxy, or does the galaxy determine how its black hole grows?
A team led by Benjamin L. Davis set out to answer this question not through direct observation, but through causal discovery — a statistical framework that identifies the direction of cause and effect from data rather than simply confirming correlation. The result depended on galaxy shape, and to test its reliability, the team turned to cosmological simulations.
Causal discovery separates correlation into cause and effect
Running an experiment on a real galaxy is impossible — observation is all astronomers have. But causal discovery methods can analyze data from hundreds of galaxies and determine which variable changes first and which one responds with a time lag.
Applying this approach to real galaxies confirmed earlier findings: in spiral galaxies, the black hole causally drives its host galaxy's physical parameters. In elliptical galaxies, the pattern reverses — the black hole behaves as a passive companion, growing almost in lockstep with the galaxy rather than dictating its development.
The key open question was whether this split is a fixed rule of nature, or whether it changes over time within a single galaxy's life.
NIHAO simulations track how the causal direction flips over time
To answer that, the team used NIHAO — a suite of cosmological zoom-in hydrodynamical simulations that model the evolution of individual galaxies from the early Universe to the present day in fine detail.
Unlike real observations, which capture a galaxy at a single moment, a simulation lets researchers follow the entire history: how a galaxy's black hole mass (M●) and central stellar velocity dispersion (σ0) changed over billions of years of evolution.
The result confirmed the core hypothesis and added a time dimension to it. The causal direction between black hole and galaxy noticeably flips between the epoch before the peak of star formation and the epoch after it. While a galaxy is still gas-rich and actively forming stars, the black hole drives the process through AGN feedback — powerful energy outflows from active galactic nuclei that gradually shut down star formation. Once the peak of star formation has passed and gas is depleted, the black hole's role turns passive: it simply keeps pace with the galaxy's own growth.
The M–σ formula overestimates early black hole masses by roughly a hundredfold
The most practical consequence of this study concerns observations from the James Webb Space Telescope (JWST). It routinely detects supermassive black holes in distant, young galaxies dating back to just hundreds of millions to a few billion years after the Big Bang. Their masses are usually estimated using the standard M–σ formula, and the results look anomalous — some black holes appear far too massive for such young, low-mass host galaxies, defying existing growth models.
The authors propose a different explanation. The standard M–σ formula was calibrated mostly on elliptical galaxies in the local Universe — systems where star formation has long since stopped and the black hole is a passive passenger. But distant, young galaxies in the early Universe are predominantly gas-rich spiral systems, where the opposite causal mechanism applies.
Applied to such galaxies, the standard formula overestimates black hole mass by roughly a hundredfold (two orders of magnitude). The researchers developed updated, causally-informed scaling relations that yield significantly lower mass estimates for black holes at high redshift.
Updated causally-informed scaling relations predict high-z black hole masses that are approximately two orders of magnitude less massive, and thus not overmassive with respect to local z=0 SMBH–galaxy mass ratiosfrom the paper's abstract, Astrophysical Journal, 2026
If these revised estimates hold up, many of the "overmassive" black holes JWST has been finding in the early Universe could turn out to be entirely ordinary for their age and galaxy type. The problem may not lie with the black holes themselves, but with the formula used to measure them.
