Abstract Correlation does not imply causation, but patterns of statistical association between variables can be exploited to infer a causal structure (even with purely observational data) with the burgeoning field of causal discovery. As a purely observational science, astrophysics has much to gain by exploiting these new methods. The supermassive black hole (SMBH)–galaxy interaction has long been constrained by observed scaling relations, which is low-scatter correlations between variables such as SMBH mass and the central velocity dispersion of stars in a host galaxy's bulge. This study, using advanced causal discovery techniques and an up-to-date data set, reveals a causal link between galaxy properties and dynamically measured SMBH masses. We apply a score-based Bayesian framework to compute the exact conditional probabilities of every causal structure that could possibly describe our galaxy sample. With the exact posterior distribution, we determine the most likely causal structures and notice a probable causal reversal when separating galaxies by morphology. In elliptical galaxies, bulge properties (built from major mergers) tend to influence SMBH growth, while, in spiral galaxies, SMBHs are seen to affect host galaxy properties, potentially through feedback in gas-rich environments. For spiral galaxies, SMBHs progressively quench star formation, whereas, in elliptical galaxies, quenching is complete, and the causal connection has reversed. Our findings support theoretical models of hierarchical assembly of galaxies and active galactic nuclei feedback regulating galaxy evolution. Our study suggests the potentiality for further exploration of causal links in astrophysical and cosmological scaling relations, as well as any other observational science.

Abstract Observations indicate that early-type galaxies exhibit varying slopes in the relation between their central stellar surface density and stellar mass (Σ 1 – M ⋆ ). Low-mass galaxies tend to follow a steep slope, close to 1, while the slope flattens for high-mass early-type galaxies. In our study, we investigate the Σ 1 – M ⋆ scaling relation and its evolution using the Numerical Investigation of Hundred Astrophysical Objects (NIHAO) suite of cosmological simulations and compare our findings with recent results from the MaNGA survey. Our analysis shows that NIHAO galaxies successfully reproduce the observed scaling relation based on the MaNGA survey. Our analysis suggests that active galactic nucleus (AGN) feedback plays a critical role in flattening the Σ 1 slope, by expelling gas from galactic centers, leading to a decrease in both stellar and dark matter density as the gravitational potential becomes shallower. To further support our findings, we conduct high-resolution N -body simulations, which confirm that (sudden) gas removal does substantially alter the stellar density in the central region, consistent with the results from NIHAO. Furthermore, our numerical experiments show that even if the same amount of gas is reaccreted on a typical (longer) freefall time, it is not able to restore the original stellar density. Our study concludes that AGN-feedback-assisted gas removal presents a plausible explanation for the decline in central stellar surface density as observed in massive elliptical galaxies.