Symmetry in fundamental parameters of galaxies on the star-forming main sequence

ABSTRACT The Star-Forming Main Sequence (SFMS) serves as a critical framework for understanding galaxy evolution, highlighting the relationship between star formation rates (SFR) and stellar masses $M_*$ across cosmic time, for star forming galaxies. Despite its significance, the origin of the 0.3–0.4 dex dispersion in the SFMS remains a topic of debate. Uncovering the origin of dispersion is crucial for understanding the evolution of galaxies. Using a large sample of approximately 500 000 galaxies, we reveal a set of clear and systematic symmetries in the distribution of key structural properties – effective radius ($R_{\rm e}$), stellar surface density ($M_*/R_{\rm e}^2$), and morphology – on the SFMS. This symmetry implies that galaxies with high (above SFMS) and low (below SFMS) SFRs share similar fundamental parameters. Moreover, galaxies with smaller $R_{\rm e}$ or higher $M_/R_{\rm e}^2$ exhibit greater dispersion in SFR. This dispersion reflects the response to fluctuations in cosmic accretion flows, while the SFR itself represents the time-averaged effect over the gas consumption time-scale. Shorter gas consumption time-scales, associated with higher $M_/R_{\rm e}^2$, lead to greater SFR dispersion. Our results reveal that the variation of SFR originates from the oscillation of accretion flow and is regulated by the stellar surface density.