Symmetry in Fundamental Parameters of Galaxies on the Star-forming Main Sequence

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. Despite its significance, the origin of the 0.3-0.4 dex dispersion in the SFMS remains a key unresolved question. Uncovering the origin of dispersion is crucial for understanding the evolution of galaxies. Using a large sample of approximately 500,000 galaxies, we reveal an unprecedented symmetry 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 timescale. Shorter gas consumption timescales, 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.