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. 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.

Figures (13)

• Figure 1: Star formation main sequence for the sample with 556,764 galaxies from SDSS DR7. (a), the black solid line represents the main sequence relationship of SFR and $M_*$: $\log {\rm SFR}=0.83\times \log {M_*}-8.33$. The dashed line represents the boundary between SF and quenched galaxies by shifting the SFMS down 1 dex. (b) the deviation from the SFMS is defined as $\Delta \rm SFMS = \log \rm SFR - 0.83 \times \log M_{*} - 8.33$. The standard deviation of $\Delta \rm SFMS$ is approximately $\sigma = 0.42$ dex. The distribution of $\Delta \rm SFMS$ for SF galaxies is asymmetric, with an excess on the left, likely due to contributions from quenched or Green Valley galaxies. To correct this, the right-side distribution is symmetrically mirrored to the left, resulting in a more balanced distribution with a reduced dispersion of 0.33 dex.
• Figure 2: The regression relationship of $R_{\rm e}$ and $M_*$. The best-fit regression between $R_{\rm e}$ and $M_*$ is given by $\log [R_{\rm e}/ \rm kpc] = 0.22 \times \log [M_*/ M{\odot}$M_⊙$] - 1.46$. The residual of $R_{\rm e}$ is defined as $\Delta \log R_{\rm e} = \log R_{\rm e} - \log R_{\rm e}(M_*)$. Blue contours represent the isodensity lines for SF galaxies, while red contours represent those for quenched galaxies. Since our focus is on the dispersion of the SFMS, we only analyze the dependence of $R_{\rm e}$ on $M_*$ for SF galaxies.
• Figure 3: The regression relationship of $M_*/R_{\rm e}^2$ and $M_*$. The best regression relationship for $M_*/R_{\rm e}^2$ and $M_*$ is $\log [M_*R_{\rm e}^{2-}/ M{\odot}$M_⊙$\rm kpc^{-2}]$ = 0.66$\times \log [M_*/ M{\odot}$M_⊙$]$ +1.80. The residual of $M_*/R_{\rm e}^2$ are $\Delta \log [M_*/R_{\rm e}^2]$=$\log [M_*/R_{\rm e}^2]$ - $\log [M_*/R_{\rm e}^2](M_*)$. Blue contours represent the isodensity lines for SF galaxies, while red contours represent those for quenched galaxies. Since our focus is on the dispersion of the SFMS, we only analyze the dependence of $M_*/R_{\rm e}^2$ on $M_*$ for SF galaxies.
• Figure 4: Symmetry for the galaxy effective radius on the SFMS. The galaxy effective radius ($R_{\rm e}$) exhibit symmetry along the SFMS, i.e., the closer to SFMS, the larger the $R_{\rm e}$. The positive dependency between $R_{\rm e}$ and $M_*$ makes this symmetry appear less pronounced.
• Figure 5: Symmetry Phenomenon on the SFMS. (a, c): After accounting for their dependence on $M_{}$, the residual galaxy effective radius ($R_{\rm e}$) and stellar surface density ($M_*/R_{\rm e}^2$) exhibit symmetry along the SFMS. Deviations correspond to smaller $R_{\rm e}$ or higher $M_*/R_{\rm e}^2$. To visualize this symmetry, the $R_{\rm e}$ and $M_*/R_{\rm e}^2$ values for each data point were averaged over a 0.1-dex surrounding range. The black straight line represents the SFMS, while the dashed line below marks the boundary between star-forming and quenched galaxies. (b, d): On the SFMS, the average $\Delta \log R_{\rm e}$ reaches its maximum value and decreases as it deviates from the SFMS. Conversely, the average $\Delta \log M_*/R_{\rm e}^2$ is smallest on the SFMS and increases as it deviates from the SFMS.