COSMOS-Web: A history of galaxy migrations over the stellar mass-star formation rate plane

The stellar mass-star formation rate ($\mathrm{M_*}$-$\mathrm{SFR}$) plane is a fundamental diagnostic for distinguishing galaxy populations. However, the evolutionary pathways of galaxies within this plane across cosmic time remain poorly understood. This study aims to observationally characterize galaxy migration in the $\mathrm{M_*}$-$\mathrm{SFR}$ plane using reconstructed star formation histories (SFHs) of galaxies at $z < 4$. Our goal is to provide insights into the physical processes governing star formation and quenching. We analyze a sample of 299,131 galaxies at $z < 4$ from the COSMOS-Web NIRCam survey ($m_{\mathrm{F444W}} < 27$, 0.54 deg$^2$). Using non-parametric SFH modeling with CIGALE, we derive physical properties and reconstruct SFHs. To trace galaxy evolution, we define migration vectors, quantifying their direction ($\Phi_{\mathrm{dt}}$ [deg]) and velocity norm ($r_{\mathrm{dt}}$ [dex/Gyr]) on the $\mathrm{M_*}$-$\mathrm{SFR}$ plane. The reliability of these vectors is assessed using the Horizon-AGN simulation. We find that main-sequence galaxies exhibit low-amplitude migration with scattered directions, suggesting oscillations within the main sequence. Their progenitors predominantly lie on the main sequence 1 Gyr earlier. Starburst galaxies show rapid mass assembly ($50\%$ within 350 Myr) and originate from the main sequence, while passive galaxies display uniformly declining SFHs. Massive passive galaxies emerge as early as $3.5 < z < 4$, increasing in number density over time. Only $<20\%$ of passive galaxies were starbursts 1 Gyr prior, indicating diverse quenching pathways. By reconstructing SFHs to $z < 4$, we present a coherent picture of galaxy migration in the $\mathrm{M_*}$-$\mathrm{SFR}$ plane, linking evolutionary phases to their star formation signatures.