MaNGA DynPop. VII. A Unified Bulge-Disk-Halo Model for Explaining Diversity in Circular Velocity Curves of 6000 Spiral and Early-Type Galaxies

We derive circular velocity curves (CVCs) from stellar dynamical models for $\sim 6000$ nearby galaxies in the final data release of the Sloan Digital Sky Survey-IV MaNGA survey with integral-field spectroscopy, exploring connections between the inner gravitational potential (traced by CVC amplitude/shape) and galaxy properties. The maximum circular velocity ($V_{\mathrm{c}\mathrm{i}\mathrm{r}\mathrm{c}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$) and circular velocity at the half-light radius ($V_{\mathrm{c}\mathrm{i}\mathrm{r}\mathrm{c}}(R_{\mathrm{e}}^{\mathrm{m}\mathrm{a}\mathrm{j}})$) both scale linearly with the stellar second velocity moment ${\sigma }_{\mathrm{e}}^2\equiv ⟨V^2+{\sigma }^2⟩$ within the half-light isophote, following $V_{\mathrm{c}\mathrm{i}\mathrm{r}\mathrm{c}}^{\mathrm{m}\mathrm{a}\mathrm{x}}\approx 1.72{\sigma }_{\mathrm{e}}$ (7$\mathrm{\%}$ error) and $V_{\mathrm{c}\mathrm{i}\mathrm{r}\mathrm{c}}(R_{\mathrm{e}}^{\mathrm{m}\mathrm{a}\mathrm{j}})\approx 1.62{\sigma }_{\mathrm{e}}$ (7$\mathrm{\%}$ error). CVC shapes (rising, flat, declining) correlate strongly with structural and stellar population properties: declining curves dominate in massive, early-type, bulge-dominated galaxies with old, metal-rich stars and early quenching, while rising CVCs prevail in disk-dominated systems with younger stellar populations and ongoing star formation. Using a unified bulge-disk-halo model, we predict CVC shapes with minimal bias, identifying three governing parameters: bulge-to-total mass ratio ($B\mathrm{/}T$), dark matter fraction within $R_{\mathrm{e}}$, and bulge Sersic index. The distribution of CVC shapes across the mass-size plane reflects evolutionary pathways driven by (i) in situ star formation (spurring bulge growth) and (ii) dry mergers. This establishes CVC morphology as a diagnostic for galaxy evolution, linking dynamical signatures to structural and stellar population histories.