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

Abstract We derive circular velocity curves (CVCs) from stellar dynamical models for ∼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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">circ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">max</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> ) and circular velocity at the half-light radius ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">circ</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">maj</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> </mml:math> ) both scale linearly with the stellar second velocity moment <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>≡</mml:mo> <mml:mo stretchy="false">〈</mml:mo> <mml:msup> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">〉</mml:mo> </mml:math> within the half-light isophote, following <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">circ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">max</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>≈</mml:mo> <mml:mn>1.72</mml:mn> <mml:msub> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> </mml:math> (7% error) and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">circ</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">maj</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> <mml:mo>≈</mml:mo> <mml:mn>1.62</mml:mn> <mml:msub> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:msub> </mml:math> (7% 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/T), dark matter fraction within R e , and bulge Sérsic 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.