Negative Dynamical Timescales in Pressure-Supported Galaxies

This paper demonstrates that the unified dynamical timescale τ defines a genuine kinematic phase of galaxies, extending beyond rotation-supported disks to pressure-supported spheroids. Using large-sample integral-field spectroscopy, we show that galaxies dominated by random stellar motion occupy a distinct dynamical regime characterized by negative values of τ\tauτ. Pressure-supported systems are identified through a purely kinematic classification based on the ratio of ordered to random stellar motion (v/σv/\sigmav/σ), independent of morphology, photometric structure, or star-formation indicators. A Kolmogorov–Smirnov change-point analysis applied to stellar population age distributions (Dn4000) demonstrates that the transition between rotation- and dispersion-dominated systems is robust across stellar mass and redshift subsamples. We find that while the precise numerical value of the kinematic proxy separating regimes varies modestly with sample selection, the sign of τ\tauτ remains invariant. This establishes that negative τ\tauτ does not arise from classification choices, but reflects a physically distinct dynamical phase in which the scale of confinement exceeds the scale of dynamical coherence. Together with earlier work establishing τ\tauτ as independent of star-formation activity, these results demonstrate that τ\tauτ is a galaxy-scale parameter applicable across the Hubble sequence. The findings unify disk and spheroidal systems within a single dynamical framework and motivate further investigation into how evolutionary history governs baryonic outcomes within a given kinematic phase.