Turning Galaxy Rotation Curves into Radial Cosmic Chronometers: A Nexus Paradigm Approach

TL;DR

This paper introduces a novel method to derive galaxy assembly histories from rotation curves, transforming kinematic data into radial cosmic chronometers without dark matter halo fitting.

Contribution

It presents a new approach linking galaxy rotation curves to formation redshifts and lookback times, enabling direct reconstruction of galaxy evolution.

Findings

Recovered diverse radial age structures in galaxy samples.

Demonstrated the method's consistency with known galaxy formation scenarios.

Provided a kinematic chronometer as a new observable for galaxy evolution.

Abstract

We present a method for transforming galaxy rotation curves into radially resolved dynamical chronometers, enabling reconstruction of galaxy assembly histories directly from kinematic data. Within the Nexus Paradigm, the baryonic Tully-Fisher relation provides an estimate of the dynamical mass profile $ M_{dyn}(r)=v^4/Ga_0$, where $a_0=H_0/2\pi $.By Comparing this with independently derived intrinsic baryonic mass profiles, $M_{int}(r)$, obtained from stellar S\'ersic fits and gas surface density measurements, we construct the ratio $ M_{dyn}(r)/M_{int}(r)$, which maps directly to a formation redshift via $ 1+z_{form}(r)=(M_{dyn}/M_{int})^{1/4}$. Inverting this relation with$\Lambda CDM$ cosmology yields a radial lookback-time profile, $t_{lb}(r)$, representing the time since the last dynamical reconfiguration at each radius. Applying this framework to a pilot sample of SPARC galaxies spanning high-and low -surface-brightness systems, together with the Milky Way, we recover diverse radial age structures, including flat profiles consistent with coherent disk assembly and stratified profiles indicative of inside-out growth. The method operates without dark-matter halo fitting and provides a kinematic chronometer complementary to stellar-population and chemical-evolution approaches. While the inferred ages depend on the accuracy of baryonic mass reconstruction and local applicability of the evolving baryonic Tully-Fisher relation, the results demonstrate that galaxy rotation curves encode time-resolved dynamical information. This establishes the radial dynamical chronometer as a new observable for probing galaxy evolution and testing gravitational frameworks.