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

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 $a_0=H_0/2π$.By Comparing this with independently derived intrinsic baryonic mass profiles, $M_{int}(r)$, obtained from stellar Sérsic 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}$. Inverting this relation with$ΛCDM$ 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.

• The paper introduces a novel method for extracting radial cosmic chronometers from galaxy rotation curves by leveraging the evolving baryonic Tully-Fisher relation.
• The method applies high-quality SPARC rotation curve data to compute local lookback times, revealing distinct assembly modes in HSB, LSB galaxies, and the Milky Way.
• The technique bypasses traditional dark matter halo fitting, offering a new framework for testing gravitational theories and refining galaxy formation models.

Transforming Galaxy Rotation Curves into Radial Cosmic Chronometers: The Nexus Paradigm Approach

Introduction

This work develops a methodology for directly extracting the radial assembly history of galaxies from rotation curve data, exploiting the evolving baryonic Tully-Fisher relation (BTFR) as derived in the Nexus Paradigm (NP) framework. Traditionally, galaxy formation histories are reconstructed indirectly via stellar population synthesis, chemo-dynamical analyses, or morphological diagnostics. The approach presented here constructs a local dynamical chronometer from rotation curves without resorting to dark-matter halo fitting, reframing kinematic data as a time-resolved probe of galaxy evolution.

Theoretical Framework

The NP posits a quantized spacetime wherein Ricci solitons provide a geometrization of dark energy and dark matter phenomena, leading naturally to flat galaxy rotation curves (Marongwe 2024; Marongwe et al. 2025a,b). Within this context, the BTFR normalization is not static but evolves with cosmic time. The BTFR derivation,

$$M_\text{int}(r) = M_\text{dyn}(r) \exp\left[\int_{t_\text{form}}^{t_0}H(t)dt\right]$$

(or, in the $\Lambda$CDM limit, $$1 + z_\text{form}(r) = [M_\text{dyn}(r)/M_\text{int}(r)]^{1/4}$$),

connects the ratio of dynamically inferred mass to observed baryonic mass at each radius to a formation redshift. Inversion within the $\Lambda$CDM cosmology framework thus yields a local lookback-time profile, $t_{lb}(r)$, representing the time since the last major dynamical reconfiguration at each galactocentric radius.

Unlike standard interpretations in $\Lambda$CDM or MOND (where BTFR is effectively static for disk galaxies), the NP introduces explicit cosmological evolution, allowing scatter in the BTFR to track assembly epoch rather than unmodeled baryonic or halo diversity.

Methodology

The chronometric method requires high-quality observed rotation curves, usually drawn from the SPARC database, and radially resolved baryonic mass profiles constructed independently from stellar light (Sérsic fits, mass-to-light calibration) and HI/H$_2$ gas distributions. The dynamically inferred mass profile, $M_\text{dyn}(r)$, is obtained from the BTFR with explicit time dependence. By forming the local ratio $M_\text{dyn}(r)/M_\text{int}(r)$, a formation redshift $z_\text{form}(r)$ and corresponding lookback-time profile are computed for every radius. Monte Carlo error propagation robustly accounts for photometric, dynamical, and model uncertainties.

The technique is applied to both high-surface-brightness (HSB) and low-surface-brightness (LSB) galaxies, as well as the Milky Way. Importantly, the method maintains full radial resolution and does not presume spherical symmetry or a universal formation scenario.

Results and Key Claims

High-Surface-Brightness Galaxies

Strong radial gradients in dynamical age are consistently observed. Systems like NGC 2841 display canonical inside-out growth: the central $\Lambda$04 Gyr region transitions to outer regions of $\Lambda$12 Gyr, supporting a dissipative collapse followed by secular disk assembly. Other HSBs show secular or even coeval assembly modes, with the NP chronometer able to recognize these variations directly from kinematic data. The results robustly reproduce observed rotation curves without adopting ad hoc dark-matter halo profiles.

Low-Surface-Brightness Galaxies

LSBs (e.g., UGC 128, F568-3) exhibit shallow, nearly flat dynamical age gradients, indicative of diffuse, quasi-coherent assembly over several Gyr. There is no evidence for early, rapid collapse or major merger-driven restructuring. This outcome, supported by independent star formation histories and stellar population ages from the literature, demonstrates the method's consistency and discriminative power regarding galactic evolutionary mode.

The Milky Way

For the Milky Way, the chronometer reconstructs a uniformly young relaxation age ($\Lambda$2–$\Lambda$3 Gyr) across the disk, matching the independently known dynamical activity (bar/spira-driven migration, recent satellite and accretion events, warping, and lopsidedness). This flat age profile indicates ongoing dynamical perturbations and disk mixing, distinct from the stratified assembly seen in more quiescent HSBs. Such a result validates the method by cross-referencing multifaceted empirical records.

Physical Interpretation

The inferred dynamical age at each radius is the time since the last equilibrium-resetting event (major merger, tidal disturbance, significant secular instability)—not the median stellar-population age. The BTFR scatter is thereby reinterpreted as physical signal encoding local assembly timing. Disks near the present-day BTFR normalization are dynamically young; systematic offsets characterize older or less-relaxed systems.

Theoretical and Practical Implications

• Direct Kinematic Assembly Mapping: This method renders rotation curves as time-resolved dynamical observables, offering independent and radially resolved cosmic chronometers.
• Testing Gravity Theories: The approach is specific to the NP, where BTFR normalization evolves and the ratio-to-redshift mapping is valid. In contrast, static MOND and vanilla $\Lambda$4CDM lack this local chronometric interpretability.
• Complementarity: The NP chronometer is naturally complementary to population-synthesis, metallicity, and chemo-dynamical clocks. Cross-validation across methods will further constrain galaxy formation models.
• Bypassing Dark Matter Halo Fitting: The framework skirts dark matter halo decomposition entirely, leveraging a direct mapping from kinematics to mass via the evolving BTFR.

Limitations and Future Directions

The principal uncertainty lies in the accuracy of reconstructed baryonic mass profiles (especially stellar mass-to-light ratios and gas measurements). The underlying assumption that the evolving BTFR applies locally within disk galaxies warrants further empirical validation on larger, more diverse samples and via hydrodynamical simulations. Future work aims at expanding the galaxy sample, comparing the NP chronometer with $\Lambda$5CDM and MOND predictions, and tighter integration with chemo-dynamical and stellar age diagnostics.

Conclusion

The methodology introduced establishes galaxy rotation curves as direct, radially resolved cosmic chronometers. Under the Nexus Paradigm, each radial shell’s dynamical age (since last major restructuring) is extracted from the local ratio of dynamical to baryonic mass, using the evolving BTFR specific to NP quantum gravity. Application to SPARC galaxies and the Milky Way reveals diverse assembly modes—inside-out stratification in HSBs, diffuse assembly in LSBs, and globally young ages in the dynamically perturbed Milky Way. The approach circumvents dark matter halo fitting, enhances the interpretive power of rotation curves, and sets a new path for empirical tests of gravitational theories and galaxy formation scenarios. Further validation and cross-calibration will determine the chronometer’s ultimate utility and discriminating power for resolving the physics of galactic evolution.

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Reference: "Turning Galaxy Rotation Curves into Radial Cosmic Chronometers: A Nexus Paradigm Approach" (2604.17597)