Evolving Baryonic Tully-Fisher Relation Unifies Galaxies and Clusters with a Fixed Slope of and Time-Dependent Normalization

The Baryonic Tully-Fisher relation, a fundamental link between a galaxy’s mass and its rotation speed, has long been considered a cornerstone of galactic astronomy. Stuart Marongwe from the University of Botswana and Stuart Kauffman from the University of Pennsylvania, along with their colleagues, now demonstrate that this relationship extends seamlessly from individual galaxies to the largest structures in the universe, galactic clusters. Their work resolves a recent puzzle concerning the offset observed between galaxies and clusters on the standard BTFR, revealing it arises naturally from the passage of cosmic time. By establishing an evolving form of the BTFR, the team unifies mass-velocity scaling across an unprecedented five orders of magnitude, offering a powerful new framework for understanding how cosmic structures form and evolve.

Recent studies indicate that galaxy clusters occupy a parallel but offset relation, raising questions about the universality of the BTFR. Here, scientists demonstrate that the offset between galaxies and clusters arises naturally from cosmic time evolution. Using an evolving BTFR derived from the Nexus Paradigm of quantum gravity, they show that the normalization of the relation evolves as an exponential function of cosmic time, while the slope remains fixed. The authors propose that the BTFR isn’t merely a set of observed trends, but a fundamental connection evolving with the universe, framed within the Nexus paradigm, suggesting a deeper underlying physics. The core argument challenges the traditional view of the BTFR as a simple correlation, positing it as a fundamental relationship whose evolution reveals insights into galaxy and cluster formation. The research synthesizes data from various sources, including observations of galaxies and clusters at different redshifts, and compares findings with predictions from standard cosmological models and alternative theories.

The study emphasizes the role of baryonic matter, normal matter, in driving the BTFR, suggesting it is a more fundamental driver than dark matter, and utilizes weak lensing reconstructions to improve mass model accuracy, particularly for clusters. Key findings confirm that the BTFR evolves with redshift, indicating changes in the physical processes governing galaxy and cluster formation over cosmic time. The findings present challenges to the standard cosmological model, particularly in explaining the observed BTFR evolution without invoking excessive dark matter, and are more consistent with alternative theories. The study highlights the crucial role of baryonic physics, gas dynamics, star formation, and feedback processes, in shaping the BTFR, proposing a unified law connecting galaxies, clusters, and the cosmos.

Future research will focus on sophisticated hydrodynamical simulations incorporating time-evolving quantum effects, and observations with next-generation telescopes like the James Webb Space Telescope, Euclid, and the Square Kilometre Array to directly test the predicted redshift-dependent normalization shifts in the BTFR. Further refinement of stellar mass models, incorporating chemical evolution, is also crucial for accurately determining the baryonic content of galaxies. The research confirms that this offset arises naturally from differences in when galaxies and clusters formed, rather than requiring separate scaling laws for each. Experiments reveal that the normalization of the BTFR evolves as an exponential function of cosmic time, while maintaining a consistent slope of approximately 4 across five orders of magnitude in baryonic mass. The team applied an evolving BTFR framework, showing that galaxies, typically assembling at higher redshifts, and clusters, forming at lower redshifts, both adhere to the same universal scaling law.

Measurements confirm the offset between galaxies and clusters is a consequence of their differing formation epochs, bridging a gap in understanding cosmic structure formation. This work builds upon the well-established BTFR for galaxies, which links total baryonic mass to characteristic rotation velocity with remarkably low intrinsic scatter. Extending this relation to galaxy clusters required adapting velocity proxies, such as galaxy velocity dispersion and circular velocities derived from X-ray observations, but the team successfully demonstrated a consistent scaling. Results demonstrate that clusters trace a parallel BTFR, offset by a small amount in logarithmic baryonic mass, but this offset is fully explained by the evolving normalization linked to cosmic time. By allowing the normalization of the relation to change over time, while maintaining a constant slope, the model successfully unifies the scaling behaviors of both galaxies and clusters across a wide range of baryonic masses. Galaxies, forming earlier in cosmic history, exhibit lower baryonic masses at a given rotational velocity, while later-forming clusters align with a higher normalization, reflecting the influence of cosmic expansion on baryon-dark matter interactions. The research confirms a predicted offset between the relations for galaxies and clusters, aligning with observational data spanning five orders of magnitude in baryonic mass.

This unification extends beyond empirical agreement, offering new insights into how cosmic structures assemble within the standard cosmological model, incorporating principles from quantum gravity. The consistent slope suggests fundamental gravitational equilibria within dark matter halos, while the evolving normalization highlights the role of cosmic expansion in modulating interactions between baryons and dark matter. The authors acknowledge that further research, particularly at higher redshifts, will continue to refine understanding of these processes and validate the model’s predictions regarding mass growth and the influence of gas accretion and feedback.