The effect of the environment-dependent stellar initial mass function on the baryonic Tully Fisher relation

Abstract: We investigate the impact of an environment-dependent galaxy-wide stellar initial mass function (gwIMF) on the baryonic Tully-Fisher relation (BTFR). The integrated galaxy-wide IMF (IGIMF) theory, which incorporates variations in stellar populations due to star formation history (SFH) and metallicity, provides a more accurate framework for understanding systematic deviations in galaxy scaling relations than that given by an invariant gwIMF. By considering how the mass-to-light ratio of the stellar population is influenced by metallicity and SFH, we show that high-mass galaxies have their masses in stars and remnants underestimated under the assumption of a constant mass-to-light ratio. In contrast, low-mass, gas-dominated galaxies are less affected. Our results suggest that the discrepancies between the true and observed BTFR are primarily driven by the evolving nature of the stellar IMF, particularly in galaxies with slowly declining SFHs. The IGIMF theory offers a solution to the observed offsets in the BTFR, especially for high-mass galaxies, where the rotational velocities are higher than predicted by MOND. We conclude that incorporating the IGIMF provides a more accurate description of galaxy dynamics, revealing the importance of stellar population characteristics in refining our understanding of the baryonic mass-velocity relationship. This study underscores the necessity of accounting for the variation of the gwIMF when interpreting the BTFR, particularly in the context of alternative gravitational theories like MOND.