Limited imprint of high-mass IMF variations on sodium abundances in main-sequence galaxies

Growing evidence suggests that the stellar initial mass function (IMF) varies systematically across galaxies, deviating from the canonical Milky Way form. Such variations would modify the integrated nucleosynthetic yields, and hence the abundance patterns used in stellar population synthesis studies. How these could impact, in particular, the sodium abundance (and sodium-to-oxygen ratios) in star-forming galaxies is not well understood. In this work, we systematically study how high-mass IMF variations affect sodium enrichment using a one-zone galactic chemical evolution model. The model incorporates star formation histories from semi-analytic simulations and is calibrated to match the observed galaxy mass--metallicity relation. We find that varying the IMF high-mass end (and the IMF slope) could only alter the sodium abundance by less than 0.1 dex, across galaxies with stellar masses from $10^9\,\mathrm{M}_\odot$ to $10^{11}\,\mathrm{M}_\odot$. This result is robust under different stellar models and galaxy evolution assumptions, primarily because sodium production is similar to that of oxygen. We conclude that sodium abundance is largely insensitive to changes in the high-mass IMF, unlikely to compromise the use of sodium indices as IMF diagnostics in stellar population studies.