Can current models predict the local black hole merger rate?

After four observational runs, the Ligo-Virgo-Kagra collaboration estimated a local binary black hole (BBH) merger rate density of $R_{0,\textrm{LVK}}\simeq 14-26\,\textrm{Gpc}^{-3}\,\textrm{yr}^{-1}$ within the 90% credible interval. Some previous studies already pointed out that, when a realistic evolution of the metallicity-dependent cosmic star formation rate density (SFRD) is adopted, theoretical models predict a local BBH merger rate density that exceeds the observed value by at least a factor of $\sim 10$ (Sgalletta et al. 2025). In this paper, we confirm and strengthen this claim by constructing an empirical model for the SFRD and metallicity evolution that includes a correction accounting for iron abundance. The adopted metallicity relation is flexible, enabling us to bracket the wide range of observational uncertainties. We show that, even under the most conservative assumptions regarding both the SFRD and the metallicity relation, the local BBH merger rate density is overestimated by a factor $> 10$. Attempts to reconcile the predicted and observed merger rates by modifying only the metallicity-dependent SFRD would require unrealistically high metallicities ($Z>Z_\odot$) even in low-mass galaxies at high redshift. This finding indicates that revisions to the treatment of stellar and binary evolution are necessary to achieve consistency between theoretical predictions and observations. We suggest that even a modest steepening of the delay-time distribution could help alleviate this tension.