GalIMF–E-MILES library: Impact of an environment-dependent initial mass function on stellar population spectra

We present, for the first time, model spectra of single-age, single-metallicity stellar populations computed with the E-MILES evolutionary synthesis code incorporating an environment-dependent, variable galaxy-wide initial mass function (gwIMF). This gwIMF, calculated using the GalIMF code, is rooted in the integrated galactic initial mass function (IGIMF) theory, which predicts IMF variations as a function of the star formation rate and the metallicity. By coupling these two codes, we generated a comprehensive library of single-burst stellar population spectra uniquely sensitive to gwIMF variations. Through detailed comparisons with the canonical Milky-Way IMF, we reveal how both the spectral energy distributions and key stellar absorption features systematically evolve with age under different IMF conditions. Our results uncover clear spectral signatures tied to IMF variability, emphasising the critical role of star formation and chemical enrichment histories in shaping the integrated light observed in galaxies. Based on our work, specific absorption spectral indices emerge as powerful diagnostics, and they open new pathways to empirically test IMF variations and refine models of galaxy formation and evolution. All synthetic spectra generated in this study are publicly available and constitute a valuable resource for future observational and theoretical investigations.