The effect of the environment-dependent stellar initial mass function on the photometric properties of star-forming galaxies

Abstract: (Abridged) Observational estimates of galaxy properties rely on the inherent galaxy-wide initial mass function (gwIMF), which systematically varies with the global SFR and metallicity, as proposed by the integrated-galactic IMF (IGIMF) theory and supported by empirical evidence. We incorporate PARSEC and COLIBRI stellar isochrones into the GalIMF code, a galaxy chemical evolution (GCE) model featuring real-time updates of environment-dependent gwIMFs. This newly developed photometric GalIMF (photGalIMF) code allows the calculation of photometric properties for galaxies with diverse stellar populations. Subsequently, we analyze observed luminosities and metallicities of local star-forming galaxies to deduce their stellar masses assuming that they have constant SFRs over 13.6 Gyr. We also compute SFR$-$H$\alpha$ luminosity relations for varying stellar metallicities using a separate stellar population synthesis code based on PEGASE. Comparing the IGIMF theory to the canonical universal IMF, our analysis reveals that estimates of the stellar masses and SFRs for local star-forming galaxies differ by factors of $\approx 2$ and 10, respectively. The computed gas-depletion timescale increases with gas mass, implying lower star formation efficiencies in more massive galaxies, possibly due to stronger feedback regulation, aligning with theoretical expectations. Additionally, the characteristic stellar mass buildup timescale increases with stellar mass, indicating that massive disk galaxies initiate star formation earlier than their low-mass counterparts. The photGalIMF code enables self-consistent computations of galactic photometry, self-consistently with GCE modelling within the context of an environment-dependent gwIMF. Utilizing Ks-band and H$\alpha$ luminosities of galaxies, the outcomes include galaxy mass, SFR, and fitting functions for the SFR correction factor.