For three decades it has been speculated that the stellar initial mass function (IMF) is more biased towards massive stars in starburst environments, especially in massive galaxies at high-redshift, which could explain the overabundance of magnesium (mostly synthesised in high-mass stars) with respect to iron (mostly produced by type Ia supernovae with relatively low-mass progenitors) observed in local elliptical galaxies. However, differences in star-formation time scales and/or the presence of selective galactic outflows could act in a similar way. More recently, the so-called integrated galaxy-wide IMF (IGIMF) theory has been developed, according to which the galaxy-wide IMF lacks massive stars in lower-mass star-forming systems, and privileges high-mass star formation in higher-mass systems. This is also evident from broadband photometric and Hα emission studies of thousands of star forming galaxies. According to the theory and cosmological simulations, the most extreme IMF variations should be seen in large galaxies that shine at high redshifts, where they experience the most powerful starbursts that the Universe ever saw, with star formation rates possibly in excess of 500–1000 M_⊙/yr. Classical methods of IMF determination, limited at optical, UV, and near-IR wavelengths, cannot probe such ‘monsters’ because of the dust obscuration of stellar light. On the other hand, element and isotopic abundances measured in the interstellar medium (ISM) at millimeter/submillimeter wavelengths provide fundamental new constraints for the stellar IMF in these extreme objects.

In previous work, we have demonstrated that the isotopic ratios of CNO elements, in particular the ¹³C-to-¹⁸O ratio measured from the optically thin ¹³CO and C¹⁸O lines in molecular gas, are indeed excellent IMF probes for galaxies. This opens up a new window to deduce the stellar IMF in dust-shrouded galaxies using ALMA, especially for submillimeter galaxies at redshift z~1–7 that are heavily obscured in the optical. We find a clear boost of the ¹⁸O-to-¹³C ratio in all starburst galaxies, and a top-heavy IMF appears to be the only reasonable explanation. Yet, significant uncertainties are still present, when we want to extend this line of inquiry to other isotopic abundances (e.g., those of N, Si, and S), to better constrain the IMF slopes using their synergy, and to measure isotopic abundances using fine-structure atomic lines, ionised lines, and high-lying molecular lines using space telescopes, such as SOFIA, Herschel, JWST, and SPICA.

With this proposal, we aim at building up an international team whose members have all the necessary expertise to (i) reduce significantly the uncertainties present in abundance measurements, (ii) extend the measurements to different types of galaxies, from dwarfs to ellipticals, at both high and low redshifts, (iii) improve –or develop from scratch– the theoretical tools that are necessary for a full exploitation and interpretation of the data. Our team is composed of ten scientists from five European countries and from China. It includes experts in numerical simulations, semi-analytical models of galaxy formation in a cosmological context, state-of-the-art hydro-dynamical simulations, stellar evolution and nucleosynthesis, chemical evolution, IGIMF theory, as well as experts in ISM physics, molecular line observations and data analysis. Because of the team composition, and to help self-supported external experts from both European countries and China to attend the meetings, our team would benefit from one 5-day meeting in ISSI, Bern, and one 5-day meeting in ISSI-BJ, Beijing.