Spectroscopic analyses of gravity-sensitive line strengths give growing evidence towards an excess of low-mass stars in massive early-type galaxies ( ETGs ) .
Such a scenario requires a bottom-heavy initial mass function ( IMF ) .
However , strong constraints can be imposed if we take into account galactic chemical enrichment .
We extend the analysis of Weidner et al .
and consider the functional form of bottom-heavy IMFs used in recent works , where the high-mass end slope is kept fixed to the Salpeter value , and a free parameter is introduced to describe the slope at stellar masses below some pivot mass scale ( M < M _ { P } = 0.5 M _ { \odot } ) .
We find that no such time-independent parameterisation is capable to reproduce the full set of constraints in the stellar populations of massive ETGs – resting on the assumption that the analysis of gravity-sensitive line strengths leads to a mass fraction at birth in stars with mass M < 0.5 M _ { \odot } above 60 % .
Most notably , the large amount of metal-poor gas locked in low-mass stars during the early , strong phases of star formation results in average stellar metallicities [ M/H ] \lesssim - 0.6 , well below the solar value .
The conclusions are unchanged if either the low-mass end cutoff , or the pivot mass are left as free parameters , strengthening the case for a time-dependent IMF .