Stellar initial mass function varies with metallicity and time

Most structural and evolutionary properties of galaxies strongly rely on the stellar initial mass function (IMF), namely the distribution of the stellar mass formed in each episode of star formation 1 – 4 . The IMF shapes the stellar population in all stellar systems, and so has become one of the most fundamental concepts of modern astronomy. Both constant and variable IMFs across different environments have been claimed despite a large number of theoretical 5 – 7 and observational efforts 8 – 15 . However, the measurement of the IMF in Galactic stellar populations has been limited by the relatively small number of photometrically observed stars, leading to high uncertainties 12 – 16 . Here we report a star-counting result based on approximately 93,000 spectroscopically observed M-dwarf stars, an order of magnitude more than previous studies, in the 100–300 parsec solar neighbourhood. We find unambiguous evidence of a variable IMF that depends on both metallicity and stellar age. Specifically, the stellar population formed at early times contains fewer low-mass stars compared with the canonical IMF, independent of stellar metallicities. In more recent times, however, the proportion of low-mass stars increases with stellar metallicity. The variable abundance of low-mass stars in our Milky Way establishes a powerful benchmark for models of star formation and can heavily affect results in Galactic chemical-enrichment modelling, mass estimation of galaxies and planet-formation efficiency. A direct star-counting method of about 93,000 M-dwarf stars in the solar neighbourhood indicates a variable stellar initial mass function that depends on both metallicity and stellar age.