The initial mass function of field stars with mass ⩽1 M⊙ varies with metallicity

ABSTRACT We investigate a volume-limited sample of Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) main-sequence stars with masses from 0.25 to 1 ${\rm M}_{\odot }$ and distances of 150–350 pc to explore how the stellar initial mass function (IMF) varies with metallicity. We correct the spectroscopic selection function by comparing the stellar number densities with the photometric ones at the same colour and magnitude. From these corrected number density distributions, we derive the IMF for each metallicity subsample. Fitting a broken power-law function to each IMF with a fixed break point at 0.525 ${\rm M}_{\odot }$, we find that the power-law indices increase with [Fe/H] for both mass regimes: $\alpha _1$ (mass $\le$ 0.525 ${\rm M}_{\odot }$) rises from 0.54 $\pm$ 0.21 to 1.40 $\pm$ 0.07 and $\alpha _2$ (mass $>$ 0.525 ${\rm M}_{\odot }$) increases from 1.40 $\pm$ 0.16 to 1.86 $\pm$ 0.04 as [Fe/H] varies from −1 to +0.5 dex. This demonstrates that low-mass stars make up a larger fraction in metal-rich environments than in metal-poor environments. We perform simulations to assess the impact of unresolved binaries on the IMF power-law indices. After correction, the binary-adjusted $\alpha$ values retain a similar metallicity-dependent trend. Furthermore, by examining the IMF of the aggregate sample, we find that the corrected indices ($\alpha _{\rm {1,corr}} = 1.48 \pm 0.03$, $\alpha _{\rm {2,corr}} = 2.17 \pm 0.03$) are consistent with the Kroupa IMF values ($\alpha _1 = 1.3 \pm 0.5$ and $\alpha _2 = 2.3 \pm 0.3$). Finally, we verify the robustness of our results by testing different break points and mass bin sizes, confirming that the IMF’s dependence on [Fe/H] remains consistent.