The Initial mass function of field stars with mass $\leq$ 1 $M_{\odot}$ varies with metallicity

Abstract

We investigated a volume-limited sample of LAMOST main-sequence stars with masses from 0.25 to 1 $M_{\odot}$ and distances of 150-350 pc to explore how the stellar initial mass function (IMF) varies with metallicity. We corrected 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 derived IMFs for each metallicity sub-samples. Fitting a broken power-law function in each IMF with a fixed break point at 0.525 $M_{\odot}$, we found the power-law indices increase with [Fe/H] for both mass regimes: $\alpha_1$ (mass $\leq$ 0.525 $M_{\odot}$) rises from 0.54 $\pm$ 0.21 to 1.40 $\pm$ 0.07 and $\alpha_2$ (mass>0.525 $M_{\odot}$) grows from 1.40 $\pm$ 0.16 to 1.86 $\pm$ 0.04 as [Fe/H] varies from -1 to +0.5 dex. It demonstrates that low-mass stars make up a larger fraction in metal-rich environments than in metal-poor ones. We performed simulations to assess the impact of unresolved binaries on the IMF power-law indices. After correction, the binary-adjusted $\alpha$ values retained a similar metallicity-dependent trend. Furthermore, by examining the IMF of the aggregate sample, we found the corrected indices ($\alpha_{\rm{1,corr}} = 1.48 \pm 0.03$ , $\alpha_{\rm{2,corr}} = 2.17 \pm 0.03$) are consistent with Kroupa's IMF values ($\alpha_1 = 1.3 \pm 0.5$ and $\alpha_2 = 2.3 \pm 0.3$). Finally, we verified 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.