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

Dan Qiu, Chao Liu, Jennifer A. Johnson, Jiadong Li, Bo Zhang

TL;DR

This study probes whether the field-star IMF in the mass range $0.25 \le M/M_\odot \le 1$ varies with metallicity by analyzing a volume-limited sample from LAMOST DR9. It corrects the spectroscopic selection function using photometric densities, derives metallicity-binned IMFs from vertical-density integration, and fits each IMF with a broken power-law anchored at $0.525\ M_\odot$ using Bayesian MCMC. The results show that both IMF slopes, $\alpha_1$ and $\alpha_2$, increase with metallicity, with $\alpha_1$ rising from $0.54\pm0.21$ to $1.40\pm0.07$ and $\alpha_2$ from $1.40\pm0.16$ to $1.86\pm0.04$ as [Fe/H] goes from $-1$ to $+0.5$ dex; after accounting for unresolved binaries, the corrected indices remain metallicity-dependent and the aggregate IMF is consistent with Kroupa's. Robustness checks show the trend persists for different break points and mass-bin sizes. The work supports a metallicity-modulated IMF in the solar neighborhood and provides a path toward extending the analysis to lower masses with future surveys like SDSS-V.

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: $α_1$ (mass $\leq$ 0.525 $M_{\odot}$) rises from 0.54 $\pm$ 0.21 to 1.40 $\pm$ 0.07 and $α_2$ (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 $α$ values retained a similar metallicity-dependent trend. Furthermore, by examining the IMF of the aggregate sample, we found the corrected indices ($α_{\rm{1,corr}} = 1.48 \pm 0.03$ , $α_{\rm{2,corr}} = 2.17 \pm 0.03$) are consistent with Kroupa's IMF values ($α_1 = 1.3 \pm 0.5$ and $α_2 = 2.3 \pm 0.3$). 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.

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

TL;DR

This study probes whether the field-star IMF in the mass range varies with metallicity by analyzing a volume-limited sample from LAMOST DR9. It corrects the spectroscopic selection function using photometric densities, derives metallicity-binned IMFs from vertical-density integration, and fits each IMF with a broken power-law anchored at using Bayesian MCMC. The results show that both IMF slopes, and , increase with metallicity, with rising from to and from to as [Fe/H] goes from to dex; after accounting for unresolved binaries, the corrected indices remain metallicity-dependent and the aggregate IMF is consistent with Kroupa's. Robustness checks show the trend persists for different break points and mass-bin sizes. The work supports a metallicity-modulated IMF in the solar neighborhood and provides a path toward extending the analysis to lower masses with future surveys like SDSS-V.

Abstract

We investigated a volume-limited sample of LAMOST main-sequence stars with masses from 0.25 to 1 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 , we found the power-law indices increase with [Fe/H] for both mass regimes: (mass 0.525 ) rises from 0.54 0.21 to 1.40 0.07 and (mass>0.525 ) grows from 1.40 0.16 to 1.86 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 values retained a similar metallicity-dependent trend. Furthermore, by examining the IMF of the aggregate sample, we found the corrected indices ( , ) are consistent with Kroupa's IMF values ( and ). 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.

Paper Structure

This paper contains 20 sections, 12 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Data
  3. Atmospheric parameters of dwarf stars
  4. Determination of stellar mass
  5. Volume completeness
  6. Method
  7. Select Function Correction
  8. Determination of stellar IMF
  9. The power-law model of stellar IMF
  10. Results
  11. IMF Power-law indices as a function of $\rm [Fe/H]$
  12. Comparison with Li23
  13. Discussion
  14. Binaries correction
  15. Simulation
  16. ...and 5 more sections

Figures (13)

  • Figure 1: The flowchart outlines the procedure for determining stellar masses. Detailed descriptions of each step are provided in subsections \ref{['subsec:metallicity']} and \ref{['subsec:mass']}.
  • Figure 2: The metallicity versus the effective temperature of 1308 LAMOST M dwarfs. The metallicities, calibrated with Equation (\ref{['eq:deltafeh']}), are inherited from the F, G, or K dwarf companions, whereas the $T_{\rm eff}$ are taken from the LASPM pipeline.
  • Figure 3: The left panel shows the comparison in $\rm [Fe/H]$ of 308 test M dwarfs between the reference values $\rm [Fe/H]_{FGK}$ and the SLAM predictions $\rm [Fe/H]_{SLAM}$. The right panel presents the distribution of the differences, i.e., $\rm \Delta [Fe/H]$= $\rm [Fe/H]_{FGK}-[Fe/H]_{SLAM}$. Its mean and standard deviation values are 0.01 and 0.17, respectively.
  • Figure 4: The top-left panel shows the comparison between [Fe/H]$\rm_{SLAM}$ and those determined from APOGEE DR17 ([Fe/H]$\rm_{AP}$). The black dashed line is the one-to-one relation. The grayscale (white → dark gray) encodes the stellar number density in each [Fe/H]$\rm_{SLAM}$ and [Fe/H]$\rm_{AP}$ bin, with darker tones indicating higher densities. The corresponding histogram of the metallicity difference $\rm \Delta [Fe/H] (=[Fe/H]\rm_{SLAM}-[Fe/H]\rm_{AP})$ is displayed in the top-right panel. The bottom two panels are the same as the top two panels, but use the metallicities of Birky-2020ApJ...892...31B as the reference.
  • Figure 5: The top-left panel shows the mass comparison between our work ($M_*$) and that of Li23 ($M_{Li23}$). A white-to-dark-gray scale encodes the logarithmic stellar counts within each $M_*$–$M_{Li23}$ bin. The distribution of mass difference $\Delta \rm{mass}=M_*-M_{Li23}$ is displayed in the top-right panel. The two bottom panels are the same as the top ones, but for the mass comparison between our work and that of Mann-2019ApJ...871...63M ($M_{\rm{mann19}}$).
  • ...and 8 more figures