The stellar initial mass function (IMF) is one of the most important astrophysical distribution function, and is defined as the mass distribution for stars formed in a single star-formation event and when they just enter the main-sequence stage. The measurement of IMF is challenging even in the solar neighbourhood where IMF can be extracted by star-counting. This is because the definition of the IMF should be handled cautiously, and there are multiple corrections should be made from observation to a well-founded measurement. We present a new parametrisation of the stellar IMF in the 100-pc solar neighbourhood, leveraging the astrometric and photometric data from Gaia DR3: we model the colour-magnitude diagram of the field star population while accounting for observational uncertainties, Malmquist bias, Lutz-Kelker bias, the effect of varying mass-luminosity relation caused by mixture of different metallicity, and the effect of unresolved binaries. In particular, we synthesise the binaries with a process imitating the dynamical evolution observed in star clusters to model their present-day mass-ratio distribution. We derive a stellar IMF consistent with canonical IMFs but with significantly reduced uncertainties: α₁=0. 81^+0. 06-₀. ₀₅, α₂=2. 12^+0. 04-₀. ₀₄, and a break point at m₁ₑ₄₀₊=0. 41^+0. 01-₀. ₀₁ M_. Our model also constrains the binary fraction to 25\% and the Gaia DR3 angular resolution to 1. 31^+0. 24-₀. ₂₉ arcsec. We also provide the ξ-parameter for our IMF to be 0. 5075-₀. ₀₀₅₁^+0. 0112 for the users to compare our result with other work.
Wang et al. (2025) studied this question.