Stellar initial mass function in the 100-pc solar neighbourhood

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 mbreak=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.