Stellar initial mass function in the 100-pc solar neighbourhood

Abstract: 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 \textsl{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: $\alpha_1=0.81^{+0.06}_{-0.05}$, $\alpha_2=2.12^{+0.04}_{-0.04}$, and a break point at $m_{\mathrm{break}}=0.41^{+0.01}_{-0.01}$ $\mathrm{M_{\odot}}$. Our model also constrains the binary fraction to $\sim$25\% and the \textsl{Gaia} DR3 angular resolution to $1.31^{+0.24}_{-0.29}$ arcsec. We also provide the $\xi$-parameter for our IMF to be $0.5075_{-0.0051}^{+0.0112}$ for the users to compare our result with other work.