Stellar initial mass function in the 100-pc solar neighbourhood

The stellar initial mass function (IMF) is among the most fundamental distributions in astrophysics, defined as the mass spectrum of stars produced in a single star-formation event. Even in the solar neighbourhood, where measurements can be conducted via star counting, disentangling the IMF from observational effects remains challenging. In this work we introduce a new parametrisation of the stellar IMF in the 100-pc solar neighbourhood, leveraging the high-precision 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, variations in the mass-luminosity relation arising from metallicity differences, and the effects of unresolved binaries. In particular, we synthesise the binary population with a process imitating the dynamical evolution observed in star clusters to enforce that all components are drawn from the same IMF, while simultaneously recovering the observed present-day mass-ratio distribution. We determine an averaged stellar IMF over $0.25<m<1.0~M_{\odot}$ that aligns with canonical IMFs but achieves significantly tighter constraints: $\alpha_1=0.75^{+0.06}_{-0.04}$, $\alpha_2=2.07^{+0.04}_{-0.03}$, and a break point at $m_{\mathrm{break}}=0.40^{+0.01}_{-0.01}$ $\mathrm{M_{\odot}}$. Our inference also yields an averaged binary fraction over $0.25<m<1.0~M_{\odot}$ of approximately 26\%, and constrains the \textsl{Gaia} DR3 angular resolution to $1.11^{+0.11}_{-0.08}$ arcsec. We also provide the $\xi$-parameter for our IMF, which is $0.5070_{-0.0096}^{+0.0068}$, to facilitate direct comparison with other IMF determinations.