Stellar initial mass function in the 100-pc solar neighbourhood

ABSTRACT 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 parametrization of the stellar IMF in the 100-pc solar neighbourhood, leveraging the high-precision 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, variations in the mass–luminosity relation arising from metallicity differences and the effects of unresolved binaries. In particular, we synthesize 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 $0.25\lt m\lt 1.0~{\rm M}_{\odot }$ 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 $m_{\mathrm{break}}=0.40^{+0.01}_{-0.01}$ $\mathrm{{\rm M}_{\odot }}$. Our inference also yields an averaged binary fraction over $0.25\lt m\lt 1.0~{\rm M}_{\odot }$ of approximately 26 per cent, and constrains the Gaia Data Release 3 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.