Study of the Gaia luminosity function of low-mass stars with the Besançon Galaxy Model

Context. The Gaia (Early) Data Release 3 provides a large sample of stars with precise parallaxes, distances and photometry from the brightest stars to the stellar-substellar limit. The Gaia Catalogue of Nearby Stars permits to have a complete view of the stellar content of the solar neighbourhood. Aims. Comparing simulations of the stellar content in the solar neighbourhood and the Gaia Catalogue of Nearby Stars, we plan to constrain the Initial Mass Function of field stars down to the stellar-substellar limit. Methods. We construct the luminosity function of the Gaia Catalogue of Nearby Stars in the 2MASS J-band. We compare it to luminosity functions from the literature, and show it reproduces features previously observed. Using the Besançon Galaxy Model, we observe the effects of different litterature Initial Mass Functions on simulated luminosity functions. We compare them with the luminosity function of the Gaia Catalogue of Nearby Stars in the Gaia G-band. Conclusions. We show that published IMFs do not permit to simulate luminosity functions comparable with the GCNS observed one, particularly for faint stars. Our updated model will allow to constrain the IMF of field stars thanks to Gaia data.