The stellar initial mass function of the solar neighbourhood revealed by Gaia

I use a sample of more than 120 000 stars in the solar neighbourhood, with parallaxes, magnitudes and colours estimated with unprecedented accuracy by the second data release of the Gaia mission, to derive the initial mass function of the Galactic disc. A full-forward technique is used to take into account, for the population of unresolved binaries, themetallicity distribution and the star formation history, including their variation across the Galactic disc, as well as all the observational effects. The shape of the initial mass function is well represented by a segmented power law with two breaks at characteristic masses. It has a maximum at M-circle dot 0.15 M-circle dot with significant flattening (possibly a depletion) at lower masses and a slope of a = -1.34 +/- 0.07 in the range 0.25 < M/M-circle dot < 1. Above 1M(circle dot), the initial mass function shows an abrupt decline with a slope ranging from a =-2.68 +/- 0.09 to a =-2.41 +/- 0.11, depending on the adopted resolution of the star formation history.