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, the metallicity distribution, the star formation history and their variation across the Galactic disk 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~0.15 Ms with significant flattening (possibly a depletion) at lower masses and a slope of alpha=-1.34 +/- 0.07 in the range 0.25<M/Ms<1. Above 1 Ms the IMF shows an abrupt decline with a slope ranging from alpha=-2.68 +/- 0.09 to alpha=-2.41 +/- 0.11 depending on the adopted resolution of the star formation history.