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We analyse the high-quality Hertzsprung-Russell diagram (HRD) derived fromGaia data release 2 for the Solar Neighbourhood. We start building analmost-complete sample within 200 pc and for |b|>25 deg, so as to limit theimpact of known errors and artefacts in the Gaia catalog. Particular effort isthen put into improving the modelling of population of binaries, which producetwo marked features in the HRD: the sequence of near-equal mass binaries alongthe lower main sequence, and the isolated group of hot subdwarfs. We describe anew tool, BinaPSE, to follow the evolution of interacting binaries in a waythat improves the consistency with PARSEC evolutionary tracks for single stars.BinaPSE is implemented into the TRILEGAL code for the generation of "partialmodels" for both single and binary stellar populations, taking into account thepresence of resolved and unresolved binaries. We then fit the Gaia HRD via MCMCmethods that search for the star formation history (SFH) and initial binaryfraction (by mass) that maximise the likelihood. The main results are (i) thebinary fraction derived from the lower main sequence is close to 0.4, whiletwice larger values are favoured when the upper part of the HRD is fitted; (ii)present models predict the observed numbers of hot subdwarfs to within a factorof 2; (iii) irrespective of the prescription for the binaries, the starformation rate peaks at values 1.5e-4 Msun/yr at ages slightly above 2 Gyr, andthen decreases to 0.8e-4 Msun/yr at very old ages.

Dissecting the Gaia HR diagram within 200 pc