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tokens: is able to remove binary stars, and (b) that the removed fraction of stars in the range where we expect unresolved binary or triple stars is higher, in line with the previous point (a). We note that the filtering removes a substantial fraction of multiple systems. In particular, Gaia cannot find astrometric solutions typically for binaries. The exact fraction of binaries filtered out by which of the criteria is however a non-trivial problem and cannot be quantified here as this would depend on detailed modeling of the space craft and the stellar population at the distance of the ONC, see for example Michalik et al. (2014) . 4.2. PMS isochrones Stellar models have been computed using the most recent version of the Pisa stellar evolutionary code (see e.g., Tognelli et al. 2011 ) described in detail in previous papers (see Randich et al. 2018 ; Tognelli et al. 2018 , and references therein). We simply recall the main aspects relevant for the present analysis. The reference set of models adopts a solar calibrated 4 mixing length parameter, namely α ML = 2.0. However, for the comparison we also used a much lower value, namely α ML = 1.00 (low convection efficiency models) which produces cooler models with inflated radii (see e.g., Tognelli et al. 2012 , 2018 ). Evolutionary tracks of mass ≥1.20 M ⊙ have been computed adopting a core convective overshooting parameter β ov = 0.15, following the recent calibration of the Pisa models by means of the TZ Fornacis eclipsing binary ( Valle et al. 2017 ). From the models (in the mass range 0.1−20 M ⊙ ) we obtained isochrones in the age range [0.1, 100] Myr with a variable spacing in age (down to δ t = 0.1 Myr), allowing for a very good age resolution. For the reference set of models we used [Fe/H] = +0.0, corresponding to an initial helium abundance Y = 0.274 and metallicity Z = 0.013 given the Asplund et al. (2009) solar heavy-element mixture. We have converted the theoretical results into the OmegaCAM r and i absolute A B magnitudes using bolometric corrections we computed using a formalism similar to that described in Girardi et al. (2002) , employing the MARCS 2008 synthetic spectra library ( Gustafsson et al. 2008 ), which is available for T eff ∈ [2500, 8000] K, log g ∈ [ − 0.5, 5.5], and [Fe/H] ∈[−2.0, +0.5] completed with the Castelli Kurucz (2003) models for T eff > 8000 K. Next we compared the evolutionary models with the data in order to identify the best fitting isochrones for the observed PMS populations. This was performed by using the same Bayesian maximum likelihood technique described in Randich et al. (2018) . Briefly, the method computes the distance of each star in the observational plane from a given isochrone extracted from our database. The square of the distance is used to define the likelihood of a single star. Then, the total likelihood is defined as the product of all the single star likelihoods. The parameters to be recovered in this work are the age t and the reddening E (