tokens: net yield of the chemical element X per stellar generation, y X , and the yield of X from Type Ia SNe, m X , Ia . Other fundamental assumptions in the model are given by the DTD for the Type Ia SN rate and the prescription for the SFR law. An observational constraint for the calibration of the gas infall history is given by the radial profile of the present-day total surface mass density, tot ( r , t G ), which is very difficult to retrieve from an observational point of view. In this work, we apply our model to reproduce the observed chemical abundance patterns at the solar neighbourhood, where r S 8kpc; hence, we normalize the infall law, as given in equation ( 12 ), by requiring the following constraint: where we assume t G 14Gyr, a single infall episode, and tot ( r S , t G )54M pc 2 , which represents the present-day total surface mass density at the solar neighbourhood (see also Micali, Matteucci Romano 2013 , which refers to the work by Kuijken Gilmore 1991 ). The best model is defined as the one capable of reproducing the observed trend of the [O/Fe] versus [Fe/H] chemical abundance pattern, which represents the best observational constraint for the chemical evolution models of the MW. Our best models are characterized by the following values of the free parameters: L 2Gyr 1 , for our best model with the linear SchmidtKennicutt law, and SFR 0 2M pc 2 Gyr 1 , for our best model with the non-linear SchmidtKennicutt law; the infall time-scale for the gas mass growth of the MW disc is 7Gyr; the mass loading factor is 0.4. Finally, the best models assume the single-degenerate scenario for the Type Ia SN rate. We remark on the fact that the predicted [Fe/H]-[O/Fe] relation in the MW is fitted by construction using fixed values for the key free parameters L (or SFR 0 ), and . It is worth noting that the values of our best parameters are in agreement with previous recent studies (see e.g. Minchev, Chiappini Martig 2013 ; Nidever etal. 2014 ; Spitoni etal. 2015 ); in particular, a typical infall time-scale 7Gyr and star formation efficiency 1Gyr 1 are necessary to reproduce also the observed age-metallicity relation and the metallicity distribution function of the G-dwarf stars in the solar neighbourhood (Matteucci 2001 , 2012 ; Pagel 2009 ). Once the best set of free parameters is determined, we fix them and explore the effects of assuming different DTDs for the Type Ia SN rate and different prescriptions for the relation between the SFR and the surface gas mass density, gas ( r , t ). In this way, we can demonstrate the flexibility of our method for solving the chemical evolution of galaxies by taking into account the major systematics in the theory. 3 THE OBSERVED DATA SET The data set for the observed [Fe/H][O/Fe] and [Fe/H][Si/Fe] relations in the solar neighbourhood is shown in Fig. 1 (a) and Fig. 1 (b), respectively, where the data from different works are drawn with different colours. Our set of data includes both MW halo stars from
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O B-Model I-Model I-Model O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O B-Model I-Model I-Model O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion B-Citation I-Citation O B-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O