We generalize the analytic solutions presented in Pantoni et al. (2019) by including a simple yet effective description of wind recycling and galactic fountains, with the aim of self-consistently investigating the spatially-averaged time evolution of the gas, stellar, metal, and dust content in disc-dominated late-type galaxies (LTGs). Our analytic solutions, when supplemented with specific prescriptions for parameter setting and with halo accretion rates from $N-$body simulations, can be exploited to reproduce the main statistical relationships followed by local LTGs; these involve, as a function of the stellar mass, the star formation efficiency, the gas mass fraction, the gas/stellar metallicity, the dust mass, the star formation rate, the specific angular momentum, and the overall mass/metal budget. Our analytic solutions allow to easily disentangle the diverse role of the main physical processes ruling galaxy formation in LTGs; in particular, we highlight the crucial relevance of wind recycling and galactic fountains in efficiently refurnishing the gas mass, extending the star-formation timescale, and boosting the metal enrichment in gas and stars. All in all, our analytic solutions constitute a transparent, handy, and fast tool that can provide a basis for improving the (subgrid) physical recipes presently implemented in more sophisticated semi-analytic models and numerical simulations, and can offer a benchmark for interpreting and forecasting current and future spatially-averaged observations of local and higher redshift LTGs.
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