Abundances of light elements in dwarf stars of different ages are important constraints for stellar yields, Galactic chemical evolution and exoplanet chemical composition studies. We have measured C and N abundances and $^{12}$C/$^{13}$C ratios for a sample of 63 solar twins spanning a wide range in age, based on spectral synthesis of a comprehensive list of CH,A-X and CN,B-X features using HARPS spectra. The analysis of 55 thin disc solar twins confirms the dependences of [C/Fe] and [N/Fe] on [Fe/H]. [N/Fe] is investigated as a function of [Fe/H] and age for the first time for these stars. Our derived correlation [C/Fe]-age agrees with works for solar-type stars and solar twins, but the [N/Fe]-age correlation does not. The relations [C,N/Fe]-[Fe/H] and [C,N/Fe]-age for the solar twins lay under-solar. $^{12}$C/$^{13}$C is found correlated with [Fe/H] and seems to have decreased along the evolution of the local thin disc. Predictions from chemical evolution models for the solar vicinity corroborate the relations [C,N/Fe]-[Fe/H], $^{12}$C/$^{13}$C-age and [N/O]-[O/H], but do not for the $^{12}$C/$^{13}$C-[Fe/H] and [C/O]-[O/H] relations. The N/O ratio in the Sun is placed at the high end of the homogeneous distribution of solar twins, which suggests uniformity in the N-O budget for the formation of icy planetesimals, watery super-earths and giant planets. C and N had different nucleosynthetic origins along the thin disc evolution, as shown by the relations of [C/N], [C/O] and [N/O] against [O/H] and age. [C/N] and [C/O] are particularly observed increasing in time for solar twins younger than the Sun.
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