uvby-$\beta$ photometry of solar twins: the solar colors, model atmospheres, and the Teff and metallicity scales

Solar colors have been determined on the uvby-$\beta$ photometric system to test absolute solar fluxes, to examine colors predicted by model atmospheres as a function of stellar parameters (Teff, log g, [Fe/H]), and to probe zero-points of Teff and metallicity scales. New uvby-$\beta$ photometry is presented for 73 solar-twin candidates. Most stars of our sample have also been observed spectroscopically to obtain accurate stellar parameters. Using the stars that most closely resemble the Sun, and complementing our data with photometry available in the literature, the solar colors on the uvby-$\beta$ system have been inferred. Our solar colors are compared with synthetic solar colors computed from absolute solar spectra and from the latest Kurucz (ATLAS9) and MARCS model atmospheres. The zero-points of different Teff and metallicity scales are verified and corrections are proposed. The Teff calibration of Alonso and collaborators has the poorest performance (~140 K off), while the relation of Casagrande et al. (2010) is the most accurate (within 10 K). We confirm that the Ramirez & Melendez (2005) uvby metallicity calibration, recommended by \'Arnad\'ottir et al. (2010) to obtain [Fe/H] in F, G, and K dwarfs, needs a small (~10%) zero-point correction to place the stars and the Sun on the same metallicity scale. Finally, we confirm that the c_1 index in solar analogs has a strong metallicity sensitivity.