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SDSS Absolute Magnitudes for Thin Disc Stars based on Trigonometric Parallaxes

We present a new luminosity-colour relation based on trigonometric parallaxes for thin disc main-sequence stars in SDSS photometry. We matched stars from the newly reduced Hipparcos catalogue with the ones taken from 2MASS All-Sky Catalogue of Point Sources, and applied a series of constraints, i.e. relative parallax errors ($σ_π/π\leq0.05$), metallicity ($-0.30\leq[M/H]\leq0.20$ dex), age ($0\leq t \leq 10$ Gyr) and surface gravity ($\log g>4$), and obtained a sample of thin disc main-sequence stars. Then, we used our previous transformation equations (Bilir et al. 2008a) between SDSS and 2MASS photometries and calibrated the $M_{g}$ absolute magnitudes to the $(g-r)_{0}$ and $(r-i)_0$ colours. The transformation formulae between 2MASS and SDSS photometries along with the absolute magnitude calibration provide space densities for bright stars which saturate the SDSS magnitudes.