Metallicity calibration and photometric parallax estimation: II. SDSS photometry

Abstract

We used the updated [Fe/H] abundances of 168 F-G type dwarfs and calibrated them to a third order polynomial in terms of reduced ultraviolet excess, $\delta_{0.41}$ defined with $\mathit{ugr}$ data in the SDSS. We estimated the $M_{g}$ absolute magnitudes for the same stars via the re-reduced Hipparcos parallaxes and calibrated the absolute magnitude offsets, $\Delta M_{g}$, relative to the intrinsic sequence of Hyades to a third order polynomial in terms of $\delta_{0.41}$. The ranges of the calibrations are $-2<\mbox{[Fe/H]}\leq 0.3~\mbox{dex}$ and $4< M_{g}\leq 6~\mbox{mag}$. The mean of the residuals and the corresponding standard deviation for the metallicity calibration are 0 and 0.137 mag; while, for the absolute magnitude calibration they are 0 and 0.179 mag, respectively. We applied our procedures to 23,414 dwarf stars in the Galactic field with the Galactic coordinates $85^{\circ }\leq b\leq 90^{ \circ }$, $0^{\circ }\leq l\leq 360^{\circ }$ and size 78 deg². We estimated absolute magnitude $M_{g}$ dependent vertical metallicity gradients as a function of vertical distance $Z$. The gradients are deep in the range of $0< Z\leq 5~\mbox{kpc}$, while they are very small positive numbers beyond $Z=5~\mbox{kpc}$. All dwarfs with $5< M_{g}\leq 6~\mbox{mag}$ are thin-disc stars and their distribution shows a mode at $(g-r)_{0}\approx 0.38~\mbox{mag}$, while the absolute magnitudes $4< M_{g} \leq 5$ are dominated by thick disc and halo stars, i.e. the apparently bright ones ($g_{0}\leq 18~\mbox{mag}$) are thick-disc stars with a mode at $(g-r)_{0}\sim 0.38~\mbox{mag}$, while the halo population is significant in the faint stars ($g_{0}>18~\mbox{mag}$).