The period-luminosity relation of RR Lyrae stars in the SDSS photometric system

We provide the first detailed study of the RR Lyrae period-luminosity (PL) relation in the ugriz bandpasses of the Sloan Digital Sky Survey (SDSS) filter system. We argue that tight, simple PL relations are not present in the SDSS filters, except for the redder bandpasses i and (especially) z. However, for all bandpasses, we show that by incorporating terms involving a (fairly reddening-independent) "pseudocolor" C₀ ≡ (u - g)₀ - (g - r)₀, we can obtain tight (nonlinear) relations. We provide such theoretically calibrated relations in the present paper, which should be useful in deriving precise absolute magnitudes (hence distances) and intrinsic colors (hence reddening values) even to individual field RR Lyrae stars. For applications to cases in which photometry in all five passbands may not be available, we also provide simple (although less precise) average PL relations for the i and z bandpasses, which read as M_z = 0:839 - 1.295 log P + 0.211 log Z and M_i = 0.908 - 1.035 log P + 0.220 log Z. Similarly, simple period-color relations for (r - i)₀, (g - r) ₀, and (u - z)₀ are also provided.