Period-Color and Amplitude-Color Relations at Maximum and Minimum Light for RR Lyrae Stars in the SDSS Stripe 82 Region

Investigation of period-color (PC) and amplitude-color (AC) relations at the maximum and minimum light can be used to probe the interaction of the hydrogen ionization front (HIF) with photosphere and the radiation hydrodynamics of the outer envelopes of Cepheids and RR Lyraes. For example, theoretical calculations indicated that such interactions would occur at minimum light for RR Lyrae and result in a flatter PC relation. In the past, the PC and AC relations have been investigated by using either the $(V-R)_{MACHO}$ or $(V-I)$ colors. In this work, we extend previous work to other bands by analyzing the RR Lyraes in the Sloan Digital Sky Survey Stripe 82 Region. Multi-epoch data is available for RR Lyraes located within the footprint of the Stripe 82 Region in five ($ugriz$) bands. We present the PC and AC relations at maximum and minimum light in four colors: $(u-g)_0$, $(g-r)_0$, $(r-i)_0$ and $(i-z)_0$, after they are corrected for extinction. We found that the PC and AC relations for this sample of RR Lyraes show a complex nature in the form of flat, linear or quadratic relations. Furthermore, the PC relations at minimum light for fundamental mode RR Lyrae stars are separated according to the Oosterhoff type, especially in the $(g-r)_0$ and $(r-i)_0$ colors. If only considering the results from linear regressions, our results are quantitatively consistent with the theory of HIF-photosphere interaction for both fundamental and first overtone RR Lyraes.