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Curvature induced polarization and spectral index behavior for PKS 1502+106

A comprehensive study of multifrequency correlations can shed light on the nature of variation for blazars. In this work, we collect the long-term radio, optical and $γ$-ray light curves of PKS 1502+106. After performing the localized cross-correlation function analysis, we find that correlations between radio and $γ$-ray or $V$ band are beyond the $3σ$ significance level. The lag of the $γ$-ray relative to 15 GHz is $-60^{+5}_{-10}$ days, translating to a distance $3.18^{+0.50}_{-0.27}$ parsec (pc) between them. Within uncertainties, the locations of the $γ$-ray and optical emitting regions are roughly the same, and are away from the jet base within $1.2$ pc. The derived magnetic field in optical and $γ$-ray emitting regions is about $0.36$ G. The logarithm of $γ$-ray flux is significantly linearly correlated with that of $V$ band fluxes, which can be explained by the synchrotron self-Compton (SSC) process, the external Compton (EC) processes, or the combination of them. We find a significant linear correlation in the plot of $\log\prod$ (polarization degree) versus $\log νF_ν$ at $V$ band, and use the empirical relation $Π\sim \sin^n θ'$ ($θ'$ is the observing angle in the comoving frame blob) to explain it. The behaviors of color index (generally redder when brighter at the active state) and $γ$-ray spectral index (softer when brighter) could be well explained by the twisted jet model. These findings suggest that the curvature effect (mainly due to the change of the viewing angle) is dominant in the variation phenomena of fluxes, spectral indices, and polarization degrees for PKS 1502+106.