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Long-term optical polarization variability of the tev blazar 1es~1959+650

A detailed analysis of the optical polarimetric variability of the TeV blazar 1ES 1959+650 from 2007 October 18 to 2011 May 5 is presented. The source showed a maximum and minimum brightness states in the R-band of 14.08$\pm$0.03 mag and 15.20$\pm$0.03 mag, respectively, with a maximum variation of 1.12 mag, and also a maximum polarization degree of $P=$(12.2$\pm$0.7)%, with a maximum variation of 10.7%. From August to November 2009, a correlation between the optical $R$-band flux and the degree of linear polarization was found, with a correlation coefficient $r_{pol}$=0.984$\pm$0.025. The source presented a preferential position angle of optical polarization of $\sim153^{\circ}$, with variations of $10\degr$-$50\degr$, that is in agreement with the projected position angle of the parsec scale jet found at 43 GHz. From the Stokes parameters we infer the existence of two optically-thin synchrotron components that contribute to the polarized flux. One of them is stable, with a constant polarization degree of 4%. Assuming a stationary shock for the variable component, we estimated some parameters associated with the physics of the relativistic jet: the magnetic field, $B\sim$0.06 G, the Doppler factor, $δ_{0}\sim$23, the viewing angle, $Φ\sim2.4\degr$, and the size of the emission region $r_b\sim5.6\times10^{17}$ cm. Our study is consistent with the spine-sheath model to explain the polarimetric variability displayed by this source during our monitoring.