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 maximum and minimum brightness states in the R band of 14.08 +/- 0.03 mag and 15.20 +/- 0.03 mag, respectively, with a maximum variation of 1.12 mag, and a maximum polarization degree of P = (12.2 +/- 0.7)%, with a maximum variation of 10.7%. From 2009 August to November, a correlation between the optical R-band flux and the degree of linear polarization was found with a correlation coefficient r(pol) = 0.984 +/- 0.025. The source presented a preferential position angle of optical polarization of similar to 153 degrees, with variations of 10 degrees-50 degrees, which 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 similar to 0.06 G, the Doppler factor, delta(0) similar to 23, the viewing angle, Phi similar to 2 degrees.4, and the size of the emission region r(b) similar to 5.6 x 10(17) cm. Our study is consistent with the spine-sheath model of explaining the polarimetric variability displayed by this source during our monitoring.