On-sky demonstration of optical polaroastrometry

A method for measuring the difference between centroids of polarized flux and total flux of an astronomical object - {\it polaroastrometry} - is proposed. The deviation of the centroid of flux corresponding to Stokes parameter $Q$ or $U$ from the centroid of total flux multiplied by dimensionless Stokes parameter $q$ or $u$ respectively, was used as a signal. The efficiency of the method is demonstrated on the basis of observations made in the $V$ band by using an instrument combining features of a two-beam polarimeter with a rotating half-wave plate and a speckle interferometer. The polaroastrometric signal noise is 60-70 $\mu$as rms for a total number of accumulated photoelectrons $N_e$ of $10^9$ from a 70-cm telescope; this corresponds to a total integration time of 500 sec and an object magnitude $V=6$ mag. At smaller $N_e$ the noise increases as $\approx 1.7^{\prime\prime}/\sqrt{N_e}$, while at larger $N_e$ it remains the same owing to imperfection of the half-wave plate. For main sequence stars that are unpolarized and polarized by interstellar dust and the Mira type variable R Tri the signal was undetectable. For the Mira type variable $\chi$ Cyg the polaroastrometric signal is found to be $310\pm70$ and $300\pm70$ $\mu$as for Stokes $Q$ and $U$ respectively; for $o$ Cet these values are $490\pm100$ and $1160\pm100$ $\mu$as. The significant value of the polaroastrometric signal provides evidence of the asymmetry of the polarized flux distribution.