Optical spectropolarimetry with incomplete data sets

Linear spectropolarimetry is a photon-hungry'' observing technique, requiring a specific sequence of observations to determine the Stokes Q and U parameters. For dual-beam spectropolarimeters, the parameters can be ideally determined using observations at N=2 retarder plate positions. The additional polarization signal introduced by instrumental effects requires the redundancy of N=4 observations to correct for these effects. We wish to determine if the instrumental signature corrections’', eQ and eU, are identical for observations with dual-beam spectropolarimeters. For instances when observations were acquired at N=3 retarder plate angles, we wish to determine if the complete measurement of one Stokes parameter and the associated instrumental signature correction can be used to determine the other Stokes parameter. We constructed analytical and Monte Carlo models of a general dual-beam spectropolarimeter to study the factors affecting the assumption eQ=eU. We compared these models with VLT FORS1 spectropolarimetry. We find that eQ-eU=0, with the variance around zero (\Delta(eQ-eU)) being directly related to the signal-to-noise ratio of the observations. Observations of a polarized standard star, over the period 2002-2007, show that the assumption of eQ-eU=0 is generally true, although the absolute values of eQ and eU vary between observational epochs. Incomplete spectropolarimetry datasets can be analyzed under the assumption that eQ=eU. This property of the analysis of spectropolarimetry, with dual beam spectropolarimeters, can be used to assess the quality of the reduction for complete data.