Calibration Errors in Interferometric Radio Polarimetry

Residual calibration errors are difficult to predict in interferometric radio polarimetry because they depend on the observational calibration strategy employed, encompassing the Stokes vector of the calibrator and parallactic angle coverage. This work presents analytic derivations and simulations that enable examination of residual on-axis instrumental leakage and position-angle errors for a suite of calibration strategies. The focus is on arrays comprising alt-azimuth antennas with common feeds over which parallactic angle is approximately uniform. The results indicate that calibration schemes requiring parallactic angle coverage in the linear feed basis (e.g., the Atacama Large Millimeter/submillimeter Array) need only observe over 30 degrees, beyond which no significant improvements in calibration accuracy are obtained. In the circular feed basis (e.g., the Very Large Array above 1 GHz), 30 degrees is also appropriate when the Stokes vector of the leakage calibrator is known a priori, but this rises to 90 degrees when the Stokes vector is unknown. These findings illustrate and quantify concepts that were previously obscure rules of thumb.