System equivalent flux density of Stokes I, Q, U, and V of a polarimetric interferometer

Abstract

Aims. We present the system equivalent flux density (SEFD) expressions for all four Stokes parameters: I, Q, U, and V. Methods. The expressions were derived based on our derivation of SEFD I (for Stokes I) and subsequent extensions of that work to phased array and multipole interferometers. The key to the derivation of the SEFD Q, U, and V expressions is to recognize that the noisy estimates of Q, U, and V can be written as the trace of a matrix product. This shows that the SEFD I is a special case, where the general case involves a diagonal or anti-diagonal 2 × 2 matrix interposed in the matrix multiplication. Following this step, the relation between the SEFD for I as well as Q, U, and V immediately becomes evident. Results. We present example calculations for a crossed dipole based on the formulas derived and the comparison between simulation and observation using the Murchison Widefield Array (MWA).