Tackling the Unique Challenges of Low-frequency Solar Polarimetry with the Square Kilometre Array Low Precursor: The Algorithm

Coronal magnetic fields are well known to be one of the crucial parameters defining coronal physics and space weather. However, measuring the global coronal magnetic fields remains challenging. The polarization properties of coronal radio emissions are sensitive to coronal magnetic fields. While they can prove to be useful probes of coronal and heliospheric magnetic fields, their usage has been limited by technical and algorithmic challenges. We present a robust algorithm for precise polarization calibration and imaging of low-radio frequency solar observations and demonstrate it on data from the Murchison Widefield Array, a Square Kilometer Array (SKA) precursor. This algorithm is based on the Measurement Equation framework, which forms the basis of all modern radio interferometric calibration and imaging. It delivers high dynamic range and fidelity full Stokes solar radio images with instrumental polarization leakages $<1\%$, on par with general astronomical radio imaging, and represents the state-of-the-art. Opening up this rewarding, yet unexplored, phase space will enable multiple novel science investigations and offer considerable discovery potential. Examples include detection of low-level of circularly polarization from thermal coronal emission to estimate large-scale quiescent coronal fields; polarization of faint gyrosynchrotron emissions from coronal mass ejections for robust estimation of plasma parameters; and detection of the first-ever linear polarization at these frequencies. This method has been developed with the SKA in mind and will enable a new era of high fidelity spectro-polarimetric snapshot solar imaging at low-radio frequencies.