Towards a Robust Estimate of the Solar Photospheric Poynting Flux and Helicity Flux

The observed solar photospheric magnetic fields and Doppler velocities are frequently used to quantify the Poynting flux and helicity flux. Multiple methods have been developed for this purpose, but their estimates of the Poynting flux and helicity flux often differ from one another. Here we study the performance of three widely used methods on NOAA active region 12673:"PTD-Doppler-FLCT Ideal"(PDFI),"Differential Affine Velocity Estimator for Vector Magnetograms"(DAVE4VM), and an extension of the latter with Doppler velocity constraint (DAVE4VMwDV). We find that the values of the accumulated energy and helicity differ significantly between the three methods, even in signs. Using the Helmholtz-Hodge decomposition, we show that Doppler velocity can contribute significantly to the Poynting flux and helicity flux through the non-inductive (curl-free) electric field. The different, ad hoc treatments of the Doppler and transverse velocities in three methods are directly responsible for the discrepancies. We discuss the desired future observations that can better constrain these methods.