What Can DKIST/DL-NIRSP Tell Us About Quiet-Sun Magnetism?

Quiet-Sun regions cover most of the Sun's surface; its magnetic fields contribute significantly to the solar chromospheric and coronal heating. However, characterizing the magnetic fields of the quiet Sun is challenging due to their weak polarization signal. The 4-m \textit{Daniel K. Inouye Solar Telescope} (\textit{DKIST}) is expected to improve our understanding of the quiet-Sun magnetism. In this paper, we assess the diagnostic capability of the Diffraction-Limited Near Infrared Spectropolarimeter (DL-NIRSP) instrument on \textit{DKIST} on the energy transport processes in the quiet-Sun photosphere. To this end, we synthesize high-resolution, high-cadence Stokes profiles of the \ion{Fe}{1} 630~nm lines using a realistic magnetohydrodynamic simulation, degrade them to emulate the \textit{DKIST}/DL-NIRSP observations, and subsequently infer the vector magnetic and velocity fields. For the assessment, we first verify that a widely used flow-tracking algorithm, Differential Affine Velocity Estimator for Vector Magnetograms, works well for estimating the large-scale ($> 200$ km) photospheric velocity fields with these high-resolution data. We then examine how the accuracy of inferred velocity depends on the temporal resolution. Finally, we investigate the reliability of the Poynting flux estimate and its dependence on the model assumptions. The results suggest that the unsigned Poynting flux, estimated with existing schemes, can account for about $71.4\%$ and $52.6\%$ of the reference ground truth at $\log \tau =0.0$ and $\log \tau = -1$. However, the net Poynting flux tends to be significantly underestimated. The error mainly arises from the underestimated contribution of the horizontal motion. We discuss the implications on \textit{DKIST} observations.