How does the limited resolution of space plasma analyzers affect the accuracy of space plasma measurements?

We investigate the systematic errors in measured plasma velocity distribution functions and their corresponding velocity moments, arising from the limited energy and angular resolution of top-hat electrostatic analyzers. For this purpose, we develop a forward model of a concept analyzer that simulates observations of typical solar wind proton plasma particles with their velocities following a Maxwell distribution function. We then review the standard conversion of the observations to physical parameters and evaluate the errors arising from the limited resolution of the modeled instrument. We show that the limited resolution of the instrument results in velocity distributions that underestimate the core and overestimate the tails of the actual Maxwellian plasma velocity distribution functions. As a consequence, the velocity moments of the observed plasma underestimate the proton density and overestimate the proton temperature. Moreover, we show that the examined errors become significant for cold and fast plasma protons. We finally determine a mathematical formula that predicts these systematic inaccuracies based on specific plasma inputs and instrument features. Our results inform and contextualize future evaluations of observations by analyzers in various plasma regimes.