An analytical theory for the resolution attainable using eclipse mapping of exoplanets

Abstract: We present an analytic theory for the resolution attainable via eclipse mapping of exoplanets, based on the Fourier components of the brightness distribution on the planetary disk. We find that the impact parameter determines which features can and cannot be seen, via the angle of the stellar edge relative to the axis of the orbit during the eclipse. We estimate the signal-to-noise ratio as a function of mapping resolution, and use this to determine the attainable resolution for a given star-planet system. We test this theory against numerical simulations and find good agreement; in particular, our predictions for the resolution as a function of stellar edge angle are accurate to the simulated data to within 10% over a wide range of angles. Our prediction for the number of spatial modes that can be constrained given a light curve error is similarly accurate. Finally, we give a list of exoplanets with the best expected resolution for observations with the NIRISS SOSS, NIRSpec G395H, and MIRI LRS instruments on JWST.