An Analytic Characterization of the Limb Asymmetry -- Transit Time Degeneracy

Atmospheres are not spatially homogeneous. This is particularly true for hot, tidally locked exoplanets with large day-to-night temperature variations, which can yield significant differences between the morning and evening terminators -- known as limb asymmetry. Current transit observations with the James Webb Space Telescope (JWST) are precise enough to disentangle the separate contributions of these morning and evening limbs to the overall transmission spectrum in certain circumstances. However, the signature of limb asymmetry in a transit light curve is highly degenerate with uncertainty in the planet's time of conjunction. This raises the question of how precisely transit times must be measured to enable accurate studies of limb asymmetry, in particular with JWST. Although this degeneracy has been discussed in the literature, a general description of it has not been presented. In this work, we show how this degeneracy results from apparent changes in the transit contact times when the planetary disk has asymmetric limb sizes. We derive a general formula relating the magnitude of limb asymmetry to the amount by which it would cause the apparent time of conjunction to vary, which can reach tens of seconds. Comparing our formula to simulated observations, we find that numerical fitting techniques add additional bias to the measured time, of generally less than a second, resulting from the occultation geometry. We also derive an analytical formula for this extra numerical bias. These formulae can be applied to planning new observations or interpreting literature measurements, and we show examples for commonly studied exoplanets.