What's in Your Transit? Towards Reliably Getting $5\times$ More Science from Exoplanet Transit Data

Exoplanetary science heavily relies on transit depth ($D$) measurements. Yet, as instrumental precision increases, the uncertainty on $D$ appears to increasingly drift from expectations driven solely by photon-noise. Here we characterize this shortfall (the Transit-Depth Precision Problem, TDPP), by defining an amplification factor, $A$, quantifying the discrepancy between the measured transit-depth uncertainty and the measured baseline scatter on a same time bin size. While in theory $A$ should be $\sim\sqrt{3}$, we find that it can reach values $\gtrsim$10 notably due to correlations between $D$ and the limb-darkening coefficients (LDCs). This means that (1) the performance of transit-based exoplanet studies (e.g., atmospheric studies) can be substantially improved with reliable priors on LDCs and (2) low-fidelity priors on the LDCs can yield substantial biases on $D$--potentially affecting atmospheric studies due to the wavelength-dependence of such biases. For the same reason, biases may emerge on stellar-density and planet-shape/limb-asymmetry measurements. With current photometric precisions, we recommend using a 3$^{\rm rd}$-order polynomial law and a 4$^{\rm th}$-order non-linear law, as they provide an optimal compromise between bias and $A$, while testing the fidelity for each parametrization. While their use combined with existing LDC priors (10-20% uncertainty) currently implies $A\sim10$, we show that targeted improvements to limb-darkening models can bring $A$ down to $\sim2$. Improving stellar models and transit-fitting practices is thus essential to fully exploit transit datasets, and reliably increasing their scientific yield by $5\times$, thereby enabling the same science with up to $25\times$ fewer transits.