Simulating the M-R Relation from APF follow up of TESS targets: Survey design and strategies for overcoming mass biases

We present simulations of multi-year RV follow up campaigns of the {\it TESS} small exoplanet yield on the Automated Planet Finder telescope, using four different schemes to sample the transiting planets' RV phase curves. For planets below roughly 10 M$_\oplus$ we see a systematic bias of measured masses that are higher than the true planet mass, regardless of the observing scheme used. This produces a statistically significant difference in the mass-radius relation we recover, where planet masses are predicted to be too high and too similar across the entire super-Earth to Neptune radius range. This bias is due in part to only reporting masses that are measured with high statistical significance. Incorporating all mass measurements, even those that are essentially only upper limits, significantly mitigates this bias. We also find statistically significant differences between the mean number of planets measured at the 1-, 3-, and 5$\sigma_{\rm K}$ level by the different prioritization schemes. Our results show that prioritization schemes that more evenly sample the RV phase curves produce a larger number of significant mass detections. The scheme that aims to most uniformly sample the phase curve performs best, followed closely by the scheme which randomly samples, and then an in quadrature sampling approach. The fourth scheme, out of quadrature, performs noticeably worse. These results have important implications for determining accurate planet compositions and for designing effective RV follow up campaigns in the era of large planet detection surveys such as $K2$, $TESS$, and $PLATO$.