The Planetary Mass-Radius Relation and its Dependence on Orbital Period as Measured by Transit Timing Variations and Radial Velocities

Abstract

The two most common techniques for measuring planetary masses - the radial velocity (RV) and the transit timing variations (TTVs) techniques - have been observed to yield systematically different masses for planets of similar radii. Following Steffen (2016), we consider the effects of the observational biases of the two methods as a possible cause for this difference. We find that at short orbital periods ($P<11$ day), the two methods produce statistically similar results, whereas at long periods ($P>11$ day) the RV masses are systematically higher than the TTV ones. We suggest that this is consistent with an RV detection-sensitivity bias for longer periods. On the other hand, we do find an apparently significant difference between the short and the long-period planets, obtained by both observing techniques-the mass-radius relationship parameterized as a power law has a steeper index at short periods than at long periods. We also point out another anticipated observational bias between the two techniques - multiple planet systems with derived RV masses have substantially larger period ratios than the systems with TTV mass derivation.