Nature versus Nurture: Investigating the Effects of Measurement Uncertainties in the Assessment of Potential Trends between Planetary and Stellar Properties

Correlations between planetary and stellar properties, particularly age, can provide insight on planetary formation and evolution processes. However, the underlying source of such trends can be unclear, and measurement uncertainties and small sample sizes can leave doubt as to whether an observed trend truly exists. We use a Bayesian framework to examine how uncertainties in measured parameters influence the odds ratios of competing hypotheses for the source of an observed trend. We analyze three reported trends from the literature. In each application, while uncertainties do affect the numerical value of the odds ratios, our conclusions remain the same whether or not uncertainties are taken into account: hot Jupiter eccentricities are circularized over time, obliquities of hot Jupiter hosts are driven by stellar temperature, and there is not enough evidence to favor a trend of 2:1 orbital resonances with age over a chance relation. Updated samples for the 2:1 resonance and obliquity cases do not change the original conclusions. Simulated 2:1 resonance data show that sample size may be more important than measurement precision for drawing a firm conclusion. However, if 2:1 resonances get disrupted on a wide range of timescales, an age trend will be inherently difficult to confirm over a chance relation, even with a large sample. For some applications, full incorporation of measurement uncertainties may be too computationally expensive, making it preferable to use the framework without uncertainties and perform additional tests to examine the effects of highly uncertain measurements.