Detectability and Error Estimation in Orbital Fits

TL;DR

This paper investigates the detectability of two resonant planets via radial velocity data, highlighting the limitations based on planet masses and data quality, and analyzes errors in orbital parameter estimation from synthetic data.

Contribution

It provides new insights into the detectability thresholds for resonant exoplanets and characterizes error distributions in orbital fits from synthetic datasets.

Findings

Jovian resonant planets are hard to detect if their masses differ by more than a factor of 4.

Outer planet eccentricity is systematically overestimated in orbital fits.

Biases in amplitude estimates are linked to initial conditions near stable ACRs.

Abstract

We estimate the conditions for detectability of two planets in a 2/1 mean-motion resonance from radial velocity data, as a function of their masses, number of observations and the signal-to-noise ratio. Even for a data set of the order of 100 observations and standard deviations of the order of a few meters per second, we find that Jovian-size resonant planets are difficult to detect if the masses of the planets differ by a factor larger than $\sim 4$. This is consistent with the present population of real exosystems in the 2/1 commensurability, most of which have resonant pairs with similar minimum masses, and could indicate that many other resonant systems exist, but are presently beyond the detectability limit. Furthermore, we analyze the error distribution in masses and orbital elements of orbital fits from synthetic data sets for resonant planets in the 2/1 commensurability. For various mass ratios and number of data points we find that the eccentricity of the outer planet is systematically over estimated, although the inner planet's eccentricity suffers a much smaller effect. If the initial conditions correspond to small amplitude oscillations around stable apsidal corotation resonances (ACR), the amplitudes estimated from the orbital fits are biased toward larger amplitudes, in accordance to results found in real resonant extrasolar systems.