Skip to main content# Analyzing the Detectability of Secondary Exoplanets using Markov Chain Monte Carlo Simulation

Presentation #417.05 in the session Exoplanet Radial Velocities and Transits: Techniques.

Published onJun 29, 2022

Analyzing the Detectability of Secondary Exoplanets using Markov Chain Monte Carlo Simulation

Radial-velocity measurements have long been an important tool in exoplanet detection. By approximating the radial-velocity curve of a star as a sine wave, we can make good estimates of a stellar companion’s characteristics. However, in multi-planet systems, such estimates are dominated by the radial-velocity signal from the largest, shortest-period planet. Secondary exoplanets, with smaller masses and larger orbital periods, contribute smaller trends to the star’s overall radial velocity, and as a result, their signals are often undetectable against a large background of noise. Using residuals of radial-velocity data from stars known to host hot Jupiters, we present our analysis of the detection thresholds at which secondary exoplanets’ signals become detectable. Using Markov chain Monte Carlo analysis, we take the residuals from each host star, add in the radial-velocity signal from 10^{4} to 10^{5} different Keplerian orbits while varying semimajor axis and planetary mass, and attempt to detect the injected signal against the background noise. Our goal is to determine, for a given set of radial-velocity measurements, the minimum mass that a secondary exoplanet must ascertain in order to be detectable at a certain distance from the star. Our research also compares the result from testing the detectability of a purely-random set of planetary masses and semimajor axis lengths with the result from picking a semimajor axis length and gradually lowering the planetary mass until it is undetectable. The second method described comes from Bowler et. al. 2010, “Retired A Stars and Their Companions. III. Comparing the Mass-Period Distributions of Planets around A-Type Stars and Sun-Like Stars,” upon which much of the inspiration for this work is based.