A visual walkthrough of my dissertation research on using radial velocity precursor data to optimize direct imaging observation scheduling for exoplanet missions.
Future direct imaging missions are likely to use Radial Velocity (RV) data to inform their observation schedules. RV works by measuring the Doppler shift of a star's light caused by the motion of orbiting planets, effectively making the star appear blue when it's moving towards us and red when it's moving away.
Animation showing the Doppler shift of a star's light caused by the motion of orbiting planets.
An unfortunte reality of radial velocity measurements is that we cannot separate a planet's mass from its orbital inclination. This means that a planet could be either an Earth or a Jupiter, depending on its orbital orientation. This animatino shows two planets with the exact same radial velocity signal but one has the mass of the Earth and the other has the mass of Jupiter.
Comparing an Earth-mass planet (top) to a Jupiter-mass planet (bottom) viewed edge-on. The radial velocity signal depends on both mass and orbital inclination.
To manage this ambiguity we can randomly sample different inclinations and calculate the mass corresponding to it. That allows us to make probabilistic statements of the planet's visibility to a coronagraphic mission.
RV measurements over time reveal the orbital period and eccentricity, but leave inclination and true mass partially unconstrained.
The first step of determining when a planet will be visible is applying the "geometric constraint" from the coronagraph. Coronagraph's have an inner and outer working angle that define an annular region where the planet can be detected. Given a set of consistent orbits, we can apply the geometric constraint to determine when the planet will be in the observable region. Note that this is a helpful heuristic, but there's some nuance because a very bright planet may still be visible outside of the observable region.
We can calculate the probability that a planet will not be obscured by the coronagraph. The shaded region in this animation represents the region of the image that is obscured by the coronagraph.
The photometric constraint is the other major constraint used to forecast when a planet will be visible. If a planet is too faint it cannot be detected even if it is in the observable region. If we apply both the geometric and photometric constraints we can determine when a planet will be visible and determine it's probability of detection.
The photometric constraint is based on the ratio of the brightness of the planet to the brightness of the star.
The previous animations showed a very idealized RV signal. In reality, the signal is affected by other factors such as multi-planet systems, stellar activity, instrument noise, and atmospheric turbulence.
A realistic RV signal generated from a 7 planet system and noise.
To determine which planets exist around a star we must "fit" the RV signal to the data. This is a complex process that involves Bayesian inference to determine the most likely set of planets that could have generated the RV signal.
Fitting orbits the the RV signal generated above. Only three planets were fit with high enough confidence to be included are shown as a set of possible orbits after resolving the mass/inclination ambiguity.
We can then calculate the probability of detection for each planet that was found by the RV fitting process and use that to inform direct imaging observations. By combining the geometric and photometric constraints with the orbital uncertainties from RV data, we can optimize when to observe each target star to maximize the chance of detecting and characterizing its planets.
For more detail, see the last chapter of my dissertation.