NASA’s Kepler Mission has discovered many multiplanet systems.  One of my personal favorites, and the first one I studied, is KOI-94 (now Kepler-89).

KOI-94 is unusual among multiplanet systems because one of its planets is Jupiter-sized, and the others are all small.  The Jupiter-sized planet, KOI-94 d, orbits its star in just 22 days (1/4 the orbital period of Mercury).  Although this orbit is short compared to our own Jupiter’s orbit (11 years), it is much longer than the so-called “hot” Jupiters that orbit their stars in under 5 days!  Many “hot” Jupiters have very low densities, including one with a density lower than styrofoam, and we do not understand how they got so puffy.  Intermediate “warm” Jupiters like KOI-94 d serve as a laboratory in which we can test theories of planet inflation.

 In the summer of 2012, my teammates and I determined the mass of the warm Jupiter.  To do this, we measured 26 “radial velocities” (RVs) of KOI-94 with the Keck telescope on Mauna Kea, Hawaii.  The radial velocity is the instantaneous speed of the star in the direction away from the observer.  A planet orbiting a star exerts a gravitational force on the star, and so both the star and the planet orbit the center of mass of the system.  By measuring how fast the star was moving toward and away from us at various times, we determined the mass of the warm Jupiter.  We also placed upper limits on the masses of the three smaller planets.  KOI-94 d has a mass comparable to Saturn’s and a size comparable to Jupiter’s, and so it is very slightly inflated compared to the cold giant planets in our solar system.

KOI-94 RVs
The velocity of the star KOI-94 along a radial axis (“radial velocity”, or RV) in meters per second vs. time in days. The star moves due to the gravitational influence of all of its planets, but especially the warm Jupiter KOI-94 d.

We also compared KOI-94 d to all of the other planets with measured masses and densities.  We realized that there is an empirical relationship between the planet mass, radius, and stellar irradiation (flux).  The mass-radius-flux relation can be used to predict a planet’s radius, given its mass and the energy flux received from the star.

Planet radius (in units of Earth’s radius) vs. planet mass (in units of Earth’s mass) for the planets with measured masses and radii, as of fall 2012. The planets are split in half: the half that receive more energy from their star (“incident flux”) are colored red/orange, and the half that receive less energy are colored blue/purple. The exoplanets are small circles, the solar system planets are big triangles with labels, and the KOI-94 planets are big stars with labels.