McMahan Observatory

Exoplanets

Exoplanets, or extra-solar planets, are planets orbiting stars other than the sun. While we can't see these planets directly even with the largest telescopes, large telescopes can detect the red and blue Doppler shift of the light from the star as the orbiting planet causes the star to "wobble" toward and away from the Earth as it orbits around the center of mass (barycenter) of the extra solar system. Most exoplanets are discovered by the Doppler shift method, but some have been discovered by observing small variations in the light reaching us from the planet's host star (transit method). If the exoplanet orbit, the host star and the Earth are essentially in the same plane, the exoplanet will transit in front of the star as viewed from Earth. During the transit, the planet blocks some of the light from the star that reaches Earth when the planet is not transiting. This causes a very slight reduction in the "brightness" (magnitude) of the star during the transit. The amount of reduction in light flux will depend on the size of the planet and how close it is to the star.

Observing exoplanet transits gives important information about these remote planets and their relationships to host stars. Doppler shift only measures the wobble of the star on a direct line from the earth to the star. Unless the earth is exactly in the plane of the exoplanet orbit, the planet actually accelerates the star more than is detected by the Doppler shift. In the extreme case in which the orbit of the planet is in the plane perpendicular to the line between the Earth and the star, no Doppler shift would be detectable from the Earth because the acceleration would be in a direction perpendicular to the line line of site from the Earth. There would be essentially no change in the radial velocity of the star in relation to the Earth, and there would be no Doppler shift. Therefore, Doppler shift only gives a lower boundary for the acceleration of the star. It can understate the acceleration, and therefore, the mass of the orbiting planet by a factor of SIN(i) where "i" is the angle of inclination from the plane perpendicular to the line of site from the earth to the star.

To determine the mass of the planet you need he mass of the star, the acceleration of the star and the period of rotation. Astronomers estimate the mass of the star from the star's spectrum. The spectrum tells us the type of star and its position on the HR diagram. There is a direct relationship between a star's type and its mass. Estimates of this relationship has been developed and refined during more than a century of observation and research, but there is still a significant amount of error in any given estimate of stellar mass. Given the star's mass, the period of rotation of the planet and the acceleration of the star, determining the mass of the planet is then a classical mechanical problem, which for circular orbits, is similar to determining residual imbalance in rotating machinery. It is easy to see however that the estimate of the planet's mass involves a number of estimates, each one of which adds uncertainty to the result.

If an exoplanet can be observed in transit, much of the uncertainty involved in determining the angle of the orbital plane can be eliminated and the mass of the planet can be determined more precisely. The fact that the planet transits the host star means that the plane of orbit lies nearly on the line of site. Further refinement of the path of the planet across the face of the star and, therefore, the angle of inclination of the orbit can be obtained from the shape of high time resolution light curves spanning the entire transit, including ingress and egress.

In addition to improving mass estimates of an exoplanet, transits also allow its size and therefore its density to be estimated. To date there does not seem to be an obvious relationship between the mass of exoplanets and their density. It is important to understand if such relationships exist because they can shed light on possible planet formation models. Data so far argues against a single-value function but there could still be a determinable function that takes on distinct values depending on initial or other conditions. Much more data on planet sizes and densities and their relationship, if any, to planetary orbits, will be required to formulate and test planet and system formation theories.

Amateur astronomers can help in this effort. Observing, imaging and analyzing exoplanet transits is within the capabilities of amateur astronomers. The McMahan Observatory uses a 250 mm (10") Dahl-Kirkham variant of the cassegrain telescope with an SBIG ST7 CCD camera. With this good but relatively modest equipment, good skies, and careful CCD technique, it is possible to capture statistically significant light flux variations down to .01 magnitudes with time resolution of two minutes for stars of 12th magnitude and brighter.