Saturday, November 13, 2010

Weighing Up Extrasolar Moons

An extrasolar planet is a planet which orbits a star other than the Sun and from the Paris Observatory’s online Extrasolar Planets Encyclopedia, there are about 500 known extrasolar planets as of November 2010. This number is expected to increase dramatically in the next several months with follow-up observations of the hundreds of candidate transiting extrasolar planet released in the first data set by NASA’s Kepler space observatory - a ‘planet hunting’ space telescope. A transiting extrasolar planet is one which periodically blocks a small fraction of the light from its parent star as its orbit happens to bring it in front of the star.

As the number of known extrasolar planets continues to increase rapidly, it undoubtedly brings up the possibility of detecting moons orbiting around these extrasolar planets. Detecting moons around extrasolar planets will be very challenging since such objects are expected to be smaller and less massive than the Earth. However, NASA’s Kepler space observatory might have the sensitivity necessary to detect the largest of such moons around extrasolar planets. Moons around extrasolar giant planets that are close to the size of the Earth can be particularly interesting because a large number of extrasolar giant planets are know to orbit their parent stars at ‘comfortable’ distances where Earth-like surface conditions are possible on such moons!

Recently, I did some research on transit timing variations (TTV) and transit duration variations (TDV) caused by the presence of a planet’s moon perturbing the periodic transit of the planet in front of its parent star. I used the methods outlined in two papers published by David M. Kipping in 2008 and in 2009 respectively, and wrote a program which allows me to play around with the parameters. I used stars, planets and moons of different masses in various combinations and orbital configurations. Additionally, I also used various TTV and TDV inputs to determine the corresponding mass of the moon and the corresponding planet-moon orbital configuration that is responsible the various signals.

In one of my analysis, I have a star with the mass of our Sun and a planet with the mass of the Earth which orbits the star at a mean distance of 100 million kilometers. This planet has a moon that is one-twelfth its mass and the moon orbits the planet at a mean distance of 130000 kilometers. It is also assumed that the planet takes 40000 seconds to transit in front of its parent star. As the periodic transits of the planet in front of its parent star is measured, the moon will induce an observed TTV of around 20 seconds and a TDV of around 35 seconds.

In light of a paper by David M. Kipping (2010) entitled “How to Weigh a Star Using a Moon”, I wrote a separate program to study the methods outlined in this paper. Basically, if a star has a planet, and if that planet has a moon, and if both of them transit in front of their parent star, then the sizes and masses of the star, planet and moon can be precisely measured. Furthermore, knowing the size and mass of an object allows its bulk composition to be constrained. This particular method employs the TTV and TDV signals, and it requires a star to have both a planet and moon that transit it. Although no star is yet know to have both a planet and moon that transit it, NASA’s Kepler space observatory is expected to discover several of such systems.

This method of measuring the mass of a moon of an extrasolar planet is rather interesting because such a moon is likely to be less massive than the Earth and the mass of such an object will not be measurable with radial velocity measurements. Therefore, a method like this offers a means to accurately pin down the masses and sizes of the star, planet and moon respectively. The masses of moons measured in this way could well be the smallest masses that can be directly measured outside of our Solar System.