A recent query about how astronomers work out the mass and radius of planets found through microlensing — such as the so-called ‘super-Earth’ recently discovered 9000 light years from our Sun — prompted Centauri Dreams to query one of the principals in that discovery. Andrew Gould, leader of the MicroFUN collaboration and professor of astronomy at Ohio State University, was kind enough to clarify how this fascinating science proceeds. Herewith his response:
We obtain a planet-star mass ratio from a fit to the light curve. This parameter (q) is a standard output from fits to microlensing curves generated by binary lenses (two point masses, e.g., star and planet). Now, for low-magnification microlensing events, such as OGLE-2005-BLG-390Lb (which was announced by the PLANET team in January), it is generally possible to estimate the mass just by looking at the light curve. And in those cases it can be explained easily to the non-expert (although PLANET did not do this in their article). However, in high-magnification events like OGLE-2005-BLG-169Lb, we get a mass ratio out of our computer codes, but there is no known simple way to make an estimate directly by looking at the light curve.
We estimate the star mass M based on some characteristics of the event plus a Galactic model. Thus we derive a planet mass, m = qM. We will be able to do better on the star mass when we get images of the host star as it moves away from the source (assuming we can get Hubble time for this).
We have no direct information about the radius. In the article, we put forward two ideas about the nature of the planet. One is that it is like Neptune, with a rock and ice core surrounded by a thick padding of gas. Then it would presumably have a radius like Uranus and Neptune, about 4 earth-radii. However, because it is in the region of its solar system that is just out past the “snow line” (where Jupiter and Saturn are in our solar system), we prefer the idea that it is a failed core of a Jupiter-like planet. Then it would be all rock and ice, probably roughly 2 gm/cm³ uncompressed (and so about 2.5 gm/cm³) compressed. This would give it a radius of about 3 earth-radii.
On the matter of terrestrial-size worlds, Gould added that he was hopeful that such planets could be detected within a few years, but noted that they would still be 10,000 to 20,000 light years away. Thus the beauty, and frustration, of microlensing. It seems the most likely way we’ll find our first Earth-mass planets, but the physics involved all but guarantees they’ll be distant indeed.