Sunday, July 19, 2015

The transit method

The transit method is one of the most important techniques to detect and to study extrasolar planets. Using this method, up to date 1210 exoplanets have been found (, the majority by the unbelievably successful NASA Kepler mission, but also by the European mission CoRoT and many ground-based programs.

Planets orbiting their host star can, if we look at the system from a favorable viewing angle, pass in front of the stellar disk. For most systems we will never see planetary transits because the orbits do not have the right inclination. But if we look at thousands of stars we will have - by chance - some planets moving between their host stars and us. When this happens, part of the star's light is blocked by the exoplanet and does not reach the Earth anymore.

The upper part of the diagram explains this in detail. The large yellow circle is the disk of the star and the small blue circle is the planet orbiting around it. From our point of view the orbit is only tilted a little bit, so when the planet orbits around its host star it will cross the stellar disk (although not directly in the center). If the plane of the orbit was tilted a little bit more, the planet would transit the star closer to the edge; if the tilt is large enough, it would not transit at all.

The lower part of the diagram shows the lightcurve, which is the measured brightness with time, of the system as it would be observed from our point of view. It is important to understand that for most systems we cannot resolve the star and the planet, which means we measure the brightness of both - star and planet. We cannot take a picture of the system as I plotted it; even in an image of the best telescopes we have, the system would always look like a point. Most systems are so far away that we have not yet the technology to separate planet and star.

For simplicity I assume here that the planet itself emits no light at all. In reality, this is not true, but for many systems the contribution of the planet is so small that you cannot see it.

In the diagram the same planet is plotted four times at different positions of its way around the star. In the lightcurve these four positions are indicated on the time axis. I will explain these four situations in detail:

  1. The planet is not yet on the stellar disk. In the lightcurve the brightness of the system is at 100 % because all of the light coming from the star can be see.
  2. The planet just moved onto the stellar disk. During the time period when the planetary disk moves on the stellar disk, but is not yet complete on it, the brightness goes down steeply. This is the beginning of the transit, which is also called ingress.
  3. Now the planet is completely on the stellar disk and the brightness dropped down to a lower level. As long as the entire disk of the planet is on the star, the brightness stays down there. This flat bottom is again a simplification; in reality, the brightness will change, even during the transit, because the stellar disk is not equally bright in all parts. In particular, it is darker at the edges than in the center, which is referred to as limb-darkening. However, I will ignore this effect here. Important is that the brightness goes down to a constant value of 0.99, so the light we receive from the system is 1 % less than when there is no transit. It is easy to understand where this comes from: The planetary disk blocks 1 % of the stellar disk, so 1 % of the light cannot reach us anymore. You now know the size of the planet relative to the star. The relative disk size is 1 %, the relative radius is the square-root of ita: 10 %. In our example the radius of the planet is 10 % the radius of the star. This is the beauty of the transit method: Just by measuring the depth of the transit, which can be easily done by anybody, we know the radius of the planet.
  4. The planet moved on its orbit to the other side of the star. When it moved off the disk, which is called egress, the lightcurve went up steeply back to the 100 % brightness it had before the transit. Now the planet moves around the star and will in a certain period of time, depending on its orbital period, come back for another transit.
Like every other technique the transit method has strong and weak points. On the plus side: It is a conceptually easy method and requires only to measure brightnesses of many stars. From the lightcurve you easily get two important, fundamental properties of the planet: its radius relative to the star and its orbital period, which is how long the planet takes to move once entirely around the star. From this you can already learn quite a lot about the planet. However, on the down side: The probability to see a transit is low; even worse, it depends on the planet's distance from its host star. I will certainly talk about this in a separate post, but it means that far out planets are very hard to detect. One might also considered it as a weak point that it is not possible to measure a planet's mass from its transit - at least not in every case and in a simple manner. Since the mass is a very fundamental property, one has to get the mass somehow, which usually is by using the radial velocity (RV) technique.

In the end I would like to mention that until about a year ago it was not considered to be good practice to announce a new planet just because transits in a lightcurve were found. There are some other problems I did not mention here, which make it possible that the "transits" you observe do not really come from a planet. So one always had to check the system with the RV technique; only if the planet was found there, too, it was accepted as a real exoplanet. However, this has changed lately and you do not always have to backup a transit detection anymore. Although this might be based on good reasons, some astrophysicists are not very happy with it - maybe I will talk about this controversy in some other post.

a. Simple geometry: The area A of a circular disk is πR2. If you have the area ratio and want the radius ratio you have to square-root the first to get the latter.