The Kepler team have found several thousand exoplanet candidates. The number of targets showing transit-like signals is increasing on a nearly daily basis as we search through light curves. However, these candidates are just that, candidates. Even though the planet candidates list is thought to have a high degree of fidelity, meaning that the vast majority of candidates are indeed real planets (somewhere in the region of 90%), it requires significant amounts of time and resources to turn a planet candidate into a planet.
I’ll start by being careful with my terminology. The Kepler team use two terms when deciding a candidate is a planet. Confirmation and validation. The former generally only used when we have spectroscopic radial velocity follow-up observations. These are measurements of the wobble induced on the star by the mass of the planet. The planet and star orbit a common point in space. When the planet is moving towards us the star moves away, and vice versa. When the star moves away it gets a little redder and when it moves towards us it get a little bluer. We measure these shifts and it tells us how fast the star is moving in along out line of sight.
Radial velocity measurements in combination with a transit give the planet’s mass and radius. A radial velocity detection of a planetary mass object (normally taken to be less than 13 Jupiter masses) is very unlikely to be erroneous and we are therefore happy to confirm the existence of a planet.
In order to measure a radial velocity a planet must be close enough and massive enough to have a measurable effect on the star. The best instruments currently available are sensitive to a periodic change in radial velocity of around 1 m/s and even getting this precision requires a bright star. The Earth causes a radial velocity pull on the Sun of around 10 cm/s, measuring with this precision is out of the question with currently available instruments. We therefore require another method to use another method if we want to turn small planet candidates into planet.
Validation of a planet
Validation of a planet applies when we use a statistical argument to say that it is much more likely that the transit signal is caused by a planet passing in front of the the target star (I’ll call it star A) that it is to be caused by something else.
There are 4 main ‘something else’, or false positive, scenarios we consider.
- A background eclipsing binary
- A background planetary system
- An eclipsing binary physically associated with the star A
- A transiting star-planet system physically associated with star A
(*There is some debate on whether a planet orbiting a star other than star A should really be considered a false positive. It is still a planet but it does contaminates our statistics on how many small planet are in the Galaxy.*)
A background eclipsing binary is a system of two stars that are appear fainter than star A, usually because they are far away (although they could be intrinsically faint stars which are, counter-intuitively, in the foreground between us and star A). The two fainter stars pass in front of one another much like a transiting planet does and cause a periodic dip in brightness. Because star A is much brighter than the eclipsing system, the eclipse depth appears to be much shallower than it really is and hence the eclipse looks similar to planet transiting star A.
A background planetary system is much the same as scenario (1) but the fainter system contains a star and a planet instead of two stars. If we think the transit is of a planet around the larger star A, we get the planet radius wrong. If we are not careful this scenario could cause us to claim a Jupiter-sized planet is Earth-sized.
Scenario (3) is what is known as a hierarchical triple. There are three stars in the system, star A and two lower mass stars which eclipse each other and orbit around the same center of mass as star A. This is more common than one would initially think guess. Around half of all stars are members of binary systems and in the region of 10% of these are triple or multiple star systems. The light from star A washes out the eclipse of the smaller stars and the eclipse looks much more shallow than it intrinsically is.
Finally, there is the case where a star-planet system orbits star A. The depth of the transit is decreased by the presence of extra light from star A and we get the planet radius wrong.
We try to obtain high resolution images using fancy techniques like adaptive optics imaging which changes the shape of one of the telescope’s mirrors to correct for the movement of the air in the atmosphere. These images allow us to see very close to the star and therefore look for other stars nearby in the image that could cause the transit-like signal. Typically if we don’t see star nearby star A we are able to say there are no stars further than 0.1 arcseconds away (0.00003 degrees) which could cause the transit-like signal. We are then able to make use of models of our Galaxy to predict the probability that there is a star in the right brightness range and within the allowed separation from star A that could mimic the transit signal. It is common for us to be able to say there is less than one in a million chance of a there being an allowed background star. When we take into account the probability that a background star is an eclipsing binary or hosts a planet the result is usually that it is very unlikely that there is a background eclipsing binary or star-planet system.
Ruling out a physically associated star-planet or eclipsing binary system can be much more challenging. We can again use the high resolution imaging but it is much more likely that a companion star is very close to star A than is the case for a background star. One thing on our side is that the shape of the transit can be used to rule out a stellar eclipse: eclipses are usually much more ‘V-shaped’ than the typically ‘U-shaped’ planet transit. We can often say that we cannot fit the shape we observe with a stellar binary. It is also possible to rule out planet transits around a smaller star because the timescale of the ingress and egress (the part of a transit where the planet is moving into and out of transit) does not agree with the transit depth as both these piece of information yield the planet radius. However, we really need good signal-to-noise in order to place firm constraints on the ingress and egress durations. Even so, it always gives us some information even if it is not particularly constraining and this can be used to calculate a false positive probability.
The final step is to sum up the combined false positive probabilities from the different scenarios and compare that to the probability that the transit signal is due to a planet transit around star A. If the transit scenario is much more likely (say 1000 times more likely) than a false positive we claim the planet is validated. On other occasions we have to hold our hands up and say we can’t rule out the false positive scenario with a high enough degree of confidence and the source of the signal remains a planet candidate.
The case where stars host multiple planet candidates, such as that found by the Planet Hunter in the paper by Chris Lintott, is a particularly interesting one. This is because the probability that the a multi-planet candidate system contains a false positive is much lower than for single planet candidates system, somewhere in the region of 50 times less likely. This makes validation much easier.
Planet Hunters have already shown they can find these multi-planet system. Keep searching a more will appear, especially long period ones. There is a good chance that there is an Earth-like planet hiding somewhere in the data currently available.
