The Goldilocks Trap: Guest post from Andrew Vanderburg, PhD student at Harvard

This guest post is from Harvard astronomy graduate student Andrew Vanderburg.  Andrew is better known for his extensive work on the NASA K2 mission, including the discovery of a disintegrating minor planet orbiting a white dwarf!   Andrew and I collaborated on a paper that is published in the Monthly Notices of the Royal Astronomical Society, and is available in pre-print form here: http://arxiv.org/abs/1604.03143.  I remember when I had the genesis of the idea for this paper -  I was at the American Astronomical Society meeting in Washington DC in January of 2014; I excitedly rushed around the meeting to other exoplanet scientists bouncing the idea off of them.  Several of them would end up being co-authors on our paper.  No one had thought of this angle before. However, soon thereafter an excellent series of observational papers would come out from Paul Robertson demonstrating that we were on to something.  Read on for more from Andrew!

A major goal for astronomers studying exoplanets is to learn how common is it to find small, rocky planets orbiting in their stars’ habitable zones -- that is, orbiting just far enough away from their host star for the planet to have liquid surface water (and possibly alien life). One of the most promising ways to address this question is by closely monitoring the star’s radial velocity, or the speed at which stars are traveling towards or away from us here on Earth. We can detect the presence of planets around these stars because they tug on their host stars very slightly as they orbit. For the past 20 years, radial velocity measurements have been one of the most successful methods for discovering exoplanets.

Radial velocity measurements of the first exoplanet discovered around a sun-like star. The planet tugging on the star as it orbits causes a wobble in the radial velocity.

As our technology has improved and we learned to measure radial velocities (or RVs for short) more and more precisely, the situation has become a bit more complicated. It turns out that other processes on stars can cause apparent changes in its radial velocity, which can either mask (or more disturbingly) mimic the signatures of small exoplanets. One of the main culprits are starspots, which are the same as sunspots on our own Sun. When starspots rotate in and out of view as the star spins, they can cause RV variations which look a lot like the wobble of exoplanets that orbit their stars every time the star rotates.

Recently, there have been several high-profile cases where starspots have likely fooled astronomers into believing a planet orbited a star (see for example http://www.space.com/26432-potentially-habitable-exoplanets-gliese-581-existence.html). For astronomers trying to find small planets orbiting in their host stars’ habitable zones, this is a scary lesson! For one thing, two planets which we thought might be at the right temperature for liquid surface water to exist actually never existed. And for another, how will we ever be able to confidently say that a particular signal is a planet instead of starspots?

For these reasons, Peter and I decided to investigate the phenomenon of stellar activity (like starspots) mimicking and masking habitable exoplanets. We wanted to figure out under what circumstances could this type of planetary deception take place and how we might avoid it when searching for habitable exoplanets in the future.

We performed an analysis using a mixture of theoretical stellar models, observational data from NASA’s Kepler space telescope, and empirically determined relations describing the rotation of stars. First, we figured out the periods at which starspots can mimic exoplanets. We thought that these periods should be related the period of the star’s rotation (because spots will rotate in and out of view every time the star rotates), and our analysis confirmed that intuition. We were a bit surprised, however, to see how important the “harmonics” of the star’s rotation period are for stellar activity. It turns out that starspots can mimic planets orbiting at one half the star’s rotation period, or one third the star’s rotation period, just as easily as at the rotation period itself. We also found that even if there is a real planet orbiting near the star’s rotation period, it’s considerably more difficult than usual to detect it with radial velocity measurements.

Once we knew the importance of the star’s rotation period (and its harmonics), we used gyrochronology relations to predict the rotation periods for stars of different masses and ages. As stars age, they start to spin more and more slowly, and gyrochronology is the study of how that deceleration happens. Generally, more massive stars spin faster than lower mass stars. So cool, low-mass M-dwarfs have longer rotation periods, which means that any spurious planet detections would happen at similarly long periods.

Finally, we compared the periods where we expect spurious planet detections from our analysis to orbital periods of exoplanets in the habitable zone. The habitable zone also depends on the mass of the star -- for stars like the sun, the habitable zone is at periods around 1 year (like the Earth). But for smaller stars, the orbital periods of habitable zone exoplanets are shorter because these stars are intrinsically fainter, and to stay warm enough for liquid water to form, you need to be closer to the star.

It turns out that stars about half the mass of the sun have rotation periods close enough to the orbital period of habitable zone exoplanets, and therefore, we expect to see stellar rotation mimicking habitable-zone exoplanets around this type of star. This is the exact type of star where starspots have previously been found to mimic habitable zone exoplanets, and we could see more of the same until better ways have been found to separate out the signatures of starspots and genuine exoplanets. Until then, our take-away message is that if you’re looking for habitable-zone exoplanets around stars about half the size of the sun, buyer beware! You risk being fooled by stellar activity.

The time-scales of stellar activity from starspots that confuse radial velocity measurements.  For M dwarfs, habitable zone exoplanets have orbital periods (green stripe) that are in the same range as rotation periods (grey region).  We've nicknamed this overlap the "Goldilocks trap."  Similarly, the amplitudes of the apparent and real radial velocity changes are in the same ranges too.