Tracking exoplanets via orbital mechanics isn’t easy. Plenty of variables could affect how a planet moves around its star, and determining which ones affect any given exoplanet requires a lot of data and a lot of modeling.
A recent paper from researchers led by Kaviya Parthasarathy from National Tsing Hua University in Taiwan published in New Astronomy tries to break through the noise and determine what is causing the transit timing variations (TTVs) of HAT-P-12b, more commonly known as Puli.
Puli is a “sub-Saturn” exoplanet that orbits the star HAT-P-12, also known as Komondor. Both the star and its planet are named after dog breeds as they reside in the constellation Canes Venatici and lie about 463 light years away from Earth. Nothing is particularly special about the star or the planet, except that they have had a lot of data collected on them.
The paper analyzed 46 light curves watching Puli traverse in front of Komondor. Some were previously published, whereas others, including some ground-based observations and some new data from the Transiting Exoplanet Survey Satellite, were never before analyzed.
The most noticeable feature of Puli’s transits was its variability. This feature, known in the literature as transit timing variations, was pretty significant, coming in at an “amplitude” of 156 seconds of variability, meaning that the planet would occasionally pass in front of the star either over two minutes earlier or two minutes later than expected given a “regular” orbital period. That might not seem like much, but orbital mechanics are very precise, so that much variation was definitely a sign of something else affecting Puli’s orbit.
To figure out what, the researchers resorted to statistical analysis. They tried four different orbital models to see which one was the best first. First, they looked at a “linear” model representing a perfectly periodic transit. Given the variability in the transit times, that model did not fit the data well.
An orbital decay model, which represents whether the planet’s orbit is slowing due to being pulled into the host star, didn’t fit particularly well either. It represented a slow but steady rate of change, which would have seen the transits’ time change consistently in one direction over the course of the observations.
Another model, the apsidal model, tried to understand what would happen with a slightly eccentric orbit that could be reflected in different start and end times of Puli’s transit. This one fit better than the other two models, but wasn’t the best fit for the data.
That title goes to a sinusoidal model, representing another planet’s gravitational influence on Puli’s transits. This model caught a periodic signal in the TTVs that was translated into a companion planet with a period of 6.24 orbital days and a mass about 2% the size of Jupiter. The output of the sinusoidal model estimated a TTV amplitude of 2.6 minutes, almost spot on what it actually was.
To rule out other factors, the authors considered the Applegate mechanism, whereby changes in the star itself could affect TTV measurements. This mechanism includes factors like the star’s magnetic activity or a change in its “oblateness,” or how much it bulges at its center, which could dramatically impact the orbital timing of a transiting exoplanet. However, the predicted amplitude from this effect was only about 0.4 seconds, not anywhere near enough to explain the more than two-minute deviation found in the data.
Luckily, Komondor had enough data collected on it that the authors could do this kind of deep dive to discover a potential new planet—not every exoplanetary system is so lucky. But as we start to collect more data on more exoplanet systems, there will undoubtedly be unseen companion planets lurking in them. The more we can run the sort of analysis described in the paper, the more of them we are likely to find.
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