The Von Trapp Family Planets: A Sixth Planet Confirmed for K2-138

Title: K2-138 g: Spitzer Spots a Sixth Planet for the Citizen Science System

Authors: Kevin K. Hardegree-Ullman, Jessie L. Christiansen, David R. Ciardi, Ian J. M. Crossfield, Courtney D. Dressing, John H. Livingston, Kathryn Volk, Eric Agol, Thomas Barclay, Geert Barentsen, Björn Benneke, Varoujan Gorjian, Martti H. Kristiansen

First Author’s Institution: Caltech / IPAC-NExScI

Status: Accepted for publication in AJ, available on arXiv

What do you get when you have five exoplanets that sing and add a sixth? Why, the K2-138 system of course! 

Discovered in 2018 through the Exoplanet Explorers program, K2-138 was the first system found by citizen scientists with K2, the extension mission of the original Kepler program. By spotting regular dips in K2 light curves, the citizen scientists were able to find four sub-Neptune exoplanets, with an additional super-Earth discovered after further analysis. All the planets were found to be in a near perfect 3:2 resonance chain, meaning their orbital periods follow successive ratios of each other – as discussed in this Astrobite.

But, the K2-138 system had more to offer! The analysis which discovered the super-Earth also spotted two additional dips in the K2 light curves, roughly 42 days apart. Dips like these, shown by the dark blue lines, and the letter g, in Figure 1, indicate that a sixth planet might transit K2-138, waiting to be confirmed by the authors of today’s paper.

A two panel figure showing the light curves of K2-138 over a period of 80 days. The top panel shows the raw flux of the star K2-138. The flux is represented by a solid black line which varies semi-periodically wtih varying amplitudes, peaking at 100.5% and 99% of the star's normal relative flux. Small colored lines extend vertically from the black line to show the transits of the planets and occur at the same period of each planet. The lines are typically 0.1% long. From shortest period to longest, planet b is shown with red lines, planet c with orange lines, planet d with yellow lines, planet e with green, planet f with light blue and the potential planet g with dark blue. Directly beneath this, the bottom panel shows the flux of K2-138 flattened. The black line is now constant at 100% relative flux across the 80 day width of the graph. The transit depth lines are still shown in the same colours as before, but are also now marked with the letter of each planet. The lines now extend between 0.1% for planet b, to 1.2% for planet e, with the other planets at depths in between. Grey circles are scattered around the lines showing the individual flux measurements.

Figure 1: The top panel shows the raw K2 light curve, while the bottom panel shows the same light curve flattened to highlight the planetary transits. In both panels transits of each planet in the system are shown with colored lines. The potential planet g is represented by the darkest blue lines. Adapted from Figure 2 from the paper.

To determine the origins of these mystery dips, the authors used the Spitzer Space Telescope to stare at K2-138 for 11 hours, centered around the predicted transit time of the proposed sixth planet. By fitting the original K2 and new Spitzer data, a clear transit event, shown in Figure 2, was found in the Spitzer observations within an hour of the expected time, confirming the existence of a sixth planet, K2-138g.

Figure showing the transit light curve of K2-138g with two plots next to each other. Both plots share the same y axis "Relative Flux" which varies between 1.002 and 0.996. Both plots have an x axis of "Hours from Mid-Transit", varying between -4 and 4, with the plot centered around 0. On the left, the K2 transit model is shown by a blue line at 1.0 relative flux, dropping down 0.999 during transit. The transit lasts between approximately -2 and 2 hours from mid-transit has a slightly rounded bottom. Two transits are plotted on top of the model, with data points roughly every 20 minutes. The first transit is shown by yellow circles and the second by red triangles, with a relatively large amount of scatter around the blue transit model. The plot on the right shows the Spitzer transit. The transit model is again plotted in blue and has a near identical shape to the K2 model, but this time has a flatter bottom. Grey circles are significantly scattered around the model line showing all the Spitzer flux measurements. To show the transit shape of the data more clearly, the grey points are binned to 20 minutes intervals and shown by red circles with small error bars, closely following the transit model.

Figure 2: The transit light curves from the K2 and Spitzer observations. In the left panel, yellow circles and red triangles show each of the two transits seen by K2. In the right panel, grey points show the Spitzer observations. The red circles show the data binned to 20 minute intervals, showing the drop in flux caused by the transiting planet. In both panels, the blue line gives the fitted transit model. Adapted from Figure 5 in the paper.

Orbiting at over twice the distance of planet f, the sub-Neptune K2-138g is something of a loner compared to its tightly packed siblings. With its 42 day orbit, K2-138g is not only one of the longest period K2 planets found to date,  makes K2-138 the K2 system with the most discovered planets yet. 

While the transit durations of the two light curves in Figure 2 are nearly identical, the Spitzer data shows K2-138g to have a slightly larger transit depth, and hence radius. As the two transit lengths are consistent within one sigma, the authors note that the limited number of data points in the K2 transits mean that any outliers could skew the results, causing the slight discrepancy with Spitzer.

The More the Merrier

While planets b, c, d, and e are in near 3:2 resonance with their respective neighbours, the outer planets f and g are not. Given this fact, along with the sizeable gap in orbital period between f and g, could there be additional planets in the system yet to be discovered? It seems possible. If the pattern of resonances continued beyond planet f, resonant orbits would be expected at periods of around 20 and 30 days, but more observations are needed to confirm whether any such planets exist.

Figure showing the orbital separations of 8 multiplanet systems. Each system is represented by a horizontal line across the figure with a/R* across the x axis from 0 to 175. The systems are in order of stellar size with the largest at the top. Each line has a thickness representative of it's stellar size, and is a different color from a gradient of pink at the top through yellows and oranges until the final system in red. The planets in each system are plotted on the lines to show their orbital separations from their host stars. The systems from top to bottom are Kepler-90, Kepler-11, Kepler-20, K2-138, HD 219134, Kepler-80, TOI-178 and TRAPPIST-1. Kepler-11, Kepler-20, K2 138, HD 219134 and Kepler-80 have planets bunches together at low values of a/R*, with an additional planet at a much larger orbital seperation. The other systems have more uniform spacing between each of their planets.

Figure 3: The orbital spacings of a selection of multiplanet systems, in order of the size of their stellar hosts from largest at the top. Each system is shown by a coloured line with a width corresponding to the size of the host star. Transiting planets are represented by circles scaled to the line width, enlarged 10x for clarity. Non-transiting planets are shown in blue. The large separation between the two outer planets of K2-138 is similar to that seen in the Kepler-11, Kepler-20, HD 219134, and Kepler-80 systems. Figure 10 from the paper.

K2-138g isn’t unique in its socially distanced orbit, however. Around half of the 9 other exoplanet systems with 6 or more planets also have a large gap between their outermost planets, as seen in Figure 3. While this apparent trend could be the result of planet formation processes, planets at large orbital radii can be harder to detect, so observational biases might be at play.

A Benchmark System 

With its tightly packed resonant inner planets and abundance of sub-Neptunes, the authors argue that the K2-138 system is a more than worthy target of follow-up observations. The inner planets provide an excellent opportunity to study their potential transit-timing variations (TTVs), discrepancies in the regular periods of planets, and observations have already been scheduled. Alongside radial velocity (RV) data, this could enable precise mass measurements and see the potential discovery of additional planets. While the planets have atmospheric signals too small to be studied with the James Webb Space Telescope, they are prime targets for the European Space Agency’s upcoming ARIEL mission. The system’s five sub-Neptunes could provide a key test bed for comparative studies of the atmospheres of a planet category not seen in our solar system.

Whatever the future holds, it certainly seems likely that we’ll be hearing more from K2’s most musical system in the years to come!

Astrobite edited by Brent Shapiro-Albert

Featured image credit: NASA / JPL-Caltech / R. Hurt (IPAC)

About Lili Alderson

Lili Alderson is a second year PhD student at the University of Bristol studying exoplanet atmospheres with space-based telescopes. She spent her undergrad at the University of Southampton with a year in research at the Center for Astrophysics | Harvard-Smithsonian. When not thinking about exoplanets, Lili enjoys ballet, film and baking.

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