Exoplanetology Beyond Kepler

Useful synergies continue to emerge among our instruments as we ponder the future of exoplanet studies. Consider the European Space Agency’s PLATO mission (PLAnetary Transits and Oscillations of stars). Operating from the L2 Lagrangian point, PLATO will use 34 telescopes and cameras on a field of view that includes a million stars, using transit photometry, as Kepler did, to find planetary signatures. Working at optical wavelengths, PLATO will look for nearby Earth-sized and ‘super-Earth’ planets in the habitable zone of their stars.

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This mission is scheduled to be launched in 2024, an interesting date because it’s also the year that the European Extremely Large Telescope (E-ELT) is scheduled to see first light. Huge new installations like these, although ground-based, are so powerful that they should be able, with the help of adaptive optics, to study planetary atmospheres on the PLATO-discovered planets. Thus we get the best of both worlds, with repairable and upgradable ground telescopes fleshing out the data gathered by our space instruments, just as today we can use Kepler data to find planet candidates and then confirm them using radial velocity studies from the ground.

The TESS mission (Transiting Exoplanet Survey Satellite) launches earlier (probably in 2018) but offers the same kind of synergies with other instruments. Both TESS and PLATO, for example, will hand off data to the James Webb Space Telescope, scheduled for a 2018 launch. Here again we can look for deepened studies of the targets other missions have found. And in the process, we can be assured that we’ll enrichen our catalog of extrasolar worlds.

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Just what we might find is the subject of new work by Michael Hippke (Institute for Data Analysis, Neukirchen-Vluyn, Germany) and Daniel Angerhausen, a postdoc at NASA GSFC. Writing in The Astrophysical Journal, the duo explain in one recent paper that while planets with sizes and orbits similar to Mars or Mercury will be out of reach (around solar-class stars, at any rate), planets the size of Venus or Earth should show up readily for TESS and PLATO. The optimum target for life-hunters, of course, is an Earth-class world in an Earth-like orbit, and both instruments are believed to be capable of finding these. From the paper:

In this work, we have shown that future photometry will be able to detect Earth- and Venus-analogues when transiting G-dwarfs like our Sun… Larger sized planets (> 2R?) will be detected in a single transit around G-dwarfs, in low stellar noise cases, and assuming one can find them in the first place. The search techniques for such single transits will require further research and validation, and will likely be performed remotely, due to the large storage requirements.

But Hippke and Angerhausen’s interests extend beyond planets. They believe that a large planet like Jupiter that has several large moons should produce a characteristic signature, allowing its ‘exomoons’ to be detected. The detection would be marginal, as Angerhausen explains: “We wouldn’t have a clear detection, and we wouldn’t be able to say whether the planet had a single large moon or a set of small ones, but the observation would provide a strong moon candidate for follow-up by other future facilities.”

Let me drop back quickly to one of Hippke’s papers from early 2015, which explored exomoon candidates from the Kepler data, using what is known as the orbital sampling effect, which stacks numerous planet transits and tries to extract an exomoon signature. In this paper, Hippke used numerical simulations to inject exomoon signals into real Kepler data. This is useful because it shows us that there is a size limit to what we can find, one that TESS and PLATO should be able to improve on. The paper finds that for suitable planets with orbits between 35 and 80 days, an exomoon’s detectable radius is approximately 2120 kilometers, or about a third the radius of Earth, while for longer period planets, even larger moons are the minimum.

Such moons go beyond what we generally see in our system, but as the paper notes:

…our solar system might not be the norm – we have no Hot Jupiters, warm Neptunes, or Super-Earths in our solar system, and thus no reference for typical moons around such planets. Also, there is a strong selection bias, based on the detection limits…, and in addition the simple fact that the strongest dips are most significant. The first moons to be found will likely be at the long (large/massive) end of exomoon distribution, as was the case for exoplanets.

Hippke is surely right that the first moons found will be at the larger end of the size range, just as the first exoplanets we detected were massive worlds in close orbits that were the easiest to see with our instruments. For more on Hippke’s work and the methods he employs, see the article he wrote for Centauri Dreams, Exomoons: A Data Search for the Orbital Sampling Effect and the Scatter Peak.

But back to the Hippke and Angerhausen paper I started with. It notes that while the detection of moons will remain problematic for planets analogous to those in our own system, moons around planets orbiting quiet M-dwarf stars should be easier to detect. This paper, “Photometry’s bright future: Detecting Solar System analogues with future space telescopes,” focuses in directly on the capabilities of instruments like TESS and PLATO in offering datasets beyond Kepler’s.

Here again the authors deploy the Orbital Sampling Effect:

The OSE can be used to detect a significant flux loss before and after the actual transit (if present), which might be indicative of an exomoon in transit. The basic idea is that at any given transit the moon(s) must be somewhere: They might transit before the planet, after the planet, or not at all – depending on the orbit configuration. But by stacking many such transits, one gets, on average, a flux loss before and a flux loss after the exoplanet transit.

And bear in mind that moons are only one of the things we might expect to extract from TESS and PLATO data. Right now we have one detected ring system, around the planet J1407b, a massive ring more than 200 times larger than Saturn’s. The authors show that a transiting planet with a ring system produces a definitive signal. Even Trojan asteroids, which lead and follow a planet by 60 degrees in its orbit, should be in range for detection. In a third paper, the authors use Kepler data, injecting synthetic Trojan light curves to search for the limits of detectability. From the paper:

Our result gives an upper limit to the average Trojan transiting area (per planet) corresponding to one body of radius < 460km at 2? confidence. We find a significant Trojan-like signal in a sub-sample for planets with more (or larger) Trojans for periods >60 days.

The authors call these results tentative and suggest that improved data from TESS and PLATO should help us refine them. “As good as the Kepler data are, we’re really pushing them to the limit, so this is a very preliminary result,” adds Hippke in this NASA news release. “We’ve shown somewhat cautiously that it’s possible to detect Trojan asteroids, but we’ll have to wait for better data from TESS, PLATO and other missions to really nail that down.”

All of which tells us that we have much to expect from TESS and PLATO and the instruments that will subsequently home in on the targets they have provided. The papers are Hippke, “On the detection of Exomoons: A search in Kepler data for the orbital sampling effect and the scatter peak,” The Astrophysical Journal Vol. 806, No. 1 (abstract / preprint); Hippke and Angerhausen, “Photometry’s bright future: Detecting Solar System analogues with future space telescopes,” accepted at The Astrophysical Journal (preprint); and Hippke and Angerhausen, “A statistical search for a population of Exo-Trojans in the Kepler dataset,” accepted at The Astrophysical Journal (preprint).

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Pluto’s Circumbinary Moons

Kepler-47 is an eclipsing binary some 4900 light years from Earth in the direction of the constellation Cygnus. It’s a system containing two transiting circumbinary planets, meaning the planets orbit around the binary pair rather than around one or the other star. That configuration caught the eye of Simon Porter, a postdoc at the Southwest Research Institute, because the configuration is so similar to another circumbinary system, the one involving four small moons around Pluto/Charon. In both cases, we have a binary at the center of the orbit. Porter writes about the configuration in this post from the New Horizons team.

In the case of Pluto, the binary could be considered a binary planet, with Charon the other half of the duo. Both are orbited by a system of four moons, each of them less than 50 kilometers in diameter, the moons orbiting around the system’s center of mass. New Horizons, the gift that keeps on giving, has already sent some striking images of these small moons, but we have even better imagery yet to come as we continue to download data from the craft’s Long Range Reconnaissance Imager (LORRI), the high resolution camera that has given us so so many unforgettable images already. But I’ll open the week with an image not from LORRI but from the Multispectral Visible Imaging Camera, just to provide a sense of context and a bit of awe.

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Image: Pluto’s haze layer shows its blue color in this picture taken by the New Horizons Ralph/Multispectral Visible Imaging Camera (MVIC). The high-altitude haze is thought to be similar in nature to that seen at Saturn’s moon Titan. The source of both hazes likely involves sunlight-initiated chemical reactions of nitrogen and methane, leading to relatively small, soot-like particles (called tholins) that grow as they settle toward the surface. This image was generated by software that combines information from blue, red and near-infrared images to replicate the color a human eye would perceive as closely as possible. Credit: NASA/JHUAPL/SwRI.

Blue atmospheric haze in the Kuiper Belt is not something anyone was expecting. SwRI’s Carly Howett offers a read on what we’re seeing:

“That striking blue tint tells us about the size and composition of the haze particles. A blue sky often results from scattering of sunlight by very small particles. On Earth, those particles are very tiny nitrogen molecules. On Pluto they appear to be larger — but still relatively small — soot-like particles we call tholins.”

This JHU/APL news release has more, explaining current thinking that tholins form in the upper atmosphere as ultraviolet light breaks nitrogen and methane molecules apart, allowing them to form increasingly complex negatively and positively charged ions that recombine to form macromolecules. Small particles can grow out of the process, with volatile gases condensing to coat their surfaces before they fall back to the surface, adding to its reddish hue.

But back to the system of moons. The closest to New Horizons during the July encounter was Nix, of which LORRI has delivered three close-ups so far. Have a look at the object as, in the second view, it reveals its ‘potato-like’ aspect — the elongation is lost in the first image because we’re looking down the long axis. What stands out here is the size of that crater. Are we looking at a fragment of an older moon, as Porter speculates, or was Nix just lucky to have survived a shot that could leave a crater of that size on such a small surface? A crescent Nix shows up on the far right, which may yield information on the surface of the diminutive moon.

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Image: Pluto’s moon Nix is viewed at three different times during the New Horizons July 2015 flyby. Credit: NASA/JHUAPL/SwRI.

Now have a look at Nix as seen through the Ralph/Multispectral Visible Imaging Camera. Here we’re working with only a quarter of LORRI’s resolution, but we’ve got color now and can discern that most of Nix is white, while that provocative crater and the ejecta it produced show up as reddish. It’s a natural assumption that Nix’s interior is made up of much darker material than the surface. “We don’t actually know what either the dark or the light material is,” writes Porter, “nor will we be able to tell until we download the Nix data from the Ralph-Linear Etalon Imaging Spectral Array (LEISA) composition mapping spectrometer.”

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Image: Pluto’s moon Nix is shown in high-resolution black-and-white and lower resolution color. Credit: NASA/JHUAPL/SwRI.

Below is Hydra as seen through LORRI, with the caveat that this moon was on the other side of Pluto during close approach, so we don’t have the same level of resolution we had for Nix. Porter notes a certain similarity in aspect with another object that caught our attention this summer: Comet 67P/Churyumov-Gerasimenko, around which the ESA’s Rosetta spacecraft continues its operations. In both cases, we have the possibility of a low-speed collision which melded two originally separate objects. The images of Styx and Kerberos that we’ll get later in the year, by the way, should be of roughly the same resolution as this image of Hydra.

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Image: Pluto’s moon Hydra as seen from NASA’s New Horizons spacecraft, July 14, 2015. Credit: NASA/JHUAPL/SwRI

New Horizons also detected surface water ice on Pluto, with areas showing the most apparent water ice signatures corresponding to areas that appear red in other recent images of Pluto. Figuring out how water ice interacts with the reddish tholins is going to take some work.

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Image: Regions with exposed water ice are highlighted in blue in this composite image from New Horizons’ Ralph instrument, combining visible imagery from the Multispectral Visible Imaging Camera (MVIC) with infrared spectroscopy from the Linear Etalon Imaging Spectral Array (LEISA). The strongest signatures of water ice occur along Virgil Fossa, just west of Elliot crater on the left side of the inset image, and also in Viking Terra near the top of the frame. A major outcrop also occurs in Baré Montes towards the right of the image, along with numerous much smaller outcrops, mostly associated with impact craters and valleys between mountains. The scene is approximately 450 kilometers across. Note that all surface feature names are informal. Credit: NASA/JHUAPL/SwRI.

In addition to the sheer thrill of seeing places as tiny as Nix at some level of detail, not to mention the often startling and mesmerizing views of Pluto and Charon themselves, I note the fact that exoplanets have become so common that we can draw analogies from our catalogues to describe what we see in our own system, as Simon Porter did in his description of Pluto’s moons. The world has changed so much in the past twenty years of exoplanet hunting, meaning that our view of ourselves and our place in the universe has been much enriched, and we have a panoply of planetary configurations to draw on as we consider how solar systems are made.

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Exomoons: A Data Search for the Orbital Sampling Effect and the Scatter Peak

Exomoons continue to be elude us, though they’re under intense study. One detection strategy is called Orbital Sampling Effect, as explained in the article below. I’ll let Michael Hippke describe it, but the intriguing fact is that we can work with these methods using existing datasets to refine our techniques and actively hunt for candidates. Michael is a researcher based in Düsseldorf, Germany. With a background in econometrics, statistics and IT, he mastered data analysis at McKinsey & Company, a multinational management consulting firm. These days he puts his expertise to work in various areas of astrophysics, and most recently appeared here in our discussion of his paper on Fast Radio Bursts (see Fast Radio Bursts: SETI Implications?).

by Michael Hippke

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Our own Solar System hosts 8 planets (plus Pluto and other “dwarf planets”), but 16 large moons with radii over 1,000km. And we have detected thousands of exoplanets – planets orbiting other stars – but not a single exomoon. The question of their existence is interesting, as some exomoons might in fact be habitable. Lately, there has been some speculation that, overall, there might be more habitable moons than planets in the universe. Consequently, we really want to know more about moons!

Moons are, by definition, smaller than their host planets, and thus harder to detect. Various search methods have been proposed – with the HEK project (Hunt for Exomoons with Kepler), led by David Kipping, being the most prominent team. A novel, promising method has been developed by René Heller in 2014, dubbed the “orbital sampling effect” (OSE). As with exoplanet transits, this method stacks many (dozens or ideally hundreds) of planet transits, and searches for the signature of a moon in this stack. While planet transit shapes are rather simple, the moon curves turn out the be very complex.

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Image: A star with a transiting planet and its moon. The angled area shows the inclination of the moon orbit. Orbit positions beyond the dashed line are not undergoing transit, and are thus not observable.

In my recent work, I have processed data from the Kepler space telescope to search for this effect. I also worked with the “scatter peak,” an exomoon detection method described by Attila Simon (Konkoly Observatory, Hungary) and team in 2012. It is based on the fact that the geometrical exomoon configuration is very likely different during every exoplanet transit: On some transits, the moon might be ahead of the planet, on other transits behind it. When stacking many transits, at a given phase folded time, one gets a flux loss in some cases, and not in others. This results in increased scatter (photometric noise) when compared to out-of-transit times.

While the sole use of the scatter peak is problematic due to stellar noise, it can be used to confirm or reject certain signals. Not surprisingly, the struggle against stellar noise, instrumental jitter and other glitches has required the development of a complex statistical framework. While the Kepler data quality is at the very limit for exomoon hunting, a few very interesting results could be achieved.

The first result is sensitivity. What moons can we detect with Kepler and the OSE? Learning the answer to this will be useful for the assessment of future time-series photometry space missions, such as TESS or PLATO 2.0. With Kepler, the limit seems to be about 0.3 — 0.4 Earth radii for a moon to be detected, which is about the size of Ganymede. In many cases, where the host stars are dimmer, or noisier, only larger moons can be detected. Despite these limitations, my work shows that the OSE is a promising method, which will one day, with better data quality and/or processing, likely succeed and find moons!

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Image: The smallest radii detectable with the OSE in Kepler data are ~0.4 Earth radii. In many cases, the data and method only allows for the detection of larger moons. These are calculated limits, not real observations.

The second result is the ‘average moon’ effect. While no single moon could be detected, it is possible to “super-stack” a larger sample of planet-OSEs to estimate the average moon size in different samples. For very short-period planets with orbits shorter than about 15 days, no moons are seen. This is in agreement with stability arguments: The closer the planet to the star, the more the star “pulls” on the moon and tries to swallow it. The critical distance is not perfectly clear, but believed to be at ~15-day orbits. In my analysis, I find that the average moon signal comes up for periods over 35 days. In the sample of 35- to 80-day orbits, I find an average moon radius of about 2,000km (roughly like our moon). This estimate doesn’t tell how many planets actually have moons, or how many multiple moon systems are included in this average. It is for future studies (and telescopes) to determine this. But it is exciting that one can try.

The third result is about individual candidates. A small sample of planets shows prominent OSE-like signals justifying an in-depth analysis. It must be clearly said that, very likely, all of these will turn out to be false-positives. For some cases, it might even be possible to show that they cannot be moons, for example because some configurations are not stable over longer time frames. But this is not a bad result, for when we find false-positives, we can add the detection mechanism for these to our algorithm, and improve future searches.

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Image: Planet transit (straight line), moon effect due to the OSE (dashed line) and real datapoints (dots with error bars). In this case of Kepler-264b, the data are in favour of a moon interpretation, although this cannot be considered a detection, as detailed in the paper.

Personally, I would expect that the first moon(s) that will be found will be at the long (large/massive) end of exomoon distribution, as was the case for exoplanets. This comes from a selection bias: Large things are easier to see, and will thus be detected first. It will not mean that all moons are giants, as not all planets are Hot Jupiters (which were the first planets detected). Interesting times are ahead!

For more information, the paper is Hippke, “On the detection of Exomoons: A search in Kepler data for the orbital sampling effect and the scatter peak.” It has been accepted by the Astrophysical Journal for publication. A preprint is available.

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Large Exomoons Shown to Be Detectable

The search for sub-planetary scale features in other solar systems continues, with encouraging news from the Hunt for Exomoons with Kepler project. A moon around a distant exoplanet is a prize catch, but as we’ve also seen recently, scientists are weighing the possibilities in detecting exoplanetary ring systems (see Searching for Exoplanet Rings). Confirming either would be a major observational step, but exomoons carry the cachet of astrobiology. After all, a large moon around a gas giant in the habitable zone might well be a living world.

David Kipping (Harvard University) and colleagues at HEK have released a new study that tackles the question of how detectable exomoons really are. Published online today by the Astrophysical Journal, the paper examines 41 Kepler Objects of Interest, bringing the total number of KOIs surveyed by HEK thus far up to 57. The paper demonstrates that the process is beginning to move out of the realm of computer simulations and assumption-laden theory to actual data from Kepler. The paper’s goal is to determine how small a moon could be detected in each case given the kind of signatures that flag an exomoon’s presence.

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Image: After surveying nearly 60 exoplanets for moons, the HEK team have derived empirical limits for each world, demonstrating an ability to detect even the smallest moons capable of sustaining an Earth-like atmosphere (“Mini-Earths”) for 1 in 4 cases studied. Whilst a confirmed discovery remains elusive, the painstaking survey of 60 planets spanning several years reveals what is possible with current technology. Credit: The Hunt for Exomoons with Kepler (HEK) Project.

An examination of an exoplanet that does not turn up an exomoon thus leads to a statement of how massive a moon has been excluded by the current data, which means the team is learning much about the sensitivity of its methods. From the paper:

… based on empirical sensitivity limits, we show for the first time that the HEK project is sensitive to even the smallest moons capable of being Earthlike for 1 in 4 cases (after accounting for false-positives). In terms of planet-mass ratios, we find even that the Earth-Moon mass-ratio is detectable for 1 in 8 of cases, posing a challenge but not an insurmountable barrier. Mass ratios of ? 10?4, such as that of the Galilean satellites, have never been achieved. However, if Galilean-like satellites reside around lower-mass planets than Jupiter, of order ? 20 M?, then we do find sensitivity, as demonstrated by the limit of 1.7 Ganymede masses achieved for Kepler-10c.

This is encouraging news, for the team can now make statements about the actual mass of a detectable exomoon. In 1 of 3 planets surveyed, an exomoon with Earth’s mass is detectable. Kipping believes that we can move down to the smallest moon thought capable of supporting an Earth-like atmosphere and still detect it in 1 of 4 of the cases studied. No exomoons have yet been detected but we are learning just what our capabilities are. Says Kipping:

“Here we report on our null results and the first estimate of empirical sensitivities. Ultimately, we would like to actually discover a clear signal and are pursuing some interesting candidates we hope will pan out. Either way though, I like to recall what the Nobel Prize winning American physicist Richard Feynman said about science: ‘Nature is there and she’s going to come out the way she is, and therefore when we go to investigate it we shouldn’t pre-decide what it is we’re trying to do except to find out more about it’.”

HEK_Sensitivity_MassRatios

Image: The Moon has about 1% the mass of the Earth posing a challenge for the HEK team, since such configurations are detectable for 1 in 8 planets surveyed. The much larger Pluto-Charon mass-ratio of 11.6% is much more detectable. Credit: Hunt for Exomoons with Kepler Project.

No exomoons turn up in the 41 KOIs surveyed in the study, with four, KOI-0092.01, KOI-0458.01, KOI-0722.01 and KOI-1808.01, showing up as false positives for an exomoon. Stellar activity is a likely cause, as the paper comments:

When dealing with a handful of transits, quasi-periodic distortions to the transit profile, such as those due to spots… can be well fitted by the flexible exomoon model. However, since an exomoon is not the underlying cause, this model lacks any predictive power and thus should fail F2a [a follow-up test described in the paper]. We therefore suggest that stellar activity is likely responsible for these four instances.

KOI-1808.01, in fact, passes the basic criteria for an exomoon detection, but the paper explains that the observed transit signal is distorted by the effects of star spots. Transit timing variations observed at KOI-0072.01 (Kepler-10c) seem to point to an additional planet in the system rather than an exomoon.

Thirteen of the KOIs produce some kind of spurious detection, assigned by the paper to effects like perturbations from unseen bodies, stellar activity or instrumental artifacts. Through the range of KOIs the project has studied thus far (57), 46 null detections are found from which upper limits on an exomoon’s mass can be derived. The paper reminds us that “…exomoons live in the regime where correlated noise is present and one must employ methods to guard against it when seeking such signals.”

The declared purpose of the Hunt for Exomoons with Kepler project is to ‘determine the occurrence rate of large moons around viable planet hosts,’ a task with implications for the abundance of life in the universe, for if habitable moons are common, there could be more of them than habitable planets, and conceivably more than one orbiting a single planet. An additional benefit of studying exomoons is that they can teach us about solar systems formation by showing us planet/moon systems in a variety of configurations.

The paper is Kipping et al., “The Hunt for Exomoons with Kepler (HEK): V. A Survey of 41 Planetary Candidates for Exomoons,” submitted to the Astrophysical Journal (preprint).

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Searching for Exoplanet Rings

Not long ago we looked at the discovery of what appears to be a disk orbiting the huge gas giant J1407b (see Enormous Ring System Hints of Exomoons). The example of Saturn is one thing that makes us wonder whether rings might exist around exoplanets, but of course in our own Solar System we also have Jupiter, Uranus and Neptune as hosts of ring systems of different sizes. In the case of J1407b, we’re not strictly sure that the object is a planet. If it’s actually a brown dwarf, we might be observing a protoplanetary disk in a young system.

I’m not surprised when it comes to looking for ring systems around exoplanets that David Kipping (Harvard-Smithsonian Center for Astrophysics) should be in the mix. Working with Jorge Zuluaga (University of Antioquia) and two of their students, Kipping is co-author of a paper discussing how we might identify what are now being called ‘exorings.’ As illustrated in the figure below, an exoplanet’s transit signature is a key, taking advantage of the fact that a planet with a ring system will produce a longer, deeper transit than the same planet without any rings.

RingTransit

Image: Schematic representation of the transit of a ringed planet in front of its star. When compared with the light curve of an non-ringed analogue (dashed line) the transit of a ringed planet is deeper (the relative flux diminishes by a larger fraction) and longer. Credit: Jorge Zuluaga/David Kipping.

The trick here is to separate the effect of a larger planet seen in transit from a smaller world with a ring system. The paper explains that in transit studies, objects that appear larger than expected are often classed as false positives, a category that the authors think merits a careful look in case what is being rejected is actually a planet with a ring system. From the paper:

The transits of a Saturn-like ringed-planet are up to ?3 times deeper than that expected for a spherical non-ringed one. These deep transits will be interpreted as produced by a planet ?1.7 times larger. Additionally, if independent estimations of its mass were also available, the density of the planet will be underestimated by a factor of ?5. Thus, instead of measuring Saturn’s density ?0.7 g/cm3 , this planet would seem to have an anomalously low density of ?0.14 g/cm3 . Even under more realistic orientations (cosiR ? 0.2) the observed radius will be ?20% larger and the estimated density almost a half of the real one.

It is conceivable, then, that some ‘false-positive’ transits conceal a population of planets with rings.

An effect based on asterodensity profiling that the authors call the ‘photo-ring’ effect also comes into play. Here we examine the transit depth and its duration. The first is related to the size of the star, while the second depends on orbital velocity and the mass of the star. Out of this information we can estimate the star’s density, a result that can be compared with independent density calculations from methods like asteroseismology or the transits of other planetary companions to see if the results coincide. A discrepancy may be telling: The presence of rings around the transiting world, the authors argue, leads to an underestimation of stellar density.

Interestingly, the two effects we seek (anomalous transit depths and photo-ring effect) are complementary with respect to the orientation of the ring plane. For large inclinations and obliquities (face-on rings), the effect on transit depths is significant whilst the photo-ring effect is negligible. Alternatively, if rings have relatively low obliquities (edge-on rings), then the photo-ring effect will be considerable but the depth anomaly small.

PhotoRing

Image: Magnitude of the so-called Photo-ring effect predicted by Zuluaga, Kipping et al., at different projected inclinations and tilts (small “saturns”). Credit: Jorge Zuluaga/David Kipping.

The strategies that emerge from this study are thus complementary. We can look for already confirmed transiting planets that appear to have anomalously low densities for further study. We can also reinvestigate our catalog of false-positives due to anomalously large transit depths to see if any of these could mask a ringed planet’s signature. Finally, we can search for transit signals that show the ‘photo-ring’ effect, looking for discrepancies in density calculations.

None of this implies that studying transit lightcurves itself does not remain significant:

We stress that the method presented here is complementary to the methods developed to discover exorings through detailed light curve modelling (Barnes & Fortney 2004; Ohta et al. 2009; Tusnski & Valio 2011). As explained earlier, the role of these methods will be very important once a suitable list of potential exoring candidates [is] found. It is, however, also important to note the great value of light curve models developed under the guiding principle of computational efficiency (semianalytical formulae, efficient numerical procedures, etc.), such as the basic models presented here.

We thus have a relatively straightforward technique for surveying our transiting planet catalogs for ringed-planet candidates, looking for that subset that can be subjected to more detailed lightcurve analysis. The paper is Zuluaga et al., “A Novel Method for Identifying Exoplanetary Rings,” accepted for publication at Astrophysical Journal Letters (preprint).

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