Tag Archives: kepler

Shifting Eclipses – K2’s Second Multi-planet System

On March 20th this year, the moon will pass between Earth and the Sun sending a slither of Northern Europe into darkness. For those in the UK, this partial eclipse will be the most impressive eclipse until three minutes of totality at 4:56pm on September 23rd, 2090. Calculating something so far ahead seems like an impressive feat but in fact astronomers can precisely work out exactly when and where eclipses will occur for not just the next hundred, but the next million years. Such is the way for most transiting exoplanets too, the calculations for which could probably be valid in thousands of years.

477859main_KeplerSinglePanelStill[1]But a new planetary system, discovered by a team that includes Warwick astronomers (including me), doesn’t yet play by these rules. It consists of two planets orbiting their star, a late K star smaller than our sun, in periods of 7.9 and 11.9 days. The pair have radii 7- and 4-larger than Earth, putting them both between the sizes of Uranus and Saturn. They are the 4th and 5th planets to be confirmed in data from K2, the rejuvenated Kepler mission that monitors tens of thousands of stars looking for exoplanetary transits. (36 other planet candidates, including KIC201505350b & c, have been released previously).

But it is their orbits, rather than planetary characteristics, that have astronomers most excited. “The periods are almost exactly in a ratio of 1.5” explains Dave Armstrong, lead author of the study. This can be seen directly in how the star’s brightness changes over time. This lightcurve appears to have three dips of different depths, marked here by green, red and purple dips. ”Once every three orbits of the inner planet and two orbits of the outer planet, they transit at the same time”, causing the deep purple transits.

K2 Paper Lightcurve

But this doesn’t just make for an interesting lightcurve; the closeness of these periods to a 3/2 ratio also causes other weird effects. “The planets perturb each other and change their period every orbit, so they never quite transit when you expect”, explains Arms. These shifts are called Transit Timing Variations (or TTVs).

An Example of TTVs in a 2-planet system
TTVs in a 2-planet system (credit: Eric Ford)

The size of these TTVs is related to the mass of the planets, and some previous multi-planet systems have been weighed in this way. When the team went back to observe the larger planet less than 9 months later, they found that the transit time had shifted by more than an hour. And their period ratio of 1.5035 means the resulting TTVs are likely to continue increasing over a few years, potentially shifting the system more than a day from it’s current rhythm.

These TTVs also help prove that the planets are real. Their presence means that both objects are interacting with each other, so the planets must orbit the same star rather than being, say, two different background binaries. The team also used these shifts in transit time to constrain the planet masses, showing them to be less than 1.2 and 2.04 times that of Jupiter.

rvgif2[1]Not only is this one of the most interesting multi-planet systems yet discovered by Kepler, it is also one of the brightest (12th magnitude), making ground-based follow-up much easier than many Kepler systems. Most interestingly, precise spectrographs like HARPS and SOPHIE will be able to measure the tiny to-and-fro shift in the star’s velocity caused by the gravitation pull of planet on the star. This radial velocity would give a precise mass for the planets in the system and for the first time allow masses found by TTVs to be directly compared to those from RVs.

Fomalhaut_planet_341px[1]Examples of 3:2 resonance can be found everywhere in planetary science, including between Pluto & Neptune’s orbits, in the Kirkwood gap of the Asteroid Belt, and even between the planets around pulsar PSR1257+12. It is also thought that Jupiter and Saturn may have, at one point, become caught in a 3:2 resonance as they migrated inwards. This scenario, of planets caught in 3:2 resonance migrating inwards, could explain how these two sub-Jupiter sized planets came to be in such an unusual orbit.

These two planets could also help settle other dilemmas. “We’d like to answer questions like ‘Did they form there?’, ‘Did they migrate there and get stuck?’ and ‘will they eventually get ejected from the system, or crash into the star?’” suggests Armstrong. The best way to do this is simply by watching future transits and monitoring just how in-sync the planets really are. And maybe one day we could even begin to predict their eclipses as confidently as we can with those happening here on Earth.


The paper, submitted to A&A, can be found on ArXiV here. My work on the paper involved developing the tools to find the transiting planets in the K2 lightcurve.

Kepler’s Last Stand: Verification by Multiplicity

TNG_LaPalmaFor 3 months a year, the TNG telescope on the island of La Palma turns its high-precision spectrometer (HARPS-N) towards the constellations of Cygnus and Lyra. This is the field of view that NASA’s Kepler space telescope stared at for more than 3 years, detecting thousands of potential new exoplanets using the transit method. There the TNG scans hundreds of Kepler’s potentially planet-holding stars looking for tiny changes in their radial velocity. If detected, this signal will indicate the presence of a real planet, confirming once and for all what Kepler first hinted at many months before. This is the process that, up until now, has been used to definitively find the majority of Kepler’s 211 planets.

New ‘discoveries’ in context

That appeared to change in the blink of an eye this week with the confirmation of 715 new planets using a new catch-all statistical technique. But how did the Kepler team confirm all these new worlds, and can they really be considered real planets?

Without further observations with instruments such as HARPS, Kepler’s 3000 planetary candidates cannot usually be called definite planets. This is because a number of other signals could mimic the transit signal of a star, including tightly bound double-stars that graze one other as they orbit, or unseen dim stars that have binary companions. Alternatively the cameras themselves could be acting up, producing periodic, transit-like signals in the data. Last year a team used simulations of the Kepler data to estimate that around 10% of the candidates were likely to be such false positives.

Kepler Candidates by size

So how can more than 700 worlds be confirmed at once, without any manual work from telescopes on the ground? The answer is through performing statistics on Kepler’s planets. Of a zoo of 190,000 stars observed, Kepler discovered 3000 potential planets, of which 10% are likely to be spurious signals. As a rough estimate then (and the Kepler team go into much more effort than this), the random probability of finding a false positive is 300/190,000, or a rate of only 0.16%.

That number on its own cannot help confirm planets. The trick comes when thinking about Kepler’s hundreds of multiple planet systems. The likelihood of a single-planet system randomly having another false positive also in the data is extremely low. In fact, applying that rough number to the 1000 best single-planet candidates tells us only around 2 of those multiplanet systems should have a spurious planet. Similar calculations can be done for even rarer systems with two false positives, two planets and a false positive, etc.

Possible False Positve Signals

This rate can also be significantly improved by excluding any targets more likely to give these spurious signals. For example, the authors removed more than 350 potential planets from the initial sample for many reasons. Some had instrumental artefacts seen in other stars or had transits close to the limit of detection. Others with V-shaped transits were eliminated as these are more likely to be grazing binary stars. The team also studied the images Kepler took to check for possible transits on a secondary star, eliminating anything where the transit did not in the star’s central position.

Using these cuts, the study narrowed down the search to 851 planets around 340 stars. Applying statistics and using the estimate that 10% of currently detected planets might be false positives, the team found that 849 of the 851 planets were likely to be planets. This corresponds to a certainty of 99.8%,  just greater than 3σ, which in astronomy is usually enough to constitute a detection. This is how “verification by multiplicity” works.

Confirmed Kepler Planets by Size

Of these, 715 are previously un-confirmed worlds. Nearly all are relatively small planets, with radii going from the same as Earth up to that of Neptune. Four of these new planets may also reside in their star’s habitable zone, the region where liquid water could exist on the surface.

As amazing as it would be to nearly double the number of exoplanets overnight, some doubts remain about this method. By eliminating astronomical follow-ups, no extra information can be gleaned. For example, without performing radial velocity measurements, the mass of these planets will never be known. And without other accurate astronomical studies, we cannot accurately determine the nature of the star, and therefore the radius of the planet.

The main difference, though, comes from the impersonal nature of verification by multiplicity. Previous confirmation methods assessed the probability of each candidate being a planet individually. By performing the confirmation in bulk we will know, thanks to the statistics, that at least 2 planets are imposters*. But if exoplanet astronomers can learn to live with that doubt, such planets may well be accepted as confirmed worlds and this simple idea will see the single biggest influx of validated exoplanets in history.

* Here’s another way to compare those statements. Imagine you have two pills. One produces a 0.2% chance of death. The other causes the loss of two fingers (0.2% body mass). By adding these planets to the list of exoplanets, we may well gain a whole new body of worlds, but there will be painful amputations to come in the future.

The two papers, which will be released on March 10th in ApJ, can be found here (Lissauer, 2014) and here (Rowe, 2014).

UPDATE: The new planets are proving reasonably contentious. The exoplanet counter on NASA’s planetquest sits at 1690 , wheras the Paris-based exoplanet.eu remains on 1078. Time will tell whether astronomers accept these as true planets or simply string candidates.

What can PLATO do for exoplanet astronomy?

As readers of my previous post will no doubt know; the future looks grim for exoplanetary science. Kepler is dead, Hubble will soon follow and we face a long wait before the next generation of planet-hunting instruments. But this week, exoplanet astronomers glimpsed another ray of hope. The next £500million of European Space Agency money looks likely to go to PLATO; an incredible exoplanet-hunting mission set to be even better than Kepler.


With an array of 34 telescopes mounted on a sun-shield, PLATO hopes to do things a little differently from both Kepler and TESS. Like those missions, it too will monitor thousands of stars looking for the minute dip in light caused by the passage of a planet in front of its parent star. However, it is in both breadth and depth that PLATO excels; with the combined light of dozens of cameras allowing 5% of the sky to be monitored to incredible accuracy at any one time.

Plato’s likely field of view, with 2-3yr stops in red

More than a million stars could be scrutinised for Earth-sized planets by Plato, giving an expected planet haul an order of magnitude higher than Kepler. Plato will also not be tied down into staring at the same stars, instead monitoring 50% of the sky on eight 30-day positions and two longer 3-year fields. This will allow dozens of Earth-like planets with potentially habitable temperatures to be discovered.

The main criticism of the now-defunct Kepler mission was the faintness of these stars (between magnitude 7 and 17). This meant the vast majority of its planetary candidates were impossible to follow up and confirm. The wide field and large array of cameras on Plato allow the brightest stars to be monitored (mag 4-16). That will mean even tiny Earth-sized worlds found by Plato can be followed up and confirmed by ground-based telescopes.

The concept of Astroseismology

This ability to survey bright stars also allows astronomers to perform extremely sensitive measurements of the stars themselves. By using variations in starlight caused by ripples on the star’s surface, astronomers can accurately pin down not only the size of the star but also the age of the star system. This means, not only can Plato find exoplanets around bright stars, but it can also determine the size and age of many of these planets to a precision only previously dreamed of.

The Transiting Exoplanet Survey Satellite (TESS), to launch in 2017, seems superficially to be a similar mission to Plato. It will potentially discover hundreds of planets before Plato even gets off the ground in 2024. However, the limited sensitivity of its cameras mean it is completely blind to Earth-like worlds around sun-like stars. Astroseismology is also off-limits for TESS, meaning the size of any worlds it does discover will be highly uncertain. Unlike Plato, it will also move between patches of sky every 30 days, allowing only hot, short-period planets to be found.

The only truly habitable planet yet known

With all other new telescopes, both in space and on the ground, limited to finding super-Earths around small stars, Plato is the only mission on the table truly capable of discovering an Earth-like world around a star like our Sun. And by targeting bright stars that allow atmospheric follow-up, it is not impossible to think that, as well as the first truly habitable planet, Plato could find the first inhabited one too.

However, the decision process for ESA’s Cosmic vision (M3 class) is still ongoing. It would be highly unusual for ESA member states to overturn the mission recommended by the science committee, but in the political cauldron that is ESA anything is possible. If Plato does get through unscathed, it will bring riches not just to the universities, countries and industries involved, but more significantly to the world of science as a whole.


The paper detailing mission design and expected science results can be found at: http://arxiv.org/abs/1310.0696 . The official ESA mission page has similar information at: http://sci.esa.int/plato/

A comparison of Kepler Candidate planets (the majority of which are too faint for follow-up observations) against likely PLATO candidates (significantly brighter, eg with a lower magnitude)

The hunt for an exo-Earth: How close are we?

This blog was first published as a guest post on Andrew Rushby’s excellent II-I- blog.


In the 1890s Percival Lovell pointed the huge, 24-inch Alvan Clark telescope in Flagstaff, Arizona towards the planet Mars. Ever the romantic, he longed to find some sign of life on the Red Planet: To hold a mirror up to the empty sky above and find a planet that looked a little bit like home. Of course, in Lovell’s case, it was the telescope itself that gave the impression of life, imposing faint lines onto the image that he mistook for canals. But, with Mars long since relegated to the status of a dusty, hostile world, that ideal of finding such a planet still lingers. In the great loneliness of space, our species yearns to find a world like our own, maybe even a world that some other lineage of life might call home.

A hundred years after Lovell’s wayward romanticism, the real search for Earth-like planets began. A team of astronomers at the University of Geneva used precise spectroscopy to discover a Jupiter-sized world around the star 55-Peg. This was followed by a series of similar worlds; all distinctly alien with huge gas giants orbiting perishingly close to their stars. However, as techniques improved and more time & money was invested on exoplanet astronomy, that initial trickle of new worlds soon turned into a flood. By 2008 more than 300 planets had been discovered including many multi-planet systems and a handful of potentially rocky planets around low-mass stars. However, the ultimate goal of finding Earth-like planets still seemed an impossible dream.


In 2009 the phenomenally sensitive Kepler mission launched. Here was a mission that might finally discover Earth-sized planets around Sun-like stars, detecting the faint dip in light as they passed between their star and us. Four years, 3500 planetary candidates and 200 confirmed planets later, the mission was universally declared a success. Its remarkable achievements include a handful of new terrestrial worlds, such as Kepler-61b and 62e, orbiting safely within their star’s habitable zones. However, despite lots of column inches and speculation, are these planets really the Earth 2.0s we were sold?

Even more damning is the size of these planets. Rather than being truly Earth-like, the crop of currently known ‘Habitable planets’ are all super-Earths. In the case of Kepler’s goldilocks worlds, this means they have radii between 1.6 and 2.3 times that of Earth. That may not sound too bad, but the mass of each planet scales with the volume. That means, when compression due to gravity is taken into account, for such planets to be rocky they would need masses between 8 and 30 times that of Earth. With 10ME often used as the likely limit of terrestrial planets, can we really call such planets Earth-like. In fact, a recent study of super-Earths put the maximum theoretical radius for a rocky planet as between 1.5 and 1.8RE, with most worlds above this size likely being more like Mini-Neptunes.

So it appears our crop of habitable super-Earths may not be as life-friendly as previously thought. But it is true that deep in Kepler’s 3500 candidates a true Earth-like planet may lurk. However the majority of Kepler’s candidates orbit distant, dim stars. This means the hope of confirming these worlds by other techniques, especially tiny exo-Earths, is increasingly unlikely. And with Kepler’s primary mission now ended by a technical fault, an obvious question arises: just when and how will we find a true Earth analogue?

Future exoplanet missions may well be numerous, but are they cut out to discover a true Earth-like planet? The recently launched Gaia spacecraft, for example, will discover hundreds of Gas Giants orbiting Sun-like stars using the astrometry technique, but it would need to be around a hundred times more sensitive to discover Earths. New ground-based transit surveys such as NGTS are set to be an order of magnitude better than previous such surveys, but still these will only be able to find super-Earth or Neptune-sized worlds.

TESS_satellite (1)

Similarly, Kepler’s successor, the Transiting Exoplanet Survey Satellite which is due to be launched in 2017, will only be able to find short-period planets with radii more than 50% larger than Earth. HARPS, the most prolific exoplanet-hunting instrument to date, is also due for an upgrade by 2017. Its protégée is a spectrometer named ESPRESSO that will be able to measure the change in velocity of a star down to a mere 10cms-1. Even this ridiculous level of accuracy is not sufficient to detect the 8cms-1 effect Earth’s mass has on the Sun.

While such worlds may well have surfaces with beautifully Earth-like temperatures, there are a number of problems with calling such worlds definitive Earth twins. For a start the majority of these potentially habitable planets (such as Kepler-62e) orbit low-mass M and late K-type stars. These are dimmer and redder than our Sun and, due to the relative distance of the habitable zone, such planets are likely to be tidally locked. The nature of such stars also makes them significantly more active, producing more atmosphere-stripping UV radiation. This means, despite appearances, ‘habitable’ planets around M-dwarfs are almost certainly less conducive to life than more sun-like stars.


So despite billions spent on the next generation of planet-finders, they all fall short of finding that elusive second Earth. What, precisely, will it take to find this particular Holy Grail? There is some hope that the E-ELT (European-Extremely Large Telescope), with its 35m of collecting area and world-beating instruments will be able to detect exo-earths. Not only will its radial velocity measurements likely be sensitive enough to find such planets, it may also be able to directly image earth-analogues around the nearest stars. However, with observing time likely to be at a premium, the long-duration observations required to find and study exo-earths could prove difficult.

Alternatively, large space telescopes could be the answer. JWST will be able to do innovative exoplanet research including taking direct images of long-period planets and accurate atmospheric spectra of transiting super-Earths and giants. Even more remarkably, it may manage to take spectra of habitable zone super-Earths such as GJ 581d. But direct detection of true Earth-analogues remains out of reach. An even more ambitious project may be required, such as TPF or Darwin. These were a pair of proposals that could have directly imaged nearby stars to discover Earth-like planets. However, with both projects long since shelved by their respective space agencies, the future doesn’t look so bright for Earth-hunting telescopes.

After the unabashed confidence of the Kepler era, the idea that no Earth-like planet discovery is on the horizon may come as a surprisingly pessimistic conclusion. However not all hope is lost. The pace of technological advancement is quickening. Instruments such as TESS, Espresso, E-ELT and JWST are already being built. These missions may not be perfectly designed to the technical challenge of discovering truly Earth-like planets, but they will get us closer than ever before. As a civilisation we have waited hundreds of years for such a discovery; I’m sure we can hold out for a few more.

Gaia: Planets and Parallax

In six hours’ time, A Soyuz rocket will blast of from Guyana with the hope of delivering a €1billion Christmas present to astronomers across the world. That present will be Gaia, ESA’s flagship science mission, which hopes to revolutionise how we look at the galaxy around us by providing a 3D map of a billion stars and finding hundreds of new exoplanets.


So what is Gaia? It is essentially the most sensitive camera ever to be pointed at the heavens. That may sound the same as most space telescopes, but its specifications mean it will be able to pinpoint the location of stars with accuracy previously only dreamed of. Using a 1.5m mirror and a Gigapixel CCD camera, it will image more than a billion stars at least 70 times over a 5 year mission to provide the most accurate catalogue of stars in the Milky Way ever seen.

It is not the sensitivity of the telescope that is extraordinary, however, but rather its angular resolution. Consider the previous such mission, Hipparcos. It was capable of resolving objects tens of thousands of times closer together than the human eye, for example even from 200km away, it’s camera was capable of spotting two lights placed only a millimetre apart. This corresponds to the order of milliarcseconds, or 1/3600000th of a degree. Gaia, on the other hand, will be able to resolve stars mere microarcseconds apart. That is equivalent to being able to read 20pt text from 30,000km above Earth, or resolving two bright lights only 170m apart at the distance of Pluto.

Astronomical Parallax

What this amazing technological shift means is that Gaia will not only be able to compile the most accurate catalogue of star positions in history, it will also be able to map them in 3D. It may seem strange, but measuring the distance to a far-away point source like a star is nearly impossible. For nearby stars the shift of Earth’s position during the course of the year can act as a sort of cosmic depth perception, with the location of nearby stars wobbling subtlety between July and January, depending on how far away they are. It is this Parallax effect that, thanks to the incredible resolution of Gaia, will enable the distance to 1% of the stars in our galaxy to be precisely measured.


But when this effect due to the motion of Earth is corrected for, what motion is left? It’s likely the star will be moving in some direction through the galaxy relative to our solar system. This straight-line speed is the star’s ‘proper motion’ and can be as high as 10.3 arcsecs per year. But that’s not the only thing Gaia might spot. Stars are also tugged at by the gravitational pull of all nearby objects. This is most prominently done by planets in the stars vicinity. For example, an observer 30 lightyears away would see the sun shift by nearly 500µas due to the orbit of Jupiter. That means Gaia would see the Sun perform a slow ellipse across the sky every 5 years each time Jupiter orbits.

Planets Gaia can detect bounded in Blux lines. Upper line: Sun-like star. Lower line: M-dwarf

The biggest signals come from Gas Giant planets circling far from their stars, and Gaia will be able to search the nearest 400,000 stars for such worlds. Due to its 5-year mission, it will find these Jupiter analogues between 1 and 4AU. With any luck, more than 1000 candidates will be found; potentially doubling the current crop of exoplanets. And with Kepler dead and TESS still on the drawing board, Gaia may well become our best tool to mine the skies for new planets.

Even more interesting for exoplanet astronomers is that Gaia will find planets missed by other detection techniques. Both the transit and radial velocity methods are more sensitive to close-in planets, and have such discovered hundreds of bloated Hot Jupiters circling close to their star. Gaia, on the other hand, will be able to scan regions much further from the star. This will potentially answer the question of whether these Hot Jupiter systems are common or if other solar systems are more like our own stellar back

Another remarkable feat that Gaia will be able to achieve is pinning down the exact mass of some exoplanets. Worlds discovered by radial velocity give us an estimate of their size based on the to-and-fro motion of the star due to planets. Astrometry by Gaia will be able to give the side-to-side motion and determine in what precise inclination the planets are in. By tying down the planets orbit like this, their mass can be precisely determined.


Gaia, if successfully launched in the next few hours, will be capable of incredible feats. First and foremost, it’s incredible parallax measurements will turn astronomy from a two-dimensional star map into a complex three dimensional system where the distances to almost every object is known precisely. And tagged on for free are another thousand potential exoplanets to add to the exponentially growing list of alien worlds! If all goes well in Guyana at 9am, a collective sigh of relief will emanate from astronomers worldwide, and it might just signal the start of a new era of astronomy.

Infographic on Gaia:


A Planet for Every Star?

Astronomers have now found an astonishing 1000 exoplanets. But that pales in comparison to the 100 billion stars in our galaxy. So how can we say whether planets are the norm? And is it possible to find a star that is definitively a planet-free zone?

The current crop of alien worlds comes from a limited selection of well-studied stars. Rather than try to directly spot what is the equivalent of a fleck of dust in a spotlight, astronomers use changes in the light of the star itself to tease out the signal of a planetary companion.


This can be done in a variety of ways, each of them with their own shortcomings. Often the method of discovery itself means that only a tiny selection of flukily-aligned planets will have the potential of being discovered.

For example, the Kepler spacecraft was staring at over 100,000 stars to try to detect the drop in light as exoplanets crossed their star. However, the probability of the average planet making this crossing is extraordinarily low. A planet orbiting at 1AU (the same distance from its star as Earth) will be found in only 1 in 200 such systems! To put that in perspective; for each Earth-like planet found by Kepler, 199 more stars with planets exactly like our own will have been be tossed aside.


The other common detection technique, known as radial velocity, is marginally less wasteful. This uses the to-and-fro of the star imprinted in the colour variations (or spectra) to find the delicate gravitational tug of a planet. While this works for planets in most orbits, if they happen to circle their star in a face-on orientation, no signal will be received at all. For both cases, this means that even if no planetary signal is detected at all, we can’t definitively say there isn’t one there.

These techniques are also only sensitive to planets larger than a certain size. While the Kepler mission was able to find Earth-sized worlds, similar transit surveys from the ground will only ever be able to find large Gas Giants. Any Mars or Mercury-sized planets will be missed entirely. Radial Velocity is also limited by size, with Neptune or Super-Earth-sized worlds the current limit. These searches are both also bias towards planets close to their stars. To detect worlds at Earth distances is a much trickier prospect than those scraping the surface of their stars.

So many planets will be missed entirely. How can we talk with any certainty about the number of planets in the whole Galaxy?


Well, because the exact problems with these techniques are known, astronomers can estimate how many planets we expect to find. If we know the number of stars studied and the probability of an orbit being perfectly aligned, we can use the number of planets found to estimate the number of planets around all stars.

For example, a study of gravitational lensing by planets showed that on average every star has a planet larger than 5 Earth Masses from 0.5 to 10AU. Similar studies have also been done with Kepler, finding basically the same number: More than one planet bigger than Earth from 0 to 2AU around every star. It should also be noted that these results also only cover a tiny portion of potential planets. Distant Jupiters or low-mass rocky planets were missed completely. So, as our searches become more and more sensitive to small and distant worlds, those numbers can only go up. It’s likely that on average every star in the Milky Way has its own Solar System with multiple planets.

But what about lonely, planet-less worlds? There are certain to be stars without any planetary material wandering the cosmos. For example, those dislodged from triple-star systems, as can happen due to gravitational resonance and scattering, might not hold onto any planetary material. But until we’re able to study a star in perfect detail and definitively say no planets exist, we are forced to stick with what has become the default setting: all stars have planets, and it’s just a matter of time until we find them.