# TRAPPIST 1 and planet statistics?

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From what I understand, the TRAPPIST 1 system was discovered using the transiting method looking at 20 ultra-cool small stars. I'm not sure how many have been observed since this study.

What I wonder is, what would we expect to see if all 20 had planets? I'm not sure how many planetary systems in this and future similar studies we would expect to see edge on. What about radial velocity measurements?

Did we just get lucky with TRAPPIST 1?

The probability of observing a planet transit is approximately $(R_p + R_s)/a$, where $R_p$ and $R_s$ are the planet and stellar radius respectively and $a$ is the semi-major axis of the planet's orbit. This assumes that planetary orbits are circular and randomly oriented with respect to our line of sight to the star (for which there is little or no counter-evidence).

In the case of Trappist-1, it has an estimated radius of $R_p=0.11R_{odot}$, the planetary companions have radii and semi-major axes of (in units of Earth radii and au respectively) (1.09,0.011), (1.06, 0.015), (0.77,0.021), (0.92,0.028), (1.05, 0.037), (1.13, 0.045), (0.75, 0.059).

Using approximation above, then the transit probabilities are 0.051, 0.037, 0.026, 0.020, 0.015, 0.012, 0.009 respectively.

Now these probabilities cannot be treated as independent of one another, since it is quite likely (though this is still the subject of research) that planets will naturally tend to inhabit the same orbital plane (the Trappist-1 planetary orbit inclinations are within 0.2 degrees of each other - flatter than the solar system). Thus you are much more likely to see second and subsequent transits in a system with one transiting planet than you are in a star picked at random. On the other hand, a system with lots of planets that are not quite in the same orbital plane gives an increased chance of seeing one of them transit.

Either way, you can see from the probabilities above that seeing one and only one transiting system of this type from 20 targets, even if all of them had similar planetary systems, is not at all unexpected.

Radial velocity studies of such systems are difficult, but currently being attempted. Trappist-1 has an apparent J magnitude of 11.4, which is very challenging for current telescopes and instrumentation to get high resolution spectroscopy.

## Celestia Forums

NASA has just announced that in the TRAPPIST-1 system there are 7 Earth-sized planets and 3 of them are in the habitable zone.

TRAPPIST-1A - the star
Name 2MASS J23062928-0502285
Alternate name TRAPPIST-1
Right ascension α = 23h 06m 29.28s
Declination δ = -05º 02' 28.5''
Constellation Aquarius
Apparent magnitudes V = 18.80 ± 0.08, R = 16.47 ± 0.07,
I=14.0 ± 0.1, J = 11.35 ± 0.02, K = 10.30 ± 0.02
Parallax 82.58 ± 2.58 mas
Distance 12.1 ± 0.4 pc
Mass 0.080 ± 0.007 M☉
Density 50.7 -2.2+1.2 ρ☉
Effective temperature 2559 ± 50 K
Luminosity 0.000525 ± 0.000036 L☉
Metallicity [Fe/H] +0.04 ± 0.08
Age > 500 Myr

TRAPPIST-1b
Orbital period 1.51087081 ± 0.00000060 days
Mid-transit time 2 457 322.51736 ± 0.00010 (Julian Date)
Transit depth 0.7266 ± 0.0088
Scale parameter (a/R★) 20.50 -0.16+0.31
Impact parameter 0.126 ± 0.085 R☉
Transit duration 36.40 ± 0.17 minutes
Orbital inclination 89.65 ± 0.25º
Orbital eccentricity < 0.081
Semi-major axis 0.01111 ± 0.00034 AU
Mass 0.85 ± 0.72 M⊕
Density 0.66 ± 0.56 ρ⊕
Equilibrium temperature (A=0) 400.1 ± 7.7 K

TRAPPIST-1c
Orbital period 2.4218233 ± 0.0000017 days
Mid-transit time 2 457 282.80728 ± 0.00019 (Julian Date)
Transit depth 0.687 ± 0.010
Scale parameter (a/R★) 28.08 -0.42+0.22
Impact parameter 0.161 ± 0.080 R☉
Transit duration 42.37 ± 0.22 minutes
Orbital inclination 89.67 ± 0.17º
Orbital eccentricity < 0.083
Semi-major axis 0.01521 ± 0.00047 AU
Mass 1.38 ± 0.61 M⊕
Density 1.17 ± 0.53 ρ⊕
Equilibrium temperature (A=0) 341.9 ± 6.6 K

TRAPPIST-1d
Orbital period 4.049610 ± 0.000063 days
Mid-transit time 2 457 670.14165 ± 0.00035 (Julian Date)
Transit depth 0.367 ± 0.017
Scale parameter (a/R★) 39.55 -0.59+0.30
Impact parameter 0.17 ± 0.11 R☉
Transit duration 49.13 ± 0.65 minutes
Orbital inclination 89.75 ± 0.16º
Orbital eccentricity < 0.070
Semi-major axis 0.02144 ± 0.00065 AU
Mass 0.41 ± 0.27 M⊕
Density 0.89 ± 0.60 ρ⊕
Equilibrium temperature (A=0) 288.0 ± 5.6 K

TRAPPIST-1e
Orbital period 6.099615 ± 0.000011 days
Mid-transit time 2 457 660.37859 ± 0.00035 (Julian Date)
Transit depth 0.519 ± 0.026
Scale parameter (a/R★) 51.97 -0.77+0.40
Impact parameter 0.12 ± 0.10 R☉
Transit duration 57.21 ± 0.71 minutes
Orbital inclination 89.86 ± 0.11º
Orbital eccentricity < 0.085
Semi-major axis 0.02817 ± 0.00085 AU
Mass 0.62 ± 0.58 M⊕
Density 0.80 ± 0.76 ρ⊕
Equilibrium temperature (A=0) 251.3 ± 4.9 K

TRAPPIST-1f
Orbital period 9.206690 ± 0.000015 days
Mid-transit time 2 457 671.39767 ± 0.00023 (Julian Date)
Transit depth 0.673 ± 0.023
Scale parameter (a/R★) 68.4 -1.0+0.5
Impact parameter 0.382 ± 0.035 R☉
Transit duration 62.60 ± 0.60 minutes
Orbital inclination 89.680 ± 0.034º
Orbital eccentricity < 0.063
Semi-major axis 0.0371 ± 0.0011 AU
Mass 0.68 ± 0.18 M⊕
Density 0.60 ± 0.17 ρ⊕
Equilibrium temperature (A=0) 219.0 ± 4.2 K

TRAPPIST-1g
Orbital period 12.35294 ± 0.00012 days
Mid-transit time 2 457 665.34937 ± 0.00021 (Julian Date)
Transit depth 0.782 ± 0.027
Scale parameter (a/R★) 83.2 -1.2+0.6
Impact parameter 0.421 ± 0.031 R☉
Transit duration 68.40 ± 0.66 minutes
Orbital inclination 89.710 ± 0.025º
Orbital eccentricity < 0.061
Semi-major axis 0.0451 ± 0.0014 AU
Mass 1.34 ± 0.88 M⊕
Density 0.94 ± 0.63 ρ⊕
Equilibrium temperature (A=0) 198.6 ± 3.8 K

TRAPPIST-1h
Orbital period 20 -6+15
Mid-transit time 2 457 662.55463 ± 0.00056 (Julian Date)
Transit depth 0.352 ± 0.033
Scale parameter (a/R★) 117 -26+50
Impact parameter 0.45 ± 0.25 R☉
Transit duration 76.7 ± 2.5 minutes
Orbital inclination 89.80 ± 0.07º
Orbital eccentricity unknown
Semi-major axis 0.063 -0.013+0.027 AU
Mass unknown
Density unknown
Equilibrium temperature (A=0) 168 -28+21 K

TRAPPIST-1x
It is possible that other planets exist around TRAPPIST-1. Further observations may tell us about their presence.

## Exoplanets: The TRAPPIST-1 System

The hunt for exoplanets is one of the fastest-growing enterprises in astronomy, and for very good reason. An exoplanet, or extra-solar planet, is any planet that orbits a star other than our own Sun. These planets vary in size and distance from their star. If we can find planets with similar composition and features to Earth, we may discover extraterrestrial life, or a potential future home for humanity. This page will explore one of the most bountiful results of the exoplanet search, TRAPPIST-1, anaylsing the composition of this planetary system and the methods used by astronomers to discover it, and how research of this planet will proceed in the future.

Background on TRAPPIST-1

Artist’s impression of TRAPPIST-1 being transited by two of its seven known planets 1

While thousands of exoplanets have been discovered, only a fraction of these could have the ability to sustain life. The TRAPPIST system is a product of the exoplanet hunt that has yielded unusually high results. TRAPPIST-1 is an ultra-cool dwarf star 39.5 light-years away that is roughly the size of Jupiter and roughly 84 times as massive, and was first discovered using the TRAPPIST (the TRansiting Planets and Planestesimals Small Telescope). Additional planets were discovered using multiple other telescopes such as Spitzer Space Telescope and Liverpool Telescope. 2 At 7 discovered exoplanets, TRAPPIST-1 has more detected planets than any other system. 5 of these planets are of similar size to Earth, with 3 of these orbiting in the habitable zone. 3

Discovery of the TRAPPIST Exoplanets – The Transit Method

Light curve shows the decrease in brightness of the star as the planet passes between it and the observer 6

The Transit Method allowed astronomers to discover the exoplanets that orbit TRAPPIST-1, as well as many others. It makes use of the simple idea idea that an exoplanet which crosses between its host star and Earth once an orbit will block a very small amount of light each time. Therefore, astronomers monitor the night sky in search of periodically dimming stars. An astronomer can tell that this object is truly a planet and not a foreign object in the galaxy by continually observing that star, making sure that this “dimming” happens once every orbital revolution and over the same length of time as the planet’s “year” goes by. 7 Typically, a star will lose between 0.1% and 1% of its overall brightness depending on how large the planet passing over it is. The time the planet takes to pass between the observer and the star is dependent on the distance between the planet and the star. 7 The repetition of the planet passing in-between the observer and the star helps astronomers observe the planet’s astrosphere. As the planet passes over the star, some of the starlight passes through the atmosphere of the planet, and scientists then analyze the colors of the light to learn more about the composition of the atmosphere. 8 Free oxygen in the atmosphere is a potential indicator of life. 7

The transit method comes with many advantages, but also quite a few disadvantages. Some advantages would include it being the most sensitive method for locating exoplanets, it can be used in conjunction with other methods to determine planetary density based on the mass and size of said exoplanet, as well as determining the atmospheric composition of the exoplanet. The disadvantages include the dependency of a transit to occur, the small window the scientist has to view said transit, the multiple transits needed to conclude that the object is in fact an exoplanet and the tendency to throw false positives. All of these add to a successful method in finding exoplanets, even though it relies heavily on luck and chance. 9

All the planets in the TRAPPIST-1 system pass in front of their star, which enable astronomers to observe their transit from Earth. Scientists monitored repeated shadows that displayed during transit. This helped them resolve the composition of the planets, by tracking the rate of time the planets took to surpass the star, allowing them to measure the masses of the planets, therefore evaluating the densities and therefore their bulk composition – which is rocky. During transit scientists were also able to investigate the climate on these planets by looking at the light from the star that passed through the atmosphere of the planet. 2

Features of the TRAPPIST-1 System

As mentioned above, the TRAPPIST-1 system is comprised of seven planets, all ranging from diameters 0.8 and 1.1 times the diameter of the Earth. 10 Their periods are between 1.5 and 20 days, and they orbit relatively close to the star, only laying 1.6 million to 9.5 million kilometers from TRAPPIST-1. 10 There are no Jupiter’s among this crowd, as these planets range from 0.4 to 1.4 Earth masses (Jupiter is 318 Earth masses). 10,11

Astronomers have also been able to determine, based on the temperature of the star and the orbital radius of each planet, that these planets receive a similar amount of light as many planets in our own solar system. However, this does not necessarily mean they could be in the habitable zone for TRAPPIST-1, as the closest planet, TRAPPIST-1b, has an equilibrium temperature of about 400 Kelvin, which translates to about 127℃, well beyond the boiling point of water. 2 At the other end of the spectrum, TRAPPIST-1h (the furthest planet) gets about as much light as Ceres, a dwarf planet in the asteroid belt, does from our sun, giving it a temperature of about -100℃. 12 While these extreme cases may not be able to harbour life, it is reasonable to believe that some of the planets between them may have a better environment to host living organisms similar to our own.

The potential for life within the TRAPPIST-1 system can also be analysed through observing the atmospheric conditions of each planet. An atmosphere that remains present over very long periods of time is regarded as one of the most crucial criteria necessary for obtaining habitability on a planet. Using mathematical simulations of stellar winds along with the atmospheric ion escape rate for all TRAPPIST-1 planets, a study concluded that planets further away from the star hold atmospheres more suitable for life. 16 Therefore, TRAPPIST-1h (the most outward planet) contains the atmosphere that will deteriorate at the slowest pace. According to predictions based off of the deterioration of Earth’s atmosphere, TRAPPIST-1h will support an atmosphere for approximately 109 years, while the most inward planets TRAPPIST-1b may only support an atmosphere for 108 years. 16 This is problematic for the most inward planets because the origin of life on earth took over 5𴡄 years to evolve. 16 It is not certain that all planets will evolve life on the same timetable, however it is our best approximation based on the knowledge attained thus far. The longer an atmosphere is supported, the chances also increase for more complex and even intelligible life forms to evolve. 16 TRAPPIST-1h seems like the most capable of fostering life from an atmospheric standpoint, however it does not orbit within the habitat zone, making TRAPPIST-1g (the second furthest orbiting planet) the most likely to harbour life because of its increased chances of holding liquid water.

Poster Inspired by the TRAPPIST-1 system by Amanda J. Smith 13

Future Research on the TRAPPIST-1 System – K2 and Spritzer

The TRAPPIST-1 system has given astronomers much to consider, but many questions still remain. K2 and JWST are two of the current missions that will work towards uncovering the secrets of TRAPPIST-1.
NASA’s Kepler Mission from 2009-2013 gave astronomers many things to consider while monitoring 150,00 stars including the orientation of the exoplanets planets in the galaxy. This mission came to an end due to the loss of the second of four reaction wheels. 14 Months later the K2 mission was developed using the Kepler platform and put into action in 2014. The K2 missions operate on an ecliptic plane which minimizes solar wind pressure on the spacecraft, reducing the rotational torque, nullifying pointing drift. 14 This allows the K2 missions to be controlled by thrusters and the remaining reaction wheels, allowing observation times of up to 80 days. K2 ultimately is a second chance for the damaged Kepler probe. In general, the Kepler Mission looks to study the stars that harbor planetary systems, as well as the dynamics of the planets that orbit them including orbit sizes, masses, densities and more. 14
The James Webb Space Telescope, or simply JWST, is a future NASA, ESA and CSA collaboration set to launch in October of 2018. 15 JWST is the ultimate multitasker, analysing not only the remnants of the cataclysmic Big Bang, but the formation of solar systems similar to our own, such as TRAPPIST-1.
In the future, scientists will be using K2 to get a more accurate reading if these planets truly have a rocky base, or if they are able to sustain water. 4 The planets exhibit a harmoniously resonant orbital pattern and are tightly packed. This is somewhat of a mystery because previous models of planetary formation don’t explain how this highly compact system formed. 5 Having seven planets so closely located will allow scientists to compare the atmospheric compositions and temperatures to one another using JWST in the distant future. 4

The TRAPPIST-1 exoplanets are all connected in the dynamic and mysterious TRAPPIST-1 system. As you’ve seen above, astronomers have already learned so much about the composition and atmospheres of each planet and their relation to their star, but the search for answers is far from over. Future missions like K2 and JWST look to peel back the veil not only on the remaining unknowns of this planetary system, but on the thousands of other exoplanets that have been discovered just in our own small slice of the galaxy. They will also continue to search for a model that can accurately describe the formation of these diverse systems. Using the transit method and many other useful tools, astronomers are embarking on the largest exploration in the history of mankind, mapping out new worlds in the cosmos and learning new things about the cosmos every day.

## TRAPPIST-1 planetary orbits not misaligned

Artist's impression of the TRAPPIST-1 exoplanet system. Credit: NAOJ

Astronomers using the Subaru Telescope have determined that the Earth-like planets of the TRAPPIST-1 system are not significantly misaligned with the rotation of the star. This is an important result for understanding the evolution of planetary systems around very low-mass stars in general, and in particular the history of the TRAPPIST-1 planets including the ones near the habitable zone.

Stars like the Sun are not static, but rotate about an axis. This rotation is most noticeable when there are features like sunspots on the surface of the star. In the Solar System, the orbits of all of the planets are aligned to within 6 degrees with the Sun's rotation. In the past it was assumed that planetary orbits would be aligned with the rotation of the star, but there are now many known examples of exoplanet systems where the planetary orbits are strongly misaligned with the central star's rotation. This raises the question: can planetary systems form out of alignment, or did the observed misaligned systems start out aligned and were later thrown out of alignment by some perturbation?

The TRAPPIST-1 system has attracted attention because it has three small rocky planets located in or near the habitable zone where liquid water can exist. The central star is a very low-mass and cool star, called an M dwarf, and those planets are situated very close to the central star. Therefore, this planetary system is very different from our Solar System. Determining the history of this system is important because it could help determine if any of the potentially habitable planets are actually inhabitable. But it is also an interesting system because it lacks any nearby objects which could have perturbed the orbits of the planets, meaning that the orbits should still be located close to where the planets first formed. This gives astronomers a chance to investigate the primordial conditions of the system.

Because stars rotate, the side rotating into view has a relative velocity towards the viewer, while the side rotating out of view has a relative velocity away from the viewer. If a planet transits, passes between the star and the Earth and blocks a small portion of the light from the star, it is possible to tell which edge of the star the planet blocks first. This phenomenon is called the Rossiter-McLaughlin effect. Using this method, it is possible to measure the misalignment between the planetary orbit and the star's rotation. However, until now those observations have been limited to large planets such as Jupiter-like or Neptune-like ones.

A team of researchers, including members from the Tokyo Institute of Technology and the Astrobiology Center in Japan, observed TRAPPIST-1 with the Subaru Telescope to look for misalignment between the planetary orbits and the star. The team took advantage of a chance on August 31, 2018, when three of the exoplanets orbiting TRAPPIST-1 transited in front of the star in a single night. Two of the three were rocky planets near the habitable zone. Since low-mass stars are generally faint, it had been impossible to probe the stellar obliquity (spin-orbit angle) for TRAPPIST-1. But thanks to the light gathering power of the Subaru Telescope and high spectral resolution of the new infrared spectrograph IRD, the team was able to measure the obliquity. They found that the obliquity was low, close to zero. This is the first measurement of the stellar obliquity for a very low-mass star like TRAPPIST-1 and also the first Rossiter-McLaughlin measurement for planets in the habitable zone.

However the leader of the team, Teruyuki Hirano at the Tokyo Institute of Technology, cautions, "The data suggest alignment of the stellar spin with the planetary orbital axes, but the precision of the measurements was not good enough to completely rule out a small spin-orbit misalignment. Nonetheless, this is the first detection of the effect with Earth-like planets and more work will better characterize this remarkable exoplanet system."

## TRAPPIST-1 planets provide clues to the nature of habitable worlds

This is a slice through a model composition of TRAPPIST-1 'f' which contains over 50 percent water by mass. The pressure of the water alone is enough to cause it to become high-pressure ice. The pressure at the water-mantle boundary is so great that no upper mantle is present at all instead the shallowest rocks would be more like those seen in the Earth's lower mantle. Credit: ASU

Among planetary systems, TRAPPIST-1 is of particular interest because seven planets have been detected orbiting this star, a larger number of planets than have been than detected in any other exoplanetary system. In addition, all of the TRAPPIST-1 planets are Earth-sized and terrestrial, making them an ideal focus of study for planet formation and potential habitability.

ASU scientists Cayman Unterborn, Steven Desch, and Alejandro Lorenzo of the School of Earth and Space Exploration, with Natalie Hinkel of Vanderbilt University, have been studying these planets for habitability, specifically related to water composition. Their findings have been recently published in Nature Astronomy.

Water on the TRAPPIST-1 Planets

The TRAPPIST-1 planets are curiously light. From their measured mass and volume, all of this system's planets are less dense than rock. On many other, similarly low-density worlds, it is thought that this less-dense component consists of atmospheric gasses.

“But the TRAPPIST-1 planets are too small in mass to hold onto enough gas to make up the density deficit,” explains geoscientist Unterborn. “Even if they were able to hold onto the gas, the amount needed to make up the density deficit would make the planet much puffier than we see.”

So scientists studying this planetary system have determined that the low-density component must be something else that is abundant: water. This has been predicted before, and possibly even seen on larger planets like GJ1214b, so the interdisciplinary ASU-Vanderbilt team, comprised of geoscientists and astrophysicists, set out to determine just how much water could be present on these Earth-sized planets and how and where the planets may have formed.

Calculating water amounts on TRAPPIST-1 planets

To determine the composition of the TRAPPIST-1 planets, the team used a unique software package, developed by Unterborn and Lorenzo, that uses state-of-the-art mineral physics calculators. The software, called ExoPlex, allowed the team to combine all of the available information about the TRAPPIST-1 system, including the chemical makeup of the star, rather than being limited to just the mass and radius of individual planets.

Much of the data used by the team to determine composition was collected from a dataset called the Hypatia Catalog, developed by contributing author Hinkel. This catalog merges data on the stellar abundances of stars near to our Sun, from over 150 literature sources, into a massive repository.

What they found through their analyses was that the relatively “dry” inner planets (labeled “b” and “c” on this image) were consistent with having less than 15 percent water by mass (for comparison, Earth is 0.02 percent water by mass). The outer planets (labeled “f” and “g” on this image) were consistent with having more than 50 percent water by mass. This equates to the water of hundreds of Earth-oceans. The masses of the TRAPPIST-1 planets continue to be refined, so these proportions must be considered estimates for now, but the general trends seem clear.

“What we are seeing for the first time are Earth-sized planets that have a lot of water or ice on them,” says ASU astrophysicist and contributing author, Steven Desch.

But the researchers also found that the ice-rich TRAPPIST-1 planets are much closer to their host star than the ice line. The “ice line” in any solar system, including TRAPPIST-1's, is the distance from the star beyond which water exists as ice and can be accreted into a planet inside the ice line water exists as vapor and will not be accreted. Through their analyses, the team determined that the TRAPPIST-1 planets must have formed much farther from their star, beyond the ice line, and migrated in to their current orbits close to the host star.

There are many clues that planets in this system and others have undergone substantial inward migration, but this study is the first to use composition to bolster the case for migration. What's more, knowing which planets formed inside and outside of the ice line allowed the team to quantify for the first time how much migration took place.

Because stars like TRAPPIST-1 are brightest right after they form and gradually dim thereafter, the ice line tends to move in over time, like the boundary between dry ground and snow-covered ground around a dying campfire on a snowy night. The exact distances the planets migrated inward depends on when they formed. “The earlier the planets formed,” says Desch, “the further away from the star they needed to have formed to have so much ice.” But for reasonable assumptions about how long planets take to form, the TRAPPIST-1 planets must have migrated inward from at least twice as far away as they are now.

Interestingly, while we think of water as vital for life, the TRAPPIST-1 planets may have too much water to support life.

“We typically think having liquid water on a planet as a way to start life, since life, as we know it on Earth, is composed mostly of water and requires it to live,” explains Hinkel. “However, a planet that is a water world, or one that doesn't have any surface above the water, does not have the important geochemical or elemental cycles that are absolutely necessary for life.”

Ultimately, this means that while M-dwarf stars, like TRAPPIST-1, are the most common stars in the universe (and while it's likely that there are planets orbiting these stars), the huge amount of water they are likely to have makes them unfavorable for life to exist, especially enough life to create a detectable signal in the atmosphere that can be observed. “It's a classic scenario of 'too much of a good thing,'” says Hinkel.

So, while we're unlikely to find evidence of life on the TRAPPIST-1 planets, through this research we may gain a better understanding of how icy planets form and what kinds of stars and planets we should be looking for in our continued search for life.

## Seventh TRAPPIST-1 Planet Confirmed

By: Camille M. Carlisle May 22, 2017 1

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Astronomers have confirmed the existence of the seventh planet around the ultracool dwarf star TRAPPIST-1.

Artist’s concept of what the sky might look like from one of the seven known terrestrial planets in the TRAPPIST-1 system.
ESO / M. Kornmesser

The modest M8 red dwarf star TRAPPIST-1 became famous after astronomers discovered seven small exoplanets in orbit around it. At the time the discoverers made the announcement in February, they couldn’t say much about the outermost world, labeled h: The astronomers had seen the planet — or, at least something they thought was a planet — pass in front of the star only once.

Rodrigo Luger (University of Washington, Seattle) and colleagues, including members of the original discovery team, have now confirmed planet h’s existence and some of its specs.

The team used more than 70 days of data from NASA’s repurposed Kepler spacecraft, taken as part of its K2 mission. The craft detected h crossing in front of its star four times, with an orbital period of 18.77 — just what the researchers were expecting, based on their previous observations. (They analyzed the data three different ways, too, just to be sure.) This orbit places the exoplanet well outside TRAPPIST-1’s habitable zone: The amount of energy planet h receives from the little star is on par with what dwarf planet Ceres receives from the Sun at its home in the main asteroid belt.

The transits reveal that planet h is 75% as wide as Earth, or about 40% larger than Mars. But we still don’t know the world’s mass. Researchers used tiny shifts in the other six exoplanets’ transit times to estimate their gravitational influence on one another, and hence their masses. Unfortunately, planet h’s measured transits aren’t clean enough to reveal timing shifts due to its siblings’ gravitational tugs, Luger says.

The exoplanet’s orbital period makes a complicated pattern with the periods of those around it, the authors explain May 22nd in Nature Astronomy. Normally, when we talk about such resonant orbits, we think of situations like that of Jupiter’s Galilean moons: For every circuit Ganymede makes around Jupiter, Europa makes two. TRAPPIST-1’s planets have a more complicated arrangement, called a higher-order Laplace resonance, in which the pattern is a combination of three periods that doesn’t exactly produce the straightforward, integer multiples we usually think of. For those interested in the math, the relationship is

where x and y are integers and P1, P2, and P3 are the orbital periods of planet 1, planet 2, and planet 3 in the trio of neighboring bodies you’re comparing.

For those not interested in the math, just know that for every two laps planet h makes around TRAPPIST-1, planet g makes about 3, and planet f makes (more roughly) four. The exoplanets would have migrated into this complex chain arrangement sometime after the system formed, then gotten gravitationally stuck.

The above animation shows a simulation of the TRAPPIST-1 exoplanets over 90 Earth-days, then focuses on the outer three after 15 days. The three-body resonance of the outer three planets causes the planets to repeat the same relative positions. Astronomers used this expected resonance to predict the orbital period of TRAPPIST-1h. Credit: Daniel Fabrycky / University of Chicago

### How Old Is TRAPPIST-1?

Luger’s team also tried to constrain TRAPPIST-1’s age. Dating stars as puny as this one is tough. The way a star ages depends on its mass at a measly 8% the Sun’s mass, TRAPPIST-1 will age very slowly.

Thanks to the K2 data, the astronomers could use starspots to clock the dwarf’s rotation period at 3.3 days (about twice as long as the period we previously reported). That’s middle-of-the-road for nearby, ultracool dwarf stars. Kepler also didn’t reveal much activity, but it did catch at least one notable flare. Based on the spin and activity level, the authors estimate the star’s age is between 3 and 8 billion years.

Other M dwarf astronomers agree that that’s a reasonable range. Elisabeth Newton (MIT) says that most nearby stars are younger than 8 billion years. She and her colleagues recently surveyed nearly 400 nearby M dwarfs, finding that those with periods less than 10 days generally had ages of less than 2 billion years. But she cautions that the red dwarfs her team looked at were more massive than TRAPPIST-1, and the relationship between age and rotation period depends on the star’s mass. “I don’t think that the current data we have on the rotation periods of red dwarf stars is too useful for pinning down the ages of stars as small as TRAPPIST-1,” she warns.

John Bochanski (Rider University) agrees. TRAPPIST-1’s activity level implies that it’s not “really” old, he says, but beyond that it’s hard to say. It wouldn’t surprise him if the star was a little outside the range. Meanwhile, Jeffrey Linsky (University of Colorado, Boulder) puts his bet on 2 to 5 billion years, based on the star’s heavy-element content, X-ray output, and motion through the Milky Way.

Whatever the exact number, it’s likely that TRAPPIST-1 is about as old as the Sun. That permits all sorts of speculation about habitability and alien life, but given how much remains unknown about this system, I prefer not to dabble in such musings.

Reference: Rodrigo Luger et al. “A Seven-Planet Resonant Chain in TRAPPIST-1.” Nature Astronomy. May 22, 2017.

February 6, 2018 at 12:29 pm

"Yet TRAPPIST-1 still holds more questions than answers — none of the studies released today, for example, can say whether the planets are habitable." This is a good observation here. I recently read that Mars has a chemical in the soil that is toxic. We do not know that soil on the list of potential, habitable exoplanets is compatible with plant life on earth and allows crop growing as we enjoy here on earth.

February 6, 2018 at 2:28 pm

Yup, the perchlorates in Martian soil are bad news! The good news is that you could use water to wash the soil (perchlorates are water soluble), but water may not be easily accessible on Mars.

February 10, 2018 at 1:15 pm

Hmm, 7 in a resonant chain, five more and we'll have found the 12 Tribes of Kobol!

February 10, 2018 at 2:55 pm

I keep seeing various reports on the TRAPPIST exoplanets and efforts to find a new Earth. I note this in the report here - "Planets don’t form like this. Instead, TRAPPIST-1’s planets likely formed much farther out. They migrated inward by interacting with the primordial planet-forming disk before stabilizing in their current, resonant configuration."

My note - the TRAPPIST exoplanets are all < 0.1 AU from their parent star. How did our very habitable Earth with life teeming on it, avoid forming well inside where Mercury is at today like the TRAPPIST exoplanets formed by their parent star? Questions like this are *origins science* in my view.

## REB Research Blog

According to Star Trek, Vulcans and Humans meet for the first time on April 5, 2063, near the town of Bozeman, Montana. It seems that Vulcan is a relatively nearby, earth-like planet with strongly humanoid inhabitants. It’s worthwhile to speculate why they are humanoid (alternatively, how likely is it that they are), and also worthwhile to figure out which planets we’d like to visit assuming we’re the ones who do the visiting.

First things first: It’s always assumed that life evolved on earth from scratch, as it were, but it is reasonably plausible that life was seeded here by some space-traveling species. Perhaps they came, looked around and left behind (intentionally or not) some blue-green algae, or perhaps some more advanced cells, or an insect or two. A billion or so years later, we’ve evolved into something that is reasonably similar to the visiting life-form. Alternately, perhaps we’d like to do the exploring, and even perhaps the settling. The Israelis are in the process of showing that low-cost space travel is a thing. Where do we want to go this century?

As it happens we know there are thousands of stars with planets nearby, but only one that we know that has reasonably earth-like planets reasonably near. This one planet circling star is Trappist-1, or more properly Trappist 1A. We don’t know which of the seven planets that orbit Trappist-1A is most earth-like, but we do know that there are at least seven planets, that they are all roughly earth size, that several have earth-like temperatures, and that all of these have water. We know all of this because the planetary paths of this star are aligned so that seven planets cross the star as seen from earth. We know their distances from their orbital times, and we know the latter from the shadows made as the planets transit. The radiation spectrum tells us there is water.

Trappist 1A is smaller than the sun, and colder than the sun, and 1 billion years older. It’s what is known as an ultra-cool dwarf. I’d be an ultra cool dwarf too, but I’m too tall. We can estimate the mass of the star and can measure its brightness. We then can calculate the temperatures on the planets based their distance from the star, something we determine as follows:

The gravitational force of a star, mass M, on a planet of mass, m, is MmG/r 2 , where G is the gravitational constant, and r is the distance from the star to the planet. Since force = mass times acceleration, and the acceleration of a circular orbit is v 2 /r, we can say that, for these orbits (they look circular),

Here, v is the velocity of the planet and ω is its rotational velocity, ω = v/r. Eliminating m, we find that

Since we know G and ω, and we can estimate M (it’s 0.006 solar masses, we think), we have a can make good estimates of the distances of all seven planets from their various rotation speeds around the star, ω. We find that all of these planets are much closer to their star than we are to ours, so the their years are only a few days or weeks long.

We know that three planets have a temperatures reasonably close to earths, and we know that these three also have water based on observation of the absorption of light from their atmosphere as they pass in front of their star. To tell the temperature, we use our knowledge of how bright the star is (0.0052 times Sol), and our knowledge of the distance. As best we can tell, the following three of the Trappist-1 planets should have liquid surface water: Trappist 1c, d and e, the 2nd, 3rd and 4th planets from the star. With three planets to choose from, we can be fairly sure that at least one will be inhabitable by man somewhere in the planet.

The seven orbital times are in small-number ratios, suggesting that the orbits are linked into a so-called Laplace resonance-chain. For every two orbits of the outermost planet, the next one in completes three orbits, the next one completes four, followed by 6, 9 ,15, and 24. The simple whole number relationships between the periods are similar to the ratios between musical notes that produce pleasant and harmonic sounds as I discussed here. In the case of planets, resonant ratios keep the system stable. The most earth-like of the Trappist-1 planets is likely Trappist-1d, the third planet from the star. It’s iron-core, like earth, with water and a radius 1.043 times earth’s. It has an estimated average temperature of 19°C or 66°F. If there is oxygen, and if there is life there could well be, this planet will be very, very earth-like.

The temperature of the planet one in from this, Trappist-1c, is much warmer, we think on average, 62°C (143°F). Still, this is cool enough to have liquid water, and some plants live in volcanic pools on earth that are warmer than this. Besides this is an average, and we might the planet quite comfortable at the poles. The average temperature of the planet one out from this, Trappist-1e, is ice cold, -27°C (-17°F), an ice planet, it seems. Still, life can find a way. There is life on the poles of earth, and perhaps the plant was once warmer. Thus, any of these three might be the home to life, even humanoid life, or three-eyed, green men.

Visiting Trappist-1A won’t be easy, but it won’t be out-of hand impossible. The system is located about 39 light years away, which is far, but we already have a space ship heading out of the solar system, and we are developing better, and cheaper options all the time. The Israeli’s have a low cost, rocket heading to the moon. That is part of the minimal technology we’d want to visit a nearby star. You’d want to add enough rocket power to reach relativistic speeds. For a typical rocket this requires a fuel whose latent energy is on the order mc 2 . That turns out to be about 1 GeV/atomic mass. The only fuel that has such high power density is matter-antimatter annihilation, a propulsion system that might have time-reversal issues. A better option, I’d suggest is ion-propulsion with hydrogen atoms taken in during the journey, and ejected behind the rocket at 100 MeV energies by a cyclotron or bevatron. This system should work if the energy for the cyclotron comes from solar power. Perhaps this is the ion-drive of Star-Trek fame. To meet the Star-Trek’s made-up history, we’d have to meet up by April, 2063: forty-four years from now. If we leave today and reach near light speed by constant acceleration for a few of years, we could get there by then, but only as time is measured on the space-ship. At high speeds, time moves slower and space shrinks.

This planetary system is named Trappist-1 after the telescope used to discover it. It was the first system discovered by the 24 inch, 60 cm aperture, TRA nsiting P lanets and P lanetesImals S mall T elescope. This telescope is operated by The University of Liége, Belgium, and is located in Morocco. The reason most people have not heard of this work, I think, has to do with it being European science. Our news media does an awful job covering science, in my opinion, and a worse job covering Europe, or most anything outside the US. Finally, like the Israeli moon shot, this is a low-budget project, the work to date cost less than €2 million, or about US $2.3 million. Our media seems committed to the idea that only billions of dollars (or trillions) will do anything, and that the only people worth discussing are politicians. NASA’s budget today is about$6 billion, and its existence is barely mentioned.

The Trappist system appears to be about 1 billion years older than ours, by the way, so life there might be more advanced than ours, or it might have died out. And, for all we know, we’ll discover that the Trappist folks discover space travel, went on to colonize earth, and then died out. The star is located, just about exactly on the ecliptic, in the constellation Aquarius. This is an astrological sign associated with an expansion of human consciousness, and a revelation of truths. Let us hope that, in visiting Trappist, “peace will guide the planets and love will steer the stars”.

## TRAPPIST-1 Statistics Table

This chart shows, on the top row, artist concepts of the seven planets of TRAPPIST-1 with their orbital periods, distances from their star, radii and masses as compared to those of Earth. On the bottom row, the same numbers are displayed for the bodies of our inner solar system: Mercury, Venus, Earth and Mars. The TRAPPIST-1 planets orbit their star extremely closely, with periods ranging from 1.5 to only about 20 days. This is much shorter than the period of Mercury, which orbits our sun in about 88 days.

The artist concepts show what the TRAPPIST-1 planetary system may look like, based on available data about their diameters, masses and distances from the host star. The system has been revealed through observations from NASA's Spitzer Space Telescope and the ground-based TRAPPIST (TRAnsiting Planets and PlanetesImals Small Telescope) telescope, as well as other ground-based observatories. The system was named for the TRAPPIST telescope.

The seven planets of TRAPPIST-1 are all Earth-sized and terrestrial, according to research published in 2017 in the journal Nature. TRAPPIST-1 is an ultra-cool dwarf star in the constellation Aquarius, and its planets orbit very close to it.

NASA's Jet Propulsion Laboratory, Pasadena, California, manages the Spitzer Space Telescope mission for NASA's Science Mission Directorate, Washington. Science operations are conducted at the Spitzer Science Center at Caltech, also in Pasadena. Spacecraft operations are based at Lockheed Martin Space Systems Company, Littleton, Colorado. Data are archived at the Infrared Science Archive housed at Caltech/IPAC. Caltech manages JPL for NASA.

## A seven-planet resonant chain in TRAPPIST-1

The TRAPPIST-1 system is the first transiting planet system found orbiting an ultracool dwarf star 1 . At least seven planets similar in radius to Earth were previously found to transit this host star 2 . Subsequently, TRAPPIST-1 was observed as part of the K2 mission and, with these new data, we report the measurement of an 18.77 day orbital period for the outermost transiting planet, TRAPPIST-1 h, which was previously unconstrained. This value matches our theoretical expectations based on Laplace relations 3 and places TRAPPIST-1 h as the seventh member of a complex chain, with three-body resonances linking every member. We find that TRAPPIST-1 h has a radius of 0.752 R and an equilibrium temperature of 173 K. We have also measured the rotational period of the star to be 3.3 days and detected a number of flares consistent with a low-activity, middle-aged, late M dwarf.

The star TRAPPIST-1 (EPIC 246199087) was observed for 79 days by NASA’s Kepler Space Telescope in its two-reaction wheel mission 4 (K2) as part of Campaign 12, starting on 2016 December 15 and ending on 2017 March 4. The spacecraft was in safe mode between 2017 February 1 and 2017 February 6, resulting in a five-day loss of data. On downlink from the spacecraft, the raw cadence data are typically calibrated with the Kepler pipeline 5 , a lengthy procedure that includes background subtraction, smear removal, and undershoot and non-linearity corrections. However, given the unique science drivers in this dataset, the raw, uncalibrated data for Campaign 12 were made publicly available on 2017 March 8, shortly after downlink. We download and calibrate the long cadence (exposure time texp = 30 min) and short cadence (texp = 1 min) light curves using a simple column-by-column background subtraction, which also removes smear and dark noise (see Methods). Because of its two failed reaction wheels, the rolling motion of the Kepler spacecraft due to torque imbalances introduces strong instrumental signals, leading to an increase in photometric noise by a factor of about three to five compared with the original mission. As TRAPPIST-1 is a faint M8 dwarf with Kepler magnitude Kp ≈ 16–17 (see Methods), these instrumental signals must be carefully removed to reach the

0.1% relative photometric precision required to detect Earth-size transits 6 . To this end, we detrend the long cadence light curve for TRAPPIST-1 using both EVEREST 7,8 and a Gaussian process-based pipeline, achieving an average 6 h photometric precision of 281.3 ppm, a factor of three improvement over the raw light curve. After analysis of the long cadence light curve, we detrend the short cadence light curve in the vicinity of the features of interest, achieving a comparable or higher 6 h precision (see Methods).