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The orbital motions of the TRAPPIST-1 planets form a complex chain with three-body Laplace-type resonances linking every member. The relative orbital periods (proceeding outward) approximate whole integer ratios of 24/24, 24/15, 24/9, 24/6, 24/4, 24/3,
and 24/2, respectively, or nearest-neighbor period ratios of about 8/5, 5/3, 3/2, 3/2, 4/3, and 3/2 (1.603, 1.672, 1.506, 1.509, 1.342, and 1.519). This represents the longest known chain of near-resonant exoplanets, and is thought to have resulted from
interactions between the planets as they migrated inward within the residual protoplanetary disk after forming at greater initial distances.[38][34]

The resonant chain has been shown to be necessary to keep the tightly packed system stable for long timescales,[16] and the tight correspondence between whole number ratios in orbital resonances and in music theory has made it possible to convert the
system's motion into music.[17]

Formation of the planetary system

Artist's impression of the TRAPPIST-1 planetary system.[51]
According to Ormel et al. previous models of planetary formation do not explain
the formation of the highly compact TRAPPIST-1 system. Formation in place would
require an unusually dense disk and would not readily account for the orbital resonances.
Formation outside the frost line does not explain the planets' terrestrial nature or Earth-like masses. The authors proposed a new scenario in which planet formation starts at the frost line where pebble-size particles trigger streaming instabilities,
then protoplanets quickly mature by pebble accretion. When the planets reach Earth mass they create perturbations in the gas disk that halt the inward drift
of pebbles causing their growth to stall. The planets are transported by Type I
migration to the
inner disk, where they stall at the magnetospheric cavity and end up in mean motion resonances.[52] Such inward migration increases the odds of substantial amounts of water being present on these worlds.

Tidal locking
All seven planets are likely to be tidally locked (one side of each planet permanently facing the star),[38] making the development of life there "much more challenging".[14] A less likely possibility is that some may be trapped in
a higher-order spin–
orbit resonance.[38] Tidally locked planets would typically have very large temperature differences between their permanently lit day sides and their permanently dark night sides, which could produce very strong winds circling the planets. The best
places for life may be close to the mild twilight regions between the two sides, called the terminator line.

Tidal heating
Tidal heating is predicted to be significant: all planets except f and h are expected to have a tidal heat flux greater than Earth's total heat flux.[34] With the exception of TRAPPIST-1c, all of the planets have densities low enough
to indicate the
presence of significant H2O in some form. Planets b and c experience enough heating from planetary tides to maintain magma oceans in their rock mantles; planet c may have eruptions of silicate magma on its surface. Tidal heat fluxes
on planets d, e, and
f are lower, but are still twenty times higher than Earth's mean heat flow. Planets d and e are the most likely to be habitable. Planet d avoids the runaway greenhouse state if its albedo is ≳ 0.3.[53]

Possible effects of strong X-ray and extreme UV irradiation of the system Bolmont et al. modelled the effects of predicted far ultraviolet (FUV) and extreme ultraviolet (EUV/XUV) irradiation of planets b and c by TRAPPIST-1. Their results suggest that the two planets may have lost as much as 15 Earth oceans of water (although
the actual loss would probably be lower), depending on their initial water contents. Nonetheless, they may have retained enough water to remain habitable,
and a planet orbiting further out was predicted to lose much less water.[23]

However, a subsequent XMM-Newton X-ray study by Wheatley et al. found that the star emits X-rays at a level comparable to our own much larger Sun, and extreme
ultraviolet radiation at a level 50-fold stronger than assumed by Bolmont et al. The authors
predicted this would significantly alter the primary and perhaps secondary atmospheres of close-in, Earth-sized planets spanning the habitable zone of the
star. The publication noted that these levels "neglected the radiation physics and hydrodynamics of
the planetary atmosphere" and could be a significant overestimate. Indeed, the XUV stripping of a very thick hydrogen and helium primary atmosphere might actually be required for habitability. The high levels of XUV would also be expected to make water
retention on TRAPPIST-1d less likely than predicted by Bolmont et al., though even on highly irradiated planets it might remain in cold traps at the poles or
on the night sides of tidally locked planets.[54]

If a dense atmosphere like Earth's, with a protective ozone layer, exists on planets in the habitable zone of TRAPPIST-1, UV surface environments would be similar to present-day Earth. However, an anoxic atmosphere would allow more UV
to reach the
surface, making surface environments hostile to even highly UV-tolerant terrestrial extremophiles. If future observations detect ozone on one of the TRAPPIST-1 planets, it would be a prime candidate to search for surface life.[55]

Spectroscopy of planetary atmospheres
Because of the system's relative proximity, the small size of the primary and the orbital alignments that produce daily transits,[56] the atmospheres of TRAPPIST-1's planets are favorable targets for transmission spectroscopy investigation.[57]

The combined transmission spectrum of TRAPPIST-1b and c, obtained by the Hubble
Space Telescope, rules out a cloud-free hydrogen-dominated atmosphere for each planet, so they are unlikely to harbor an extended gas envelope, unless it is cloudy out to
high altitudes. Other atmospheric structures, from a cloud-free water-vapor atmosphere to a Venus-like atmosphere, remain consistent with the featureless spectrum.[58]

Another study hinted at the presence of hydrogen exospheres around the two inner planets with an exospheric disks extending up to 7 times the planets' radii.[59]

In a paper by an international collaboration using data from space and ground-based telescopes, it was found that TRAPPIST-1 c and TRAPPIST-1 e likely
have largely rocky interiors, and that TRAPPIST-1 b is the only planet above the runaway green-house
limit, with pressures of water vapour of the order of 101-104 bar.[47]

Observations by future telescopes, such as the James Webb Space Telescope or European Extremely Large Telescope, will be able to assess the greenhouse gas content of the atmospheres, allowing better estimation of surface conditions. They may also be able
to detect biosignatures like ozone or methane in the atmospheres of these planets, if life is present there.[12][60][61][62]

Impact of stellar activity on habitability
The K2 observations of Kepler revealed several flares on the host star. The energy of the strongest event was comparable to the Carrington event, one of the strongest flares seen on the Sun. As the planets in TRAPPIST-1 system orbit
much closer to their
host star than Earth, such eruptions could cause 10–10000 times stronger magnetic storms than the most powerful geomagnetic storms on Earth. Beside the direct harm caused by the radiation associated with the eruptions, they can also pose further
threats: the chemical composition of the planetary atmospheres is probably altered by the eruptions on a regular basis, and the atmospheres can be also eroded in the long term. A sufficiently strong magnetic field of the exoplanets
could protect their
atmosphere from the harmful effects of such eruptions, but an Earth-like exoplanet would need a magnetic field in the order of 10–1000 Gauss to be shielded from such flares (as a comparison, the Earth's magnetic field is ≈0.5 Gauss).[6]

Probability of interplanetary panspermia
Panspermia is potentially orders of magnitude more likely to occur in the TRAPPIST-1 system compared to the Earth-to-Mars case and the probability of abiogenesis is enhanced.[63]

Existence of undiscovered planets
One study using the CAPSCam astrometric camera concluded that the TRAPPIST-1 system has no planets massing at least 4.6 Jupiter masses with year-long orbits
and no planets massing at least 1.6 Jupiter masses with five-year orbits. The authors of the
study noted, however, that their findings left areas of the TRAPPIST-1 system, most notably the zone in which planets would have intermediate-period orbits, unanalyzed.[64]

Radio signal search
In February 2017, Seth Shostak, senior astronomer for the SETI Institute, noted: "... the SETI Institute used its Allen Telescope Array [in 2016] to observe the environs of TRAPPIST-1, scanning through 10 billion radio channels in search of signals. No
transmissions were detected, although new observations are in the offing ..."[20]

Moons
Stephen R. Kane, writing in The Astrophysical Journal Letters, notes that TRAPPIST-1 planets are unlikely to have large moons.[65][66] The Earth's Moon has a radius 27% that of Earth, so its area (and its transit depth) is 7.4% that of Earth, which would
likely have been noted in the transit study if present. Smaller moons of 200–300 km (120–190 mi) radius would likely not have been detected.

At a theoretical level, Kane found that moons around the inner TRAPPIST-1 planets would need to be extraordinarily dense to be even theoretically possible. This is based on a comparison of the Hill sphere, which marks the outer limit of a moon's possible
orbit by defining the region of space in which a planet's gravity is stronger than the tidal force of its star, and the Roche limit, which represents the smallest distance at which a moon can orbit before the planet's tides exceed its own gravity and
pull it apart. These constraints do not rule out the presence of ring systems (where particles are held together by chemical rather than gravitational forces). The mathematical derivation is as follows:

{\displaystyle R_{H}=a_{p}{\sqrt[{3}]{\frac {M_{p}}{3M_{s}}}}} {\displaystyle R_{H}=a_{p}{\sqrt[{3}]{\frac {M_{p}}{3M_{s}}}}}

{\displaystyle R_{H}} R_{H} is the Hill radius of the planet, calculated from the planetary semi-major axis {\displaystyle a_{p}} a_{p}, the mass of the planet {\displaystyle M_{p}} M_{p}, and the mass of the star {\displaystyle M_{s}} M_{s}. Note that
the mass of the TRAPPIST-1 star is approximately 26,000 M⊕ (see data table above); the remaining figures are provided in the table below.

{\displaystyle R_{R}\approx 2.44R_{p}{\sqrt[{3}]{\frac {\rho _{p}}{\rho _{m}}}}} {\displaystyle R_{R}\approx 2.44R_{p}{\sqrt[{3}]{\frac {\rho _{p}}{\rho _{m}}}}}

{\displaystyle R_{R}} R_R is the Roche limit of the planet, calculated from the
radius of the planet {\displaystyle R_{p}} R_{p}, and the density of the planet
{\displaystyle \rho _{p}} \rho_p.

Planet {\displaystyle M_{p}} M_{p}
(Earth masses) {\displaystyle R_{p}} R_{p}
(Earth radii) {\displaystyle a_{p}} a_{p}
(AU) {\displaystyle R_{H}} R_{H}
(milliAU) {\displaystyle R_{R}} R_R
(milliAU) {\displaystyle R_{H}/R_{R}} {\displaystyle R_{H}/R_{R}} TRAPPIST-1 b 0.85 1.086 0.011 0.244 0.120 2.04
TRAPPIST-1 c 1.38 1.056 0.015 0.393 0.141 2.79
TRAPPIST-1 d 0.41 0.772 0.021 0.370 0.094 3.94
TRAPPIST-1 e 0.62 0.918 0.028 0.557 0.108 5.17
TRAPPIST-1 f 0.68 1.045 0.037 0.756 0.111 6.80
TRAPPIST-1 g 1.34 1.127 0.045 1.154 0.139 8.28
TRAPPIST-1 h 0.31 0.715 0.060 0.936 0.086 10.86
Kane notes that moons near the edge of the Hill radius may be subject to resonant removal during planetary migration, leading to a Hill reduction factor
roughly estimated as 1/3 for typical systems and 1/4 for the TRAPPIST-1 system;
thus moons are not
expected for the planets where {\displaystyle R_{H}/R_{R}} {\displaystyle R_{H}/R_{R}} is less than four. Furthermore, tidal interactions with the planet
can result in a transfer of energy from the planet's rotation to the moon's orbit, causing a moon to
leave the stable region over time. For these reasons, even the outer TRAPPIST-1
planets are believed to be unlikely to have moons.

Gallery

TRAPPIST-1 planetary system
(artist concept; animation (1:10); February 2018)



TRAPPIST-1 is a smaller (11% the size), fainter and redder star than the Sun



TRAPPIST-1 starlight may pass through transiting exoplanets to reveal atmospheric compositions using spectroscopy (artist concept)[67]


TRAPPIST-1 planets (artist concept; February 2018)



TRAPPIST-1c landscape (artist concept)



Three planets orbiting TRAPPIST-1 (artist concept)



Drops in brightness (astronomical transits) of TRAPPIST-1 over 20 days (September–October 2016; Spitzer Space Telescope and others) due to the seven
planets (noted on the bottom) blocking the star's light



Dimming of TRAPPIST-1 due to its seven known planets - large planets, more dimming; distant ones, longer (Spitzer Space Telescope)

Videos
File:A trip to TRAPPIST-1 and its seven planets.webm
Video (00:44) – A trip from Earth to TRAPPIST-1 (artist concept)


File:Artist’s impression of the ultracool dwarf star TRAPPIST-1 from close to
one of its planets.ogv
Video (00:22) – A close view of one of the seven planets orbiting TRAPPIST-1 (artist concept)


File:PIA21427 - TRAPPIST-1 Planetary Orbits and Transits.ogv
Video (01:32) – Transit data (artist concept)


File:PIA21468 - TRAPPIST-1 Planets - Flyaround Animation.ogv
Video (01:10) – Fly-around of the planets of the TRAPPIST-1 system (artist concept)


File:The seven planets of TRAPPIST-1.webm
This artist's impression video compares the seven planets orbiting the star at the same scale.

See also
HD 10180, a star with at least seven known planets
Kepler-90, a star with eight known planets
KIC 8462852, another star with notable transit data
Active SETI, the attempt to transmit messages to intelligent extraterrestrial life
Habitability of red dwarf systems
Notes
Based on photometric spectral type estimation.
Taking the absolute visual magnitude of TRAPPIST-1 {\displaystyle M_{V_{\ast }}=18.4} {\displaystyle M_{V_{\ast }}=18.4} and the absolute visual magnitude of the Sun {\displaystyle M_{V_{\odot }}=4.83} {\displaystyle M_{V_{\odot }}=4.83}, the visual
luminosity can be calculated by {\displaystyle {\tfrac {L_{V_{\ast }}}{L_{V_{\odot }}}}=10^{0.4(M_{V_{\odot }}-M_{V_{\ast }})}.} {\displaystyle {\tfrac {L_{V_{\ast }}}{L_{V_{\odot }}}}=10^{0.4(M_{V_{\odot }}-M_{V_{\ast }})}.}
The surface gravity is calculated directly from Newton's law of universal gravitation, which gives the formula {\displaystyle g={\tfrac {GM}{r^{2}}}} {\displaystyle g={\tfrac {GM}{r^{2}}}}, where M is the mass of the object, r is
its radius, and G is
the gravitational constant. In this case, a log g of ≈5.227 indicates a surface gravity around 172 times stronger than Earth's.

--- SoupGate-Win32 v1.05
* Origin: www.darkrealms.ca (1:229/2)