# FeaturedI 7 exoplanets around TRAPPIST-1

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1. May 19, 2017

### lpetrich

Here are some preprints from arxiv about TRAPPIST-1 and its planets:

[1703.01424] Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1 -- the announcement paper for the seven planets. Some of them had been written about in earlier publications, however.

[1703.04166] A terrestrial-sized exoplanet at the snow line of TRAPPIST-1 (12 Mar 2017) -- from the K2 observations, it's been possible to get the mass of planet h.

[1704.02957] Limits on the Stability of TRAPPIST-1 (10 Apr 2017) -- "Due to uncertain system parameters, most orbital configurations drawn from the inferred posterior distribution are unstable on short timescales, even when including the eccentricity damping effect of tides."

[1704.04290] Updated Masses for the TRAPPIST-1 Planets (13 Apr 2017) -- some of the mass values revised downward, and a mass estimate for h. The new masses are more dynamically stable, and e, f, g, and h are most consistent with being water worlds, planets with superdeep water oceans. Planet b is likely a water world also, planet d straddles the all-rock line, and planet c is between all-rock and all-iron, much like the Earth and Venus.

2. Jun 13, 2017

### Staff: Mentor

OU astrophysicist identifies composition of Earth-size planets in TRAPPIST-1 system
Now we need JWST and E-ELT to study their atmospheres.

3. Jun 13, 2017

### lpetrich

It's in arxiv as [1704.02261] Plausible Compositions of the Seven TRAPPIST-1 Planets Using Long-term Dynamical Simulations

I'll also put in the masses found from [1704.04290] Updated Masses for the TRAPPIST-1 Planets, as determined from Transit Timing Variations (TTV"s).

I calculated the test parameter for Student's t test for the differences between the two results:
$$t = \frac{x_2 - x_1}{\sqrt{\sigma_1{}^2 + \sigma_2{}^2}}$$
where the x's are the values to be compared and the σ's are their standard deviations.
• b: 0.88+0.62-0.53 ... 0.79+-0.27 ... -0.15
• c: 1.35+0.61-0.59 ... 1.63+-0.63 ... +0.32
• d: 0.42+0.25-0.21 ... 0.33+-0.15 ... -0.35
• e: 0.55+0.51-0.35 ... 0.24+0.56-0.24 ... -0.47
• f: 0.68+0.17-0.18 ... 0.36+-0.12 ... -1.48
• g: 1.39+0.76-0.69 ... 0.566+-0.038 ... -1.19
• h: 0.47+0.26-0.26 ... 0.086+-0.084 ... -1.41
So most of the updated-mass results are less than most of the dynamical-stability results, with only one exception, a small one. This is enough to force planets e, f, g, h down from being mostly rocky to being mostly watery.

Li Zeng's page Planet Models contains some tables of radius as a function of mass for various compositions: iron to rock to water, then hydrogen-helium. The most detailed table: has "100%fe 95%fe 90%fe 85%fe 80%fe 75%fe 70%fe 65%fe 60%fe 55%fe 50%fe 45%fe 40%fe 35%fe 30%fe 25%fe 20%fe 15%fe 10%fe 5%fe rocky 5%h2o 10%h2o 15%h2o 20%h2o 25%h2o 30%h2o 35%h2o 40%h2o 45%h2o 50%h2o 55%h2o 60%h2o 65%h2o 70%h2o 75%h2o 80%h2o 85%h2o 90%h2o 95%h2o 100%h2o cold_h2/he max_coll_strip"
The rock used was MgSiO3 in a perovskite structure.

4. Jun 14, 2017

### lpetrich

The TRAPPIST-1 planets have the remarkable property of being in a chain of mean-motion resonances. Mean motion = mean angular velocity = (2*pi)/period.

This chain has ratios
8:5:3:2, 3:2, 4:3:2
It includes all 7 known planets of the TRAPPIST-1 star.

One can find a "resonance gap" angular velocity from
$$\omega_{res} = \frac{n_2 \omega_1 - n_1 \omega_2}{n_2 - n_1}$$
where the n's are the resonance numbers and the ω's are angular velocities.

The resonances all share a fundamental frequency, a frequency that corresponds to a period of around 1.35 years. I checked on the observations of TRAPPIST-1, and I found:
• La Silla, Chile, 60cm, TRAPPIST-South -- 2015 Sep 17 - Dec 31, ... 2016 Apr 30 - Oct 11
• Oukaïmeden, Morocco, 60cm, TRAPPIST-North -- 2016 Jun 1 - Oct 12
• India, 2m, Himalayan Chandra Telescope (HCT) -- 2015 Nov 18
• Paranal, Chile, 8m, Very Large Telescope (VLT) -- 2015 Nov 8
• Hawaii, US, 3.8m, UK Infrared Telescope (UKIRT) -- 2015 Dec 5, 6, 8, 10, 11, ... 2016 Jun 24, Jul 16, 18, 29, 30, Aug 1
• La Palma, Canary Islands, 4.3m William Herschel Telescope -- 2016 Aug 23 - 35
• Sutherland, South Africa, 1m, South African Astronomical Observatory -- 2016 June 18, 19, 21, 22, Jul 2, 3
• Spitzer Space Telescope -- 2016 Feb 21, Mar 3, 4, 7, 13, 15, Sep 19 - Oct 10
• Kepler Space Telescope -- 2016 Dec 15 - 2017 Feb 1, 2017 Feb 6 - Mar 4
TRAPPIST = TRansiting Planets and PlanetesImals Small Telescope

So TRAPPIST-1 has been observed off-and-on over from 2015 Sep 17 to 2017 Mar 4, nearly 1 1/2 years, a little more than my calculated resonance period.

But TRAPPIST-1's observers have likely scheduled some additional observing time, and they may already have started some more observations of the star.

[1605.07211] Temperate Earth-sized planets transiting a nearby ultracool dwarf star
[1703.01424] Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1
[1703.04166] A seven-planet resonant chain in TRAPPIST-1
[1704.04290] Updated Masses for the TRAPPIST-1 Planets

5. Jun 14, 2017

### halbhh

Regarding the surprising idea earlier that Trappist 1 is a "quiet" star, that's now to be replaced with this -- "The energy distribution of the 42 observed flares shows that TRAPPIST-1 belongs to the more active group of M-dwarfs."
https://phys.org/news/2017-04-frequent-flaring-trappist-1unsuited-habitability.html

So, then the expected effect of frequent flaring would be....atmospheric loss, unless a very unusually strong magnetic field is present, and also intense radiation. But this was only the typically expected situation, isn't that right, because red dwarfs typically are active (but now I see the thread the needle idea that until this large amount of small flares is considered, that previously it was thought if the planets formed far away during a more intense flaring stage and then with the hypothesis the star is quieter (but even for larger flares, just precisely how much frequency, since it could only take a 1 or a few direct hits of bigger flares to end any life as we know it?) then the planets migrate into near a hypothesized 'quiet' star, so the April results are closing that scenario down more firmly. When first announced about the 7 planets and the phrase "Earth like", this was the first thought that came to mind -- flares. If even before the frequent flares shown back in April, the scenario was depending on so many just-right outcomes, then we should never have thought "good candidates", but instead "long shot candidates".

Last edited: Jun 14, 2017
6. Jun 14, 2017

### lpetrich

So those planets would be much like Venus and Mars -- most of their surface and atmospheric water stripped off. That raises the question of what would happen to an ocean planet. How much of such a planet's super ocean would survive to the present? Would it all get stripped off, leaving a rocky core?

7. Jun 14, 2017

### Staff: Mentor

The density measurements are for the current situation. We don't know how large the initial oceans were, but if the density now indicates large oceans then apparently a large ocean survived. Or the planet is made out of something we don't expect.

8. Jun 14, 2017

### halbhh

An ocean world is an interesting possibility. It would be good to see a simulation, because of the fact that the flares are not that weak, and the planets so very much closer than Earth. Even with a nicely high magnetic field say twice as strong as Earth's (an optimistic scenario?), I'd guess before seeing the simulation that it is not enough protection that close to the star. The ocean could protect against the radiation intensity, but not against the atmosphere loss unless the magnetic field is enough, and if a larger flare hits, that level of 'enough' is very high I'm guessing, since I read these little red dwarfs can flare just as strongly as our much larger sun. Do coronal mass ejection intensities fall off with the square of distance, or are they held together magnetically? The planets are 25 - 35 times closer than Earth is to the Sun.... 900 times intensity would matter, and then how could the magnetic field be enough? And even if it was merely linear, even just a factor of 25 is pretty drastic. I'd want to see the simulation. (Of course, in time, our observations will trump the simulations.)

Here's one paper I see from a wiki:

^ Khodachenko, Maxim L.; et al. (2007). "Coronal Mass Ejection (CME) Activity of Low Mass M Stars as An Important Factor for The Habitability of Terrestrial Exoplanets. I. CME Impact on Expected Magnetospheres of Earth-Like Exoplanets in Close-In Habitable Zones". Astrobiology. 7 (1): 167–184. Bibcode:2007AsBio...7..167K. doi:10.1089/ast.2006.0127. PMID 17407406.

"Abstract
Low mass M- and K-type stars are much more numerous in the solar neighborhood than solar-like G-type stars. Therefore, some of them may appear as interesting candidates for the target star lists of terrestrial exoplanet (i.e., planets with mass, radius, and internal parameters identical to Earth) search programs like Darwin (ESA) or the Terrestrial Planet Finder Coronagraph/Inferometer (NASA). The higher level of stellar activity of low mass M stars, as compared to solar-like G stars, as well as the closer orbital distances of their habitable zones (HZs), means that terrestrial-type exoplanets within HZs of these stars are more influenced by stellar activity than one would expect for a planet in an HZ of a solar-like star. Here we examine the influences of stellar coronal mass ejection (CME) activity on planetary environments and the role CMEs may play in the definition of habitability criterion for the terrestrial type exoplanets near M stars. We pay attention to the fact that exoplanets within HZs that are in close proximity to low mass M stars may become tidally locked, which, in turn, can result in relatively weak intrinsic planetary magnetic moments. Taking into account existing observational data and models that involve the Sun and related hypothetical parameters of extrasolar CMEs (density, velocity, size, and occurrence rate), we show that Earth-like exoplanets within close-in HZs should experience a continuous CME exposure over long periods of time. This fact, together with small magnetic moments of tidally locked exoplanets, may result in little or no magnetospheric protection of planetary atmospheres from a dense flow of CME plasma. Magnetospheric standoff distances of weakly magnetized Earth-like exoplanets at orbital distances <or=0.1 AU can be shrunk, under the action of CMEs, to altitudes of about 1,000 km above the planetary surface. Such compressed magnetospheres may have crucial consequences for atmospheric erosion processes."

Last edited: Jun 14, 2017
9. Jun 14, 2017

### halbhh

Was just seeing this --

"But actual mathematical models conclude that, even under the highest attainable dynamo-generated magnetic field strengths, exoplanets with masses like that of Earth lose a significant fraction of their atmospheres by the erosion of the exobase's atmosphere by CME bursts and XUV emissions (even those Earth-like planets closer than 0.8 AU—affecting also GK stars— probably lose their atmospheres)."

Ouch.

https://en.wikipedia.org/wiki/Habitability_of_red_dwarf_systems

Totally worth observing, but I'm expecting no atmosphere. My guess is we need a solar system much more similar to our own to find something we ourselves would be able to inhabit other than underground (though I'd be pleased to find out otherwise, it just doesn't seem realistic given current information).

10. Jun 14, 2017

### Staff: Mentor

A deep ocean could replenish the atmosphere for quite some time (even Earth has about 300 times the atmospheric mass as oceans, and we are not living on an ocean planet), simply by evaporating. Oceans only go away once all the water has escaped - and you need both hydrogen and oxygen to escape. If only hydrogen escapes, you might get a very dense oxygen/water atmosphere.

11. Jun 14, 2017

### lpetrich

TRAPPIST-1 also has sizable starspots, judging from its light curve in Figure 2 of the improved-masses paper. The star rotates with a period of around 3 days.

Figure 3 in that paper shows how orbit fits were improved by adding the Kepler "K2" observations. It shows observed TTV's and calculated TTV curves from a large number of randomly-generated orbits. That random generation was a result of Markov-Chain Monte Carlo (MCMC) fitting, something that seems much like simulated annealing. Randomly change the parameters, and if they improve the fit, accept them, but if they don't, then accept them with probability exp(-(Enew - Eold)/T), where the E's are error values and T is a sort of temperature.

For b to g, the new curves are well inside the old curves, meaning that the with-K2 mass estimates are both smaller and with smaller error bars than the without-K2 ones. My estimated amplitudes: b: 2 min, c: 2 min, d: 25 min?, e: 10 min?, f: 40 min, g: 30 min.

Planet h has three distinct sets of TTV fits, with a few outlying fits. The most populous set having an amplitude of about 100 min.

From the seven-planets announcement paper, transit durations are b: 36.40+-0.17 min, c: 42.37+-0.22 min, d: 49.13+-0.65 min, e: 57.21+-0.71 min, f: 62.60+=0.60 min, g: 68.40+-0.66 min, h: 76.7+2.7-2.0 min

This may explain the error bars and scatter of the b and c TTV measurements. The scatter is much less for the outer ones.

12. Jan 1, 2018

### Stavros Kiri

13. Feb 6, 2018

### Staff: Mentor

14. Feb 9, 2018

### lpetrich

[1802.01377] The nature of the TRAPPIST-1 exoplanets -- the most recent paper on them at arxiv.

Not So Strange New Worlds - NASA Spitzer Space Telescope, Imagining the Planets of TRAPPIST-1 - NASA Spitzer Space Telescope

These planets likely have a few percent of water by mass, and this translates into something like

b: 400, c: 200, d: 250, e: ~0, f: 250, g: 400, h: 150, all km of depth

with error bars around 100 km of depth. The Earth has 0.023% water by mass, with average depth 3.7 km and planetwide average 2.6 km.

15. Feb 9, 2018

### DrStupid

How reliable is the relationship between mean density and water content? Are there alternative explanations for low densities (e.g. small metal cores)?

16. Feb 11, 2018

### lpetrich

Small iron cores would work, yes. In fact, that likely explains the densities of Mars and the Moon -- they are less dense than what one would expect from the Earth's composition.

So in the case of as much rock as possible, only three of the moons would have sizable oceans -- b: 250, d: 150, g: 250 km depth.

17. Feb 20, 2018

### ExoExplorer

Planets b, c, and possibly d are all in runaway greenhouse state, so their low densities are likely the result of massive and thick steam atmospheres not a layer of ocean or ice. Little water building up bars of water vapor envelope can already explain the radius and masses of the inner three planets without involving large quantity of water in the condensed form.

18. Feb 23, 2018

### lpetrich

There's a little something called Scale height - Wikipedia:

$$H = \frac{kT}{mg}$$

For our planet's atmosphere at the surface and 290 K, it is 8.5 km.

At 1000 K and 1 Earth gravity, the scale height is 47 km -- not much compared to the sizes of these planets.

Hydrogen has a much larger scale height, about 420 km.

Hubble delivers first insight into atmospheres of potentially habitable planets orbiting TRAPPIST-1 | ESA/Hubble planets d, e, and f likely do not have a lot of hydrogen in their atmospheres, or else that telescope would have observed different effective sizes at different wavelengths.