Better Masses for TRAPPIST-1's Seven Planets

[lpetrich]

I had earlier posted on Seven planets orbiting a star. Now, some follow-up.

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

Very technical:
[1703.01424] Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1 (early 2017)
[1704.04290] Updated Masses for the TRAPPIST-1 Planets (early 2017)
[1802.01377] The nature of the TRAPPIST-1 exoplanets (the most recent one)

The TRAPPIST-1 planets are observed by the transit method, by watching them cross across their star and block some of their star's light. That method gives their sizes, but not much else about them. However, the planets are in orbital resonances, and that amplifies their perturbations of each others' motions. This produces observable Transit Timing Variations (TTV's), and this effect has been used to determine the masses of several exoplanets, including the TRAPPIST-1 ones.

Planet	Distance	Period	Mass	Radius	Eq Temp
b	0.012	1.51	1.017	1.121	392
c	0.016	2.42	1.156	1.091	335
d	0.022	4.05	0.287	0.784	282
e	0.029	6.10	0.772	0.910	246
f	0.036	9.21	0.934	1.046	215
g	0.047	12.35	1,148	1.148	194
h	0.062	18.77	0.331	0.773	169

Units: AU, Earth days, Earth mass and radius, K

As you can see, the error bars are much improved over the earlier calculations, and we now have good masses for all these planets. Combined with their radii, this gets their average densities in g/cm^3:

b: 4.00, c: 4.87, d: 3.40, e: 5.64, f: 4.50, g: 4.18, h: 3.96

That's only enough to determine planets' compositions if the planets are made of only two materials. But we can plausibly expect at least three: iron, rock, and water, meaning that a planet might be mostly rock, or else some mix of iron, rock, and water, while having the same mass and density.

So I used the paper's estimate of the iron/rock ratio, a little bit less than for the Solar System. I find these relative masses of water:

b: 0.05, c: 0.02, d: 0.05, e: ~0, f: 0.02, g: 0.04, h: 0.03

Error bars: ~ 0.1

Those numbers don't look like much, but the Earth has 0.00023 for its oceans. Those oceans' average depth is 3.7 km, and averaged over all the planet's surface, 2.6 km. So I find these estimated ocean depths in km:

b: 400, c: 200, d: 250, e: ~0, f: 250, g: 400, h: 150

Error bars: ~ 100

So with that composition, at least 6 of the 7 planets have superdeep oceans by Earth standards.

 

[Malintent]

This is my first visit to this thread. I am hear to say that every time I see this thread title, it makes me want a beer.

Trappist is a Belgium style ale that uses some fairly ancient yeast strains that are unique to the Belgium Trappist Monk's Abbeys.

It was the Trappist Monks (I think) that changed the Church's position on drinking beer during Lent (or was it on the Sabbath, I forget). 1,500 years before McDonalds got the FDA to categorize French Fries as a Vegetable for the purposes of allowing their products into school cafeterias, the Trappists got the Church to categorize Beer as a kind of Bread, for the purposes of being able to drink during a "holy time".

 

[lpetrich]

A month ago, someone expanded the article  TRAPPIST-1 by a factor of 2. I edited that article to indicate more clearly why moons are unlikely. If they are too close, they get pulled apart, while if they are too far, they tend to escape. Unlike in the Solar System, the TRAPPIST-1 planets have narrow stable regions for possible moons. In any case, there is no well-established observation of *any* exomoons, despite many exoplanets being likely to have them.

[2010.01074] Refining the transit timing and photometric analysis of TRAPPIST-1: Masses, radii, densities, dynamics, and ephemerides

The planets' radii are now known to within 1%, and the planets' masses to within 5%, and 3% for four of them. This is because of their gravitational interactions, something that makes transit timing variations (TTV's). These are amplified by the orbital resonances of the planets:

8:5, 5:3, 3:2, 4:3, 3:2

The planets have resonance periods of around 1.3 years. Neighboring triplets have "Laplace resonances" with combinations:

(2,-5,3), (1,-3,2), (2,-5,3), (1,-3,2), (1,-2,1)

This is much like the moons of Jupiter Io, Europa, and Ganymede, which have 2:1 resonances and a (2,-3,1) combined Laplace resonance. For those three moons, 2*lng(Io) - 3*lng(Europa) + lng(Ganymede) = 180d to lowest order (lng = celestial longitude in orbit plane), but comparable values for the TRAPPIST-1 system are different, though approximately constant.

There is no evidence of an eighth planet with a mass much like the known planets' masses and in an orbit not far outside the known planet's orbits.

 

[lpetrich]

We have only two observed physical quantities for each planet, its mass and its radius, and that means that structure models with more than two components are only partially constrained, like structure models with iron, rock, and water. If a planet's core is large, then it must also have a lot of water. But if its core is small, then it must have very little water.

Let's look at the Solar System. Mercury: 75%, Venus: ?, Earth: 31%, Moon: 1-3%, Mars: 24%.

A lot of variation. For Mars-sized or Earth-sized cores, planets b, c, and d have very thin oceans, if any. Planet e has 0.3% or 2.9% water, planet f 1.9% or 4.5%, planet g 3.5% or 6.4%, planet h 3.0% or 5.5%.

The Earth's oceans have 0.2% of the Earth's mass, and their average depth is 3.7 km, or 2.7 km relative to the Earth's total land surface. For 4% of mass, this is about 20 times as much, or an average depth of 54 km.

[2101.08172] Characterisation of the hydrospheres of TRAPPIST-1 planets -- not sure how they estimated planet-core sizes

[2110.03340] TRAPPIST-1: Dynamical analysis of the transit-timing variations and origin of the resonant chain

We analyze the recently published best-fit solution of the TRAPPIST-1 system, which consists of seven Earth-size planets appearing to be in a resonant chain around a red dwarf. We show that all the planets are simultaneously in 2-planet and 3-planet resonances, apart from the innermost pair for which the 2-planet resonant angles circulate. By means of a frequency analysis, we highlight that the transit-timing variation (TTV) signals possess a series of common periods varying from days to decades, which are also present in the variations of the dynamical variables of the system. Shorter periods (e.g., the TTVs characteristic timescale of 1.3 yr) are associated with 2-planet mean-motion resonances, while longer periods arise from 3-planet resonances. By use of N-body simulations with migration forces, we explore the origin of the resonant chain of TRAPPIST-1 and find that for particular disc conditions, a chain of resonances - similar to the observed one - can be formed which accurately reproduces the observed TTVs. Our analysis suggests that while the 4-yr collected data of observations hold key information on the 2-planet resonant dynamics, further monitoring of TRAPPIST-1 will soon provide signatures of 3-body resonances, in particular the 3.3 and 5.1 yr periodicities expected for the current best-fit solution. Additional observations would also give more precise information on the peculiar resonant dynamics of the innermost pair of planets, and therefore additional constraints on formation scenarios.