Will NASA Reveal Oxygen in TRAPPIST-1 Exoplanet Atmospheres?

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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.
 
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[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.
 
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How reliable is the relationship between mean density and water content? Are there alternative explanations for low densities (e.g. small metal cores)?
 
DrStupid said:
How reliable is the relationship between mean density and water content? Are there alternative explanations for low densities (e.g. small metal cores)?
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.
 
lpetrich said:
[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.
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.
 
There's a little something called Scale height - Wikipedia:

[tex]H = \frac{kT}{mg}[/tex]

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.