[ExI] Double-Earth (Was: kepler study says 8.8e9 earthlike planets)

[Anders Sandberg]

OK, now I have the time to run my code, based on what I have gathered 
from the exoplanet literature. Welcome to dry and wet Double-Earth:

A lot hinges on whether we assume Double-Earth started out beyond the 
iceline and moved inwards, in which case it will be really wet, or 
started out close to the sun and never got much volatiles. In the first 
case the mass will be about 3 Earths and the average density 37% of 
Earth, with a surface gravity of 0.73 g and an escape velocity of 13.6 
km/s. This will have an ocean hundreds of kilometres deep, surrounding a 
rocky core covered with high pressure warm ices. In the second case the 
mass will be 15 Earths, the density will be 167%, gravity 3.4 g and 
escape velocity 30 km/s.

Note that if the component rock contributes water like on Earth, a 
planet with 15 times the mass but only 4 times the area will have 3.75 
times deeper hydrosphere, assuming everything equal.  That means 16 km 
deep oceans - "dry" Double-Earth might still be a waterworld.

Now we need to make some guesses at atmosphere and temperatures. The 
basic temperature for a greybody with Earthlike albedo at this orbital 
distance (1 AU around a sun-like star) is 250 K, if we add the 36 K 
greenhouse correction of Earth this becomes 13 degrees C average.

In the wet case the scale height is 11.3 km - air pressure will be 36% 
less at this altitude. The temperature needed for a molecular species to 
escape is 1.49 times on Earth: in this case hydrogen certainly escapes 
and I think helium will escape (it depends on the exosphere temperature, 
something that is hard to calculate). Methane and ammonia could be 
retained, but if there is life and oxygen they will have been turned 
into carbon dioxide and nitrogen.

In the dry case scale height is 2.4 km: clouds will be very low. The 
retention temperature is 7.5 times Earth - dry Double-Earth could 
potentially retain hydrogen gas. This means that potentially it could 
have gathered a much denser atmosphere from the beginning, potentially 
turning into a gas giant. Note however that by assumption we had it form 
in the "dry" zone near the star, so it might not have accumulated that 
much. We should still expect it to have a denser atmosphere than the wet 
case.

If we make the assumption that the surface pressure is proportional to 
surface gravity (might make sense in this particular case) wet 
Double-Earth has surface pressure 0.73 and dry Double-Earth surface 
pressure 3.4 atmospheres. Let's also assume the mean wind speed is a 
terrestrial 10 m/s - again, this is hard to evaluate without running a 
full model. Finally, most doubtfully, let's assume the rotation period 
is 24 hours.

In this case wet Double-Earth gets air density 0.9 Earths. The radiative 
timescale of 1.8 days and advection timescale of 1.4 days - this means 
that the weather is complex like on Earth, and responds rather quickly 
to seasons (ah, I implicitly assumed an Earth-like axial tilt: things 
will get really strange if it is more extreme). Wet will have about 9-10 
jet-streams (Earth has about 7). Dry Double-Earth instead has surface 
air density is 4.3 times Earth, fast timescales and 10 jet streams. Not 
too alien.

Weather is partially driven by buoyancy. On wet Double-Earth this is 
weaker: clouds will be taller and move more ponderously, while on dry 
Double-Earth the higher gravity will make small density differences 
generate more force: flatter, more intense convection. The strength of 
hurricanes depends on the temperature difference between the ocean and 
the stratosphere; I do not know how to calculate this, but I note that 
in the absence of land they can run much longer before drifting too far 
towards the poles that they dissipate. I am a bit uncertain about 
whether latitudinal mixing is strong enough to keep the poles too warm 
to form ice sheets or not. I suspect the lack of land will destabilize ice.

If we assume 20% oxygen, then dry Double-Earth will have 537 mmHg 
partial pressure oxygen - toxic to humans. Even worse, the partial 
pressure of CO2 will be 10.4 mmHg - causing hypercapnia in humans. 
Still, local life could likely evolve to handle that with little 
problem. Wet Double-Earth looks pretty OK for humans.

The radiogenic heating (assuming an Earthlike composition) of dry 
Double-Earth is 3.34 times higher than on Earth, 0.29 W/m^2. Still not 
enough to melt the crust into an Io-like volcanic mess, but it is far 
more active. Wet Double-Earth will have less radiogenic heating than 
Earth, although this is complicated by the very different composition. I 
still get continental drift (hence churning the ice crust), but it is 
not as vigorous and it will stop earlier (reducing convection in the 
deep ocean, likely strongly reducing the available minerals to life).

Mountains on wet Double-Earth will tend to be 1.37 times taller than on 
Earth, but they will all be on the bottom of the super-deep ocean. On 
dry Double-Earth they will be just 0.29 times the height - the local 
Mount Everest will be just 2.4 km. Given my guess at mean ocean depths, 
this means that it will indeed be a waterworld.

If one buys the idea that Coriolis-Lorenz dynamos in the core scales as 
sqrt(density/period) the magnetic field of wet Double-Earth will be 60% 
of Earths, while dry Double-Earth 130% - not an enormous difference, 
although wet Double-Earth will be less protected. Note that it has an 
enormous store of volatiles to bleed off, though. The higher cosmic 
radiation might be nasty for beings on the surface, but the water 
absorbs it fine.

The optical depth of the atmospheres on the Double-Earths will be the 
same as on Earth (because of my assumption of pressure = surface 
gravity), so you can see the same distance. The vertical optical depth 
is 1.37 times more than Earth on wet Double-Earth: the sky is more 
milky, but not too alien. On dry Double-Earth it is just 1.1: almost 
normal. If you were to fly a plane, it would however turn dark blue at a 
much lower altitude.

On the oceans, waves would be moving differently. On wet Double-Earth 
they would move at 85% of Earth speed, while on dry Double-Earth 184%. 
The height would of course scale inversely with gravity: 136% on wet 
Double-Earth, but just 29% on dry Double-Earth. So the seas would be 
choppier but slower in the wet case (but the waves will have more energy 
per square meter), while the dry case would have fast low swells.

To sum up: both Double-Earths are waterworlds, but one is *deep*. 
Neither has any land. Both might have interesting deep sea vent 
ecologies, the wet case around vents in the high pressure ice and the 
dry case more terrestrial-style vents (which are more common than on 
Earth). On the surface the ocean has weather like on Earth, either 
strangely tall or fiercely squat clouds. Life could probably thrive on 
both worlds, but would be limited by minerals: no land, no surface 
weathering, and hence less minerals added to the oceans. Getting into 
space from wet Double-Earth is about as tough as on Earth, while dry 
Double-Earth is pretty tough to get away from.

-- 
Dr Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University