Not to mention the whole crust solidifying into a collection of I assume igneous rock, thereby requiring eons to form new sediment which can be used to create soil, grow things. Weathering will go quite slow if, as you suggest, most of the water boils away and escapes.
IIRC the last “snowball earth” ended when there was enough CO2 pushed into the atmosphere to create global warming and melt the frozen environment. Of course, without plant life, there would be no oxygen - presumably like Mars it would all be tied up bound into assorted crust compounds. (Carbonates, silicates, iron oxides, etc.)
Plus the heat to get that deep would probably help with differentiation, the heavier elements would settle out at the bottom of the melt meaning no more metals to mine until the volcanos, random meteors, and plate tectonics stirred things up again.
From quick google checks there are active lava fields that get re-colonised with lichens and other hardy plants within a century or less, but these are coming from the surrounding unaffected land in a functioning global climate.
The same with post-glacial melt colonisation.
Your terraforming will have to assume there is nothing, except bare igneous rock to start with. However a lot of it would be pulverised into dust-gravel sized particles, which certainly helps. The main break-down mechanisms - biological action, weather and water - all require a climate to have formed. As others have noted, much of your atmosphere and water have been blown away.
A well-cycled colonisation introducing water, selected nutrients and genetically modified bugs and plants to start beefing up the surface of your New Earth could probably be creating something resembling soil in a couple of centuries. A global self-sustaining biosphere would probably take many millenia, but I’d suspect closer to 100,000 years than a million.
I wonder whether a bespoke biosphere created from a single grand design would be more prone to catastrophic failure across the globe from a simple change than the clunky but resilient one with all its built-in diversity we have now.
It would be wrong in GQ to mention Slartibartfast, but you’d want advice from a good terraformer regardless.
As far as the time to cool back down goes: we can estimate it by using the Stefan-Boltzmann Law. Viewed as an isolated system in space, the only way that the heat of the impacts can be lost is via radiative transfer into space. We’ll assume that the heat capacity of the crust is essentially constant with respect to temperature. We also ignore heat conductance from deeper inside the autoclaved Earth, and assume that the temperature of the crust is uniform throughout the cooling process. None of these are particularly good assumptions, but hopefully the answer will still be correct to within an order of magnitude.
If you make all of these assumptions, the surface temperature is governed by the differential equation
C_V dT/dt = - sigma * A * T[sup]4[/sup].
where C_V is the heat capacity of the entire crust, sigma is the Stefan-Boltzmann constant, and A is the surface area of the Earth. If you solve this equation to find the amount of time that elapses between the crust having a temperature of T[sub]i[/sub] and T[sub]f[/sub], it works out to be
where d = 15 km is the thickness of the crust; c[sub]v[/sub] = 0.84 kJ/kg K is the specific heat of the crust (I used basalt, but other numbers could be justified); rho is the density of the crust (3 g/cm^3 for basalt); and all temperatures are measured in Kelvin (T[sub]f[/sub] = 300 K, T[sub]i[/sub] = 1300 K.)
Dropping all these numbers in, I get a cooling time of ~250 years. As noted above, this is a very rough estimate, and there are many complicating factors:
[ul][li]I assume that the planet’s surface can radiate directly into space. The presence of an atmosphere will effectively act like a blanket and slow down the cooling, perhaps substantially.[/li][li]I assume that there is no heat transferred from the mantle into the crust. The additional heat from below will also slow the surface cooling.[/li][li]I assume that the crust is essentially the same temperature at all times. If the thermal conductance of the crust is low, you might get the surface cool enough to stand on before the lower parts of the crust have cooled all that much, which would make my number an overestimate.[/li][/ul]All in all, I’d be relatively confident in saying that it would take “centuries to millennia” for the surface to cool enough to be inhabitable.
Ah excellent, thank you. So send a suitably massive impactor ahead - or, more likely, a probe to make a suitable planetoid into an impactor - and let the generation ship follow in a few millennia. No hurry.
It’s not clear that a 15km melt is deep enough. Even that would take a long time to cool.
Fortunately, this biochemist expects Panspermia, so I expect the bugs on planet X to be no more lethal than the bugs on planet Y.
Go on down and die for a bit, until you figure out cures, or your immune system adjusts. That’d beat heck out spending 200K years in cold sleep waiting for things to cool down, only to wake up and find you did not melt deep enough.
