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I'm imagining an artificial planet of almost pure water constructed by an advanced aquatic species. It's "almost pure" because they included enough impurities in the water for life to thrive, resulting in a composition similar to Earth's seawater. This species wants the entire volume of the planet to be liquid so that it's habitable to life (even if the depths would only be habitable to life adapted to high pressures). They don't want any high-pressure ice in the core. That brings me to my question: how big could this artificial water planet be and not have an ice core?

Note that gravity isn't a concern here, as the artificial planet would be enclosed in a transparent membrane that stops the water being lost to space even if the gravity is low, and its inhabitants can acclimate to a range of potential gravity levels.

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    $\begingroup$ Do you care that an all water world would lack a decent phosphorus supply for hosting any vegetable life? $\endgroup$ – L.Dutch - Reinstate Monica♦ Dec 1 '20 at 9:18
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    $\begingroup$ Phosphorus would be dissolved in the water (as phosphate ions), and the same applies to other nutrients. $\endgroup$ – Pitto Dec 1 '20 at 9:39
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    $\begingroup$ Not that much water boils off into space on Earth so why should it on your world? I don't think you need the membrane. It would be even less likely on a world larger than Earth. $\endgroup$ – Slarty Dec 1 '20 at 10:00
  • $\begingroup$ @Slarty Perhaps "boiling" wasn't the right word: I thought that the artificial planet would likely have less gravity than Earth, so without an enclosing membrane it would lose its atmosphere and thus its water. $\endgroup$ – Pitto Dec 1 '20 at 10:06
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    $\begingroup$ @slarty At Earth size all but the top 100km would be solid ice due to the pressure, that is the point of this poster's question. $\endgroup$ – PcMan Dec 1 '20 at 11:10
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1000-10000km Depending on conditions oceans could be very deep indeed. If the planet had a very high proportion of water and had a warm enough core, then thousands of kilometers should be possible. The limiting factor would be the formation of ice, however according modest extrapolations from this phase diagram it would appear that water might remain a liquid at pressures of 100 GPa at temperatures well in excess of 500 degrees C.

At 1 metre depth the pressure is around 10,000 Pa so that might allow 10,000km of ocean. Even allowing for compression that’s still thousands of kilometers. A 10000km deep ocean would obviously not be possible on Earth as Earths diameter is only around 12000km. But it might be possible on a bigger planet. If Earth’s crust and mantle were replaced by lighter water then there would be a significant depth increase. See this link for related information.

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    $\begingroup$ At temperatures above 374 C, you run into a different problem: the water turns into a supercritical fluid. $\endgroup$ – Mark Dec 1 '20 at 18:41
  • $\begingroup$ @Mark Yes it depends what you mean by a liquid. Above around 650K there is no phase boundary between gas and supercritical fluid. Pressure changes only serve change the density of the substance. Above around 22 GPa there is no phase boundary between a liquid and a super critical fluid. Temperature changes only serve to change the density of the substance. Water exiting from some hydrothermal deep sea vents on Earth is actually a supercritical fluid. $\endgroup$ – Slarty Dec 1 '20 at 22:52
  • $\begingroup$ the 1m - 10000 Pa relation holds true in terran surface gravity. On a planet with less mass the gravity will be lower. The gravity is not constant through the depth of the planet. $\endgroup$ – mart Dec 22 '20 at 8:20
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I pulled out the program I used to answer this question, plugged in some numbers for different temperatures, and got the following:

Temperature Radius
647 K (374 C) 2916 km
373 K (100 C) 2626 km
298 K (25 C) 2063 km
273 K (0 C) 1827 km

The hotter your planet is, the larger it can get. At the lower end, you've got a thin skin of ice surrounding a ball of water with a radius of about 1800 km, slightly larger than Earth's Moon. At the high end, your membrane is pressurizing a 2900-km radius ball of barely-subcritical water to a surface pressure of 22 MPa (about 200 times Earth's atmospheric pressure).

As the temperature drops below 0 C, the layer of surface ice gets thicker, but you don't lose the ability to have a liquid core until the temperature drops to 251 K (-22 C). At the high end, if you raise the temperature any further, the water transitions to a supercritical fluid. It's up to you to decide if you want to call this a liquid or not.

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Insulate your membrane or choose a good sun

In this system, any heat would escape outward. If you have heat inside, the only way it can leave is through the surface. You said that the planet is enclosed in a membrane, so make that membrane insulated to keep heat from inside escaping to the outside.

Now, this will have the side-effect of not allowing any heat in either. So how can you keep the ocean liquid? I'd say your best bet is tidal heating. The idea behind this is that rotating around a big object will cause the liquid to move around, generating heat. Moons like Europa and Io have vast sub-surface oceans because of tidal heating, Europa even having twice the volume of water of Earth despite being smaller than our moon.

If that's not enough heat, you can always have some sort of heater to input extra energy into the system when it runs low on energy.

Given that, I think you could get easily large enough to thousands of species. If heaters don't work for your story, you'll have to make it small enough for the sun's energy to heat the whole thing. I can't give you any specs on this, because it depends on the sun. You'll need to be as close to the sun as possible, but you have to be outside the Roche limit, or your planet will break apart. So brighter sun = more energy that can get to your planet, but that usually is paired with larger sun = the further away your planet has to be, allowing less of that energy to reach it. You'd want the brightest yet smallest mass sun possible to get the largest planet.

The next part of the answer will deal with the assumption that you're using my first solution, because you'll probably want to go bigger than the sun allows.

Now here's your problem: How are these creatures getting their energy? There probably aren't sufficient nutrients in the water (okay, you said they put impurities in the water, but it'll have to be constantly replenished) and definitely no source of energy (unless you're also constantly throwing food in as well). Energy would have to come from the sun, which is blocked out by our insulation. If we removed the insulation, the inside might freeze, but at least energy is going into the system.

And really, even if your inside is liquid without a membrane or anything like that blocking the sun, it wouldn't be habitable to life. Deep-sea ocean life on Earth is only possible because of hydrothermal vents, which couldn't be present in a solely-water world. These vents input energy and nutrients into the system, because absolutely no light from the sun is reaching that depth.

So, in conclusion, the only way I know to have a large, 100% habitable planet is to constantly feed energy and food into the system or to have an ultra-hot yet very small sun. If that works for your story, great. If not, just make it a watery planet without having to worry about ice at the core or anything like that. That way you can have hydrothermal vents and stuff to keep the inhabitants alive. That's my suggestion. It'll also have a lower Roche limit than a 100%-water planet so it can be closer to the sun and get more energy from it.

I hope that helps you. If not, let me know and I'm happy to add anything you need to my explanation.

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  • $\begingroup$ Thanks for the answer. But just to be clear, the membrane is transparent to visible light (I've edited the question to reflect this). So sunlight can still warm up the planet and provide energy for living organisms. $\endgroup$ – Pitto Dec 1 '20 at 9:42
  • $\begingroup$ @Pitto Well, if you google it, you can find some insulators that are light-permeable. They might work pretty well. You could even try and get a greenhouse-affect going, that might also do the trick. Light comes in, bounces around, and can't really get out very easily. If that doesn't work either, the part about placing it near the sun and wanting a hot but small sun still apply. $\endgroup$ – Benjamin Hollon Dec 1 '20 at 9:49
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    $\begingroup$ A greenhouse effect would occur with any material that's transparent to visible light but opaque to infrared. But the nature of the membrane isn't really relevant to my question; my question is about the size of the planet. $\endgroup$ – Pitto Dec 1 '20 at 9:54
  • $\begingroup$ @Pitto As I said in the answer, the exact size you can get depends on the sun. The hotter the sun, the more energy the planet gets, but the larger the sun, the further away from it you have to be. To get the largest possible planet, you want the highest possible ratio of sun energy to sun mass. Without exact numbers on what type of sun you're using, there's not really a way to give you an exact number on how large your planet can be. $\endgroup$ – Benjamin Hollon Dec 1 '20 at 10:00
  • $\begingroup$ I've never heard of the sun being a constraint on planetary size, do you have any links to support this? $\endgroup$ – Pitto Dec 1 '20 at 10:07

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