# Have there been any determinations of the water pressure in Europa's ocean just below the ice?

In this Astronomy SE answer to How can "Geysers" on Europa reach heights of 100km? there is discussion of the possible role of pressure at the top of Europa's ocean in the ability of the recently observed vapor plumes to reach 100 to 200 kilometers above the surface. Europa has a surface gravity of about 1.3 $$m/s^2$$ and it would take a velocity of 500 $$m/s$$ to rise ballistically to 100 kilometers for example.

In this question I am just asking if there have been any determinations, either inferred from observations or from simulations, of the pressure of the water at the top of the ocean where it meets the ice. Something quantitative? A number, even roughly?

If it's highly variable with time due to tidal effects, then it's the highest pressure that's more interesting.

A first guess might be that the pressure is what you'd get by calculating the weight per unit area of the ice above. In that case, if there is a crack, the water would rise approximately to the surface of the ice and the pressure would drop to approximately zero. What I am after is if there is ever any substantial pressure beyond this - does the pressure ever deviate so much higher than that, that it would become important in the discussion of cryovolcanos, geysers, and jets?

But here I'm just asking about determinations of pressure. above: Diagram of Europa's Ice surface and subsurface ocean, from the JPL News feature Scientists Find Evidence of 'Diving' Tectonic Plates on Europa.

• Questions on planetary science and observations by Hubble seem to fall on the dividing line between Astronomy and Space Exploration. The original was asked there, and I've asked the follow up here.
– uhoh
Sep 27, 2016 at 18:03
• Why would the average ocean pressure matter in this case? What you're really looking for is the pressure in confined regions: news.nationalgeographic.com/news/2011/11/… Sep 27, 2016 at 18:05
• Those regions are in flux. As the ice moves, it increases the pressure in the "lakes". Sep 27, 2016 at 18:06
• @called2voyage time average - not spatial average. I forget that people can't hear me think some times. The pressure in the ice is complicated, but the pressure in water should be quite smoothly varying. It's hydraulics.
– uhoh
Sep 27, 2016 at 18:07
• Ok, but I'm still confused because you're asking about the top of the ocean and it is not clear to me that the ocean is what is relevant at all, unless you just mean all bodies of liquid water: jpl.nasa.gov/news/news.php?feature=4285 Sep 27, 2016 at 18:08

It is easy to calculate. The ice is reported to be 15 to 25 km deep. Simply take the weight of the ice in Europa's gravity over one square meter of the top of the ocean.

Calculation in Wolfram Alpha

You get 24 MPa, or about 240 atmospheres for 20 km of ice.

However that ice sitting on the ocean is in equilibrium, just as ice is floating in a glass of water, and so that pressure cannot be a source of energy for cryo-volcanism. You need some other energy input, which in this case would be Jupiter tidal forces.

• Thanks, but I'm asking if there are any determinations of pressure beyond a simple estimate, not how to calculate it. Since the system is dynamic, there's a solid core, an ice crust, maybe tidal forces, it may not be so simple. "A first guess might be that the pressure is what you'd get by calculating the weight per unit area of the ice above.... What I am after is if there is ever any substantial pressure beyond this..." A link to a paper or abstract - paywalled is fine in this case.
– uhoh
Sep 28, 2016 at 1:57
• I don't mean to suggest this pressure is the thing that can drive cryovolcanism on Europa. That's how I got started on this but really I'm just curious if the pressure at the liquid/ice interface is thought to ever deviate from what you'd get from the weight of the ice. The Wolfram alpha link is nice - a lot easer than typing all the MathJax and it's live and useful as well. Even gives the energy density equivalent in $Bq/m^3$ of radon decay - enquiring minds want to know!
– uhoh
Sep 28, 2016 at 2:29
• uhoh: I'm confused by your reference to the system being dynamic. Although I haven't looked at the answer's calculation, as described it assumes hydrostatic equilibrium. If that isn't satisfied, there has to be some substantial energy source to increase the pressure and a lot of strength in the ice to withstand it. What are your thoughts? Feb 1 at 20:28