# Thermodynamics behind the heating of Saturn's moon Enceladus

I was wondering if somebody could explain to me how does the process of Enceladus being heated up satisfy the laws of thermodynamics, more precisely the conservation of energy.

Or should I ask where is the payment for the giant geysers on that moon? In layman terms, please!

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From looking it up and taking a quick glance, the moon is only 500 km in diameter, which means it would have been cooled off for a while thoroughly. But towards the core, it could still be several hundreds of degrees (possibly), heating the water towards the center and making it expand towards the surface. What do you think?

Janus
Staff Emeritus
Gold Member
The primary suspect for the internal heat is from tidal heating. Enceladus is in an orbital resonance with Dione which can causes a periodic change in orbital eccentricity. In essence, Enceladus moves in and out a bit from Saturn as it orbits and this causes a flexing of the crust due to the changing tidal force from Saturn. The friction from this flexing generates heat.

Generator Gawl
I know that, but let me rephrase my question:

A slingshot manuever borrows momentum from the target object, the slinging body essentially borrows moment from the parent body, slowing it down while speeding itself up. An arrowbreaking manuever skims the parent object's atmosphere, enacting the exact opposite trading of forces and energy.

By that logic, where exactly is the energy for the flexing coming from? What forces are being converted? There is no "free lunch" in the universe, so where is the "bill" for the flexing? How does the effect satisfy the laws of thermodynamics?

From looking it up and taking a quick glance, the moon is only 500 km in diameter, which means it would have been cooled off for a while thoroughly. But towards the core, it could still be several hundreds of degrees (possibly), heating the water towards the center and making it expand towards the surface. What do you think?
Mr. Gawl, Cassini already confirmed that Saturn's gravitational pull is generating this effect, besides, water is an excellent thermal conductor, it is highly unlikely that any kind of internal heating wouldn't have lasted for long.

Generator Gawl
Bandersnatch
By that logic, where exactly is the energy for the flexing coming from? What forces are being converted? There is no "free lunch" in the universe, so where is the "bill" for the flexing? How does the effect satisfy the laws of thermodynamics?
The energy dissipated by tidal heating (see: 'tidal dissipation') comes either from the orbital energy of the components of a system, or from their rotational kinetic energy.
To clarify: Orbit here means the orbit of the satellite and the parent body around their common barycentre, and not the heliocentric orbit (unless it's the solar tides that are being considered).

In a 2-body system such as Earth-Moon it's relatively easy to pinpoint where the energy comes from. It becomes harder with N>2 body systems, such as that of Saturn and its moons, but as a rule of thumb, in the end it's all paid for by the rotation of the parent body.

So then eventually its going to stop spinning and get tidally locked, then no more friction?

Janus
Staff Emeritus
Gold Member
So then eventually its going to stop spinning and get tidally locked, then no more friction?
Enceladus is already tidally locked in the sense of its rotation. The flexing is caused by its moving in out out from Saturn. The energy for this comes from its orbit. Over time the eccentricity of this orbit would typically become more and more circular. This is where Dione comes in. It's tug on Enceladus helps to keep the orbit eccentric. (at the expense of its own orbital energy.) However, on the other hand, tidal action between these two moons and Saturn, transfers rotational energy from Saturn to the Moons ( like Earth transfers rotational energy to the Moon), so ultimately, you could say that the slowing of Saturn's rotation helps power the internal heat of Enceladus

Or you could say Enceladus is one of the minute reasons Saturn is slowing its rotation. We must be careful with our semantics here, we do not know what the instigator is of the forces at hand!

Chronos
Gold Member
In light of our recent findings on Pluto, et al, a bit of doubt about the mechanisms behind the heating of Enceladus is probably warranted.

You better explain how one is related to the other otherwise I will accuse you of trying to change the topic!

Bandersnatch
You better explain how one is related to the other otherwise I will accuse you of trying to change the topic!
Perhaps I might, assuming this is what Chronos meant.

The Pluto-Charon system is approximately fully-synchronised. I.e., both bodies are tidally locked to each other. The remaining bodies in the system are not terribly massive, so their tidal influences ought to be minor - as evidenced by the tidal lock of the main bodies.

And yet, the surface of Pluto shows relatively limited cratering despite a collision-heavy environment (lots of junk floating around out there).
It's as if some source of heat was periodically melting the ices comprising the surface, smoothing it out.
Whether that has anything to do with tidal dissipation, and is not caused by e.g. the heat of collisions themselves, or anything else whatsoever, is unknown. But it's a nice topic for research, and who knows what we might learn once data from the New Horizons probe starts flowing in.

Or you could say Enceladus is one of the minute reasons Saturn is slowing its rotation. We must be careful with our semantics here, we do not know what the instigator is of the forces at hand!
I wouldn't put it that way, unless by the many 'minute reasons' you mean the many satellites (and rings) of the planet - after all, each of those migrating outwards 'steals' angular momentum from Saturn's rotation.

It's pretty well-understood that angular momenta in orbiting systems are being exchanged due to tidal interactions (i.e., gravity and friction).

You know, you have addressed this situation with unusual intrigue, you all appeared to have dodged the question and danced around it like politicians!

Would it not be easier to say just that there isn't enough data available to make an adequate answer?

Bandersnatch
You asked where does the energy come from, and the answer was from orbital and rotational energy.

As yes, I suppose you're right... and its probably my own fault for flagging the question as intermediate...

D H
Staff Emeritus
Or you could say Enceladus is one of the minute reasons Saturn is slowing its rotation.
This isn't just a minute reason. Ultimately, it is the sole reason. It's not the orbits, as suggested by Janus. Those moons are receding outwards. That requires energy rather than yielding energy. The energy source for that tidal recession is the same energy source for the tidal heating: Saturn's rotation. Those moons are very, very slowly slowing down Saturn's rotation rate.

That said, Enceladus remains a bit of a mystery. Equilibrium tidal heating plus internal heating would suggest an output of about 1.4 gigawatts. What has been observed is several times that. Apparently Enceladus is not in an equilibrium state; we happen to be seeing Enceladus at a time where it is excited tidally at significantly more than that suggested by equilibrium condition.

That said, Enceladus remains a bit of a mystery. Equilibrium tidal heating plus internal heating would suggest an output of about 1.4 gigawatts. What has been observed is several times that. Apparently Enceladus is not in an equilibrium state; we happen to be seeing Enceladus at a time where it is excited tidally at significantly more than that suggested by equilibrium condition.
Apparently I knew that, which is why I came here in the first place. Could it be that it has some decaying radioactive elements inside its core?

Chronos
Gold Member
Youe dismissive replies to reasonable suggestions is little more than a debating tactic.

D H
Staff Emeritus
Apparently I knew that, which is why I came here in the first place.
Apparently not. If you already knew that you would have cited Meyer and Wisdom, "Tidal heating in Enceladus," Icarus 188.2 (2007): 535-539, which finds "that equilibrium tidal heating cannot account for the heat that is observed to be coming from Enceladus."

Could it be that it has some decaying radioactive elements inside its core?
No. That is estimated to be only 0.3 GW.

Note that I wrote equilibrium tidal heating, as did Meyer & Wisdom. The most obvious solution is that Enceladus is not in a deep equilibrium resonance with Dionne. The processes of entering and exiting orbital resonances are rather chaotic, and there may be resonances at play. Perhaps that deep, stable equilibrium is not possible. Perhaps the models used by Meyer & Wisdom (and others) are incomplete. Or perhaps Saturn's rings and its inner moons are rather young (where tens to hundreds of millions of years qualifies as "young"), and Enceladus is still dissipating some of its primordial heat. Or perhaps there's another answer.

In any case, it's still a bit of a mystery, and that's a good thing. Science needs its mysteries to keep science moving forward.