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Timing Titan’s Tidal Migration

Finding out that Titan is migrating away from Saturn should cause little surprise. Our own Moon moves away from the Earth at about 38 millimeters per year (even as Earth’s rotation slows ever so slightly, lengthening the day by 23 microseconds every year). Titan’s gravitational pull on Saturn causes frictional processes inside the giant world that ultimately impart energy to Titan, moving it away from its host in a similar way. The surprise attendant to a new paper on this phenomenon is the size of the movement, about 100 times greater than had been expected.

The paper explains the migration process like this:

Tidal friction within Saturn causes its moons to migrate outwards, driving them into orbital resonances that pump their eccentricities or inclinations, which in turn leads to tidal heating of the moons.

What we’re wrestling with here are the processes of energy dissipation in giant planets, which determine the timescale for their moons’ tidal migration. The theory advanced in this work may explain them.

The paper appears in Nature Astronomy, with Valéry Lainey (Paris Observatory) as lead author. Two teams of scientists used both astrometric and radiometric datasets, two different approaches into the same question, to measure Titan’s orbit over a ten year period. Astrometry produced measurements of Titan’s position in relation to background stars, tapping data from the Cassini orbiter. The radiometry work measured Cassini’s velocity as it was affected by the gravitational influence of Titan, revealed by analysis of the spacecraft’s radio transmissions during ten close flybys of the giant moon.

Usefully, the two datasets produced results in tight agreement. Co-author Jim Fuller (Caltech) proposed in 2016 that Titan’s migration rate would be considerably faster than predicted by standard tidal theories. Fuller’s idea was that Titan’s effect on Saturn, a gravitational squeeze at a particular frequency, would create strong oscillations, what the paper refers to as “inertial waves,” inside the planet. The process is a tidal forcing effect known as ‘resonance locking.’ Saturn’s oscillations, Fuller believed, would cause energy to be dissipated, allowing Titan to migrate outward at a faster rate only weakly sensitive to orbital distance.

The Cassini data from two different analyses confirm what Fuller has been saying. Indeed, whereas the prediction had earlier been that Titan would be migrating outward at 0.1 centimeters per year, the actual number is 11 centimeters per year. Resonance locking means that we can’t assume that moons like Titan form at the orbital distance at which we see them now. Instead, we see at Saturn a system that Fuller believes evolved far more dynamically.

Image: A giant of a moon appears before a giant of a planet undergoing seasonal changes in this natural color view of Titan and Saturn from NASA’s Cassini spacecraft. Titan, Saturn’s largest moon, measures 5,150 kilometers across and is larger than the planet Mercury. This mosaic combines six images — two each of red, green and blue spectral filters — to create this natural color view. The images were obtained with the Cassini spacecraft wide-angle camera on May 6, 2012, at a distance of approximately 778,000 kilometers)from Titan. Image scale is 29 miles (46 kilometers) per pixel on Titan. Credit: NASA/JPL-Caltech/Space Science Institute.

So we’re beginning to re-think how planets affect the orbits of their moons. These results suggest that Titan started out much closer to Saturn, with the system of moons expanding more quickly than earlier thought. Rather than assuming that outer moons like Titan migrated outward more slowly than inner moons, we learn that these outer moons can migrate at a similar rate. Migration turns out to be even more complex than first believed, with results at Saturn that have implications for how we study far more distant systems including exoplanets around host stars. Thus the paper’s conclusion:

Resonance locking could operate in other moon systems, such as the Jovian system, where it might drive the outward migration of Io/Europa/Ganymede and predicts a much smaller effective Q [the tidal quality factor] for Callisto if it is caught in a resonance lock. Resonance locking can also act in stellar binaries and exoplanetary systems, but it will not always dominate tidal dynamics, for instance, at very close separations when equilibrium tidal dissipation is more important, or when resonances are saturated by chaotic or non-linear effects. But resonance locking could be especially important at wider separations where equilibrium tidal dissipation is negligible (as it is for Titan’s migration), or in situations when a star or planet evolves on a relatively short timescale owing to a rapid evolutionary phase, accretion, magnetic braking or gravitational wave-driven inspiral.

The paper is Lainey et al., “Resonance locking in giant planets indicated by the rapid orbital expansion of Titan,” Nature Astronomy 8 June, 2020 (abstract).

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{ 12 comments… add one }
  • wdk June 11, 2020, 14:11

    Wish that I understood more about the tidal models of gas giants vs. terrestrial planets. But my suspicion is that there might be differences in assumptions about how much of a gas giant’s body is subject to fluid
    manipulation by a secondary body such as a moon. With the Earth we think of tides in terms of the oceans. to a much less degree lower regions of magma, if we consider them at all. Gas giants potentially have very large oceans, what with atmospheres not having clearly defined lower bounds. My poster child for this subject is Neptune and Triton: a retrograde moon and retrograde winds. Coincidence?

    Then, of course, since it is observed that the radial departure of Titan
    (vs. Triton – migrating inward) is considerable, with a prehistory closer to Saturn more recent than expected, this also suggests that gas giants might have been in the business of calving terrestrial planets like ice shelves calve icebergs. Who knows, maybe we are living on one?
    But if we are to invoke a Mars-sized planet to collide with the early Earth to explain the existence of the Moon, then we have to explain where the Mars-sized planet came from too. Evidence for such processes might be lurking in the exoplanet database and the solar system impact record.

    • Michael Fidler June 12, 2020, 1:49

      What and how long before Saturn’s influence is gone and Jupiter’s take over? Where would Jupiter send this giant Comet/Planet?

    • Michael Fidler June 12, 2020, 1:50

      Maybe Europa came from Saturn!

  • charlie June 11, 2020, 15:45

    “Co-author Jim Fuller (Caltech) proposed in 2016 that Titan’s migration rate would be considerably faster than predicted by standard tidal theories. Fuller’s idea was that Titan’s effect on Saturn, a gravitational squeeze at a particular frequency, would create strong oscillations, what the paper refers to as “inertial waves,” inside the planet. ”

    So when Dr. Fuller speaks of particular gravitational squeezing at certain particular frequencies is this to be interpreted as to mean that more than one body is involved in enhancing a particular gravitational effect? Is there any further way to expound what is being said here? The reason I am asking is because it’s confusing how you can have an enhancement of a particular gravitational frequency.

    I understand what they mean by frequency here, but it becomes difficult to understand how a particular frequency is enhanced over other frequencies in the process; is there anyone out there who can add some further clarification to the matter?

  • Robert Flores June 11, 2020, 18:40

    For permanent colonization of Titan, this would be a deep time issue.

    In 1 x 10^6 years x .11 meters = 11,000 km outwards, increment to
    the radius of Titan’s Orbit.

    Does a weakening of the Tidal forces from Saturn Mean that Titan’s Hydrocarbons, would deplete if the their source was cryovolcanoes?

    Could this affect the overall surface temperature, making the nitrogen atmosphere freeze out?

    If Saturn Jupiter Sun alignment causes the extreme tidal stresses that
    cause modest “moutains” on Titan, would these turn into ‘molehills’ over time due to the lessening pull from Saturn?

    • Alex Tolley June 12, 2020, 12:05

      I think you have your decimal point a couple of places out.

      Round numbers:

      10 cm/yr = 10^-1 m = 10^-4 km.
      For 10^6 years => 10^2 km

      At that rate, Titan would be inside Titan’s Roche limit in 10 bn years, or twice the age of the solar system.

      If it had been 10^4 km/my, then this would have occurred in 100 my and Titan would have to be a very young moon of Saturn (assuming constant rates).

      • Robert Flores June 12, 2020, 22:40

        Yes, I made some errors, to say the least.

        Interesting though that the original estimate of
        Titans increase per year was .1 cm / Yr
        and the revision is 11 cm / Yr

        That is one heck of a change.

  • Geoffrey Hillend June 11, 2020, 20:40

    Although resonance locking applies to Moons gaining orbital energy around larger bodies like Saturn to Titan, I don’t think it can be applied as a general principle to all two body problems, i. e., to binary star systems since their larger mass is controlled by general relativity. For example: close binary star systems radiate gravitational energy, so their orbital distance between them decays if we include two white dwarfs, binary pulsars, neutron stars, black holes etc.

  • wdk June 12, 2020, 11:25

    Zdenek Kopal and others did a lot of work on tidal effects among binary stars. I think I have a couple other studies in the office. But in the case of stars or gas giant planets, it comes down to departures from the two body point mass systems. Were one object considerably more rigid than the other, you might be conceptualize the problem as distortions of the fluid mass into something akin to two bodies – and hence three.

    Then as well, One could imagine that in a red giant phase, if the orbiting planet or brown dwarf were substantial enough, it might spend some time immersed n the outer envelope of the primary star. Features tracked in Betelgeuse , I believe, for a time there was debate whether one was a star spot or a genuine immersed planet. I don’t know how that was resolved, but maybe by the time such a feature disappears, it could have been both.

    • charlie June 13, 2020, 17:13

      wdk,
      do u know the ans. to my ques. above?

  • wdk June 14, 2020, 23:52

    Charlie,
    The quick and straight answer is that I do not know.
    But I will keep my eyes out looking for clues.
    “Frequency” suggests “resonance” and amplification,
    but it’s just my conjecture at this point.

  • Laintal June 17, 2020, 7:20

    While on the subject of Titan I was just reading this one

    http://spaceref.com/saturn/evidence-for-volcanic-craters-on-saturns-moon-titan.html

    Interesting comments

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