PLANETPLANET

If you ever drop your keys into a river of molten lava, just let them go because, man, they’re gone. — Deep thoughts by Jack Handey

---

This series is about how planets die — it is introduced here.

What do you think of when you hear the word tides? Ocean waves?  The Moon?  Maybe sitting on a beach with an umbrella drink? (All good choices by the way)

Tides are just a side effect of gravity.  (A side effect that may sterilize more planets than any other process in the Universe — run for your lives!)

Let’s take a look at tides on Earth, which are controlled by the combined gravity of the Sun and Moon.

The Sun and Moon each create a tidal “bulge” on Earth.  That bulge makes the oceans stretch out in that direction.  When the two bulges are lined up, the overall change the the height of water is the highest — those are “Spring tides”.  When the bulges are not lined up the tides are weaker.

Those bulges are just gravity.  The gravitational force between two objects depends on how far apart they are.  Two times closer means gravity is four times as strong.

Take the Earth and Moon.  The side of Earth that faces the Moon is a little closer to the Moon.  So the Moon’s gravity pulls hardest on that side of Earth.  And the opposite goes for the far side of Earth: the Moon’s gravity is the weakest there.

From the point of view of the center of the Earth, the Moon pulls half of the Earth toward it and pushing the other half away:

That stretching force — caused by differences in gravity on different sides of the Earth — is where those tidal bulges come from. 

Every object can make a tidal bulge on every other object, but the bulges only matter when objects are close enough so gravity is strong.  For instance, the Earth creates a tidal bulge on the Moon by stretching the Moon’s rocks (since it has no oceans).  But the tidal bulge that the Earth creates on Venus is so small that it’s irrelevant.

Tides are a big deal on giant planet moons.  There is a lot of tidal action on Jupiter’s four big (Galilean) moons, especially the innermost one, Io.  Io is covered with volcanoes that are erupting pretty much all the time.  The outgassing is even visible from space!

Io’s volcanoes are driven by tides. Io has a tidal bulge created by Jupiter’s gravity, just like Earth does from the Moon’s gravity.  Except Jupiter’s gravity is a lot stronger.

The difference is that Io’s bulge is always changing shape.  This is because its orbit around Jupiter is elliptical.  It’s almost a perfect circle but not quite (it’s actually closer to being circular than Earth!). When Io is closest to Jupiter in its orbit the bulge is the biggest and when Io is farthest its bulge is smallest.

The continual change in the stretching of Io causes massive internal friction.  It’s like taking a paper clip and bending it back and forth a bunch of times. It gets hot fast. (Go ahead and try!)

As Io gets stretched and squished, friction makes heat in its interior.  This tidal heat is released by volcanoes (and actually produces a ring of plasma around Jupiter!)

The last piece of the puzzle is Io’s orbit.  Why isn’t it a circle?

Over millions and billions of years, tides couple the evolution of stars’ and planets’ and moons’ orbits (and submoons often go unstable).  Tides usually act to turn elliptical orbits into circular ones, and also to make moons show the same face to their planet.

But Io does not orbit Jupiter alone.  Its neighboring moons are constantly giving it gravitational kicks.  These kicks are nowhere near as strong as the ones Io gets from Jupiter, but they are enough to keep its orbit from becoming a perfect circle.

If we put this together we have a two ingredient recipe for tidal heating:

1. Strong gravity (for strong tides)
2. Other moons or planets (to maintain elliptical orbit)

Pretty simple, right? And guess what?  Billions and billions of potentially habitable planets follow this recipe.

Let’s start thinking about tidal heating in the context of planets orbiting stars.

Tidal heating is really strong for planets orbiting close to their stars. Most stars are smaller and fainter than the Sun.  Their habitable zones are much closer than Earth’s orbit around the Sun.  So tides are much much stronger.

This graph shows the tidal heat escaping from the surface of an Earth-sized planet in the habitable zone of different types of stars (the Sun is at 1.0).  For scale, Io’s tidal heat flux is the red horizontal dashed line, and Earth’s internal heat (from radioactivity in the core and mantle) is the green one.

Wherever the gray line is above the red one, the planet is heated across its surface more strongly than Io. This happens for planets orbiting stars that are less than about 20% of the Sun’s mass.  These are small, faint, red dwarf stars.

The graph above assumed that the planet’s orbit was nearly circular but not quite.  The planet has an orbital eccentricity of 1% (for scale, Earth’s average eccentricity is 3%).  This graph shows the tidal heating for planets with three different orbital shapes:

The tidal heat flux increases dramatically for planets on orbits that are more elliptical orbits. Even a slight change in shape makes a big difference in heat. On the other hand, the tidal heat is much lower for more circular orbits.

But what happens on a planet with a super high heat flux?  Probably something like this (with extra lightning thrown in):

The main point is: when heat is generated inside a planet, it needs to get out!  And that is what volcanoes do — they let heat out from the insides of planets.  (Yup, volcanoes are sort of like planets barfing, but it’s best to try never to think of that).

How many volcanoes do these planets have: a few high-powered ones or a zillion puny ones?

Io has a few hundred volcanoes.  Earth has about ten times more surface area than Io.  For the same amount of tidal heat, Earth would either have ten times as many volcanoes as Io, or if it had the same number of volcanoes as Io then they would each be ten times more active.  Boom!

Tidal heat can also affect a planet’s atmosphere.  The dust thrown up by a big volcanic eruption can actually block sunlight and cool off the planet — this is called volcanic winter and may be at the origin of some of Earth’s little ice ages.

But tidal heating generally heats a planet up, of course.  Enough tidal heating can trigger a runaway greenhouse effect.  The planet’s atmosphere heats up a little, which makes it heat up more, and more, and so on.  It’s a climate catastrophe!

A runaway greenhouse effect on an Earth-like planet would turn it into a Venus-like planet.  Same size and mass but much less pleasant to live on.  (Fun fact: a hellish Venus-like climate is one of four possible stable climates for Earth — see here).

Let me get to the point: tidal heating can be really bad for life.

Some tidal heating is no big deal.  Tidal heating up to Earth’s level of internal heat may actually be a good thing, as it’s possible that it could generate or help sustain plate tectonics, which acts as a planetary thermostat (via the carbonate-silicate cycle).

How much tidal heating is too much?  A runaway greenhouse would sterilize a planet, and that is triggered at about a hundred times higher heat flux than Io.

Is an Io-like level of tidal heating too much for life?  Volcanic eruptions would be constant. Instead of your local grocery store you’d have your local volcanic crater.   But it probably wouldn’t sterilize the planet. I mean, check out the Star Wars planet Mustafar:

So the limit for tidal heating to sterilize a planet is higher than Io’s heating, but not too too high (runaway greenhouse requires about 100 times more).

How many planets are strongly affected by tidal heating?

Back to our checklist for tidal heating.  First up, strong gravity.  That means that planets must be close to their stars.  About 3/4 of all stars in our Galaxy are puny little red dwarf stars.  Those stars’ habitable zones are really close-in, where tides are strong.  And 1/3 to 1/2 of all puny red stars have Earth-sized planets in their habitable zones.

Second, tidal heating requires more than one planet.  The vast majority of systems of planets around puny red stars have many planets. Check.

There are a few hundred billion stars in our Galaxy.  Let’s say 400 billion to make the numbers work out nicely. That’s about 300 billion red dwarf stars, and at least 100 billion of which have a roughly Earth-sized planet in their habitable zones.

That’s 100 billion planets!  But what exactly does tidal heating look like?

To answer this question we need to dip our toes in the dark waters of orbital dynamics.

Let’s start with Earth.  Earth’s orbit around the Sun is almost a circle but not quite.  It’s very slightly stretched-out, with an orbital eccentricity of a little less than 1%.

But Earth’s orbit is not fixed.  It changes in time because of gravitational kicks from the other planets.  Its orbital shape bounces between a just about perfect circle and an ellipse with an eccentricity of about 6%.  These oscillations happen on a timescale of about 100,000 years:

While these oscillations in orbital shape are relatively minor, they correlate strongly with Earth’s historical climate (called Milankovitch cycles).  Other oscillations in Earth’s orbital and spin properties also contribute to these cycles.

Venus, Mars, Jupiter and the other planets undergo oscillations in their orbits as well.  It’s like a see-saw: one planet can’t kick another around without feeling the back-reaction. And each planet is kicking each of the others all of the time.

In any system with many planets, the shapes of the planets’ orbits oscillate in time.  And the orbits are rarely perfect circles.

Systems of planets around red dwarf stars kick each other around just like our own planets. Earth’s orbital shape takes about 100,000 years to oscillate (see image above).

The timescale over which a planet’s orbital shape changes depends on the orbital structure of the system.  In general, planets on shorter orbits undergo faster oscillations than planets on longer orbits.  Since planets with strong tides are so close to their stars, these oscillations happen much faster than on Earth.

For planets in the habitable zone on which tides are strong — meaning around red dwarf stars — the timescale for orbital oscillations can vary between about 1 year and more than 1,000 years.

Here is an extreme example: the evolution of the orbital shape of the ~Earth-sized exoplanet TRAPPIST-1e, which orbits a tiny, ultracool dwarf star. Kicked around by its 6 neighbors, the planet’s eccentricity oscillates on a timescale of just over a year!  There are longer-term (~70 year) oscillations also, but the main frequency is ~1 year:

Remember that tidal heating is sensitive to the orbital shape!  Imagine an Earth-like planet in orbit around a red dwarf star.  Its orbit oscillates like Earth’s between a circular shape and an eccentric one.  Its rate of tidal heating goes up and down at the same rate:

Even if the tidal heating goes up and down every year it doesn’t mean that volcanism necessarily will change on such a short time frame.  Geological processes take time.

What would it be like to live on a planet like this?  Remember that the tidal interactions that create internal heat also affect a planet’s spin.  Planets become “tidally locked”, always showing the same face to their stars.

These are Eyeball planets.  Planets on closer orbits would be “hot Eyeball” planets, with super-hot day sides and a “ring of life” (the super-romantic zone of permanent sunset/sunrise) in which water could be liquid, and ice-covered night sides.

Planets on more distant orbits would be Cold Eyeball planets, completely covered in thick ice sheets except for a pond in the permanent day side.

On tidally locked planets the Sun doesn’t move in the sky.  There is no “day” because the Sun never rises or sets; depending on your location on the planet the Sun is either up or not, and it doesn’t move.  The “year” is impossible to pin down on the sunlit side, but on the night side can be figured out from the motions of the stars.  The year — the orbital period — is typically a few Earth days to a week or two, depending on the star.

The action of tides also makes the axial tilts of these planets drop to very small levels.  Earth’s axial tilt is 23.5 degrees and is the reason we have seasons.  With no axial tilt these planets would not have seasons like ours.  The only seasons on these planets come from their orbital shapes, when a portion of their elliptical orbits takes the planet closer to the star.

This is a pretty cool setup for a science fiction story. 

Imagine this: a civilization blossoms on a planet while it is in a circular orbital phase. Geologists and astronomers are just starting to understand the orbital dynamics of their home planet — and the fact that it oscillates between calm and volcanic periods — as the next volcanic age is approaching…

Then things get crazy.  Maybe warring factions battle over the small area of the planet that isn’t susceptible to volcanic destruction. Maybe there is a massive race to develop spaceflight technology, followed by a massive competition for the very limited cargo space on interplanetary flights.  Can other planets in these systems be colonized?  The best candidate for colonization might be a neighboring planet in the system has an orbital shape that oscillates out of phase (meaning, that planet’s orbit is circular when the main one’s is stretched-out, and vice versa) — by jumping back and forth between planets, a space-bearing civilization might be able to avoid the biggest volcanic blasts.

There is another, dramatic mode of tidal heating.

The example with oscillating orbital shapes is how systems behave most of the time.  But not always.

Sometimes systems become a little unstable.  Not so strongly unstable that planets crash into each other, but unstable enough to rapidly stretch out the orbits of one or more planets’.  There are a few different effects lurking in the dark waters of orbital dynamics that do this (for example, when tides drive planets across orbital resonances).

When an instability hits, a planet can jump suddenly from a circular orbit to a stretched-out one.  The rate of tidal heating skyrockets. Things can change fast.

The planet cannot become a volcanic hellhole overnight. There is a time lag — the planet’s insides must heat up from internal friction and then magma must make it all the way up to the surface. I don’t know how long this would take but I suspect it would be measured in the thousands to millions of years.

Imagine how a civilization would change on a planet whose orbit underwent a sudden dramatic shift.  They might understand how their home planet was slowly heating up and preparing to become a volcanic wasteland and would need to figure out what to do next….

Finally, how deadly is tidal volcanism on our planetary death scale? 

Strong volcanic activity cannot destroy a planet but it can dramatically alter its landscape.  It can cause massive extinctions.  In extreme cases tidally-driven volcanism could sterilize a planet, for example when a planet on a circular orbit is kicked onto a stretched-out orbit.

Of course, maybe tidal volcanism could lead to a type of natural selection for organisms that are particularly resistant to lava and wild temperature swings…

---

Resources

• Introduction to the how planets die series
• Blog posts about Hot and Cold Eyeball Planets
• How the habitable zone may be affected by tidal heating (including a simple equation for tidal heating): Barnes et al (2010)
• How tidal heating can trigger a runaway greenhouse and turn “Earths” into “Venuses”: Barnes et al (2013)
• A code to simulate the evolution of planetary systems with strong tides written by Emeline Bolmont: Bolmont et al (2015)
• How planets die from climate catastrophes (coming next week)