PLANETPLANET

Time for an astro-thought experiment.

You belong to a super-advanced civilization with the ability to shape the cosmos as you wish. You can move around black holes, stars, planets, comets and moons (like the builders of the ultimate planetary systems).

What would your civilization plan for big celebrations? What are their ‘fireworks’?

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What astronomical phenomena could create cosmic fireworks? Each would need to be short in duration and very bright. Here are a few ingredients that astronomical engineers could use to make cosmic fireworks:

• Shooting stars, also known as meteors. These are the bright lines that flash across the sky when a piece of space dust (usually about the size of a grain of sand) burns up in the atmosphere. Meteors can show up anytime, but meteor showers happen regularly when Earth passes through a trail of debris that was left behind by a comet. For example, the Orionids in late October (as well as the Eta Aquariids in early May) are associated with dust left behind by Halley’s comet hundreds of years ago.
• Impacts. Collisions in space happen on all size scales, although smaller impacts are more common. In the present-day Solar System we are lucky to occasionally catch a glimpse of a small meteoroid crashing into the Moon. Of course, the building of the planets involved a series of ever-larger collisions, culminating (for our planet) with the Moon-forming impact.
• Tidal disruption events. These happen when something is torn apart by gravity, from comets being shredded by passing too close to planets to stars being torn apart by black holes. The most famous Solar System example is comet Shoemaker-Levy 9, which was torn apart after passing close to Jupiter in 1994 (and its fragments crashed down onto Jupiter a couple years later). But you may have seen news of stars being torn apart by black holes.
• Supernova explosions. These are perhaps the ultimate astronomical explosions. They are beacons that can be observed billions of light years away, used to study the expansion history of the Universe.

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Now let’s put together two astronomical fireworks shows.

We’ll start with a show designed for us on Earth (for creatures with human-like eyes on a planet like our own). For us puny humans, shooting stars are pretty awesome (especially in a big meteor shower), but supernova explosions are only visible on rare occasions in human history. Of course, humans don’t have much experience in directly observing tidal disruption or collisions, since those are super rare. Plus, the events we could see are the same ones that are likely to wipe us out!

Earth is bombarded with meteoroids (that burn up as meteors in our atmosphere) when our planet’s orbit takes us through a trail of debris left behind by a comet. Shooting stars generally look white, but that can in some cases appear colorful if they produce super-heated gas of a particular composition.

With an audience on Earth, the best target for collisions is the Moon. We have some images of space rocks crashing into the Moon (like in the image above) — they look like bright flashes. While it would be nice to use larger-scale collisions, we don’t want to destroy the Moon or threaten our audience.

Would any tidal disruption events would be both visible to the naked eye from Earth and non-destructive for humans? The gravity of Earth and the Moon can disrupt fragile asteroids or comets (so-called `rubble-piles‘). It’s risky to use Earth as the disruptor, but the Moon can work.

Planet-scale fireworks (for viewing by humans) could be orchestrated by a carefully-coordinated series of objects flying around in the vicinity of Earth’s orbit. They might be a symphony of:

• Multi-colored shooting stars — from any direction and with any timing you want.
• Flashes on the Moon — again with any chosen timing and with different colors, creating shimmering images or spelling out words.
• Tidally-disrupted objects, creating streamers stretching across the face of the Moon.
• Explosions from hot air balloons left high up in the atmosphere, just out of eyesight (until they explode), or maybe pre-placed satellites containing explosive gases with particular colors.

I’m not going to choreograph it in any more detail because I’m too excited about the next one…

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Now let’s go bigger and build a cosmic fireworks display on the scale of the Ultimate Solar System.

My goal is to create a system that, once released to follow its natural evolution, will produce a ring of supernova explosions around a black hole. To make it work I’ll use an orbital trick called the Kozai-Lidov mechanism.

Let’s use of a special kind of supernova explosions called Type 1a. Their intrinsic brightness can be inferred from observations of their light-curves, and they have been used to demonstrate that the Universe’s expansion is currently accelerating (this research was awarded the Nobel prize in 2011).

Type 1a supernovae happen when a carbon-oxygen white dwarf slowly grows in mass until its constituent electrons (supported by electron degeneracy pressure) can longer hold their own weight. The growth in mass is thought to usually come from a close binary star that puffs up as it evolves into a giant and its outer layers spiral onto the white dwarf.

Things get bonkers when the white dwarf reaches 1.44 times the Sun’s mass (the Chandrasekhar limit). The white dwarf begins to convect internally and within a few seconds, all of the white dwarf’s carbon and oxygen undergo nuclear fusion. This triggers a colossal explosion that tears the white dwarf apart, throwing material out at ~6% of the speed of light. A Type 1a supernova typically shines about 5 billion times brighter than the Sun, fading in brightness over the course of a month or two.

I don’t want just one supernova in our cosmic fireworks, I want a whole ring of them. The easiest way I know to set up a ring of white dwarfs is by placing them in orbit around a supermassive black hole (as in the million-Earth Solar System).

[Technical paragraph] I explained how to build a ring of planets around a star in the Ultimate Engineered Solar System. It’s the same process for white dwarfs around a black hole. Let’s start with white dwarfs that are each 1.4 times the Sun’s mass, just 0.04 below the Chandrasekhar limit. We’ll use a black hole that is one-third of a million (or 333,333) times as massive (side note: this is about the same as the Earth-to-Sun mass ratio), which amounts to about 466,000 times the Sun’s mass. The Hill radius R_Hill of each white dwarf at orbital distance a is simply a times the cube root of the mass of white dwarf divided by 3 times the black hole mass [or, R_Hill = a (M_wd/3M_bh)^1/3]. Given our choice of black hole mass, the cube root is simply 0.01, or 1%. So R_Hill = 0.01 times a. In a given ring we need to space white dwarfs by at least 12 R_Hill, — the number of Hill radii per orbit is just N = 2 pi a divided by R_Hill , or 2 pi a / 0.01 a, which is just 200 pi, so N = about 628. We can fit 42 white dwarfs on stable orbits, separated by 15 R_Hill (42 is a convenient number: the answer to life, the Universe and Everything).

How can we trigger supernovae in these 42 white dwarfs?

We need to add some mass to these white dwarfs to push them over the Chandrasekhar limit. In many type Ia supernovae, mass is added gradually from a stream of gas stolen from a binary star (as in the image above). But I want to be able to time things more carefully, so I want to add a chunk of mass instantaneously to push each white dwarf over the limit as a specific time.

Let’s put a tiny star in orbit around each white dwarf. We’ll make each one 0.1 times the Sun’s mass, so when it collides with the white dwarf it will be nicely over the supernova limit. But when and how will these tiny stars collide with their white dwarfs?

Enter the Kozai-Lidov mechanism. This is an orbital phenomenon that was developed to explain the orbits of certain planetary satellites (by Lidov) and asteroids (by Kozai). The Kozai-Lidov mechanism comes into play when two orbits orbit each other, and are perturbed by another, distant object. Under certain circumstances, the perturbation from the distant object can change the shape of the two main objects’ orbits.

Here is a simple example: a satellite orbits a planet, which orbits a star. The satellite’s orbit is nearly circular, but is strongly tilted with respect to the planet’s orbit around the star. Perturbations from the star cause the satellite’s orbit to change shape, becoming less tilted but more stretched out. The satellite’s orbit can continually oscillate, with the amplitude of the orbit’s tilt (or orbital inclination) exchanging with the degree of stretched-out-ness (or orbital eccentricity). The reason for these oscillations comes from conserving orbital angular momentum. The Kozai-Lidov mechanism can do some pretty weird things, even sometimes causing orbits to flip direction (for animations of the Eccentric Kozai-Lidov mechanism, see the website of UCLA Professor Smadar Naoz).

In our setup, each supernova will be triggered by the collision between a tiny star and a white dwarf. Like in the image above, we want each tiny star to start off on a nearly circular orbit around its white dwarf that is close to perpendicular to the orbit of the white dwarf around the black hole. The star’s orbit will stretch out as it becomes less tilted until it is so stretched-out that, at closest approach, it collides with the white dwarf.

To start, we need to make sure there is enough orbital space for the star around the white dwarf. Our chosen white dwarf- to black hole mass ratio is almost exactly the Earth-Sun mass ratio, meaning that the Hill sphere is the same as Earth’s (about 1% of an astronomical unit). The star can easily have an orbit similar to the Moon’s around the Earth, although of course it will start off tilted on its edge compared with the white dwarf’s orbit around the black hole.

Here is what this system looks like (not to scale):

In designing such a system, there is a moment when it is released to follow nature. We assume that our super-advanced civilization can build something, and natural laws take care of the rest.

The Kozai-Lidov mechanism operates on a set timescale that is easy to calculate. It mainly just depends on the orbital period of the white dwarf around the black hole, and the orbital period of the star around the white dwarf. With such massive objects the orbital periods are short: it takes each white dwarf about 15 hours to orbit the black hole (for an orbit the same size as Earth’s around the Sun), and it takes each star about 1 hour to orbit its white dwarf (for an orbit the same size as the Moon’s around the Earth). This means that each Kozai-Lidov cycle takes about 9 days, so it will take half of that — four and a half days — for each star to collide with its white dwarf.

So if we build the ring of white dwarf-red dwarf binaries around the black hole and release it, the orbits of each of the red dwarf stars will start to stretch out and become less tilted. Then, about 5 days later, it will go boom! Here is my cartoon-like view:

Supernova explosions are fast. If the stars are not each set up just right then the supernovae might not be exactly simultaneous. Would this matter? Well, if one supernova went off too soon, it would mess up the even orbital spacing of the ring of white dwarfs. This would make the ring unstable, but it would not make any difference because the other supernova explosions would happen before the orbits of the white dwarfs could get too weird.

What happens next? Almost all of the mass in the 42 white dwarfs and red dwarfs would be launched into space over a span of months. Some would fall onto the black hole and create an accretion disk like the one already included in the images above. But a lot would get blasted outward. Each supernova leaves behind an expanding cloud of gas, a supernova remnant. In time this gas is mixed into the Galaxy’s gas reservoir, providing a large fraction of the heavy elements needed for rocky planets. Our 42-supernova fireworks would create a stupendous mega-supernova remnant that would remain as an eye-catching gas cloud for millennia to come.

Supernovae may not be so great for nearby planets. The barrage of high-energy photons can strip planets’ atmospheres or destroy their ozone layers, but only for relatively nearby planets (within ~20 light years). With 42 simultaneous supernovae, planets will be affected to a distance of a few times farther out (perhaps 50-100 light years). But that is just a tiny speck of any galaxy’s real estate — for scale, our Milky Way galaxy is more than 100,000 light years across.

So, how would our audience enjoy this fireworks display? It would look pretty majestic, even viewed from a long distance. We have to assume that our super-advanced friends could watch the show from a safe distance without getting fried. We also must hope that they have the attention span to watch for long enough to make it worthwhile — at least a month or so, ideally, and up to a millennium.

After I first shared this blog post on twitter, I got some feedback and guidance from supernova specialists. Here is an animation of a simulation of a ring of 42 simultaneous supernovae run by Almog Yalinewich, a researcher at the Canadian Institute for Theoretical Astrophysics (headed by my friend Juna Kollmeier, with whom I figured out whether moons can have their own moons):

In Almog’s simulation, the colors correspond to the density of gas on a logarithmic scale: dark blue is a strong concentration (as you can see at the expanding shock front) and white is a region that has been emptied out. Scaling to the size of our ring of supernovae and the relevant gas density, the duration of the simulation is about 2000 years. Pretty spectacular (as long as you stay out of the blast zone)! There is no black hole in the simulation, for now…

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Finally, you might wonder: did we hold back? Why weren’t there multiple rings of supernovae around that black hole? And what about gamma-ray bursts and other crazy astronomical events? Let me just say that — yes, there is always something bigger to build….

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Resources

• Using black holes as the central bodies in planetary systems: the Black Hole Solar System
• How to build rings of planets around stars: the ultimate Engineered Solar System
• Putting those ideas together: the million-Earth Solar System
• The sad part: The How planets die series
• Website of Almog Yalinewich, expert of supernova explosions and creator of the animation seen above.