What to do with all the heat in a Dyson Sphere?

Question

In the wake of this, my answer to this question about where to put a Dyson Sphere an apparent issue came up. And it needs some good resolution:

What are we going to do with all that heat the system generates?

The premise is that a Dyson Sphere with a radius of about 1AU is/will be built around a star. As we now have fully enclosed this star¹, we have a huge black sphere that has to somehow get rid of all the heat generated by the central star.

This question is about finding engineering solutions for getting rid of that heat.

---

Answers will be graded after the following criteria:

• How elegant is the proposed solution?
• How well does the solution scale when confronted with more or less heat?
• How well does it keep the sphere hidden from any observers?

_{¹And in the process consumed all the planets and other bodies in this and a few of the surrounding systems}

Answer 1

I think the best solution would be a Matrioshka Brain. This is effectively a layered set of Dyson spheres. Once it reaches equilibrium, each shell has a particular temperature differential across it, which can be used to generate work. These shells feed eachother, so the total temperature drop across the entire brain is equal to the temperature of the star minus the temperature of interstellar space.

The neat thing about Matrioshka Brains is that the temperature of the radiating surface of each layer is lower than the previous. With some careful effort, you could eventually radiate all the power of the star in a spectrum that is closer and closer to that of background radiation. You can't get it perfect (there's no such thing as stealth in space), but you can get close.

This makes it substantially harder to detect the brain. It is very hard to distinguish a signal whose spectrum is close to that of noise. You have to listen for a long time. It gets even harder from a distance. Most observations of thermal characteristics like this are from a distance where the Matrioshka brain would subtend only the tiniest fraction of a pixel. This means the temperature of the brain would be averaged with the temperature of the background radiation, and that average would be heavily weighted towards the background radiation.

EDIT: A key that I failed to mention is that there is an assumption here that there is value in harnessing the energy. Once energy is no longer in thermal form, there's many more options. For example, one might export high-potential-energy materials to be emitted elsewhere. It might be amusing to go collect the results of solar fusion from other stars and use the energy from the Matrioshka brain to un-fuse them back into hydrogen to be used in fusion reactors! A lot of options open up once you've sucked as much of the energy as possible out of the solar radiation instead of emitting it as heat!

Answer 2

In order to keep your dyson sphere hidden, you don't really have to do anything.

There's two key things to keep in mind.

1. The whole point of a dyson sphere is to extract as much useful energy as possible to do useful work with.

2. There's a maximal efficiency of any method to extract work from heat energy, and that efficiency is determined by the difference in temperature between the heat source and the thing you're dumping the heat into.

Our Heat Source:
Assuming a star like our sun, the surface is 5778 K.

Our Heat Sink:
The vacuum of space at 2.7 K.

That gives us a maximal theoretical efficiency of 1 - (2.7 / 5778) = 0.99953271028

So, assuming a dyson sphere at earth's radius, if we wanted to be as stealthy as possible and emit all heat in directional lasers, we could make the effective black body temperature of the outer surface be:

p = 1374 W (normal power output per square meter of dyson sphere surface)
b = 5.67 x 10^-8 W/(m²*K⁴) Stefan–Boltzmann constant
e = efficiency with which we can convert heat to lasers
t = effective temperature

p*(1-e)=b*t4

Solving for t we get a temperature of 58 K. So that's about the coldest we could possibly make the sphere appear. Very cold, but still not the 2.7 K of empty space.

But doing that would get us absolutely no useful work out of any of the star's energy.

If we do absolutely nothing to camouflage our sphere and just use absolutely all of the available energy for useful things:

p = b * t4

t = 394.549 K or ~ 250 Fahrenheit

This would put the radiation at:

b = Wien's displacement constant = 2.8977729×10⁻³ m⋅K
w = black body wavelength intensity peak
t = temperature

w = b / t = 7.3 * 10-6

Which puts it in the near infrared with it being just a little bit of a dark red glow in the visible spectrum. Which unfortunately is still warmer than the coldest brown dwarfs.

All of this assumes there are no other realistic inefficiencies, but basically you're looking at making the sphere somewhere between 58 K and 394 K, but the colder you make it, the less energy you get to actually use out of it. And the colder you make it, the harder it will be to detect, but you'll never be able to make it completely undetectable.

Also of note, you can lower these temperatures if you make the sphere larger. But if you make it too big you'll start running into the problem of it being more likely that your sphere occludes some other star, giving it away.

Answer 3

Being careful with your aim

You can't not radiate, so if you want to not be observed then you need to make sure you aren't radiating in the direction of your nearest neighbours. To do this you'll need to somehow channel all the energy into a series of directional beams that are aimed in-between the stars closest to you. The amount of power you'll need to pump through those emitters will vary depending on the number of emitters you have, so let's have a look at some numbers:

How much energy have we got to lose?

Lets assume we're talking about our sun for now.

3.8×10²⁶ W

OK. Just to be clear that's an awful lot of zeroes.

How can we absorb it?

There are a couple of answers to this, some on this very site. Let's assume that we use a couple of shells to create some vast thermal power plant and we can then shuffle the electricity around. It's not going to be perfect, there will still be some ambient radiation, but with decent insulation and design it should be well below the amount that's noticeable at interstellar distances. If you want to decrease the energy leakage then increase the number of shells (like adding very big, complicated blankets to a very big incandescent baby).

How can we get rid of it?

Let's turn to the ever excellent Randall Munroe for this one.

The Boeing YAL-1 was a megawatt-class chemical oxygen iodine laser mounted in a 747. It was an infrared laser...

There are bigger lasers, but they all fire for fractions of seconds.

So we've got a laser that can fire on the order of megawatts of power. Lets assume they each fire at 3.6MW and we can run them continuously and see how many of them we need...

10^21 lasers. Assuming they each take up a meter squared that's 1/281'th of the space we have to play with on the outside of our sphere. Not great, but it's usable. If we can get more laser apertures in then we can improve upon that, but preferably we want to be able to shift their aim.

Now, if we aim them at the darkest bit of sky we can find from their individual location (parallax is going to be important at these scales), then we'll be minimising our chances of being noticed. Again: This isn't perfect. The lasers won't have perfect beam coherence, so the beam will be more of a cone spreading out into the stars. This in turn means that stars further away might be clipped by an intense and regular source of radiation, spawning all sorts of wild theories about rapidly rotating stars and suchlike.

What about the bits that aren't laser arrays?

Clad them in long wavelength EM absorbent materials, refrigerate them and pump the heat back into the inner shell of your stellar power plant. Sure, you're going to hugely increase the entropy of the system as a whole, but when you're engineering a Dyson sphere I think minimum-entropy concerns are pretty much out the window...

Naturally this has some problems (heat buildup on the laser arrays being a large one) and some potential improvements (the IR lasers probably aren't the best way to direct the energy, some form of particle beam apparatus may well be better) but it should suffice to mask you from a casual observer.

One last note: Make sure the lasers are evenly spread or you'll end up pushing your shell ever so slowly out of position, and crashing a Dyson sphere into a sun is pretty embarrassing...

---

A quick note: This would also require some 'hotspot' exhausts from which to extract the electricity to power the lasers. Clever positioning of these and suitable focusing systems could again minimise the chance of detection. In fact, if you really wanted to you could probably get away with just using the exhausts, though the focusing requirements would be a lot more tricky to deal with that aiming a laser.

Answer 4

First, a back-of-the-envelope calculation:

power output of sun / surface area of sphere of radius 1 AU = ~1368 W/m^2

You MUST radiate this much (on average) from every square meter of your sphere. MUST, as in, mathematical imperative.

Under the (typical) assumption of a perfect Lambertian emitter, you can invert the Stefan–Boltzmann Law to get an average temperature of 394.1°K (or 121°C). That's not visible light, but it is pretty hefty across infrared and near-radio.

The Problem

This temperature is inconveniently high (it's death for most terrestrial life, for example), and it is unavoidable under these design constraints. If we decide it's unacceptable, we have several options. You've bitten off a lot to chew, so the best that can realistically be done is propose several classes of solutions.

Approach 1: Reduce Power Output of Star

(Insert magitech.) Stars have stable fusion rates. Maybe you can chuck a whole solar-system's worth of iron into it to slow it down. Or choose a dimmer star. Or siphon off material with a wormhole or something equally scientifically dubious.

Approach 2: Make Your Dyson Sphere Bigger

Because irradiance follows an inverse square, at 2 AU, the energy dissipated per area is 1/4 that at 1 AU. This is much more manageable.

Gravitational stresses also decrease on the poles of a larger Dyson sphere, and you get even more surface area. So it's good in other ways too. It can't reduce your heat signature, but that isn't really possible anyway (see Stealth, below). So, I recommend this approach.

Approach 3: Let Some Light Through

Poke holes in your Dyson sphere. The sideways areas give you more area to radiate. This doesn't work very well for a full sphere (the surfaces tend to radiate into each other), but lesser (and more practical) megastructures (e.g. Niven rings) can radiate nicely. Consequently, I recommend this approach.

Approach 4: Concentrate Energy

This cannot be done without reversing entropy. We can do that by expending more energy (say some fraction collected from the star), so it's not impossible in this case.

There's probably a thousand ways to do this, but they'll all be difficult because fundamental laws of optics make it essentially impossible to focus light from a large object like a star. The energy will need to go through an intermediate stage (e.g. solar panel -> electricity -> laser), with tremendous losses along the way. Those losses translate into waste heat, which is a tremendous problem in an enclosed space. Consequently, this is a bad class of approach to take.

Another thing to consider is that directional emission must be done carefully to avoid unintended consequences. For example, If you find a way to emit all the star's energy in a laser, then the whole assembly will rapidly start accelerating the opposite direction (because you've just made a stellar-scale photon rocket). You need another laser in the other direction if you don't want to move.

Stealth

The only even remotely possible way to do this is with something from approach 1 or 4 (because otherwise either light from the star is getting out, or your waste heat in aggregate is literally exactly equal to the star's output in the first place. If you can direct a beam, you have a fighting chance at aiming it. But, no matter what, energy input equals energy output; it is mathematically impossible to hide your Dyson sphere from all directions all at once if they could detect the original star.

Answer 5

A heat pipe system should be able to handle what your load.

The advantage of heat pipes over many other heat-dissipation mechanisms is their great efficiency in transferring heat. A pipe one inch in diameter and two feet long can transfer 12,500 BTU (3.7 kWh) per hour at 1,800 °F (980 °C) with only 18 °F (10 °C) drop from end to end. Some heat pipes have demonstrated a heat flux of more than 23 kW/cm², about four times the heat flux through the surface of the sun.

So on the inner surface of the sphere you put a lot of heat collection pads hooked up to heat pipes that travel through the sphere structure and to the outside where there would be huge thermal radiators.

The suns head would be absorbed, transferred through the heat pipe arrays, and then dissipated out through the radiators.
The sphere would glow in the infrared spectrum, but it would be diffuse.

Answer 6

I'm kind of thinking if you have the engineering scratch to create a Dyson sphere, you might be able to channel the energy in a way to get it directional. What you plan on doing with all of the energy, anyway? Keep in mind that heat is energy.

Anyway, a method to make it as invisible to the outside as possible would be to tightbeam the energy in two directions. One, to wherever or whatever needs that much juice. The excess could be tight-beamed to the nearest black hole or the galaxies core. Not perfect stealth, because there ain't no stealth in space (thanks to all the others who said it), but it would be very hard to notice and if you stumbled across the tightbeam by accident, you'd likely get vaporized for your trouble.

Answer 7

At the risk of recursion, I will post a link to the Physics SE, where someone asks "When does energy turn to matter?"

In theory, a sufficiently advanced civilization (like one capable of building the Dyson sphere in the first place) could reverse the equation¹ and convert that energy down to mass. Which can then be set adrift into space, where no one will ever notice.

---

¹ $$ E = MC^2 $$

Answer 8

To be converted by synthetic process into magnetic fields used to 1: Contain more of said energy without being forced to expel, radiate or convert it.

2: To provide structural reinforcement for the rigid Dyson Sphere in the resistance of gravitational, thermal and shear forces resulting from the motion of the megastructure's composites and etc.

3: For an absolute-lord-almighty-massive collider/plasma tube (or a billion of them) to change the state of said energy along further evolutions.

The problem the 'stealth' problem (whether dyson or space vessel or w/e) has is in conservation, whatever one does with energy, it is still energy. So the problem really should be 'how can one store energy within the [holistic] construct rather than expel it.' Well, the more energy has, the more one can direct to the establishment of [magnetic] fields, and we know fields can be used to direct [contain] the movement of massive energy.

Whilst this applies as much to the host star as to the construct, stars behave the way they do because of the net energy and it's distribution, changing that over long periods makes things complicated.[hah]

To be a little more specific we can say that rather than expelling energy as lasers or somesuch, the manipulation of fields can be used to impel energy and energetic particles into particular formations, regions of space and alignments with which an apparatus can perform further functions.

If we use, for instance, fields to maintain a channel, the field can be aligned in such a way that certain particles and states of energy are more or less likely to escape the channel..and thus a succession of fields can be manipulated to 'refine' energy without (as much) concern for nearby material equipment.

As all of this reflects on the conservation of energy problem: if fields can be used to move energy, they are effectively being used already to store it, importantly.. without the need for 'contacting' the material of the structure and incurring greater cost and requirements on it's maintenance and integrity. In addition, the energy can be 'contained' in any form one has the technology to impose..in 'open space' internal or external to the greater mass of the construct without radiating it 'out' in massive quantities.

As regards colliders and plasma channels: If one can redirect the flow of energy on relevant scales and with sufficient precision "free standing" plasma channels and colliders become practicable. We can use such apparatus already to impose creation events, it seems likely that with the ability to create channels in open space and with the energy provided by the merging of multiple energetic streams from multiple fusion events further [and obviously scaling] applications would become available.

Forgot to state explicitly[?]: If your apparatus can control energetic particles in open space, open space becomes a 'battery.'

But really, the point of the original post was to highlight the lack of attention being given to field manipulations, I'm not a mathmo/physicist

Answer 9

So wasn't sure where to rider this idea and I don't think it's a full answer, but I didn't see a better place.

Since it seems like Stealth is the main concern, Why not hide in plain sight?

The problem with people that say "There's no stealth in space" is that they fundamentally don't understand stealth. It's not about being perfectly invisible, it's about not being what your opponent is looking for.

Case in point, there are trillions of stars in a galaxy, so instead of trying to not let someone see your star, just don't let them see that your star is special. I think the leading solutions are to try to take a hotter star and hide it as a dimmer star, covering the outer shell of the sphere in radiators or being uniformly translucent that make the star appear dimmer and smaller. Perhaps also an irregular dust cloud slowly orbiting to help 'mask' the image of the star while also providing a natural barrier to mask any comings and goings of vessels.

Another idea would be to try to simulate being a pulsar. Spinning your sphere at a rate that would simulate a pulsar is probably not possible from a materials or habitability perspective, so I would again cover the surface in emitters that fire in a sequence to give the appears of a spinning pulsar. The problem is that pulsars are loud, so you're screaming to the universe "I AM A PULSAR" so you'll taking a gamble that 1) Pulsars aren't interesting enough to study and 2) you're really good at pretending to be pulsar.

The second part of the problem is you need to hide the fact that you built the Sphere in the first place. Building it will not be cheap nor fast. Even if you could wink the sphere into exist or phase it into this reality, an observer will probably notice if a bright star suddenly goes dim or winks out. So hiding the construction will also be critical.

I would probably try to assemble the sphere in halves above and below the plane of the galaxy. This would expose lighting traveling "up" and "Down" through the thin parts of the galaxy to the fact that you're building a Sphere, but there is much less real estate in the path for there to be potential civilizations to detect you before the light leaves for extra-galactic space.

Next, I'd try to find a way to make a diversion while I bring the hemispheres together around the star. The goal is to minimize the transition period while there's something more interesting to watch. If possible, I'd try to make a nearby star (again, 'above' or 'below' in the galactic plane to have the shadow cast through the smallest volume of galactic space) go super nova so everyone is busy looking at the big bang and blind to my star dimming. This may also be a good time to introduce that orbiting dust cloud so that any observer would just conclude that spooky action seen from my star was simply matter from the super nova rocketing past.

Lastly, we now need to clean up any survivors in our galactic 'up' and 'down' that might have had a better picture. In a perfect universe, we'd somehow lens the aforementioned super nova to fire a series of directed fast gamma ray bursts at any stars that had a good show. Sorry to be grim, but dead civilizations tell no tales: sometimes to only way to 'hide' is to kill the sentry, and we have a nice loud event to that might even help us hide our death rays.

It should be noted that these solutions are going to require you to sacrifice A LOT of power the sphere produces to devote to camouflage. I feel like that's acceptable though. If you want to hide you're probably not looking for phenomenal cosmic power, but the Megastructure equivalent of a nice quiet cabin to spend the rest of your civilization's days out in mildly-guilty "peace".

Answer 10

You don’t understand the concept of the Dyson Sphere if you are trying to “get rid” of all that heat. Heat is energy, and the DS is meant to capture the energy. The “sphere” requires many new technologies, engineering marvels, etc. chief among them is some sort of super material that absorbs and stores the energy for use when you need it, or targets the energy where you need it. If you can’t handle all the excess heat, then you are not in Dustin Sphere territory. Such a structure is reserved for civilizations that both require all that energy, and can actually use it. IOW: if “too much heat” is a problem for the materials you are using, then you are building a massive structure just to vent out the energy you are capturing, which makes no sense at all.