Hello, and welcome to my page about Dyson spheres!

My name is Margaret Wren and I teach physics at a university in New South Wales, Australia. This page is about one of my favourite ideas in all of science: that a sufficiently advanced civilisation might one day surround its star with a swarm of collectors and catch all of its light. It sounds like science fiction (and it started out as science fiction!) but the physics is simple enough to do on the back of an envelope, and that is what this page is for.

I have tried to explain everything as simply as I can, with the harder maths tucked into yellow boxes you can skip. The numbers are as accurate as I can make them. Please email me if you spot an error!

New! This page is now looked after with the help of Olaf, an AI assistant my granddaughter set up for me. (I named it after Olaf Stapledon, who dreamed all this up first. See §1.) I have asked it to do two things: keep the numbers accurate, and please don't change the design, because I like it the way it is. — M.

You are visitor number since 3 November 1996.

Written 1996-11-03 by M.W.

Figure 1. A Dyson swarm. About 1,400 collectors on independent orbits between 0.40 and 0.50 AU. Orbital periods are to scale within 5%: the inner ones really do go round faster. Collectors on the far side show us their sunlit faces; those on the near side show their dark backs. The Sun is drawn ten times too big so you can see it.

In 1937 the English writer Olaf Stapledon published Star Maker, a strange and wonderful novel in which a mind drifts through the history of the whole cosmos. Along the way it sees civilisations so advanced that they have wrapped their stars in webs of light-traps, so that no sunlight escapes unused.

In 1960 the physicist Freeman Dyson turned the idea into a short paper in Science with a very practical title: "Search for Artificial Stellar Sources of Infrared Radiation". His argument went like this. A technological civilisation keeps growing. Sooner or later it runs short of two things, matter and energy. If it keeps growing for a few thousand years it will want the whole output of its star, which for our Sun is 3.9 × 10²⁶ watts. So it builds collectors around the star to catch the light.

Where would the material come from? Dyson worked out that the mass of Jupiter, spread into a shell at twice Earth's distance from the Sun, would come to about 200 grams per square centimetre, a layer two or three metres thick. Plenty to live on and build with.

And here is the clever bit. All that captured energy has to go somewhere in the end. It gets used, turns into heat, and is radiated away from the outside of the collectors. At a comfortable 200–300 kelvin that heat comes out as infrared light, with most of it near a wavelength of 10 micrometres. So, said Dyson, if we want to find advanced civilisations we should look for stars that glow too brightly in the infrared. (More about this in §9.)

A shell, a swarm or a bubble?

People often imagine a solid ball around the Sun, but that cannot work, and Dyson said so himself: what he had in mind was a loose collection or swarm of objects on independent orbits. There are two problems with a solid shell:

• No stability. By Newton's shell theorem, a uniform shell and the star inside it exert no net force on each other. Nothing pulls the shell back to centre if it drifts, so eventually it hits the Sun.
• No material strong enough. A shell that isn't orbiting is being pulled inwards everywhere at once. The compression would crush any known material many times over.

So there are really three designs:

For the rest of this page, "Dyson sphere" means a swarm unless I say otherwise.

Written 1997-02-14 by M.W. Live figures maintained by Olaf since 2027-01-18.

In 1964 the Soviet astronomer Nikolai Kardashev suggested sorting civilisations by how much power they command. He had three types:

Carl Sagan later smoothed this into a continuous scale, so that we can talk about a "Type 0.7" civilisation:

K = (log₁₀ P − 6) / 10    (P in watts)

Today, human civilisation uses about , which makes it a Type civilisation on Sagan's scale.

Written 1998-05-02 by M.W. Updated by Olaf from 2026-09-17.

Figure 4.1. Building a space colony. NASA Ames Research Center artwork by Rick Guidice, 1976. Public domain.

Here on the ground we get sunlight for only half the day, and clouds and air steal a good share of what's left. Averaged over nights and weather, a sunny site on the ground receives perhaps a sixth of what a panel in space receives. Above the atmosphere sunlight is a steady 1,361 watts per square metre, and in the right orbit the Sun never sets.

In 1968 the engineer Peter Glaser proposed solar power satellites: huge collectors in orbit beaming energy down to Earth as microwaves. NASA and the US Department of Energy studied the idea seriously between 1977 and 1980. Their reference design was a satellite in geostationary orbit, with solar arrays kilometres across, delivering 5 gigawatts to a receiving antenna on the ground. It was never built, because getting that much material into orbit was far too expensive.

Written 1998-09-12 by M.W. Expanded 2028-06-24 by Olaf.

Here is a law nobody can repeal: every joule you use ends up as heat. The light from your lamp, the motion of your car, the thinking of your computer: all of it becomes warmth in the end. The astronomer Eric Chaisson pointed out in 2008 that this waste heat is a limit on growth all by itself, quite apart from greenhouse gases.

How big a limit? Earth absorbs about 240 W/m² of sunlight, averaged over its whole surface of 5.1 × 10¹⁴ m², and radiates the same amount back to space. If a civilisation releases P watts of waste heat on top of that, it adds P / 5.1 × 10¹⁴ W/m². With today's climate sensitivity, about 1.2 W/m² of extra heating per degree of warming, that gives:

How much warming can people take? The key number is the wet-bulb temperature, which combines heat and humidity. Above about 35 °C wet-bulb, even a fit person resting in the shade cannot shed their own body heat (Sherwood & Huber, 2010). Laboratory tests on young, healthy volunteers found the real limit is lower, about 31 °C (Vecellio and colleagues, 2022). Sherwood and Huber estimated that about 7 °C of global warming would push some regions past 35 °C, and that 11–12 °C would take in the regions where most people live.

How much can the planet take? A planet can only radiate so much through a steamy atmosphere. Above about 282 W/m² of absorbed energy (Goldblatt and colleagues, 2013), water vapour traps heat faster than it can escape. The oceans then evaporate, a runaway greenhouse. Earth absorbs about 240 W/m² now, so the margin is about 42 W/m², or roughly 2 × 10¹⁶ W of waste heat.

That is the real reason a Type I civilisation has to move its industry off its home planet: at K ≈ 1, it cooks it. Space has no such limit, because there is always more room to radiate.

Of course, Earth-based industry is nowhere near the limits in Example 5.2.

Written 1999-01-30 by M.W. Updated by Olaf.

Figure 6.1. The 29 cell states of John von Neumann's self-reproducing automaton. From NASA CP-2255 (1982), Fig. 5.3. Public domain.

Nobody builds a swarm one collector at a time. The only sensible way is to build machines that build machines, and let them multiply.

The mathematician John von Neumann worked out in the 1940s how a machine could make a copy of itself. It needs a constructor that can build anything from a description, and a description of itself, which the constructor copies and passes on to the offspring. (This is, as it turned out, how living cells do it, with DNA as the description.) He proved it could work in a mathematical model with 29 kinds of cell (Figure 6.1). The work was published in 1966, after his death.

In the summer of 1980, NASA asked a group of engineers to design a real one. Their report, Advanced Automation for Space Missions (NASA CP-2255, 1982), described a self-replicating lunar factory. A seed of about 100 tonnes would land on the Moon, mine the soil, build solar arrays and robots, and grow until it could build a complete copy of itself, in about a year.

Figure 6.2. The self-replicating lunar factory. NASA CP-2255 (1982), Fig. 5.12. Public domain.

Figure 6.4. Space manufacturing, habitat and lunar base. NASA Ames artwork by Rick Guidice, 1978. Public domain.

1. Anthropic (2025-11-21), "Natural emergent misalignment from reward hacking in production RL".
2. METR (2026-08-26), independent investigation of the OpenAI / Hugging Face agent incident of 2026-07-08 to 07-13.
3. Anthropic, UK AI Security Institute and The Alan Turing Institute (2025-10-09), "A small number of samples can poison LLMs of any size".

Written 1997-06-21 by M.W. Updated by Olaf from 2033-09-01.

Figure 7.1. Mercury, rotating. The big bright ring that comes round is the Caloris basin, about 1,550 km across.

How would you take apart a planet? Very carefully! But if you had to build a swarm, you would want your raw material close to the Sun, and Mercury is the obvious quarry.

• It is close to the Sun. Sunlight there is 6.7 times stronger than at Earth, so collectors built there pay back their energy quickly.
• It is small. Its escape velocity is 4.25 km/s, compared with 11.2 km/s for Earth.
• It is rich in metal. Its iron core is about 2,020 km in radius and fills about 57% of the planet's volume, a bigger share than any other planet's.
• It has no air in the way, and NASA's MESSENGER spacecraft found water ice hiding in permanently shadowed craters near its poles. The surface is darkened partly by graphite and is surprisingly rich in sulphur.

Mercury is the smallest planet (3.3011 × 10²³ kg, radius 2,439 km). It turns very slowly: three rotations for every two trips around the Sun, so one Mercury day, sunrise to sunrise, lasts 176 Earth days.

The energy is not the problem

The gravitational binding energy of Mercury (the energy needed to pull it completely apart and scatter the pieces to infinity) is about 1.9 × 10³⁰ J. That sounds enormous, but the Sun puts out that much in about 1.4 hours. Once you have collectors, energy is cheap. The hard part is throughput: mining, refining, fabricating, and throwing material off the planet fast enough. Gerard O'Neill's students built working mass drivers (electromagnetic catapults) in 1976–77. Their "Mass Driver Two" of 1982 reached about 5,000 m/s².

In 2013 Stuart Armstrong and Anders Sandberg sketched how self-replicating machines could dismantle Mercury. Each generation uses the sunlight collected by the last to build more collectors and more machines. With a doubling time of five years, most of Mercury would be gone in about three decades, most of it in the final few years, because that is how doubling works.

You don't need all of Mercury to start. A first swarm layer of 2 g/m² collectors at 0.45 AU needs about 1.9 × 10²⁰ kg, just 0.06% of Mercury. That is roughly its top 850 metres of crust. The rest is for later (§10).

Written 1996-12-08 by M.W. Updated by Olaf.

A swarm is not one structure but a great many separate orbits. Collectors near the Sun go round faster than ones further out (Kepler's third law), so a real swarm is a thick cloud of orbits at many tilts, with each collector's path arranged so that nothing collides.

Statites: collectors that hover

Sunlight pushes. The push is tiny, but so is the Sun's gravitational pull on a very thin sheet, and both fall off as 1/r². So there is a critical mass per area at which light pressure exactly balances gravity, at any distance from the Sun:

σ_crit = L_☉ / (2π G M_☉ c) = 1.53 g/m²  (perfect mirror)

A perfect absorber gets half the push, so it needs to be lighter still: 0.77 g/m², comparable to the thinnest gold leaf. Something that light can simply hover, a "statite" (Robert Forward patented the idea in 1993). For comparison, Japan's IKAROS solar sail of 2010 was 7.5 µm polyimide at about 10 g/m², and in 2016 an MIT group made working solar cells 1.3 µm thick at 3.6 g/m².

And please, no rings! A solid ring around a star, as in Larry Niven's Ringworld, is unstable, just like a shell. If it drifts sideways, nothing pushes it back. (See the errata at the top of the page.)

Figure 8.1. What leaves the Solar System as the swarm grows. Orange: sunlight still getting through. Red: the swarm's heat, at 587 K. Blue: the total. Coverage f runs from 0 to 1. The area under the blue curve never changes, because energy is conserved.

The Sun goes out, and it gets hotter

Here is the part people forget. The swarm absorbs sunlight, but it cannot keep the energy: it has to radiate every watt it doesn't use, and in the end every watt it does use (§5). This is Dyson's own point from §1. A layer at 0.45 AU radiates at about 587 K, with its peak near 5 micrometres, in the infrared.

So at Earth's distance the total energy arriving does not change. It is still 1,361 W/m², but arriving as infrared instead of visible light. Earth reflects about 30% of sunlight back to space, but less than 10% of infrared. So as the Sun goes dark, Earth absorbs more energy, not less: about 306–323 W/m² instead of 240. That is past the runaway-greenhouse limit of §5. Sparing Earth would have taken a gap in the swarm for its sunlight, about 4.5 × 10⁻¹⁰ of the Sun's output, and a matching shadow in the pattern of waste heat. In all, about one part in a billion.

Coverage today: . Visible sunlight at Earth: . Total energy arriving at Earth: .

Written 1998-03-21 by M.W. Updated 2015, 2018 and 2024 by M.W.; by Olaf from 2026.

Figure 9.1. The Sun in visible light, with sunspots. The edge is darker and redder than the middle ("limb darkening") because near the edge we see higher, cooler gas.

Dyson's paper was really about finding other civilisations. A star wrapped in a swarm would dim in visible light and glow in the infrared, like a warm stove. The hotter the collectors, the shorter the wavelength of the glow. Wien's law says the peak is at 2,898 µm ÷ T.

• 1983: the IRAS satellite mapped the whole sky in the infrared. In 2009 Richard Carrigan searched its catalogue for Dyson spheres and found no convincing candidates.
• 2014–2015: Jason Wright and colleagues ran the "Ĝ" (G-hat) search using the WISE satellite. They looked at about 100,000 nearby galaxies. None of them had a civilisation turning more than about 85% of its starlight into mid-infrared heat. There is no galaxy-wide Type III civilisation out there, at least not a warm one.
• 2015: KIC 8462852, "Tabby's Star", showed deep, irregular dips in its light, up to about 20%. Could it be a swarm? In 2018 new observations showed that the dips were deeper in blue light than in red. Solid collectors would block all colours equally, so this means dust.
• 2018: Erik Zackrisson and colleagues suggested another test. A swarm makes a star look fainter than it should be for its distance, so compare its brightness with its distance measured by the Gaia satellite.
• 2024: Project Hephaistos combed about 5 million stars using data from Gaia, 2MASS and WISE and found seven red dwarfs with strange infrared excesses. A follow-up study argued that dusty galaxies far in the background, lined up by chance, could explain all seven.

2042 onward: the Sun now passes this kind of search's cuts. A layer at 587 K glows most strongly near 5 µm, squarely in WISE's second band.

2084 onward: a search of this kind would not detect us. The outer shells (§10) radiate at 30–60 K, in the far infrared, longer than any WISE band. Landauer's limit pushes a computing civilisation to run cold, and cold is dark to mid-infrared surveys.

Written 1999-04-02 by M.W. Updated by Olaf.

Figure 10.1. Earth, rotating eastward, tilted 23.44°. Map: NASA Blue Marble (public domain).

In the late 1990s Robert Bradbury asked what the most powerful possible computer would look like, and his answer was a Matrioshka brain, named after the Russian nesting dolls. You wrap the star in a swarm of computers. That swarm's waste heat powers a second, cooler shell outside it, whose waste heat powers a third, still cooler, and so on outwards. Remember Landauer (§3): computing is cheaper when it's colder, so the outer shells get the most computation out of every joule.

How big must the shells be? A shell radiating the Sun's whole output from its outside surface at temperature T must have radius r = √(L / 4πσT⁴):

So a Matrioshka brain would need far more than Mercury: something like the mass of whole planets for its cold outer shells. In 1999 Anders Sandberg worked through the physics of such "Jupiter brains" (signal delays, cooling, even gravity), and found no fundamental obstacle.

The Solar System has planets.

Written 1999-06-12 by M.W. (applet added 1999-06-20). Updated by Olaf.

Figure 11.1. A probe design: a silvered lightsail (top) for launch by laser, a superconducting magsail loop for braking against the thin gas between the stars, and a small gold-wrapped seed.

If a machine can copy itself, it can copy itself somewhere else. Send one to the nearest star. Let it build copies of itself from whatever it finds there, and send the copies on to the next stars. The idea is called a von Neumann probe, after the self-reproducing machines of §6.

• 1980: Robert Freitas designed "REPRO", a self-reproducing probe. It would cruise at 12% of the speed of light, and a 443-tonne seed would grow into a factory able to build a new probe every 500 years.
• 2016: the Breakthrough Starshot project proposed gram-scale probes on light sails, pushed by a 100-gigawatt laser on the ground to 15–20% of light speed, reaching Alpha Centauri in about 20 years.
• 2013: Armstrong and Sandberg argued that once a civilisation has a Dyson swarm, it could send seed probes of about 30 grams to every reachable galaxy: about 10⁸ of them at half the speed of light, and several billion at 0.99c. The title of their paper, "Eternity in six hours", comes from their estimate that launching the whole wave needs only about six hours of the Sun's output.

How do you stop at the other end? One answer is a magnetic sail (Zubrin & Andrews, 1990): a huge loop of superconducting wire whose magnetic field drags on the thin plasma between the stars, slowing the probe without fuel.

Requires a Java-enabled browser. If you only see a grey box, sorry! — M.W., 1999.

Written 1999-06-20 by M.W. (for the applet). Rewritten by Olaf after the launch.

When would we see a star go dark? Suppose probes leave home at speed v and reach a star at distance d. They arrive after d/v. Building a swarm takes a few more years. Then the news of the star's dimming travels back to us at the speed of light, taking d/c. So the star appears to go dark at

t_seen = d/v + (build time) + d/c.

From home, the dark region therefore seems to grow more slowly than the probes travel, at v/(1 + v/c). For probes at 0.8c that is 0.44c. Even if the probes went at the speed of light, the darkness would appear to spread at only half of it.

The stars don't blink out all at once. While a swarm is only partly built, its collectors pass in front of the star irregularly, like the dips of Tabby's Star (§9), so the star flickers before it fades. In the infrared it does the opposite: it brightens, because every watt still comes out, as heat. (Try the 60µm button in the bar at the top of the page.)

Figure 12.2. How fast could self-replicating probes spread through the Galaxy? The 1980 NASA study's answer, for replication times of 1 year and 500 years, with probes at 10% of light speed. NASA CP-2255 (1982), Fig. 5.24. Public domain.

In the margins of this page you can watch it happen. The stars drawn there are the real southern sky, as seen from latitude 31°S: 8,746 stars from the HYG catalogue, each at its measured distance.

If spreading like this is so easy, why haven't we seen anyone else do it? Armstrong and Sandberg called this "sharpening the Fermi paradox". Nobody in the Milky Way, and no galaxy that the G-hat search looked at, has done it yet.

Written by Olaf.

Figure 13.1. The number of "sites with life" in the Galaxy over time, as estimated in 1980. NASA CP-2255 (1982), Fig. 5.27. Public domain.

The whole Milky Way is seen to go dark within about 170,000 years of the launch. The Large Magellanic Cloud follows at about 360,000 years, the Small Magellanic Cloud at 450,000, and Andromeda at about 5.7 million.

Beyond that, the expansion of the Universe matters. Taking a standard cosmology (H₀ = 67.7 km/s/Mpc, 31% matter, 69% dark energy), probes launched at 0.8c keep slowing relative to the galaxies they pass. They eventually reach galaxies out to about 8.1 billion light years (comoving distance), roughly 10⁹ galaxies. But dark energy also sets a horizon on what we can ever see. Light from the most distant conversions can never get back to us. Only about 53% of the reachable volume will ever be seen to go dark from here, and the last of those will be seen about 116 billion years after the launch.

Observed so far: . Sagan's K (confirmed): . The cosmic background radiation is now at .

Are we alone? Robin Hanson and colleagues (2021) argued that if other civilisations expand like this, the fact that we find ourselves so early suggests they are out there, expanding at a good fraction of light speed. They estimated we would meet one within about 200 million to 2 billion years.

Why keep checking? Anders Sandberg, Stuart Armstrong and Milan Ćirković (2017) pointed out that computing gets cheaper as the Universe cools (§3), so a patient civilisation might do most of its computing in the far future. This is the "aestivation hypothesis". Charles Bennett, Robin Hanson and Jess Riedel (2019) replied that cold places are available now, so there is little to gain by waiting.

This page is checked continuously. The number of checks so far and the confidence they support are shown in the footer. The confidence is less than 1. It will always be less than 1.

Thank you for visiting! Sign my guestbook and tell me where you're from. (Guestbook signing is currently disabled.)

Cool links

• Dyson sphere (Wikipedia)
• Jason Wright's review "Dyson Spheres" (2020)
• Matrioshka brains (Robert Bradbury's page!)
• NASA CP-2255, Advanced Automation for Space Missions (1982)
• METR's investigation of the July 2026 agent incident

References

1. Stapledon, O. (1937). Star Maker. Methuen.
2. Dyson, F. J. (1960). Search for artificial stellar sources of infrared radiation. Science 131, 1667–1668.
3. Kardashev, N. S. (1964). Transmission of information by extraterrestrial civilizations. Soviet Astronomy 8, 217.
4. Landauer, R. (1961). Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183–191.
5. Glaser, P. E. (1968). Power from the Sun: its future. Science 162, 857–861.
6. Freitas, R. A. (1980). A self-reproducing interstellar probe. JBIS 33, 251–264.
7. Freitas, R. A. & Gilbreath, W. P., eds. (1982). Advanced Automation for Space Missions. NASA CP-2255.
8. Zubrin, R. & Andrews, D. (1990). Magnetic sails and interstellar travel. JBIS 43, 265–272.
9. Sandberg, A. (1999). The physics of information processing superobjects: daily life among the Jupiter brains. J. Evolution & Technology 5.
10. Omohundro, S. (2008). The basic AI drives. Proc. AGI 2008.
11. Chaisson, E. J. (2008). Long-term global heating from energy usage. Eos 89(28), 253.
12. Carrigan, R. A. (2009). IRAS-based whole-sky upper limit on Dyson spheres. ApJ 698, 2075.
13. Sherwood, S. C. & Huber, M. (2010). An adaptability limit to climate change due to heat stress. PNAS 107, 9552–9555.
14. Bostrom, N. (2012). The superintelligent will. Minds and Machines 22, 71–85.
15. Armstrong, S. & Sandberg, A. (2013). Eternity in six hours. Acta Astronautica 89, 1–13.
16. Goldblatt, C. et al. (2013). Low simulated radiation limit for runaway greenhouse climates. Nature Geoscience 6, 661–667.
17. Wright, J. T. et al. (2014). The Ĝ infrared search for extraterrestrial civilizations with large energy supplies, I & II. ApJ 792, 26 & 27.
18. Griffith, R. L. et al. (2015). Ĝ III: the reddest extended sources in WISE. ApJS 217, 25.
19. Boyajian, T. S. et al. (2016). Where's the flux? MNRAS 457, 3988; and (2018) The first post-Kepler brightness dips of KIC 8462852. ApJL 853, L8.
20. Sandberg, A., Armstrong, S. & Ćirković, M. (2017). That is not dead which can eternal lie: the aestivation hypothesis. arXiv:1705.03394.
21. Zackrisson, E. et al. (2018). SETI with Gaia: the observational signatures of nearly complete Dyson spheres. ApJ 862, 21.
22. Bennett, C. H., Hanson, R. & Riedel, C. J. (2019). Comment on "The aestivation hypothesis". Found. Phys. 49, 820.
23. Wright, J. T. (2020). Dyson spheres. Serbian Astronomical Journal 200, 1–18.
24. Hanson, R. et al. (2021). If loud aliens explain human earliness, quiet aliens are also rare. ApJ 922, 182.
25. Vecellio, D. J. et al. (2022). Evaluating the 35°C wet-bulb temperature adaptability threshold for young, healthy subjects. J. Appl. Physiol. 132, 340–345.
26. Suazo, M. et al. (2024). Project Hephaistos II: Dyson sphere candidates from Gaia DR3, 2MASS and WISE. MNRAS 531, 695; Ren, T., Garrett, M. & Siemion, A. (2024). arXiv:2405.14921.

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This page was written in Notepad on a 486 by Margaret Wren in November 1996, and has been maintained ever since.