Right now KIC 8462852 is really hot, and not just because it is a F3 V/IV type star: the light curve, as measured by Kepler, has irregular dips that looks like something (or rather, several somethings) are obscuring the star. The shapes of the dips are odd. The system is too old and IR-clean to have a remaining protoplanetary disk, dust clumps would coalesce, the aftermath of a giant planet impact is very unlikely (and hard to fit with the aperiodicity); maybe there is a storm of comets due to a recent stellar encounter, but comets are not very good at obscuring stars. So a lot of people on the net are quietly or not so quietly thinking that just maybe this is a Dyson sphere under construction.
I doubt it.
My basic argument is this: if a civilization builds a Dyson sphere it is unlikely to remain small for a long period of time. Just as planetary collisions are so rare that we should not expect to see any in the Kepler field, the time it takes to make a Dyson sphere is also very short: seeing it during construction is very unlikely.
Fast enshrouding
In my and Stuart Armstrong’s paper “Eternity in Six Hours” we calculated that disassembling Mercury to make a partial Dyson shell could be done in 31 years. We did not try to push things here: our aim was to show that using a small fraction of the resources in the solar system it is possible to harness enough energy to launch a massive space colonization effort (literally reaching every reachable galaxy, eventually each solar system). Using energy from already built solar captors more material is mined and launched, producing an exponential feedback loop. This was originally discussed by Robert Bradbury. The time to disassemble terrestrial planets is not much longer than for Mercury, while the gas giants would take a few centuries.
If we imagine the history of a F5 star 1,000 years is not much. Given the estimated mass of KIC 8462852 as 1.46 solar masses, it will have a main sequence lifespan of 4.1 billion years. The chance of seeing it while being enshrouded is one in 4.3 million. This is the same problem as the giant impact theory.
A ruin?
An abandoned Dyson shell would likely start clumping together; this might at first sound like a promising – if depressing – explanation of the observation. But the timescale is likely faster than planetary formation timescales of 
But it is indeed more likely to see the decay of the shell than the construction by several orders of magnitude. Just like normal ruins hang around far longer than the time it took to build the original building.
Laid-back aliens?
Maybe the aliens are not pushing things? Obviously one can build a Dyson shell very slowly – in a sense we are doing it (and disassembling Earth to a tiny extent!) by launching satellites one by one. So if an alien civilization wanted to grow at a leisurely rate or just needed a bit of Dyson shell they could of course do it.
However, if you need something like 
In order to get a reasonably high probability of seeing an incomplete shell we need to assume growth rates that are exceedingly small (on the order of less than a millionth per year). While it is not impossible, given how the trend seems to be towards more intense energy use in many systems and that entities with higher growth rates will tend to dominate a population, it seems rather unlikely. Of course, one can argue that we currently can more easily detect the rare laid-back civilizations than the ones that aggressively enshrouded their stars, but Dyson spheres do look pretty rare.
Other uses?
Dyson shells are not the only megastructures that could cause intriguing transits.
C. R. McInnes has a suite of fun papers looking at various kinds of light-related megastructures. One can sort asteroid material using light pressure, engineer climate, adjust planetary orbits, and of course travel using solar sails. Most of these are smallish compared to stars (and in many cases dust clouds), but they show some of the utility of obscuring objects.
Duncan Forgan has a paper on detecting stellar engines (Shkadov thrusters) using light curves; unfortunately the calculated curves do not fit KIC8462852 as far as I can tell.
Luc Arnold analysed the light curves produced by various shapes of artificial objects. He suggested that one could make a weirdly shaped mask for signalling one’s presence using transits. In principle one could make nearly any shape, but for signalling something unusual yet simple enough to be artificial would make most sense: I doubt the KIC transits fit this.
More research is needed (duh)
In the end, we need more data. I suspect we will find that it is yet another odd natural phenomenon or coincidence. But it makes sense to watch, just in case.
Were we to learn that there is (or was) a technological civilization acting on a grand scale it would be immensely reassuring: we would know intelligent life could survive for at least some sizeable time. This is the opposite side of the Great Filter argument for why we should hope not to see any extraterrestrial life: life without intelligence is evidence for intelligence either being rare or transient, but somewhat non-transient intelligence in our backyard (just 1,500 light-years away!) is evidence that it is neither rare nor transient. Which is good news, unless we fancy ourselves as unique and burdened by being stewards of the entire reachable universe.
But I think we will instead learn that the ordinary processes of astrophysics can produce weird transit curves, perhaps due to weird objects (remember when we thought hot jupiters were exotic?) The universe is full of strange things, which makes me happy I live in it.
[An edited version of this post can be found at The Conversation: What are the odds of an alien megastructure blocking light from a distant star? ]
Excellent article and insightful theories. I’d like to pose a couple alternatives. It could be a Dyson sphere that stopped during construction for a variety of reasons, such as funding shortages, warfare, some other priority (existential threats?) taking up resources, or perhaps even discovering an even better source of energy mid-construction. It’s quite possible that by the time you’re *able* to make a Dyson sphere (or perhaps in this case, *during* the making of a Dyson sphere) that you wouldn’t *need* to make the Dyson sphere (because of something better). Why would it have to fall apart, regardless of age? It could be a form of advanced engineering holding it together that we are unable to fathom.
Here is some analysis I did on the extropians mail list:
This is a nice presentation and paper
http://orfe.princeton.edu/~rvdb/tex/talks/PACM07/RingTalk.pdf
http://orfe.princeton.edu/~rvdb/tex/saturn/ms.pdf
that show Maxwell (1859) was right about the stability of rings around planets (or, in this case, a ring of collectors around a star).
A ring of n objects with mass m orbiting a mass M will remain stable is m < 2.298 M/n^3. So if each Dysonlet is square with side s, area density rho and orbits at distance R, then: rho < [2.298/8 pi^3] M s /R^3. That is, the Dysonlets need to become much larger in a large sphere. If we take rho to be 0.0271 kg/m^2 (aluminium foil), at R=1 AU the smallest stable Dysonlet has side 4.9 km. Note that you can stabilize things by moving half out to a slightly wider orbit (n^3 drops by a factor of 8) but you will have to deal with the different periods producing self-shadowing. If an abandoned ring has some breakup (say meteor damage), then it seems likely that the appearance of smaller fragments can destabilize the whole array. In fact, the Kessler syndrome in this case might be *way* nastier than around Earth, since we are talking about a thick soup of collectors: almost half of the directions available for a debris piece will intersect with something else. Once there are smaller fragments, they will start gravitating towards larger densities and destabilize the overall structure.
The growth of a perturbation is roughly X”= omega^2 X + [nonlinear stuff] (omega is angular frequency), so once the array destabilizes it will go bad in about one rotation. But as the simulations on Vanderbei’s page show, it may take a long while for the disaster to trigger.
A Dyson sphere hence needs fairly active control to remain functioning, both in preventing infalling comets from causing damage and to maintain station keeping of the collectors. If it is abandoned it may remain intact for a while, but then crash rather quickly. That initial crash lasts only a few years, but the aftermath of slowly coalescing matter likely lasts over planetary formation timescales.
Partial Dyson spheres are less stable than full ones, since the forces are uneven.
I, of course, think the likelihood of it being anything artificially created is close to null, but, to poke holes in some arguments stated above…
Couldn’t a species technologically advanced enough to create a Dyson sphere be technologically advanced enough to create a sell-automated controlling/regulating system, powered on the energy of the Dyson sphere itself (thus enabling its stability well beyond the extinction of the species)? In fact, if that technology were available, wouldn’t it make even more sense to enable it to reduce the need of constant monitoring?
Also, using the argument of population growth rates exceeding energy requirements assumes that extraterrestrial life would be akin to ours. Though I agree with you that this is more likely than not, perhaps the species could have an extremely slow population growth based on its reproductive rates and lifespan, or a species that has it’s population growth in check from cultural rules (a la China’s attempt to cull their growth through government incentives), or even a life form or cultural society so totally foreign to us that we cannot even fathom the reasoning for a low to non growth rate?
Yes, automatic monitoring and maintenance is pretty likely. You don’t want to manually maintain 12.5 square AU of infrastructure. But self-maintaining shells simply imply that we would not see a decaying one, further lowering the probability of seeing anything with Kepler.
And sure, an alien species may have very different population growths. In fact, humans have population dynamics that baffles demographers from time to time (fertility, which “ought” to be what evolution has maximized us for, turns out to be very susceptible to cultural influences). But growth does not have to be just population: if you have self-replicating technology growth also includes the literal growth of infrastructure, and of course there is growth in the sense of wealth – whatever the aliens value, if more of the valuable thing is more valuable than less, they will tend to make more of it. Maintaining a totally stable population/infrastructure/economy is a pretty special state – growth rate zero has zero measure compared to negative and positive growth rates.
I don’t think the “growth is inevitable” argument is very strong. One can always imagine a civilization that has some reason not to grow beyond a certain size. But the converse argument, that advanced civilizations do not grow without bound, is equally weak: one can imagine plausible civilizations that do that too. “Environmental” claims that positive growth rates lead to collapse (see for example Brin’s classic 80s paper) only apply for certain types of resources and growth; space-based Dyson-builders seem to escape many of them rather well.
A partial Dyson could be a deliberate choice on the part of the civilisation concerned. After all, the civilisation will need to stop expanding when they reach the full carrying capacity of the solar system – why not stop before that event, and leave the option for further expansion open for some unspecified date in the future?
Every expansive civilisation must have two expansion rates – a relatively rapid expansion rate that applied when there are still unused resources, and another, much slower expansion rate that exactly balances the rate of emigration.
If an advanced civilisation realises this then they could reduce their rate of growth voluntarily long before it becomes unavoidable. This would give them the option for expansive growth at some future date, if it becomes desirable; this might seem more prudent than having nothing in reserve.
With regard to the WTF star, has anyone looked at Trojans and Hildas?
This animation of the Jupiter Hildas might help, just hit the arrow in key in the times step box. Now with Jupiter the Trojans number about one million 1km diameter asteroids, and the Hildas,only about 1200 asteroids. But this star seems to have a lot more asteroids. If one had a building site, the place to park up asteroids is at the Trojan points but they could be placed into Hilda type orbits.
http://orbitsimulator.com/gravitySimulatorCloud/simulations/1445194497760_hildas400.html
I don’t know if looking for Hildas or Trojans make much sense until you have a planet to focus on. And a Trojan cloud of asteroids still needs to be absurdly rich to show up in the light curve.
They; the Trojans; are going to “dunch” into each other. “Dunch” being a Northumbrian dialect word for a low velocity collision. They are in tadpole shaped orbits, mainly do to changes in the orbital velocity of Jupiter, and also changes in the Solar System’s barycentre. The barycentre can be outside of the Sun by about a Sun radius.
A million one km bodies are going to have bit chipped off them over four billion years. So we have a natural log distribution of big chunks of ice and rock.
This animation is just of Jupiter’s Trojans but it gives some idea of the orbits around the Lagrange points.
http://www.orbitsimulator.com/yabbfiles/Attachments/GravSim_JupiterTrojans_1Jup_Rev.gif
Here’s a link to the discussion on the Gravity Simulator notice board. You can ignore my comments (as I’m a total idiot) but the other two guys know what they’re talking about; Tony, designed the programme.
A note on that first animation, you can change your viewing angle, and you can also change masses of all the objects. (Great fun for smashing up Solar Systems 😉 )
I’ve only just seen the latest comment but it looks interesting.
http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1445078726;start=all