An interesting series papers were published in The Astrophysical Journal in 2014 by J. T. Wright and colleagues who used data from the WISE and Spitzer wide-field infrared astronomical survey data sets to try to detect Dyson spheres [1-3]. While very thought provoking, the entire premise of their study rested on the assumption that the Dyson spheres created by advanced civilisations will radiate waste heat around 290K [2:2.6.4]. This assumption allowed them to hypothesise that Dyson spheres radiating waste heat at this temperature would show up as very bright infrared sources well above the 15-50K background emission from interstellar gas and dust clouds [2:2.6.4].
Wright et al. provided no detailed reason for assuming this waste heat value other than the Carnot efficiency of a Dyson sphere around a sun-like star is 0.95 at 290K [2:2.6.3]. They felt that this was a “reasonable” value to use, since in their opinion, it balanced the materials required to build a Dyson sphere with the overall Carnot efficiency [2:2.6.4]. An important question that needs to be considered is would any advanced civilisation capable of constructing Dyson spheres throwaway 5% of the potential energy available if this waste could be avoided? If we assume they could build more efficient Dyson spheres, would it be possible for us to detect them in the infrared spectrum above the background noise?
The Carnot efficiency of a Dyson sphere is determined by the Carnot equation η = 1 − Tw / T where T is the temperature of the star (5800K for a star like our sun) and Tw is the temperature of the waste energy emitted by the sphere [2:2.6.3]. To achieve a 95% Carnot efficiency around sun-like star a Dyson sphere needs to have a radius approximately that of Earth’s orbit (i.e. 1 AU) [2:2.6.3].
As the spheres diameter grows larger, the waste energy temperature becomes lower and the efficiency higher. For example, to achieve a Carnot efficiency of 99%, the Tw would need to be ~58K assuming a sun-like star. For a Dyson sphere to radiate at this temperature it would need to have a surface area 625 times greater than one that radiates at 290K (see equation 12 of [2]). This efficiency corresponds to a sphere with a radius of ~25 AU around sun-like stars.
For reasons unknown, Wright et al. decided to use a Carnot efficiency of 99.5% (with a corresponding Tw of 29K) in their counter example as to why 95% was a reasonable efficiency for any Dyson sphere building civilisation to use. They calculated that the sphere surface area to achieve this Carnot efficiency would need to have a surface area 10,000 times larger (100AU radius), but assumed that a Dyson sphere of this size would be impractical and hence only spheres with an efficiency of 0.95 would be built.
This is an unusual assumption to make since it means any advanced civilisation capable of building a Dyson sphere would have to waste 5% of the potential energy available. A 0.99 or better Carnot efficient sphere could be built using only a small fraction of the material resources available within our solar system [2]. If you are civilisation able to build a Dyson sphere the size of Earth’s orbit, then you would be able to build one larger and much more efficient using a relatively small increase in resources and time.
The consequences of this 0.95 efficiency choice is not minor. If Wright et al. had assumed Dyson spheres are 0.99 (or better) Carnot efficient then their emission spectra would not be detectable above the background infrared emissions of interstellar gas and dust – put simply, the emission signal from efficient Dyson spheres will be swamped by infrared noise in any wide-field infrared surveys.
Unfortunately this means that all we can conclude from Wright et al. study is that there are few (or no) Dyson spheres built with a 0.95 (or less) Carnot efficiency. If Dyson spheres do exist, and they are efficient (which we should expect of any advanced civilisation capable of building such spheres), we won’t be able to spot them via infrared astronomical surveys. The good news there is a different approach for finding efficient Dyson spheres, but that is another post.
References
1. Wright, J. T., Mullan, B., Sigurdsson, S., & Povich, M. S. (2014). THE Gˆ INFRARED SEARCH FOR EXTRATERRESTRIAL CIVILIZATIONS WITH LARGE ENERGY SUPPLIES. I. BACKGROUND AND JUSTIFICATION. The Astrophysical Journal: 792:26.
2. Wright, J. T., Griffith, R. L., Sigurðsson, S., Povich, M. S., Mullan, B. (2014). THE Gˆ INFRARED SEARCH FOR EXTRATERRESTRIAL CIVILIZATIONS WITH LARGE ENERGY SUPPLIES. II. FRAMEWORK, STRATEGY, AND FIRST RESULT. The Astrophysical Journal: 792:27.
3. Griffith, R. L., Wright, J. T., Maldonado, J., Povich, M. S., Sigurdsson, S., Mullan, B. (2014). THE Ĝ INFRARED SEARCH FOR EXTRATERRESTRIAL CIVILIZATIONS WITH LARGE ENERGY SUPPLIES. III. THE REDDEST EXTENDED SOURCES IN WISE. The Astrophysical Journal: 792:28.
“Unfortunately, while they calculated the increase in sphere surface area correctly to achieve this Carnot efficiency (i.e. the sphere needs to have a surface area 10,000 times larger), they inexplicable miscalculated the corresponding radius. They stated that a 99.5% Carnot efficient Dyson sphere would need to have a radius of ~100 AU (well past Eris) [2:2.6.4], when the correct value is actually ~28 AU (a bit beyond Pluto).”
I have a quibble with you here. The authors did actually calculate the distance correctly.
At 1au , surface area is ;
4PIr^2
4*PI*1AU^2 = 4PIau^2
At 100 au , surface area is
4PI * 100au^2 = 4pi *10’000 au ^2
Crossing off 4pi from both sides(as they both have it), the distance of 100au , does produce a surface area 10’000 times greater.
” What is more important than this relatively minor mathematical error, is the assumption that a 0.95 Carnot efficiency is reasonable and that any advanced civilisation must waste 5% of the potential energy available. This assumption looks very unusual when a 0.99 or better Carnot efficient sphere could be built using only a small fraction of the material resources available within our solar system”
This is rather odd. Even one built out to the background radiation of 2.7 Kelvin, at ~11’500au would only require about 5 earth masses, if made of graphene. (at .77milligrams / meter^2) The marginal increase in efficiency does imply that the energy cost of producing a solar panel has to be below 10MJ per meter squared though though, or that maintenance is 1joule per 10’000 years per meter squared (dividing by the main sequence life time of a sun analog).
This decreasing efficiency also applies in the other direction though, with breakeven points of ~15 x 10^15 joules/m2 at 10au , 18 Terrajoules/m2 at 100 au, and 15 Gigajoules/m2 at 1000au.
However the author does not appear to mention any of this, or make any effort to calculate it.
To your first point yes you are right. I have updated the post to correct this. It does not change the main conclusion :)
Your second point is of course spot on. There is no rational reason for choosing a 0.95 Carnot efficiency other than if the authors had chosen a higher value the Dyson spheres would have been undetectable using their approach.
If you wanted to add in further constraints you could put in weights to the sails so they weren’t launched outward by the photon pressure of the sun (making them about 1000x heavier) .
If using the non stellar mass of the solar system, at 0.14% of the solar systems mass this would limit you to ~3500 au. 1 earth mass is at 155 au , 0.1 at ~50 au, and 0.01 at 16.5 au.
Now there is one benefit for one centered around ~1au in that the energy required for heating and cooling the structure would be minimal, if you wanted it at ~290Kelvin. This would for example be a good temperature for human habitable areas. However literally any other required temperature would render this distance irrelevant.
Lastly if there is maintenance costs even out to 10 au , you would be energy flow positive even if you needed to send a probe to completely replace the solar panels every year and then repair them back at earths orbit. (this is ignoring any down time or occlusion though)
I would imagine that any Dyson sphere would be arranged in shells. This would minimise the material required for the outer shell and also the photon pressure on the outer shells. The end result however the sphere(s) (swarm) are built they won’t be detectable to us above the infrared background.
Why would efficiency be the paramount parameter? The cost in materials and energy goes as the square of the radius. This implies smaller, hotter Dyson spheres.
Only if you are limited to a single sphere. The most material efficient way to build a Dyson sphere would be as a series of nested shells. The longer the wavelength the less material needed to capture the energy.
Would you use 10.000 times more material to gain that 5% in efficiency, rather that constructing a 2nd Dyson sphere around another star?
Another key point may be: what are the conditions on the inside surface of the Dyson Sphere? What’s his T? Where do we assume the alien civilization is living?
What happens to the high grade energy after they use it? It re-radiates as heat. You can’t simply absorb energy without storing it or using it. eitherway, eventually it ends up as heat no matter how efficient you are.
Unless of course you are smart AND efficient enough to use m = e/(c*c) to build the shells
The energy gets radiated away a heat. The larger you make the outer shell the more of the energy you capture and the lower the temperature of waste heat. Of course if the waste heat is close to the level of the gas and dust clouds you won’t be able to see it.
Because you don’t need to use 10,000 time more material to build the outer shell (swarm). The outer shells job is just to capture the waste heat coming off the inner shell(s) and so does not need to be more than an atom thick (on average). Actually depending on the wavelengths being captured the outer layer could be less than than an atom thick on average as the antennas on the outer swarm don’t need to be continuous.
This is something we can only speculate about and would be dependent on what the makers wanted. This is a question beyond my post which is just about if we can detect Dyson spheres in the infrared.
OK i am with you and agree with your calculations. What I still don’t understand about this … Let’s say they achieve 99.5% efficiency. Are you suggesting that once they’ve wrung out every bit of work they can muster, then the remaining heat is of such a long wavelength that it blends in to the 4 K background? Even so wouldn’t it show up as a bright spot against the broad background of glowing space dust?
BTW/ I like your other posts, especially the one on climate change. I mean putting the cost onto future generations is such a non-PC thing to say. Of course humankind have been doing this in many areas besides climate. I just thought it was a pretty gutsy thing to say out loud. Personally I have no doubt whatsoever that nothing will/can be done to rein in Homo s.’s drive for short-term gain at the expense of our their own future. And I’m known as an optimist in these parts!
Within the galaxy there are a lot of sources of higher temperature background – basically all the gas and dust clouds that around 50K. Once the Carnot efficiency of the Dyson sphere gets over 99% then they becomes impossible to detect in amongst all the other 50K objects. Wright et al. argument is a bit like the drunk looking for their keys under the lamp post, not because that is where he dropped them, but because that is where the light is best and then concluding when they couldn’t find the keys that they don’t exist.
One final point is that civilisations which store their energy rather then use it, perhaps hoping to overcome landauers principle by waiting for the universe to cool down, or doing Dyson’s eternal intelligence concept. However this also lowers their luminosity. Assuming that it stores energy at the efficiency of a carnot engine, a background temperature energy storing civilisation would be located at ~530 au, and be only 0.2% as luminous as our sun, if it were around a solar analog. This means that the distance we could detect them would be 1/20th of what it would be if they used all energy at the moment it was collected.
Similarly this means that IRAS whole sky search, ( https://www.tillett.info/2016/08/03/carnot-efficient-dyson-spheres-are-undetectable-by-infrared-surveys/ ) would only have a range of 14 parsecs rather then 300pc (were it to be optimised to that temperature)
This means that either only redgiants and B type stars would be found, giving 1/300th to 1/1000th the number of candidates if they were looking for solar luminosity spheres. Meaning only a thousand candidates would be viewable (using the number of non dyson stars of that type as a proxy for candidate number)
Or if they were looking for reducing luminosity Sol type dyson swarms, only 90 candidates would exist within the search range.