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.