We are too young for that!

Nikolai Kardashev, in his seminal 1964 paper, classified civilizations into three broad categories:

  1. a civilization with technological level close to that presently attained on the earth.
  2. a civilization capable of harnessing the energy radiated by its own star, and
  3. a civilization in possession of energy on the scale of its own galaxy.

Even since this publication, people have hypothesized different methods of detecting alien megastructures (see Figure 1 for examples). A feat of extensive galactic engineering (e.g. through many Dyson spheres) would be readily discernible in the spectrum of an object. At least this was the hypothesis for the Fermilab astrophysicist James Annis when he undertook a search for class III Kardashev civilizations. Annis argued the “most direct way to obtain power” for type II and III civilizations would be to harness stellar power. This would imply the interruption or redirection of starlight which, when performed on a galactic scale, should produce an observable change in a galaxy.

Figure 1: The Hunt is on!The search for alien mega structures! Some have argued we should use the transit method to detect transits inconsistent with a planet. Others have argued artifact SETI should focus on the thermodynamic evidence. This often means one Dyson sphere covering a star or a galaxy full of Dyson spheres. Annis himself was looking for galaxies modified by type III civilizations, such that the redirection of optical light would result in significant dimming which would present itself as an outlier on scaling relationships. Source: New Scientist

Annis made a distinction between natural galaxies and those that have been modified by a type III civilization. Galaxies are bound by their masses such that there exist gravitational-thermal scaling relationships. To derive the fundamental scaling relationships, Annis used the virial theorem and assumed the temperature of the galaxy was defined by the random velocities of its stars (e.g. similar to an ideal gas). He derived a generate relationship between the radius of a galaxy, R, the surface density, I, and the temperature, T, such that T=CIR, where C is a constant. In practice, the relationship he derived is not that simple but does emphasize that (i) self-gravitating systems have a simple relationship for R, I, and T and (ii) a natural, unperturbed galaxy shows such relationship. The relationships he uses are the Tully-Fisher relationship for spiral galaxies (LIR2) and the fundamental plane for normal elliptical galaxies (RT0.68I-0.85) and he notes a small scatter of ~10%.

Given that the relationship between these parameters was relatively consistent, this allowed Annis to look for outlier galaxies in each trend. His argument was that a type III Kardashev civilization would be “an outlier on R-I-T relations in the sense of anomalously low I, probably with a thermal IR excess, and possibly with a low surface brightness in absolute terms”. The results of his search through 31 spiral galaxies and 106 elliptical galaxies is shown in Figure 2. In this available sample, Annis found no candidate type III civilizations where at least 75% of the light would be dimmed. Annis attributed the null detection to various factors: his limit for outlier classification, instrumental effects, and potential bias against modified galaxies within current catalogs.

Figure 2: The data presented by Annis. The left figure shows the relationship for spiral galaxies while the right figure is for elliptical galaxies. The solid line is the best-fit relationship for the sample. The dashed line represents the limit of 75% dimness. Anything below (in the case of spiral galaxies) or above (in the case of elliptical galaxies) would be a likely candidate for modification by a type III civilization.

To this blogger, the most important thing is the limits Annis was able to place on the formation of type III civilizations. He presents one of the first attempts to statistically evaluate our isolation in the Universe. As a thought experiment, we can assume the appearance of a type III civilization follows a Poisson distribution (p=e-rT) and could occur at any point in time. Given that, on order, the galaxy’s age is 10 billion years, a 99% probability of a null detection would suggest an occurrence rate of r=4.61×10-10 per year or, equivalently, that it takes at least 2.1 billion years for a type III civilization to occur by chance. If each galaxy represents an independent realization of the thought experiment, then the upper limit on the occurrence rate suggests ~300 billion years must pass for a type III civilization to exist. Ergo, the Universe is too young for these civilizations.

The work by Annis suggests future searches for type III civilizations would be illogical. Future attempts have tried to address this. Most recently, Wright et. al. argue against the temporal argument raised by Annis. Wright et. al. agree with Annis in that his sample, derived from optical catalogs, may be biased against galaxies which theoretically have little to no optical emission. They also criticized the use of a random Poisson process and independent of time as this would presumably contradict the time-dependent evolution of life (e.g. from no life, to type I, type II, and finally type III civilization). Wright et. al. argue that a much larger sample, preferably in the IR, would serve as a better search, although any outlier found would still require significant vetting. Annis himself has pondered:

“Life, once it becomes spacefaring, looks like it could cross a galaxy in as little as 50 million years, and 50 million years is a very short time compared to the billion-year timescales of planets and galaxies. … Maybe spacefaring civilizations are rare and isolated, but it only takes just one to want and be able to modify its galaxy for you to be able to see it. If you look at enough galaxies, you should eventually see something obviously artificial. That’s why it’s so uncomfortable that the more we look, the more natural everything appears.”

As of now, there is no unambiguous detection of a type III civilization. This blogger is not particularly surprised by the null detection. Perhaps future searches will bear fruit, but for now the only thing for certain is that the Universe holds one type I civilization.