Kardashev classification scheme for extraterrestrial civilisations

In 1964, Nikolai Kardashev published a paper on how an extraterrestrial civilisation could maximise the information it transmitted to other stars [1]. He calculated an estimated optimum spectrum of a signal, showed that Earth’s technology of the time would be able to detect it and suggested two already detected radio signals of unknown origin could be generated by extraterrestrial intelligence. This paper is most famous, however, for proposing a classification scheme for civilisations based on their level of energy consumption. This has been adapted and expanded to become a scale for measuring technological advancement known as the Kardashev scale. Here are my notes on this seminal paper.

I am tracking all of the papers I’ve read and want to read on this topic in this roundup of the technosignatures literature.

Background radiation

The first of four parts of Kardashev’s paper deals with background radiation, which limits the range of space communication. Background radiation from the galaxy was also included in calculations by Cocconi and Morrison in the paper that first proposed searching for interstellar radio communications [2] but Kardashev includes more detail on this. He gives a formula for the noise temperature and the values for each component when looking within a galaxy and between galaxies:

\[T_N = T_n + T_t + T_q\]

Within galaxy:

\[T_N = 2 \times 10^{27} f^{-2.9} + 10^{19}f^{-2} + 4.8 \times 10^{-11}f\]

Between galaxies:

\[T_N = 2 \times 10^{26} f^{-2.9} + 4.8 \times 10^{-11}f\]

Where \(T_n\), \(T_t\) and \(T_q\) are the temperatures due to synchrotron radiation (lower between galaxies), background thermal cosmic radio emission (only within the galaxy) and quantum fluctuations in the minimum detectable signal (\(T_q = \frac{hf}{k}\), where \(f\) is frequency, \(h\) is Planck’s constant and \(k\) is Boltzmann’s constant).

Information content of communications

The second part of Kardashev’s paper concerns the information content of a signal. He uses the Shannon theorem to compute a curve for the frequency-dependent upper bound of the rate of information transmission that is the same shape of curve as the frequency-dependent noise temperature but with the sign reversed, giving a maximum and a drop off at higher and lower frequencies.

He concludes that the rate of information transmission will be equal to the bandwidth of the transmitter and that, for a reliable transmission, this would be proportional to the power of the transmitter and the area of the receiver and inversely proportional to the the noise temperature and the square of the distance between transmitter and receiver.

Energy expenditure of a civilisation

This is the most famous part of Kardashev’s paper. At the time of writing (1964) the estimated total energy expended by humanity was \(4 \times 10^{19}\) erg/second (\(4 \times 10^{12}\) Watts or 14400 TWh). About sixty years later (2018) this was around \(1.8 \times 10^{20}\) erg per second and growing at about 2.9% per year, which is just under the 2-3% Kardashev quoted in his paper as the estimate of the time.

Kardashev used a 1% growth rate to compute that humanity would consume energy equal to the output of the Sun in 3200 years and equal to \(10^{11}\) sun-like stars (i.e. a galaxy of stars) in 5800 years. He believed there would be no reason to suppose this growth would be slower and anticipated communication from a more advanced civilisation would speed it up.

Three types of civilisation

Kardashev proposed classifying civilisations into three types based on their energy consumption:

• I: similar technological level to humanity c. 1964 with an energy consumption of ~ \(4 \times 10^{19}\) erg/s
• II: ability to harness the energy radiated by its own star (e.g. constructing a Dyson sphere [3]) with an energy consumption ~ \(4 \times 10^{33}\) erg/s
• III: in possession of energy on the scale of its own galaxy, with an energy consumption ~ \(4 \times 10^{44}\) erg/s

Detecting different levels of civilisation

Kardashev viewed our detection of type I civilisations as highly improbable. He considered only the detection of type II and type III at different distances in his estimates of the quantity of information we might receive from these more advanced civilisations. For comparison, he estimated that the non-redundant body of human knowledge (in the 1960s) comprised \(10^{11}\) bits of information.

Detecting type II civilisations within our galaxy

Kardashev estimated that we could receive \(3 \times 10^{9}\) bits of information per second from a type II civilisation at a distance of 100,000 light years (within our galaxy).

Detecting type III civilisations in other galaxies

With a greater available power for transmission, a type III civilisation could send \(2.4 \times 10^{13}\) bits of information per second at a distance of 10 million light years (from within our local group of galaxies) and \(3 \times 10^{10}\) bits/s at a distance of 10 billion light years (the radius of the observable universe is estimated at 46 billion light years - this number is greater than the age of the Universe, which is 13.8 billion years, due to expansion).

Characteristics of artificial sources

Kardashev proposed four characteristics that would discriminate artificial from natural radio sources, as well as the overall shape of the artificial spectrum. An artificial source would have:

1. Very small angular dimensions (on the order of the stars)
2. Circular polarization (to avoid distortion of the information by Faraday rotation)
3. Variability in time
4. Spectral features to emphasise artificial nature of the signal

Searching for artificial radio sources

At the time this paper was published there were two radio sources of interest that did not have a known explanation. These were known as CTA-21 and CTA-102. Kardashev suggested these may be artificial since they have a similar shaped spectrum to what he expected an artificial source to look like. Both were later identified as quasars.

Kardashev suggested several other targets to search:

• The centre of the galaxy since this has the highest density of stars
• The large nebula in the Andromeda constellation
• The Magellanic Clouds
• The closest radio galaxies NGC 4486 (M87) and NGC 5128 (Centaurus A)

Summary

This paper proposes “tentative” estimates for the characteristics of artificial sources of radio signals and the limits for the transmission of information from three different types of civilisations. The classification of a civilisation by its energy consumption led to the famous Kardashev scale, which has been altered and expanded since this original publication. Many now refer to type I civilisations as those that use all the energy hitting the surface of their planet, rather than the energy consumption of humanity in the 1960s. The main point Kardashev made about type I civilisations in his paper was that they would be unable to transmit information to other civilisations over great distances but they (like us) could still receive information from a civilisation with access to much greater energy.

References

1. 1. Kardashev NS: Transmission of Information by Extraterrestrial Civilizations. Soviet Astronomy 1964, 8:217.
2. 2. Cocconi G, Morrison P: Searching for Interstellar Communications. Nature 1959, 184:844–846.
3. 3. Dyson FJ: Search for Artificial Stellar Sources of Infrared Radiation. Science 1960, 131:1667–1668.