Which Energy Sources Type II Civilization Will Utilize If They Aim To Build A Dyson Sphere Around A Black Hole? (Astronomy)

You may have came across different concepts related to advanced civilizations such as Alderson disk, Matrioshka brain etc. But, one of the famous concepts is the Dyson sphere. Its concept relies on the fact that, if an extraterrestrial intelligence has reached a level of supercivilization, it might consume an energy of its own star. For this purpose, to have the maximum efficiency of energy transformation, it would be better to construct a thin shell completely surrounding the star. For instance, if a dyson sphere is built around the Sun, the total luminosity of the Sun (L ∼ 4 × 1026 W) can be utilised, which is approximately nine orders of magnitude larger than the power intercepted by the Earth (∼ 1.7 × 1017 W). After receiving the energy from the star, the civilisation would be able to convert the energy from low-entropy to high-entropy and emanate the waste heat (e.g., in mid-infrared wavelengths) into the background, suggesting this kind of energy waste is detectable.

However, it is almost impossible to build a rigid Dyson Sphere due to the gravity and the pressure from the central star. Hence, some sorts of the concept were proposed. Such as, a Dyson Swarm, a group of collectors that orbits the central energy source. This method allows the civilisation to grow incrementally. Nevertheless, due to the orbital mechanics, the arrangement of such collectors would be extraordinarily complex. Another variant is a Dyson Bubble which contains a host of collectors as well. However, the collectors are instead stationary in space assuming equilibrium between the outward radiative pressure and the inward gravity, which are usually called “solar sails” or “light sails”.

Based on energy consumption, Kardashev classified the hypothetical civilisations into three categories (Kardashev scale). A Type I civilisation uses infant technology and consumes 4 × 1016 W (or 4 × 1023 erg s¯1), the energy of its planet. A Type II civilisation harvests all the energy of its parent star, namely 4 × 1026 W (or 4×1033 erg s¯1). A Type III civilisation represents the highest technological level, which can engulf its entire galaxy as its energy source. A typical energy used by a Type III civilisation is about 4 × 1037 W (or 4×1044 erg s¯1). To represent the civilisations that have not been able to use all of their available energy sources, Sagan suggested a logarithmic interpolation in the form of 𝐾 = 0.1(logP − 6), where 𝐾 is the Kardashev index and 𝑃 (in the unit of Watts) indicates the energy consumption. Currently, our civilisation level is approximately 0.735 and we may take 5000-10000 years to become type II.

After a type II civilization absorbs all the energy from the parent star, they would seek another energy source to maintain itself. What if that energy sources are nothing but the black holes? But, the question is, if black holes can be regarded as proper energy sources?, or if they are inefficient to provide ample energy for civilizations to thrive. Hsiao and colleagues recently answered this question in their recent paper.

They considered and discussed six types of energy sources: the Cosmic Microwave Background (CMB), the Hawking radiation, an accretion disk, Bondi accretion, a corona, and the relativistic jets from two types of black holes: a non-rotating black hole (Schwarzschild black hole) and a rotating black hole (Kerr black hole), ranging from micro, stellar-mass, intermediate-mass to Supermassive Black Hole (SMBH).

© Hsiao et al.

They showed that the collectable energy from the CMB at present by the Inverse Dyson Sphere would be too low (∼ 1015 W). Next, the Hawking radiation as a source seems to be rather infeasible since the Hawking luminosity cannot provide adequate energy (e.g., for 5 M, 𝐿Hawking ∼ 10¯30 W << 1026 W (Type II)).

On the other hand, it has been suggested that, an accretion disk, a corona, and relativistic jets could be potential power stations for a Type II civilisation.

“Our results suggest that for a stellar-mass black hole, even at a low Eddington ratio, the accretion disk could provide hundreds of times more luminosity than a main sequence star.”

If a Type II civilisation collects the energy from the accretion disk of a SMBH, the energy could boost the Kardashev index, 𝐾 ∼ 2.9. Moreover, the energy reserved in a corona and jets can provide additional energy (∼ 30%− ∼ 50% for the corona luminosity and ∼ 60%− ∼ 80% for the jets luminosity) aside from the accretion disk.

“Our results suggest that if a Type II civilisation collects the energy from jets and electromagnetic radiation simultaneously, for a SMBH with a mass similar to Sgr A*, the Kardashev index can reach ∼ 3.”

Overall, their results suggested that a black hole can be a promising source and is more efficient than harvesting from a main sequence star.

(article continues below images)

Figure 1. Example spectra of Scenario A (𝑀 = 5 M and 𝐿disk = 1600 L) (upper panel:) A hot Dyson Sphere with covering fraction 𝑅c = 20%, transfer efficiency 𝜂 = 50% , and 𝑅DS = 5000𝑅Sch. (lower panel:) A solid Dyson Sphere with covering fraction 𝑅c = 2%, transfer efficiency 𝜂 = 80%, and 𝑅DS = 7.12×106 𝑅Sch. The yellow curve suggests the accretion disk flux with the absorption of the Dyson Sphere ((1–𝑅c) times the original accretion disk flux) while the purple dot curve is the original flux of accretion disk without surrounding a Dyson Sphere. The blue curve shows the flux of the waste heat from the Dyson Sphere while the red dot-line curve indicates the total flux. The black circles, green diamonds, burgundy asterisks, blue stars, and magenta hexagrams indicate the limiting magnitude of GALEX, PAN STARRS1, VHS, WISE, and SDSS survey, respectively. © Hsiao et al.

They also discussed a possible location of a Dyson Sphere around a black hole. To absorb the accretion disk luminosity, a Dyson ring or a Dyson Swarm could be a possible structure. A Dyson Sphere should be located outside of the accretion disk, ∼ 103𝑅sch − 105𝑅sch. However, in this region, the hot temperature would melt the solid structure. In order to avoid melting of the solid Dyson Sphere, the solid Dyson Sphere (𝑇 = 3000 K) should be located at 𝑅DS ≳ 107 𝑅Sch and 𝑅DS ≳ 103 𝑅Sch for a stellar mass black hole and a SMBH, respectively. (RDS – radius of dyson sphere & RSch- Radius of Schwarzschild black hole).

Figure 2: Possible wavelengths for a hot Dyson Sphere to be detected in different black hole mass. The purple, blue, green, orange, and red regions indicate X-ray(0.01–10 nm), UV(10–400 nm), optical(400 0760 nm), NIR(760 nm – 5 𝜇m), and MIR(5 – 40 𝜇m) wavelength, respectively. The shaded region is the peak wavelength from black body radiation of the waste heat, covering a wide range of parameters of a Dyson Sphere. The region enclosed by blue, magenta, and black lines indicate stellar-mass, intermediate-mass and SMBH. Three arrows show how the peak wavelengths change with increasing parameters. The arrow lengths are arbitrary. © Hsiao et al.

The size of an accretion disk for a stellar-mass black hole is smaller than the size of the Sun, which means that a Dyson Sphere around the stellar-mass black hole can be smaller than that around the Sun. In terms of relativistic jets, a possible form of a Dyson Sphere is a Dyson Bubble. Balancing the pressure and the gravity from the black hole, a light sail could be stationary in space and can continuously collect the energy from the jets. Light sails also absorb the luminosity from the accretion disk at the same time. Their results suggested that the best way to place a light sail is close to the origin of the jets, which could save the materials to build a light sail.

Moreover, a hot Dyson Sphere around a stellar-mass black hole in the Milky Way (10 kpc away from us) is detectable in the UV(10−400 nm), optical(400−760 nm), NIR(760 nm−5 𝜇m), and MIR(5 − 40 𝜇m), which can be detected by our current telescopes (e.g., WFC3/HST and GALEX survey). For a solid Dyson Sphere, the limiting magnitude of the sky surveys such as Pan STARRS1, VISTA Hemisphere Survey (VHS) Wide-Field Infrared Survey Explore (WISE) and Sloan Digital Sky Survey (SDSS) are smaller than the flux density from the solid Dyson Sphere, which indicates that the solid Dyson Sphere is bright enough to be detected.

“The presence of Dyson Spheres may be imprinted in spectra. Performing model fitting and measuring the radial velocity will help us to identify these possible artificial structures.”, concluded authors of the study.

Featured image: Advanced Civilization Using A Dyson Sphere © Getty images

Reference: Tiger Yu-Yang Hsiao, Tomotsugu Goto, Tetsuya Hashimoto, Daryl Joe D. Santos, Alvina Y. L. On, Ece Kilerci-Eser, Yi Hang Valerie Wong, Seong Jin Kim, Cossas K.-W. Wu, Simon C.-C. Ho, Ting-Yi Lu, “A Dyson Sphere around a black hole”, MNRAS, 2021. DOI:10.1093/mnras/stab1832 preprint: https://arxiv.org/abs/2106.15181

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