On the possibility of the Dyson spheres observable beyond the infrared spectrum
ABSTRACT
In this paper we revisit the Dysonian approach and assume that a superadvanced civilisation
is capable of building a cosmic megastructure located closer than the habitable zone (HZ). Then
such a Dyson Sphere (DS) might be visible in the optical spectrum. We have shown that for
typical high melting point meta material - Graphene, the radius of the DS should be of the order
of 1011cm, or even less. It has been estimated that energy required to maintain the cooling system
inside the DS is much less than the luminosity of a star. By considering the stability problem,
we have found that the radiation pressure might stabilise dynamics of the megastructure and as
a result it will oscillate, leading to interesting observational features - anomalous variability. The
similar variability will occur by means of the transverse waves propagating along the surface of the
cosmic megastructure. In the summary we also discuss the possible generalisation of definition
of HZs that might lead to very interesting observational features.
1. Introduction A recent revival of interest to the search for advanced extraterrestrial civilisations has been provoked by the discovery of the object KIC8462852 observed by the Keppler mission (Boyajian et al. 2016). According to the data, the flux coming from the mentioned object has been characterised by dips of the order of 20%, which automatically excludes existence of a planet shading the star. It is worth noting that the detected flux has an irregular character, which has been analysed in detail and it has been shown that such a behaviour might not be caused by any measurement errors. Such a strange emission pattern of KIC8462852 and some other similar stars has been analysed in a series of papers in the context of artificial megastructures possibly constructed by a superadvanced civilisation (Wright et al. 2016; Schuetz et al. 2016; Harp et al. 2016). The idea of such cosmic mega constructions has been considered by Freeman Dyson. In his well known work (Dyson 1960) he has suggested that if the superadvanced extraterrestrials exist, which are capable of utilising the total energy of their host star (Level-II civilisation in the Kardashev scale (Kardashev 1964)), then they could have built a relatively thin spherical shell (Dyson sphere (DS) with radius ∼ 1AU surrounding the star. The author has shown that on the mentioned distance the internal surface of the DS will be in the habitable zone (HZ). Therefore, the temperature of the megastructure will be of the order of 300K, which means that it will be visible in the infrared spectrum. For finding the infrared DSs the monitoring of the sky has been performed by several instruments (Jugaku & Nishimura 2002; Slish 1985; Timofeev et al. 2000) although no real candidate was found. In the beginning of the last decade a new series of investigation has been initiated. In particular, Carrigan (2009) has examined and analysed the results of IRAS (The Infrared Astronomical Satellite) covering 96% of the sky and 16 objects has been identified as potential DSs but it has been emphasised that the subsequent investigation is necessary. According to the Kardashev’s classification the 1 Level-III civilisation is the one that is capable of consuming the whole energy of its host galaxy by enveloping each of the star by spheres. This means that the galaxy will be seen in infrared. The search for galaxy spanning civilisations has been performed by Griffith et al. (2015) where the authors analysed the data of the the Wide-field Infrared Survey Explorer (WISE) in the high mid made of and (II) the super civilisation is capable of constructing an efficient cooling system inside the shell. Generally speaking, it is clear that a LevelII civilisation might use meta materials with high melting temperatures. In particular, by considering graphene it is straightforward to show that to maintain a cold region with a temperature of the order of 300K the corresponding heat flux power (normalised on the solar luminosity) is given as Pc ≈ κS L⊙ ∆T h ≈ 2.4 × 10−6× × ∆T /h 70K cm−1 × κ 2.5 × 108erg/(cmK) × S SE ergs s−1 , (2) where the temperature gradient is calculated for ∆T = (1000 − 300)K = 700K, h = 100cm and κ = 2.5 × 108 ergs cm−1K−1 is the typical value of the thermal conductivity of graphene(Cai et al. 2010) and S - the area occupied by the extraterrestrials is normalised by the total surface area of Earth SE ≈ 5.1 × 108km2 . If one assumes that the coefficient of performance (COP) for a cooling system is of the order of 5 (typical values of modern refrigerators), the engine, to compensate the aforementioned flux to the cold area must process the energy from the cold reservoir to the hot one Pe = Pc COP ≈ 4.7 × 10−7 × 5 COP × × ∆T /h 70K cm−1 × κ 2.5 × 108erg/(cmK) × S SE ergs s−1 . (3) As we see from this estimate, only a tiny fraction of the total luminosity is required to maintain a habitable zone inside the DS if one uses meta materials (graphene), which Type-I civilisation can produce. Therefore, there is no question if the Level-II extraterrestrials can produce such materials. One has to note that although temperature dependence for graphene is not studied for a wide range of temperatures, a preliminary study shows that for high temperatures κ should decrease (Pop et al. 2012). Therefore, the corresponding value of Pe might be even less. It is worth noting that if the primary purpose to construct the DS is computation, the aforementioned estimates should be changed (Sandberg 1999). An important issue we would like to address is the stability problem of the DSs. In an ideal case the star has to be located in the centre of the sphere, but it is clear that a physical system can remain in the equilibrium state only in the absence of disturbances. In Fig. 1 we schematically show the position of the star (point S) and the DS with the centre O. By assuming that the DS is shifted by x with respect to the equilibrium position we intend to study its dynamics of motion. It is obvious that according to the Gauss’ law the gravitational interaction of the star and the spherical shell is zero. On the other hand, stars emit enormous energy in the form of electromagnetic radiation, which will inevitably act on the internal surface of the DS and consequently, the part of the surface which is closer to the star will experience higher pressure than the opposite side of the sphere. Therefore the restoring force will appear leading to the periodic motion of the megastructure. By assuming the isotropic radiation, the corresponding pressure in the direction of emission (See the arrow in Fig.1) is given by P = L 4πr2c , (4) where r = x 2 + R 2 − 2xR cosϕ 1/2 (5) is the distance from the centre of the radiation source. If one assumes that the inner surface of the DS completely absorbs the incident radiation, the corresponding force acting on the differential surface area dA is given by dF = L 4πr2c dA cos γ, (6) where γ is the angle ∠OBS. On the other hand, from the symmetry it is certain that the sphere will move along the x axis (coincident with the line OS). Therefore, the dynamics is defined by the component of the force along the mentioned direction. Then, by considering a ring with radius 2πR sin ϕ it is straightforward to show that dFx = L 4πr2c 2πR2 sinϕ cos γ cos θdϕ. (7) After taking into account the relations θ = ϕ + γ, (8) and cos γ = R − x cosϕ (x 2 + R2 − 2xR cosϕ) 1/2 (9) the x component of the total radiation force acting on the DS Fx = LR2 2c Z π 0 sin ϕ (R cosϕ − x) (R − x cos ϕ) (x 2 + R2 − 2xR cosϕ) 2 dϕ, (10) for small oscillations x/R << 1 reduces to Fx = − 4L 3c x R . (11) The minus sign clearly indicates that the force has a restoring character and consequently the dynamics of the DS is described by the following differential equation dx2 dt2 + 4L 3cRM x = 0, (12) where M = 4πρR2∆R is the mass of the megastructure, ∆R is its thickness and ρ is the density of a material the DS is made of. By combining this expression with the aforementioned equation one can show that the period of oscillation is given by PDS = 2π 3πρcR3∆R L 1/2 ≈ 33.8 × L L⊙ 1/4 × × 1000K T 3/4 × ρ 0.4g/cm3 1/2 × ∆R 100cm 1/2 yrs, (13) where the thickness of the construction is normalised on 100cm and ρ is normalised on the density of graphene. As it is clear from Eq. (13), the DS is stable oscillating with the period ∼ 33.8 yrs. One can straightforwardly show that for the mentioned temperature the required mass of a megastructure is less than the mass of Earth. On the other hand, as we have already discussed, since smaller DSs will require less material, the issue that the civilisation might address would be to increase the surface temperature of the sphere. In Fig. 2 we show the behaviour of PDS versus the surface temperature for graphene having the melting temperature, 4510K (Los et al. 2015). Here we assume that if our civilisation (almost Level-I) might produce such materials, a super advanced one is able to do more efficiently. It is clear from the plot, that the period varies from 33.8yrs to 0.53yrs. This result automatically means that the search for Dysonian megastructures could be widened and observations should be performed not only in the infrared spectrum, but in the optical band. One of the characteristic features, that might distinguish the real DS from stars is the luminosity temperature relation. For example, main sequence stars having temperature of the order of 2000K belong to low luminosity M stars (Carroll & Ostlie 2010), whereas the megastructure might emit the luminosity equal or even higher than the Solar luminosity. The temperature range we consider is (2000K; 4000K), which means that the spectral radiance peaks at wavelengths (725nm; 1450nm), having significant fraction in the optical band. Here we examined graphene as a particular example just to show that if extraterrestrials consider strong materials, their DS might exhibit an interesting behaviour different from normal stars. Another important observational fingerprint follows from the results obtained above. Due to the oscillation of the hot DS its detected flux will be variable, with the period PDS. From the figure it is clear that the values of PDS are typical timescales of variability of very long period pulsating stars, which normally belong to spectral class: F, M, S or C. But F stars usually have very high temperatures, of the order of 7000K, typical temperatures of M stars although are relatively low (2400 − 3700)K but their luminosities are almost two orders of magnitude less than the Solar luminosity. Unlike them, S and C stars are highly luminous (in comparison with the Solar luminosity) (Carroll & Ostlie 2010). Therefore, these discrepancies might be good indicators of potentially interesting objects. It is worth noting that the aforementioned examples only show a certain tendency how an observational pattern of the megastructures could be significantly different from the behaviour of variable stars. This in turn, means that an analysis of rich observational data provided by several optical telescopes might be 4 very promising. The surface of the DS is not an absolutely rigid body and therefore, it might vibrate under the in- fluence of perturbations transversal to the surface, which might be induced either by the radiation pressure or by means of the star’s wind. Therefore, another possible source of variability of DSs could be the mechanical waves generated on the 2D surface of the megaconstruction. It is straightforward to show that if a membrane is stressed with a tension per unit length, (along the surface of the DS) τ, and its mass per unit area is Σ, the transverse wave speed along the surface is of the order of υw ≈ τ Σ 1/2 . (14) Even if the construction does not envelope the star completely (Dyson Swarm) it still can have similar interesting observational features. In particular, by means of these waves the surface will vibrate exhibiting the variability of emission intensity. Unlike the completely closed surface, the Dyson swarm will experience the gravitational force from the Star leading to the following value of τ τ ≈ αGMMs 2πR3 , (15) where G ≈ 6.67 × 10−8Nm2/kg2 is the gravitational constant, Ms is the star’s mass and α is the coefficient, that depends how complete the DS is (for the closed surface α = 0). We assumed that the tension is caused by gravitation (although the possible rotation of the DS might also influence the value of τ). It is clear that the timescale, Pw, for waves to travel from one point to a diametrically opposite location is given by υw/(πR) which for Graphene will be 1.5α yrs for 2000K and 0.8α yrs for 4000K. In case of higher harmonics the corresponding values will be even less. Although we do not know the value of α and the origin of the tension is unclear, the estimate shows that an aforementioned anomalous variability might be a good sign for a potential DS. 3. Conclusion We have generalised the Dysonian approach, considering megastructures not in the HZ but closer. In the framework of the paper we assume that a super civilisation is capable of building megastructures with melting point more than 2000K − 4000K. This means that the DSs having the length scales of the order 1011cm should be visible in the optical band as well. It has been argued that the radiation pressure stabilises the DS, which potentially can lead to anomalous variability. In particular, by examining the super strong and super light material graphene and assuming that since a civilisation like us can produce it, the Level-II might have created even stronger and lighter material, it has been found that the variability would have been characterised by the timescales incompatible with known long period variable stars. The similar variability might be caused by the transverse waves on the surface of the DS, where for an incomplete megastructure it has been shown that for super strong materials the ”pulsation” period might be of the same order as in the aforementioned cases. By the present paper we wanted to show that the Dysonian approach is broader and there are more possibilities of the search for intelligent life than it is sometimes thought. In this paper we have theoretically hypothesised our approach. Though the following generalisations are beyond the scope of the present paper, it is worth noting them. One of the significant issues one has to address is the question concerning anomalous variable intensity and the possibility to detect them by existent instruments. Another issue that one should address is a certain extension of the Dysonian SETI in the context of HZs. In particular, as we have already discussed in the introduction, our approaches are very restricted. Usually the HZ is defined as an area where water can be maintained in a liquid phase, whereas if one assumes nonwater-based life (Sagan 2000) the corresponding area will be in a different location. According to Carl Sagan our chemistry is attuned to the temperature of our planet and he assumes that other temperatures might lead to other biochemistries. If this is the case the HZ will be an area where temperature might be significantly different from the temperature of liquid water. For instance, if one assumes that methane is used as a solvent instead of water, then the HZ will be an area where there are appropriate conditions to maintain methane in a liquid phase. In this case the temperature is in the 5 range 90.7K − 11.7K corresponding to the wavelength interval 26µm − 32µm. Therefore, in the framework of this paradigm, the DS in the HZ might be visible in the far IR spectrum. 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