On the Possibility of the Dyson Spheres Observable Beyond The

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Keppler object the the by of observed discovery the pro- by been voked has civilisations extraterrestrial vanced Introduction 1. h dao uhcsi eaconstructions mega cosmic such of idea The ad- for search the to interest of revival recent A ntepsiiiyo h yo pee bevbebyn th beyond observable spheres Dyson the of possibility the On fHsta ih edt eyitrsigosrainlfeatures observational possible interesting headings: very the Subject to discuss lead also might we that summary HZs the of propag In waves transverse t the megastructure. feature of considering cosmic observational means By by interesting o occur to dynamics will star. leading variability stabilise a similar oscillate, might will of pressure it luminosity radiation result the the a than that less found have much we is DS the inside uhaDsnShr D)mgtb iil nteotclsetu.We spectrum. th of optical radius the the in Graphene, - visible material 10 be of meta point might the melting than (DS) high closer Sphere typical located Dyson megastructure a cosmic a such building of capable is nti ae ervstteDsna prahadasm htasu a that assume and approach Dysonian the revisit we paper this In 11 m ree es thsbe siae hteeg eurdt ma to required energy that estimated been has It less. even or cm, colo hsc,Fe nvriyo bls,08,Tbilis 0183, Tbilisi, of University Free Physics, of School yo pee EI xrtretil life-detection Extraterrestrial; SETI; sphere; Dyson sao .&Brzin .I. V. Berezhiani & Z. Osmanov nrrdspectrum infrared ABSTRACT 1 a enepaie httesbeun investi- necessary. subsequent is the it gation that but emphasised DSs potential been 16 as has and identified sky been the has of objects 96% Astro- covering Infrared Satellite) (The IRAS and nomical initiated. of examined results decade been has the last (2009) analysed has Carrigan the investigation particular, of of In beginning series the new candidate in- In a real several no found. although by was 2000) performed 1985; al. Slish et been 2002; Timofeev Nishimura has & (Jugaku sky struments the the of in visible be of will order it the spectrum. that of infrared means be which will megastructure 300K, in tempera- the be the of will Therefore, ture DS (HZ). zone the habitable of the surface mentioned internal the on the that distance shown has author The star. pee(S ihradius (Dyson shell with spherical (DS) thin sphere could Kar- relatively they a the then built in have 1964)), (Kardashev civilisation of scale energy (Level-II dashev total star the host utilising their of capable are which codn oteKrahvscasfiainthe classification Kardashev’s the to According monitoring the DSs infrared the finding For . nmlu aiblt.The variability. anomalous - s tn ln h ufc fthe of surface the along ating Ssol eo h order the of be should DS e h eatutr n as and megastructure the f eeaiaino definition of generalisation aial oe(Z.Then (HZ). zone habitable nantecoigsystem cooling the intain ,Georgia i, eavne civilisation peradvanced esaiiyproblem, stability he aesonta for that shown have ∼ 1 AU urudn the surrounding e Level-III civilisation is the one that is capable of to the star the higher its temperature. Therefore, consuming the whole energy of its host galaxy the observational signature of this DS will be dif- by enveloping each of the star by spheres. This ferent and it might be visible in the optical spec- means that the galaxy will be seen in infrared. The trum, which according to our analysis might ex- search for galaxy spanning civilisations has been hibit anomalous variability. Relatively hotter DSs performed by Griffith et al. (2015) where the au- have been proposed by Sandberg (1999), where the thors analysed the data of the the Wide-field In- author considered the megastructures built for the frared Survey Explorer (WISE) in the high mid reason of supercomputing. 5 infrared spectrum. In total approximately 10 In general, it is worth noting that in the cur- galaxies have been monitored. They have iden- rent paper we consider existence of possibility of tified almost 100 objects which, according to the extraterrestrials with biology similar to ours. But authors, deserve further study. it is clear that this is a very limited approach, the Last two decade researchers actively discuss so-called carbon chauvinism and water chauvinism the reasons of possible failure of conventional ironically coined by Carl Sagan (Sagan 2000). In approach to the Search for Extraterrestrial In- his book he examines the possibility of noncarbon telligence (SETI) (Cirkovic 2008; Bradbury et al. and nonwater-based live that might significantly 2011). Cirkovic & Bradbury (2006) have consid- enrich a methodology of the search for extrater- ered that the so-called Dysonian method to SETI restrials. is not limited by the conventional approach and a The organisation of the paper is the following: wider view to the SETI problems is required. On in Sec. 2 we present major estimates and discuss the other other hand, a good strategy for astron- possible observational patterns of the DSs and in omy is to observe all interesting events in the sky Sec. 3 we summarise our results. in as many channels as possible. Recently a rather different view to the Dysonian approach has been 2. Main consideration published. In particular, in (Osmanov 2016) the idea of freeman Dyson has been extended and the In this section we consider a theoretical model possibility of colonisation of a nearby region of of DSs with reduced radii, estimate corresponding a pulsar by a type-II civilisation was discussed. temperatures and the consequent emission spectra It has been shown that instead of a sphere the and study the stability of the megastructure. extraterrestrials should use a ring-like megacon- Unlike the case examined by Dyson (1960), structions requiring much less material than for where the DSs were located in the star’s HZ in spheres. It has been found that locating in the this section we consider a sphere with higher sur- HZ the rings will be visible in the infrared spec- face temperature, T . This could be quite reason- trum. In the following work (Osmanov 2017) the able, because smaller megastructure requires less possibility of detection of infrared rings by modern material. By assuming the black body radiation facilities has been considered and it was found that one can show that the radius of the DS is given by in the nearby area of the solar system the moni- 1/2 toring of approximately 64 ± 21 pulsars might be L R = ≈ promising. 4πσT 4

In the framework of the paradigm that con- 1 2 2 L / 1000K ventional approaches should be widened, in the ≈ 2.14 × 1012 × × cm, (1) present manuscript we examine an unusual view L⊙ T to the Dysonian SETI. In particular, if a civilisa- where σ ≈ 5.67 × 10−5erg/(cm2K4) is the Stefan- tion has reached the level-II on the Kardashev’s 33 Boltzmann’s constant and L⊙ ≈ 3.83 × 10 ergs scale, then it might have been capable of living in- s−1 is the solar luminosity. As it is clear from side the shell of the DS even if it is not in the HZ of the above estimate the radius is almost one orders the star but closer to it. The smaller the radius of of magnitude less than one astronomical unit, a the DS the less the material it requires. therefore typical size of the DS in the HZ. Here we used it is quite reasonable to search for such megastruc- two assumptions: (I) the surface temperature is tures. On the other hand, the closer the surface less than the melting point of a material the DS is

2 made of and (II) the super civilisation is capable of An important issue we would like to address constructing an efficient cooling system inside the is the stability problem of the DSs. In an ideal shell. Generally speaking, it is clear that a Level- case the star has to be located in the centre of II civilisation might use meta materials with high the sphere, but it is clear that a physical system melting temperatures. In particular, by consider- can remain in the equilibrium state only in the ing graphene it is straightforward to show that to absence of disturbances. In Fig. 1 we schemati- maintain a cold region with a temperature of the cally show the position of the star (point S) and order of 300K the corresponding heat flux power the DS with the centre O. By assuming that the (normalised on the solar luminosity) is given as DS is shifted by x with respect to the equilibrium position we intend to study its dynamics of mo- κS ∆T −6 tion. It is obvious that according to the Gauss’ Pc ≈ ≈ 2.4 × 10 × L⊙ h law the gravitational interaction of the star and the spherical shell is zero. On the other hand, ∆T/h κ S × × × −1 stars emit enormous energy in the form of electro- −1 × 8 ergs s , 70K cm 2.5 10 erg/(cmK) SE magnetic radiation, which will inevitably act on (2) the internal surface of the DS and consequently, where the temperature gradient is calculated for − the part of the surface which is closer to the star ∆T = (1000 300)K = 700K, h = 100cm and will experience higher pressure than the opposite × 8 −1 −1 κ = 2.5 10 ergs cm K is the typical value side of the sphere. Therefore the restoring force of the thermal conductivity of graphene(Cai et al. will appear leading to the periodic motion of the 2010) and S - the area occupied by the extrater- megastructure. restrials is normalised by the total surface area of 8 2 By assuming the isotropic radiation, the corre- Earth S ≈ 5.1 × 10 km . If one assumes that E sponding pressure in the direction of emission (See the coefficient of performance (COP) for a cooling the arrow in Fig.1) is given by system is of the order of 5 (typical values of modern refrigerators), the engine, to compensate the L P = , (4) aforementioned flux to the cold area must process 4πr2c the energy from the cold reservoir to the hot one where

2 2 1/2 P 7 5 r = x + R − 2xR cos ϕ (5) P = c ≈ 4.7 × 10− × × e COP COP is the distance from the centre of the radiation × ∆T/h × κ × S −1 source. −1 × 8 ergs s . 70K cm 2.5 10 erg/(cmK) SE If one assumes that the inner surface of the DS (3) completely absorbs the incident radiation, the cor- As we see from this estimate, only a tiny frac- responding force acting on the diﬀerential surface tion of the total luminosity is required to main- area dA is given by tain a habitable zone inside the DS if one uses meta materials (graphene), which Type-I civilisa- L dF = dA cos γ, (6) tion can produce. Therefore, there is no question 4πr2c if the Level-II extraterrestrials can produce such ∠ materials. One has to note that although tem- where γ is the angle OBS. On the other hand, perature dependence for graphene is not studied from the symmetry it is certain that the sphere for a wide range of temperatures, a preliminary will move along the x axis (coincident with the study shows that for high temperatures κ should line OS). Therefore, the dynamics is deﬁned by decrease (Pop et al. 2012). Therefore, the corre- the component of the force along the mentioned direction. Then, by considering a ring with radius sponding value of Pe might be even less. It is worth noting that if the primary purpose to con- 2πR sin ϕ it is straightforward to show that struct the DS is computation, the aforementioned L dF = 2πR2 sin ϕ cos γ cos θdϕ. (7) estimates should be changed (Sandberg 1999). x 4πr2c

3 After taking into account the relations In Fig. 2 we show the behaviour of PDS ver- sus the surface temperature for graphene hav- θ = ϕ + γ, (8) ing the melting temperature, 4510K (Los et al. 2015). Here we assume that if our civilisation (al- and most Level-I) might produce such materials, a super advanced one is able to do more efficiently. − R x cos ϕ It is clear from the plot, that the period varies cos γ = 1 2 (9) (x2 + R2 − 2xR cos ϕ) / from 33.8yrs to 0.53yrs. This result automatically the x component of the total radiation force acting means that the search for Dysonian megastruc- on the DS tures could be widened and observations should be performed not only in the infrared spectrum, LR2 π sin ϕ (R cos ϕ − x) (R − x cos ϕ) but in the optical band. One of the character- Fx = 2 2 2 dϕ, 2c Z0 (x + R − 2xR cos ϕ) istic features, that might distinguish the real DS (10) from stars is the luminosity temperature relation. for small oscillations x/R << 1 reduces to For example, main sequence stars having temperature of the order of 2000K belong to low luminos- 4L x F = − . (11) ity M stars (Carroll & Ostlie 2010), whereas the x 3c R megastructure might emit the luminosity equal or even higher than the Solar luminosity. The The minus sign clearly indicates that the force has temperature range we consider is (2000K;4000K), a restoring character and consequently the dynam- which means that the spectral radiance peaks at ics of the DS is described by the following differ- wavelengths (725nm;1450nm), having significant ential equation fraction in the optical band. Here we examined dx2 4L graphene as a particular example just to show that + x =0, (12) dt2 3cRM if extraterrestrials consider strong materials, their DS might exhibit an interesting behaviour differ- where M = 4πρR2∆R is the mass of the megas- ent from normal stars. tructure, ∆R is its thickness and ρ is the density Another important observational fingerprint of a material the DS is made of. By combining follows from the results obtained above. Due to this expression with the aforementioned equation the oscillation of the hot DS its detected flux will one can show that the period of oscillation is given be variable, with the period PDS. From the fig- by ure it is clear that the values of PDS are typical

3 1/2 1/4 timescales of variability of very long period pul- 3πρcR ∆R ≈ × L × sating stars, which normally belong to spectral PDS =2π 33.8 L L⊙ class: F, M, S or C. But F stars usually have very high temperatures, of the order of 7000K, 3/4 1/2 1/2 1000K ρ ∆R typical temperatures of M stars although are rel- × × × yrs, T 0.4g/cm3 100cm atively low (2400 − 3700)K but their luminosities (13) are almost two orders of magnitude less than the where the thickness of the construction is nor- Solar luminosity. Unlike them, S and C stars are malised on 100cm and ρ is normalised on the den- highly luminous (in comparison with the Solar sity of graphene. As it is clear from Eq. (13), the luminosity) (Carroll & Ostlie 2010). Therefore, DS is stable oscillating with the period ∼ 33.8 yrs. these discrepancies might be good indicators of One can straightforwardly show that for the men- potentially interesting objects. It is worth not- tioned temperature the required mass of a megas- ing that the aforementioned examples only show a tructure is less than the mass of Earth. On the certain tendency how an observational pattern of other hand, as we have already discussed, since the megastructures could be signiﬁcantly diﬀerent smaller DSs will require less material, the issue from the behaviour of variable stars. This in turn, that the civilisation might address would be to in- means that an analysis of rich observational data crease the surface temperature of the sphere. provided by several optical telescopes might be

4 very promising. 2000K − 4000K. This means that the DSs having 11 The surface of the DS is not an absolutely rigid the length scales of the order 10 cm should be body and therefore, it might vibrate under the in- visible in the optical band as well. fluence of perturbations transversal to the surface, It has been argued that the radiation pressure which might be induced either by the radiation stabilises the DS, which potentially can lead to pressure or by means of the star’s wind. Therefore, anomalous variability. In particular, by examining another possible source of variability of DSs could the super strong and super light material graphene be the mechanical waves generated on the 2D sur- and assuming that since a civilisation like us can face of the megaconstruction. It is straightforward produce it, the Level-II might have created even to show that if a membrane is stressed with a ten- stronger and lighter material, it has been found sion per unit length, (along the surface of the DS) that the variability would have been characterised τ, and its mass per unit area is Σ, the transverse by the timescales incompatible with known long wave speed along the surface is of the order of period variable stars. τ 1/2 The similar variability might be caused by the υw ≈ . (14) transverse waves on the surface of the DS, where Σ for an incomplete megastructure it has been shown Even if the construction does not envelope the that for super strong materials the ”pulsation” pe- star completely (Dyson Swarm) it still can have riod might be of the same order as in the afore- similar interesting observational features. In par- mentioned cases. ticular, by means of these waves the surface will By the present paper we wanted to show that vibrate exhibiting the variability of emission in- the Dysonian approach is broader and there are tensity. Unlike the completely closed surface, more possibilities of the search for intelligent life the Dyson swarm will experience the gravitational than it is sometimes thought. In this paper we force from the Star leading to the following value have theoretically hypothesised our approach. of τ MM Though the following generalisations are be- τ ≈ αG s , (15) 2πR3 yond the scope of the present paper, it is worth where G ≈ 6.67 × 10−8Nm2/kg2 is the gravita- noting them. One of the significant issues one has to address is the question concerning anoma- tional constant, Ms is the star’s mass and α is the coefficient, that depends how complete the DS is lous variable intensity and the possibility to detect (for the closed surface α = 0). We assumed that them by existent instruments. the tension is caused by gravitation (although the Another issue that one should address is a cer- possible rotation of the DS might also influence the tain extension of the Dysonian SETI in the con- value of τ). It is clear that the timescale, Pw, for text of HZs. In particular, as we have already waves to travel from one point to a diametrically discussed in the introduction, our approaches are opposite location is given by υw/(πR) which for very restricted. Usually the HZ is defined as an Graphene will be 1.5α yrs for 2000K and 0.8α yrs area where water can be maintained in a liquid for 4000K. In case of higher harmonics the corre- phase, whereas if one assumes nonwater-based life sponding values will be even less. Although we do (Sagan 2000) the corresponding area will be in a not know the value of α and the origin of the ten- different location. According to Carl Sagan our sion is unclear, the estimate shows that an afore- chemistry is attuned to the temperature of our mentioned anomalous variability might be a good planet and he assumes that other temperatures sign for a potential DS. might lead to other biochemistries. If this is the case the HZ will be an area where temperature 3. Conclusion might be significantly different from the temperature of liquid water. For instance, if one assumes We have generalised the Dysonian approach, that methane is used as a solvent instead of wa- considering megastructures not in the HZ but ter, then the HZ will be an area where there are closer. In the framework of the paper we as- appropriate conditions to maintain methane in a sume that a super civilisation is capable of build- liquid phase. In this case the temperature is in the ing megastructures with melting point more than

5 range 90.7K − 11.7K corresponding to the wave- length interval 26µm − 32µm. Therefore, in the framework of this paradigm, the DS in the HZ might be visible in the far IR spectrum.

Acknowledgments

The research was supported by the Shota Rus- taveli National Science Foundation grant (DI- 2016-14).

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