aa r X i v : . [ phy s i c s . pop - ph ] J u l On a spectral pattern of the Von-Neumann probes
Osmanov Z.
School of Physics, Free University of Tbilisi, 0183, Tbilisi, Georgia
ABSTRACT
In this paper we have extended our previous work (Osmanov 2019) and considered spectralcharacteristics of interstellar non-relativistic Type-II and Type-III Von-Neumann probes. It hasbeen shown that by means of the proton capture, required for replication, strong bremstrahlungemission will be generated. We have found that for both types of civilizations the probes mightbe visible mainly in the infrared spectral band, but as it has been found the probes might bevisible in the ultraviolet as well. For both cases it was shown that differential power has dipsfor equally spaced frequencies, which might be a significant fingerprint to identify such exoticinterstellar objects.
Subject headings:
Von Neumann Probes; SETI; Extraterrestrial; life-detection
1. Introduction
In the previous paper (henceforth paper-I) wehave considered self-replicating Von-Neumann ex-traterrestrial probes (Osmanov 2019). In thiswork we considered self replicating extraterres-trial robots and estimated their lengthscales. Wefound that for making a process of colonizationof space very efficient, the probes must be verysmall. Then, in a molecular cloud the typicaltimescale of replication might be several years,which might lead to potentially detectable veryintense radiation. In Paper-I we estimated or-ders of magnitude of radiation frequency, bolo-metric luminosity and its increment, but did notstudy the spectral characteristics of emission, thestudy of which is a purpose of the present work.The idea of self-reproducing probes has been pro-posed in the last century by Von Neumann (1966).In particular, he studied the possibility of ma-chines with artificial intelligence capable of self-reproduction and the problem has been examinedin in the context of information theory and cor-responding thermodynamics. This idea also hasbeen revisited in the context of the search for ex-traterrestrial intelligence (SETI) (Cirkovic 2018).After the discovery of ”Oumuamua”’s unusual be-haviour (Bialy & Loeb 2018), the interest to thestudy of extraterrestrial probes has been revived, despite the natural explanation of the aforemen-tioned peculiarity (Bannister et al. 2019).In general, the study of techno-signatures ofadvanced extraterrestrial civilizations has beenactively discussed since a brilliant idea of Dyson(1960), who proposed to search for Type-II(Kardashev 1964) civilizations by searching for in-frared spheres (Dyson spheres - DS) built aroundstars. It is worth noting that according to Karda-shev’s classification Type-I is a technological civ-ilization which uses the total energy coming fromthe host Solar-type star to the Earth-like planet,Type-II is an advanced alien society harnessingthe total energy emitted by the star and Type-IIIcivilization is capable to use the total energy ofthe host galaxy. The interest to techno-signatureshas revived after the discovery of a strange be-haviour of the Tabby’s star’s (Name in the catalogKIC8462852) flux, characterised by unusual highdips (Boyajian et al. 2016). The problem is socomplex that Dysonian SETI should be revisitedand widened (Bradbury et al. 2011). Interestingattempts have been presented in a series of pa-pers (Semiz & Ogur 2015; Osmanov 2016, 2017;Osmanov & Berezhiani 2018, 2019; Haliki 2019;Zackrisson et al. 2018; Lacki 2019).In this context a special interest deserves ourprevious work (Paper-I) where we have studied the1on-Neumann interstellar Type-II probes . Themain aim of the paper was a) to show high ef-ficiency of small sized probes in colonising thespace and b) estimate very general characteristicsof the emission pattern. In the paper-I we have ex-amined the probes with three possible velocities:0 . c, . c, . c ( c is the speed of light) and itwas shown that number of the probes increasesdrastically by the factor of 10 during 650yrs( υ = 0 . c ), 320yrs ( υ = 0 . c ), 60yrs ( υ = 0 . c ).Which are quite realistic values because they aresmall compared to a timescale (3000yrs) requiredfor Type-I civilization to reach the level of Type-II (Dyson 1960). We have found that the probesmight be seen from radio to the infrared spec-tral band and estimated the luminosity incrementtime-scales which lie in the interval (1; 10) yrs andthe corresponding achieved luminosities might beenormous, at least of the order of 10 − erg/s .The aim of the present paper is certain exten-sion of paper-I. In particular, we are going to studythe spectral characteristics of the probes studyingenergy emitted by the unit of time per unit of fre-quency for Type-II and Type-III extraterrestrialprobes.The paper is organized in the following way: inSec. 2, we coonsider the general tools and meth-ods, applying them to Type-II and Type-III civi-lizations and obtain corresponding results and inSec. 3 we outline the summary of the results.
2. Main considerations
As we have already shown in the previous work,the mass rate for a spherical probe is given by(Osmanov 2019) dMdt = πβr m nc, (1)where r is the radius of the probe, β = υ/c is a di-mensionless velocity, c represents the speed of lightand m is the mass of a molecule the probes en-counter and n is the number density of particles ina cloud. By taking into account an expression forthe mass of the spherical probe, M = 4 πξr ρ/ r is the In paper-1 a) in Eq. (2) for the probe’s size and densitythere should be 0.01 µ m and 1 cm − and b) the optimal sizeis 10 − cm instead of 7 × − cm . f (Hz) × E f ( e r g s - H z - ) Fig. 1.— The behaviour of E f versus frequency.The set of parameters is: β = 0 . N = 100, ξ = 0 . m = m p ( m p is the proton mass), ρ =0 . g cm − , n = 10 cm − , D = 2 pc. f (Hz) × E f ( e r g s - H z - ) Fig. 2.— The dependence of E f on frequency. Theset of parameters is the same as in the previousgraph except n = 1 cm − and D = 50000 pc.2adius of the probe, β = υ/c is a dimensionless ve-locity, c represents the speed of light and m isthe mass of a molecule the probes encounter and n is the number density of particles in a cloud. Bytaking into account an expression for the mass ofthe spherical probe, M = 4 πξr ρ/
3, the timescaleof replication writes as τ = MdM/dt = 4 ξβ × ρm n × rc ≃ . × ξ . ×× . β × ρ . g cm − × cm − n × r . mm yrs, (2)where ξ denotes the fraction of the total volumefilled with the material the probe is made of ρ is the corresponding density normalised by theGraphene density (up to now the strongest ma-terial). As it is clear from the above expressiontime required for replication of a single probe isof the order of several years. This in turn meansthat in a nebula with a length-scale 2pc the mul-tiplication factor, 2 t/τ , becomes of the order 10 ,which indicates high efficiency of the process. Byassuming the initial number of robots 100, onecan straightforwardly show that an average dis-tance between probes is of the order of 1m. Thetime-scale has been estimated for the typical pa-rameters of HII interstellar atomic hydrogen cloud(Carroll & Ostlie 2010).In paper-I we have discussed that the probeswhen collecting the cloud atoms or molecules willinevitably lead to observable events. In particu-lar, it is easy to show that a single probe capturingprotons will accelerate them with the acceleration, a ∼ υ / (2 κr ) ( κ ≤ L p ≃ π κ nrce β , (3)leading to the total luminosity of the ensemble ofself-replicators L tot ≃ π κ nrce β N × t/τ , (4)where N indicates the initial number of robots.Throughout the paper we use κ = 0 .
1. As it has been shown by Osmanov (2019), for agiven medium there is a certain relation betweenthe probe size and the length-scale of a space, D ,the ensemble is supposed to occupy reaching somecritical (maximum) luminosity, L cr ξ × m nρ × Dr ≃ ln (cid:18) L cr L ( r ) (cid:19) , (5)where L = N L p is the initial total luminos-ity. Unlike the previous study, in this paperwe consider both types of advanced civilizations:Type-II, harnessing the total energy of its hoststar and Type-III utilising the energy of a galaxy(Dyson 1960). For Type-II probes the critical lu-minosity is of the order of the Solar luminosity, L ⊙ ≃ . × ergs s − , whereas for Type-IIIthe critical value should be of the order of thebolometric luminosity of the galaxy. As an ex-ample we examine the Milky Way galaxy L cr ≃ . × L ⊙ (Carroll & Ostlie 2010). The afore-mentioned equation should be solved numericallyand one can show that as for a spherical molec-ular cloud with a length-scale D ≃ . D ≃ . β = 0 . dWdω = 8 πω c × | ˆ d ( ω ) | , (6)where ω is the cyclic frequency of emission andˆ d ( ω ) = 12 π Z + ∞−∞ d ( t ) e iωt dω (7)is the Fourier component of the dipole moment.By considering the Fourier transform of its secondtime derivative, one obtains (Rybicki & Lightman2007) − ω ˆ d ( ω ) = e π Z + ∞−∞ a ( t ) e iωt dω, (8)3here e is the proton’s charge and a ( t ) is thecorresponding acceleration when encountering theprobes. If one approximates it as a constant value, a , during an interaction time τ ≃ κr/v , then itis straightforward to showˆ d ( ω ) = eaπω (cid:12)(cid:12)(cid:12) sin (cid:16) ωτ (cid:17)(cid:12)(cid:12)(cid:12) , (9)reducing Eq. (6) to the following form dWdf = 4 πe β c × (cid:18) f f (cid:19) sin (cid:18) ff (cid:19) , (10)where f ≡ βc/ (2 πκr ) and we have taken into ac-count ω ≡ πf . The derived formula characterisesa single event of a proton capture. To obtain thetotal emission per unit time and unit frequency in-terval (spectral power), E f ≡ dW/ ( dtdf ), we notethat the incident proton flux is n p cβ , then one canwrite dWdtdf = n p N ( t ) 4 πe r β × (cid:18) f f (cid:19) sin (cid:18) ff (cid:19) , (11)where N ( t ) = N × e t/τ , (12)is the total number of probes. As a next step,we are going to apply the obtained expressions toType-II and Type-III civilizations. In this subsection we examine the Von-Neumannprobes belonging to Type-II societies. For thispurpose we consider a spherical nebula with aradius of the order of 1pc, then, as we have al-ready shown the optimal length-scale of the robotshould be of the order of 0 .
013 cm leading to thecorresponding normalizing emission frequency f ≃ βc πrκ ≃ . × × β . Hz. (13)In Fig. 1 we plot the dependence of E f onfrequency. The set of parameters is: β = 0 . N = 100, ξ = 0 . m = m p ( m p is the protonmass), ρ = 0 . g cm − , n = 10 cm − , D = 2 pc.As it is clear from the figure, the spectral powerof Von-Neumann probes has a specific fingerprint: The velocities of the probes are not relativistic and there-fore, the Doppler shift does not affect the result. at certain frequencies E f diminishes. From Eq.(11) one can straightforwardly show that the spec-tral power becomes zero for the following discreetset of equally spaced frequencies f k = f πk for k = 1 , , ... . The presented spectral behaviour isdrastically different from black body spectrum aswell as from the thermal bremstrahlung, which canbe a very important factor in identifying the Von-Neumann interstellar probes. Another interestingfeature is that if one considers a different valueof β , the corresponding length-scale of the probewill be different, but the overall spectral featurewill be the same - in this sense the given spec-trum is unique. The initial number of probes 100,very rapidly multiplies and approximately in 650yrs the total number will be of the order of 10 colonising the whole nebula. One should also notethat if one maintains an annual growth rate of 1%in industry, then 3000 yrs is quite enough to reachsuch an advanced technological level, which meansthat the assumption of existence of such alien so-cieties is quite reasonable (Dyson 1960). As it has been classified by Kardashev (1964)advanced civilizations consuming almost thewhole power of their host galaxy ( ∼ × ergss − ) is the so-called Type-III society. Our owncivilization consumes approximately 4 × ergss − , which means that if an average 1% of an-nual growth is maintained our society will achieveType-III in ∼ ∼ . × L ⊙ . Then,by taking into account the number density of inter-stellar protons ∼ − for the optimal size of theprobe one obtains 0 . . × Hz.In Fig. 2 we show the behaviour of E f versus f .The set of parameters is the same as for Type-IIcivilizations except n = 1 cm − and D = 50000 pc.Likewise the previous case, one can see that emis-sion spectra of Type-III probes vanishes for a dis-creet set of frequencies f k = f πk for k = 1 , , ... with f = 1 . × Hz. For the considered valueof velocity, the time-scale of colonising the whole4alaxy is of the order of T ≃ D/ (2 βc ) ≃
16 Myr,which is by three orders of magnitude less thanthe galactic age, 10 Gyr, therefore, colonizationin the context of time-scales might be quite rea-sonable. From Eq. (12) one can straightforwardlyshow that after the mentioned time, the multipli-cation factor will be of the order of 10 leadingto the total luminosity of the order of the galac-tic luminosity. Peculiarity of the emission spec-tra, characterised by equally spaced dips and theoverall dependence on frequency, which is differ-ent from all other spectral behaviours might bea good sign to identify the Type-III interstellarVon-Neumann probes.Recently new prospects appeared thanks tothe Five-hundred-meter Aperture Spherical radioTelescope (FAST) - a single-dish radio telescope,which is going to work in the SETI projects as well(Lu et al. 2019). On the other hand, radio emis-sion of Von-Neumann probes is significant. In par-ticular, for Type-II probes the total power emit-ted in the Hydrogen line (1 .
42 GHz) will be ofthe order of 10 ergs s − , therefore FAST mightpotentially detect such objects.
3. Conclusion
We have studied the spectral characteris-tics of Type-II and Type-III Von-Neumann self-reproducing interstellar probes. For this purposewe have considered emission generated by protoncapture and examined the corresponding mecha-nism of bremstrahlung.Considering Type-II robots it has been shownthat to colonise the spherical nebula with radiusof the order of 1 pc, the optimal length-scale ofthe probe should be 0 .
013 cm, leading to emissionfrom radio to infrared. It has been found that thedifferential emission power has equally spaced dipsin frequency. The same behaviour has been foundfor Type-III interstellar probes as well (also po-tentially observable from radio to infrared), whichmight be a significant indicator to identify theseexotic robots.Generally speaking, we have analysed the emis-sion pattern for certain typical parameters. Con-sequently for different values the emission spectrawill be different, but what is very important, ageneral fingerprint - the particular behaviour, withperiodic dips - is maintained and in this sense the mentioned results are unique. Therefore, if onefinds the similar dependence of spectral power onfrequency, this might be a significant result indi-cating the existence of Von-Neumann interstellarprobes.
Acknowledgments
The research was supported by the Shota Rus-taveli National Science Foundation grant (NFR17-587).
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