The Copernican Principle Rules Out BLC1 as a Technological Radio Signal from the Alpha Centauri System
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The Copernican Principle Rules Out BLC1 as a Technological Radio Signal from the Alpha Centauri System
Amir Siraj and Abraham Loeb Department of Astronomy, Harvard University, 60 Garden Street, Cambridge, MA 02138, USA
ABSTRACTWithout evidence for occupying a special time or location, we should not assume that we inhabitprivileged circumstances in the Universe. As a result, within the context of all Earth-like planetsorbiting Sun-like stars, the origin of a technological civilization on Earth should be considered a singleoutcome of a random process. We show that in such a Copernican framework, which is inherentlyoptimistic about the prevalence of life in the Universe, the likelihood of the nearest star system, AlphaCentauri, hosting a radio-transmitting civilization is ∼ − . This rules out, a priori , BreakthroughListen Candidate 1 (BLC1) as a technological radio signal from the Alpha Centauri system, as sucha scenario would violate the Copernican principle by about eight orders of magnitude. We also showthat the Copernican principle is consistent with the vast majority of Fast Radio Bursts being naturalin origin. Keywords: technosignatures; astrobiology; search for extraterrestrial intelligence; biosignatures INTRODUCTIONThe Copernican principle asserts that we are not priv-ileged observers of the Universe. Successes of its appli-cation include the rejection of Ptolemaic geocentrismand the adoption of the modern cosmological princi-ple, which underpins the leading ΛCDM model (Peebles1993). By definition, there are fewer special than unspe-cial states in the Universe. Therefore, without evidencefor occupying a special time or location, we should notassume that we inhabit privileged circumstances in theUniverse. As a result, within the context of all Earth-like planets orbiting Sun-like stars, the origin of life onEarth should be considered a single outcome of a ran-dom process.A habitable Earth around a Sun-like star is commonbased on Kepler satellite data analyzed by Bryson et al.(2020), hence the dice have been rolled billions of timesin the Milky Way alone. Gott (1993) applied the Coper-nican principle to lifetime estimation, including for thehuman species. Spiegel & Turner (2012) conducted aBayesian analysis on the emergence of life on Earth,however their model suffers from sensitivity to arbi-trary assumptions about the boundary conditions of theprior distribution for the likelihood of the emergence oflife. Lingam & Loeb (2019) estimated the relative like- [email protected], [email protected] lihood of searches for primitive and intelligent life, us-ing a Drake-type approach. Westby & Conselice (2020)applied the Copernican principle to the search for intel-ligent life, but in forms that featured strict boundariesin time, thereby not reflecting a truly random process.Here, we use a Copernican framework that operatessolely on the assumption that we are not special, toderive a probability distribution for the likelihood of aradio-transmitting civilization developing around a Sun-like star. We investigate the implications of the resultsfor Breakthrough Listen Candidate 1 (BLC1) , a radiosignal detected from the apparent direction of the AlphaCentauri star system. In Section 2, we present notationfor the Copernican framework adopted here. In Section3, we explore the role of Poisson statistics in quantifyingthe Copernican principle. In Section 4, we describe thecomplete Monte Carlo method for applying the Coper-nican principle to the prevalence of radio-transmittingcivilizations. In Section 5, we consider the implicationsof our model for extragalactic technosignatures. Finally,in Section 6, we explore key predictions of our model. FORMALISMConsider a technosignature of life, such as radio wavetransmission, on Earth-like planets orbiting Sun-like https://sites.psu.edu/astrowright/2020/12/20/blc1-a-candidate-signal-around-proxima/ a r X i v : . [ phy s i c s . pop - ph ] J a n Siraj & Loeb stars, with some mean emergence timescale, τ µbegin , andsome mean extinction timescale, τ µend , where τ µend >τ µbegin , τ µend − τ µbegin = τ µobs , and τ µobs (cid:28) τ µbegin ∼ τ µend .A technosignature can only develop around any givenstar if τ µbegin < τ (cid:63) , where τ (cid:63) ∼ . P life = n ( { τ begin | τ begin < τ (cid:63) } ) / n ( { τ begin } ) is theprobability that a Sun-like star develops a technosigna-ture within τ (cid:63) , and P obs = τ µobs /τ (cid:63) is the probabilitythat a Sun-like star that develops a technosignature atsome time within τ (cid:63) presently hosts a technosignature,then the probability P that a Sun-like star with a sim-ilar age to the Sun presently hosts a technosignature issimply, P = P life × P obs . By definition, P is equivalentto the probability that any Sun-like star presently hostsa technosignature. POISSON PROCESSGiven that the emergence and extinction of a tech-nosignature around the Sun is both independent of theemergence and extinction of life around any other star,the average rates of emergence and extinction, Γ µbegin =1 /τ µbegin and Γ µend = 1 /τ µend , the emergence and extinc-tion of technosignatures on Earth can be modeled as aPoisson process. For a given time window during whichthe average number of events is µ , the probability of x events occurring is (Gehrels 1986), P ( x, µ ) = e − µ µ x x ! , (1)so the confidence level P that fewer than n events takeplace is, P = n − (cid:88) x =0 P ( x, µ ) , (2)and the confidence level P that at least n events takeplace is, P = 1 − n − (cid:88) x =0 P ( x, µ ) . (3)Solving Equation (2) yields the normalized average rate, µ , at percentile level P of the Poisson distribution forfewer than n events taking place. For the case of n = 1, µ = ln ( P − ) . (4)Similarly, solving Equation (3) yields the normalized av-erage rate, µ , at percentile level P of the Poisson distri-bution for at least n events taking place. For the caseof n = 1, µ = ln ((1 − P ) − ) . (5) We note that, if P is sampled repeatedly from a uniformdistribution over the interval, [0 , τ ⊕ begin , and observed extinctiontimescale, τ ⊕ end , at percentile level P of the respectivePoisson distributions, the mean emergence timescale is, τ µbegin = ( τ ⊕ begin / ln ((1 − P ) − )) , (6)and the mean extinction timescale is, τ µend = τ µbegin + ( τ ⊕ obs / ln ( P − )) . (7)By definition, for any observed technosignature onEarth, τ ⊕ begin ∼ . MONTE CARLO MODELFor radio transmission in particular, the canonicaltechnosginature, (cid:16) τ present − τ ⊕ begin (cid:17) = 132 yr. Thisraises the question, what value should be adopted for τ ⊕ obs , if a given technosignature still exists today? Weadopt the Copernican lifetime estimation method (Gott1993), a framework with no dependence on assumedboundary conditions, in which the expected survivaltimescale from the present in units of the elapsed time(observed age) at some percentile level P is, τ ⊕ obs / ( τ present − τ ⊕ begin ) = ( P − − − . (8)We then use the following method to determine a sin-gular stochastic instance of P , the probability that anSun-like star formed (cid:46) . currently hosts ra-dio technosignature on an Earth-like planet. We drawthree independent values for percentile level P from auniform distribution over the interval, [0 , P is used to compute a possible instance of τ µbegin using Equation (6). Another value of P is used tocompute a possible instance of τ ⊕ obs using Equation (8).The final value of P is used to compute a possible in-stance of τ µend using Equation (7) and the chosen value of τ ⊕ obs . Given the value of τ µbegin , Poisson statistics dictatethat the proportion of stars with at least one emergenceof a technosignature within τ (cid:63) is, P life = 1 − e − ( τ (cid:63) /τ µbegin ) , (9)where each instance of τ (cid:63) is drawn from a triangular dis-tribution with range 0 − . The age at which the Earth will experience runaway green-house heating and cross the inner edge of the Sun’s habitable zone(Schr¨oder & Smith 2008). he Copernican Principle Rules Out A Technological Civilization in the α Cen System p Figure 1.
Differential distribution of the logarithm of theprobability P life that any given Sun-like star formed withinthe past 5 . / d log P life ), derivedthrough 10 runs the Monte Carlo method described in Sec-tion 4. approximation of the star formation history (SFH) forstars with τ (cid:63) (cid:46) . ∼
20% of stars were formed within the past 5 . P obs = τ µobs /τ (cid:63) , the probability that a radio tech-nosignature is presently visible from an Sun-like star,given that a radio technosignature has existed within τ (cid:63) , P = ( τ µobs /τ (cid:63) ) · (1 − e − ( τ (cid:63) /τ µbegin ) ) · n EL , (10)where τ µobs , τ (cid:63) , and τ µbegin are stochastically determinedvia the aforementioned methods, and where the numberof Earth-like planets per Sun-like star, n EL , is drawn for50% of runs from the conservative habitable zone (HZ)lower case distribution ( n EL = 0 . +0 . − . ) and the other50% of runs from the upper case distribution ( n EL =0 . +0 . − . ), where the quoted uncertainties represent 1 − σ deviations (Bryson et al. 2020).Figures 1 - 3 display the probability distributions re-sulting from 10 runs of the above Monte Carlo methodfor P , P life , and P obs . The median value of P is ∼ × − , and because only a fraction ( ∼ . ∼ − . This is, as expected, of order the technologicalage of human civilization divided by the age of the Sun. p Figure 2.
Differential distribution of the logarithm of theprobability P obs that any given Sun-like star formed withinthe past 5 . / d log P obs ), derived through 10 runs the Monte Carlomethod described in Section 4. p Figure 3.
Differential distribution of the logarithm of theprobability P = P life × P obs that any given Sun-like starformed within the past 5 . / d log P ), derived through 10 runs the Monte Carlo method described in Section 4.5. EXTRAGALACTIC TECHNOSIGNATURESFor some electromagnetic technosignature, P ∝ r ν − S ν ηD − (∆ ν/ν ), where P is power, r is the dis-tance of the source from the observer, ν is frequency, S ν is the signal strength, η is the beam diameter in unitsof the diffraction limit, and D is the diameter of thetransmitter (Lingam & Loeb 2017). Since η ∝ θνD ,where θ is the angular size of the beam, we can expressthe original relation as, P ∝ r νS ν θ (∆ ν/ν ). Siraj & Loeb P ∼ erg s − (cid:18) r (cid:19) (cid:16) ν (cid:17) (cid:18) S ν
10 mJy (cid:19) − (cid:18) θ − rad (cid:19) (cid:18) (∆ ν/ν )10 − (cid:19) , (11)where S ν ∼
10 mJy and θ ∼ − rad would matchthe characteristic fluence of observed Fast Radio Bursts(FRBs), ( S ν θ/ ˙ θ ) ∼ θ ∼ − rad is therotation rate of the Earth, taken to be typical of Earth-like planets.For the fiducial parameters adopted Equation (11),the rate of detectable signals at Earth is, Γ ∼ − (n T / − ), where n T is the number of trans-mitters per galaxy. Since there are ∼ MilkyWay size galaxies and a few × Sun-like starsper galaxy (Lingam & Loeb 2017): according to theCopernican principle, which is consistent with ∼ − of all young Sun-like stars presently hosting radio-transmitting civilizations on Earth-like planets, even ifall radio-transmitting civilizations harness the total en-ergy of starlight reaching a habitable-zone rocky planettransmit all of that energy through a maser for a com-parable duration to the time that their civilization wasradio-transmitting, technosignatures would only consti-tute at maximum a tenth of all observed FRBs (Petroffet al. 2019). As a result, we find that the Copernicanprinciple is consistent with the vast majority of FRBsbeing natural in origin. DISCUSSIONHere, we applied the Copernican principle to anorder-of-magnitude estimate of the prevalence radio-transmitting civilizations, without boundary assump-tions that have influenced some previous Copernicanframeworks (Spiegel & Turner 2012; Westby & Con-selice 2020), and showed that BLC1 as a candidate for aradio transmission signal from the Alpha Centauri sys-tem would be in violation of the Copernican principleby about eight orders of magnitude, since the median of the derived probability distribution for any givenSun-like star presently hosting a radio-transmitting civ-ilization is ∼ − (see Figure 3). The only caveat toour conclusion is if technological life on Earth and thenearest stars is correlated, for example if the seeds for itwere planted by panspermia (natural or directed) at thesame time (Ginsburg et al. 2018). Here, we ignore thispossibility, because Homo sapiens appeared on Earth ∼ . a priori argument that falls outside of the purview of the Coper-nican principle, such as panspermia between the Earthand the Alpha Centauri system. We also showed thatthe Copernican principle is consistent with the vast ma-jority of FRBs being natural in origin.We note that searching for signatures of dead civi-lizations , such as discarded debris, self-replicating ma-chines, or pollution, would be advantageous from aCopernican perspective on three counts. First, becausethe primary reason why the Copernican principle re-sults in a pessimistic outlook on the prevalence of radio-transmitting civilizations is the fact that humanity hasonly been radio-transmitting for a very small fractionof the Earth’s lifetime, implying that even if the time-integrated abundance of radio-transmitting civilizationsis high, a snapshot at any given point in time wouldyield very few. Signatures of dead civilizations, suchas physical debris, could be longer-lasting by nature.Second, a few, highly advanced, civilizations could inprinciple produce an amount of debris that exceeds thesum of that produced by all other civilizations, mean-ing that even if such civilizations are extremely rare, asthey would have to be in order to remain consistent withthe Copernican principle, they could still dominate theoverall technosignature budget. Third, self-replicatingmachines may produce a large population of relics outof a small number of seeds.ACKNOWLEDGEMENTSThis work was supported in part by a grant from theBreakthrough Prize Foundation.REFERENCES Alzate, J. A., Bruzual, G., & D´ıaz-Gonz´alez, D. J. 2021,MNRAS, 501, 302 https://blogs.scientificamerican.com/observations/how-to-search-for-dead-cosmic-civilizations/ Bryson, S., Kunimoto, M., Kopparapu, R. K., et al. 2020,arXiv e-prints, arXiv:2010.14812Gehrels, N. 1986, ApJ, 303, 336Ginsburg, I., Lingam, M., & Loeb, A. 2018, ApJL, 868, L12Gott, J. R., I. 1993, Nature, 363, 315 he Copernican Principle Rules Out A Technological Civilization in the α Cen System5