The Copernican Principle Rules out BLC1 As a Technological Radio Signal from the Alpha Centauri System

Draft version January 13, 2021 Typeset using LATEX twocolumn style in AASTeX62

The Copernican Principle Rules Out BLC1 as a Technological Radio Signal from the Alpha Centauri System

Amir Siraj1 and Abraham Loeb1

1Department of Astronomy, Harvard University, 60 Garden Street, Cambridge, MA 02138, USA

ABSTRACT Without evidence for occupying a special time or location, we should not assume that we inhabit privileged circumstances in the Universe. As a result, within the context of all Earth-like planets orbiting Sun-like stars, the origin of a technological civilization on Earth should be considered a single outcome of a random process. We show that in such a Copernican framework, which is inherently optimistic about the prevalence of life in the Universe, the likelihood of the nearest star system, Alpha Centauri, hosting a radio-transmitting civilization is ∼ 10−8. This rules out, a priori, Breakthrough Listen Candidate 1 (BLC1) as a technological radio signal from the Alpha Centauri system, as such a scenario would violate the Copernican principle by about eight orders of magnitude. We also show that the Copernican principle is consistent with the vast majority of Fast Radio Bursts being natural in origin.

Keywords: technosignatures; astrobiology; search for extraterrestrial intelligence; biosignatures

1. INTRODUCTION lihood of searches for primitive and intelligent life, us- The Copernican principle asserts that we are not priv- ing a Drake-type approach. Westby & Conselice(2020) ileged observers of the Universe. Successes of its appli- applied the Copernican principle to the search for intel- cation include the rejection of Ptolemaic geocentrism ligent life, but in forms that featured strict boundaries and the adoption of the modern cosmological princi- in time, thereby not reflecting a truly random process. ple, which underpins the leading ΛCDM model (Peebles Here, we use a Copernican framework that operates 1993). By definition, there are fewer special than unspe- solely on the assumption that we are not special, to cial states in the Universe. Therefore, without evidence derive a probability distribution for the likelihood of a for occupying a special time or location, we should not radio-transmitting civilization developing around a Sun- assume that we inhabit privileged circumstances in the like star. We investigate the implications of the results 1 Universe. As a result, within the context of all Earth- for Breakthrough Listen Candidate 1 (BLC1) , a radio like planets orbiting Sun-like stars, the origin of life on signal detected from the apparent direction of the Alpha Earth should be considered a single outcome of a ran- Centauri star system. In Section2, we present notation dom process. for the Copernican framework adopted here. In Section A habitable Earth around a Sun-like star is common 3, we explore the role of Poisson statistics in quantifying based on Kepler satellite data analyzed by Bryson et al. the Copernican principle. In Section4, we describe the (2020), hence the dice have been rolled billions of times complete Monte Carlo method for applying the Coper- in the Milky Way alone. Gott(1993) applied the Coper- nican principle to the prevalence of radio-transmitting nican principle to lifetime estimation, including for the civilizations. In Section5, we consider the implications arXiv:2101.04118v1 [physics.pop-ph] 11 Jan 2021 human species. Spiegel & Turner(2012) conducted a of our model for extragalactic technosignatures. Finally, Bayesian analysis on the emergence of life on Earth, in Section6, we explore key predictions of our model. however their model suffers from sensitivity to arbi- trary assumptions about the boundary conditions of the 2. FORMALISM prior distribution for the likelihood of the emergence of Consider a technosignature of life, such as radio wave life. Lingam & Loeb(2019) estimated the relative like- transmission, on Earth-like planets orbiting Sun-like

[email protected], [email protected] 1 https://sites.psu.edu/astrowright/2020/12/20/blc1-a- candidate-signal-around-proxima/ 2 Siraj & Loeb

µ stars, with some mean emergence timescale, τbegin, and We note that, if P is sampled repeatedly from a uniform µ µ some mean extinction timescale, τend, where τend > distribution over the interval, [0, 1), Equations (4) and µ µ µ µ µ µ µ τbegin, τend − τbegin = τobs, and τobs τbegin ∼ τend. (5) yield identical distributions. A technosignature can only develop around any given Given a technosignature on Earth with observed µ ⊕ star if τbegin < τ?, where τ? ∼ 5.5 Gyr is the timescale emergence timescale, τbegin, and observed extinction on which Earth-like planets in the habitable zones of ⊕ timescale, τend, at percentile level P of the respective Sun-like stars remain unaffected by inevitable runaway Poisson distributions, the mean emergence timescale is, greenhouse heating due to the expansion of the parent star (Schröder & Smith 2008). µ ⊕ −1 τbegin = (τbegin/ ln ((1 − P) )) , (6) If P = n({τ | τ < τ }) / n({τ }) is the life begin begin ? begin and the mean extinction timescale is, probability that a Sun-like star develops a technosigna- µ ture within τ?, and Pobs = τ /τ? is the probability µ µ ⊕ −1 obs τend = τbegin + (τobs/ ln (P )) . (7) that a Sun-like star that develops a technosignature at some time within τ? presently hosts a technosignature, By definition, for any observed technosignature on ⊕ then the probability P that a Sun-like star with a sim- Earth, τbegin ∼ 4.5 Gyr. ilar age to the Sun presently hosts a technosignature is 4. MONTE CARLO MODEL simply, P = Plife × Pobs. By definition, P is equivalent to the probability that any Sun-like star presently hosts For radio transmission in particular, the canonical a technosignature. ⊕ technosginature, τpresent − τbegin = 132 yr. This 3. POISSON PROCESS raises the question, what value should be adopted for ⊕ τobs, if a given technosignature still exists today? We Given that the emergence and extinction of a tech- adopt the Copernican lifetime estimation method (Gott nosignature around the Sun is both independent of the 1993), a framework with no dependence on assumed emergence and extinction of life around any other star, boundary conditions, in which the expected survival the average rates of emergence and extinction, Γµ = begin timescale from the present in units of the elapsed time 1/τ µ and Γµ = 1/τ µ , the emergence and extinc- begin end end (observed age) at some percentile level P is, tion of technosignatures on Earth can be modeled as a ⊕ ⊕ −1 −1 Poisson process. For a given time window during which τobs/(τpresent − τbegin) = (P − 1) . (8) the average number of events is µ, the probability of x events occurring is (Gehrels 1986), We then use the following method to determine a sin- gular stochastic instance of P , the probability that an e−µµx Sun-like star formed 5.5 Gyr ago2 currently hosts ra- P (x, µ) = , (1) . x! dio technosignature on an Earth-like planet. We draw so the confidence level P that fewer than n events take three independent values for percentile level P from a place is, uniform distribution over the interval, [0, 1), the prior n−1 X distribution that adopts no artificial limit truncations. P = P (x, µ) , (2) One value of P is used to compute a possible instance of x=0 µ τbegin using Equation (6). Another value of P is used to and the confidence level P that at least n events take compute a possible instance of τ ⊕ using Equation (8). place is, obs n−1 The final value of P is used to compute a possible in- X µ P = 1 − P (x, µ) . (3) stance of τend using Equation (7) and the chosen value of ⊕ µ x=0 τobs. Given the value of τbegin, Poisson statistics dictate Solving Equation (2) yields the normalized average rate, that the proportion of stars with at least one emergence µ, at percentile level P of the Poisson distribution for of a technosignature within τ? is, µ fewer than n events taking place. For the case of n = 1, −(τ?/τ ) Plife = 1 − e begin , (9)

−1 µ = ln (P ) . (4) where each instance of τ? is drawn from a triangular dis- Similarly, solving Equation (3) yields the normalized av- tribution with range 0 − 5.5 Gyr, an order-of-magnitude erage rate, µ, at percentile level P of the Poisson distribution for at least n events taking place. For the case 2 The age at which the Earth will experience runaway green- of n = 1, house heating and cross the inner edge of the Sun’s habitable zone µ = ln ((1 − P)−1) . (5) (Schr¨oder& Smith 2008). The Copernican Principle Rules Out A Technological Civilization in the α Cen System 3

Figure 2. Differential distribution of the logarithm of the Figure 1. Differential distribution of the logarithm of the probability Pobs that any given Sun-like star formed within probability Plife that any given Sun-like star formed within the past 5.5 Gyr presently hosts a radio-transmitting civiliza- the past 5.5 Gyr has hosted a radio-transmitting civilization tion, given that it hosts one at some point during its lifetime at some point during its lifetime (dP/d log P ), derived 7 life (dP/d log Pobs), derived through 10 runs the Monte Carlo 7 through 10 runs the Monte Carlo method described in Sec- method described in Section4. tion4. approximation of the star formation history (SFH) for stars with τ? . 5.5 Gyr in the Solar neighborhood (Fig- ure 19, Alzate et al. 2021) over the timescale that the Earth is located within the habitable zone of the Sun (Schröder& Smith 2008). We additionally note that only ∼ 20% of stars were formed within the past 5.5 Gyr (Alzate et al. 2021). µ Since Pobs = τobs/τ?, the probability that a radio technosignature is presently visible from an Sun-like star, given that a radio technosignature has existed within τ?,

µ p µ −(τ?/τbegin) P = (τobs/τ?) · (1 − e ) · nEL , (10)

µ µ where τobs, τ?, and τbegin are stochastically determined via the aforementioned methods, and where the number of Earth-like planets per Sun-like star, nEL, is drawn for 50% of runs from the conservative habitable zone (HZ) +0.48 lower case distribution (nEL = 0.36−0.21) and the other Figure 3. Diﬀerential distribution of the logarithm of the 50% of runs from the upper case distribution (nEL = probability P = Plife × Pobs that any given Sun-like star +0.90 0.60−0.36), where the quoted uncertainties represent 1 − formed within the past 5.5 Gyr presently hosts a radio- σ deviations (Bryson et al. 2020). transmitting civilization (dP/d log P ), derived through 107 Figures1-3 display the probability distributions re- runs the Monte Carlo method described in Section4. sulting from 107 runs of the above Monte Carlo method 5. for P , Plife, and Pobs. The median value of P is EXTRAGALACTIC TECHNOSIGNATURES ∼ 3 × 10−8, and because only a fraction (∼ 20%) of For some electromagnetic technosignature, P ∝ 2 −1 −2 stars were formed within the past 5.5 Gyr, to order- r ν Sν ηD (∆ν/ν), where P is power, r is the dis- of-magnitude the probability that any given Sun-like tance of the source from the observer, ν is frequency, Sν star presently hosts a radio transmitting civilization is is the signal strength, η is the beam diameter in units ∼ 10−8. This is, as expected, of order the technological of the diﬀraction limit, and D is the diameter of the age of human civilization divided by the age of the Sun. transmitter (Lingam & Loeb 2017). Since η ∝ θνD, where θ is the angular size of the beam, we can express 2 2 the original relation as, P ∝ r νSν θ (∆ν/ν). 4 Siraj & Loeb

of the derived probability distribution for any given Sun-like star presently hosting a radio-transmitting civ- r 2 ν S −1 ilization is ∼ 10−8 (see Figure3). The only caveat to P ∼ 1025 erg s−1 ν 3 Gpc 1 GHz 10 mJy our conclusion is if technological life on Earth and the θ 2 (∆ν/ν) nearest stars is correlated, for example if the seeds for it , were planted by panspermia (natural or directed) at the 10−5 rad 10−5 same time (Ginsburg et al. 2018). Here, we ignore this (11) possibility, because Homo sapiens appeared on Earth ∼ 0.3 Myr ago (Hublin et al. 2017; Richter et al. 2017), where S ∼ 10 mJy and θ ∼ 10−5 rad would match ν before Alpha Centauri became our nearest star system. the characteristic fluence of observed Fast Radio Bursts The only plausible way to avoid violating the Coper- (FRBs), (S θ/θ˙) ∼ 1 mJy s, where θ˙ ∼ 10−4 rad is the ν nican principle here would be to invoke some a priori rotation rate of the Earth, taken to be typical of Earth- argument that falls outside of the purview of the Coper- like planets. nican principle, such as panspermia between the Earth For the fiducial parameters adopted Equation (11), and the Alpha Centauri system. We also showed that the rate of detectable signals at Earth is, Γ ∼ the Copernican principle is consistent with the vast ma- 1 yr−1 (n /10−3), where n is the number of trans- T T jority of FRBs being natural in origin. mitters per galaxy. Since there are ∼ 1010 Milky We note that searching for signatures of dead civi- Way size galaxies and a few × 1010 Sun-like stars lizations3, such as discarded debris, self-replicating ma- per galaxy (Lingam & Loeb 2017): according to the chines, or pollution, would be advantageous from a Copernican principle, which is consistent with ∼ 10−8 Copernican perspective on three counts. First, because of all young Sun-like stars presently hosting radio- the primary reason why the Copernican principle re- transmitting civilizations on Earth-like planets, even if sults in a pessimistic outlook on the prevalence of radio- all radio-transmitting civilizations harness the total en- transmitting civilizations is the fact that humanity has ergy of starlight reaching a habitable-zone rocky planet only been radio-transmitting for a very small fraction transmit all of that energy through a maser for a com- of the Earth’s lifetime, implying that even if the time- parable duration to the time that their civilization was integrated abundance of radio-transmitting civilizations radio-transmitting, technosignatures would only consti- is high, a snapshot at any given point in time would tute at maximum a tenth of all observed FRBs (Petroff yield very few. Signatures of dead civilizations, such et al. 2019). As a result, we find that the Copernican as physical debris, could be longer-lasting by nature. principle is consistent with the vast majority of FRBs Second, a few, highly advanced, civilizations could in being natural in origin. principle produce an amount of debris that exceeds the sum of that produced by all other civilizations, mean- 6. DISCUSSION ing that even if such civilizations are extremely rare, as Here, we applied the Copernican principle to an they would have to be in order to remain consistent with order-of-magnitude estimate of the prevalence radio- the Copernican principle, they could still dominate the transmitting civilizations, without boundary assump- overall technosignature budget. Third, self-replicating tions that have influenced some previous Copernican machines4 may produce a large population of relics out frameworks (Spiegel & Turner 2012; Westby & Con- of a small number of seeds. selice 2020), and showed that BLC1 as a candidate for a radio transmission signal from the Alpha Centauri sys- ACKNOWLEDGEMENTS tem would be in violation of the Copernican principle This work was supported in part by a grant from the by about eight orders of magnitude, since the median Breakthrough Prize Foundation.

REFERENCES

Alzate, J. A., Bruzual, G., & D´ıaz-Gonz´alez,D. J. 2021, Bryson, S., Kunimoto, M., Kopparapu, R. K., et al. 2020, MNRAS, 501, 302 arXiv e-prints, arXiv:2010.14812 Gehrels, N. 1986, ApJ, 303, 336 3 https://blogs.scientiﬁcamerican.com/observations/how-to- Ginsburg, I., Lingam, M., & Loeb, A. 2018, ApJL, 868, L12 search-for-dead-cosmic-civilizations/ 4 http://www.molecularassembler.com/KSRM.htm Gott, J. R., I. 1993, Nature, 363, 315 The Copernican Principle Rules Out A Technological Civilization in the α Cen System 5

Hublin, J.-J., Ben-Ncer, A., Bailey, S. E., et al. 2017, Petroff, E., Hessels, J. W. T., & Lorimer, D. R. 2019, A&A Rv, 27, 4 Nature, 546, 289 Richter, D., Grün,R., Joannes-Boyau, R., et al. 2017, Lingam, M., & Loeb, A. 2017, ApJL, 837, L23 Nature, 546, 293 Schröder, K. P., & Smith, R. C. 2008, MNRAS, 386, 155 —. 2019, Astrobiology, 19, 28 Spiegel, D. S., & Turner, E. L. 2012, Proceedings of the National Academy of Science, 109, 395 Peebles, P. J. E. 1993, Principles of Physical Cosmology Westby, T., & Conselice, C. J. 2020, ApJ, 896, 58