Determining upper limits on galactic ETI civilizations transmitting continuous beacon signals in the radio spectrum A Bayesian approach to the Fermi paradox Author: Mikael Flodin (810815-0171) [email protected] Department of Physics Royal Institute of Technology (KTH) Supervisor: Lars Mattsson June 14, 2019 Typeset in LATEX TRITA-SCI-GRU 2019:305 © Mikael Flodin, 2019 Plurality must never be posited without necessity William of Ockham, 14th century Abstract This thesis put constraints on the Fermi paradox by determining upper limits on the present time pop- ulation of galactic, radio-communicating, ETI civilizations, conditioned on the current null result of the joint SETI project. This is done via a Monte Carlo method approach, where five idealizing assumptions, (A1)-(A5), on ETI civilization characteristics are adopted, in order to simulate the likelihood of detection in current and historical SETI surveys. The upper limits are then determined by conducting a Bayesian analysis on the simulated data. The combined result from 12 different submodels, regarding galactic geometry, Equivalent Isotropic Radiated Power (EIRP) and transmitting frequency, are analyzed and presented in the thesis. The main results, depending on the submodel, yields an upper limit (3σ) in the order of thousands KI civilizations (corresponding to an EIRP of 1016 W), currently transmitting in the galaxy. The result also suggests that the presence of radio-communicating KII and KIII civilizations are sparse or nonexistent. In the hypothetical event of detecting exactly one KI signal, it can be inferred that hundreds, or thousands, similar signals, that have eluded detection, exists at Earth's position. A threshold EIRP is determined to approximately 1019 W, above which the upper limits are constant, and below which the upper limits are highly sensitive to the EIRP. The conclusion is that the Fermi para- dox is an actual paradox only if the real galactic ETI population obeys the idealized assumptions and simultaneously exceeds the determined upper limits. Key words: Bayesian analysis, ETI-civilization, Fermi paradox, Radio communication, Monte Carlo simulation, Null result. Sammanfattning Denna avhandling unders¨oker Fermi-paradoxen genom att best¨amma ¨ovre gr¨anser f¨or nuv¨ardespopula- tionen av galaktiska, radiokommunicerande, ETI-civilisationer, betingat p˚adet nuvarande nollresultatet av det sammanlagda SETI-projektet. En Monte Carlo-metod anv¨ands, d¨ar fem idealiserade antagan- den, (A1)-(A5), g¨ors om ETI-civilisationers egenskaper, f¨or att simulera sannolikheten f¨or detektion i nu aktuella och historiska SETI-studier. De ¨ovre gr¨anserna best¨ams sedan genom att utf¨ora en Bayesiansk analys p˚asimulerad data. Det sammanlagda resultatet fr˚an12 olika delmodeller, som tar h¨ansyn till galak- tisk geometri, ekvivalent isotrop utstr˚aladeffekt (EIRP) och s¨andarfrekvens, analyseras och presenteras i avhandlingen. Huvudresultatet, beroende p˚amodel, ger en ¨ovre gr¨ans (3σ) motsvarande n˚agratusen KI-civilisationer (motsvarande en EIRP av 1016 W), som f¨or n¨arvarande s¨ander signaler i galaxen. Re- sultatet indikerar ocks˚aatt f¨orekomsten av radiokommunicerande KII- och KIII-civilisationer ¨ar sparsam eller obefintlig. I det hypotetiska scenariot att exakt en KI-signal detekteras, kan det konstateras att hundratals eller tusentals liknande signaler, som har undg˚att detektion, existerar vid jordens position. Ett tr¨oskelv¨arde f¨or utstr˚aladeffekt (EIRP) best¨ams till ungef¨ar 1019 W, ¨over vilket de ¨ovre gr¨anserna ¨ar konstanta, och under vilket de ¨ovre gr¨anserna ¨ar k¨ansligt beroende av EIRP-v¨ardet. Slutsatsen ¨ar att Fermi-paradoxen endast ¨ar en faktisk paradox om den verkliga galaktiska ETI-populationen f¨oljer de idealiserade antagandena och samtidigt ¨overskrider de best¨amda ¨ovre gr¨anserna. Nyckelord: Bayesiansk analys, ETI-civilisation, Fermi-paradoxen, Radiokommunikation, Monte Carlo-simulering, Nollresultat. Glossary EIRP { Equivalent Isotropic Radiated Power ETI { Extraterrestrial Intelligence SETI { Search for Extraterrestrial Intelligence GG { Galactic Geometry (model category) EMW { Entire Milky Way (submodel) GHZ { Galactic Habitable Zone (submodel) RP { Radiated Power (model category) SPO { Static Power Output (model category) PPO { Progressive Power Output (model category) TF { Transmitting Frequency (model category) HI { Hydrogen line, 21 cm (submodel) WHR { Water-hole Region, 1.1-1.9 GHz (submodel) QR { Quiet Region, 1-10 GHz (submodel) ATA { Allen Telescope Array GBT { Green Bank Telescope SKA { Square Kilometre Array VLA { Very Large Antenna FFT { Fast Fourier Transform RA { Right Ascension (unit hours) DEC { Declination (unit degrees) RFI { Radio Frequency Interference Units 1 kpc { 1 kiloparsec = 3260 light years 1 ly { 1 light year = 9:46 × 1015 m 1 Jy { 1 Jansky = 10−26 Wm−2 1 GHz { 1 Gigahertz = 109 s−1 Foreword Are we alone in the universe? That is perhaps the oldest and most fundamental question in human history. The answer, whatever it is, would have profound implications, not only to science but for the human civilization at large. Questions about man and her position in cosmos have stimulated human philosophy for millennia. Anaximander (610-546 B.C.) discussed the concept of Cosmic Plurality, an idea of multiple, or even an infinite number, of planets harboring extraterrestrial life. The atomist Metrodorus (331-277 B.C.) strongly argued that \To consider the Earth as the only populated world in infinite space is as absurd as to assert that in an entire field only one grain will grow." During Medieval times and Renaissance, such thoughts were banned by the Catholic Church. Philosopher Giordano Bruno (1548-1600 A.D) challenged the dogmatic views of the church by claiming that \Innumerable suns exist; innumerable earths revolve around these suns in a manner similar to the way the seven planets revolve around our sun. Living beings inhabit these worlds." Refusing to reject his ideas, Bruno was sentenced for blasphemy and burned at the stake in Campo dei Fiori, Rome, on February 17, 1600 (Angelo, 2007; Fitzgerald, 2017). Bruno was a philosopher and an advocate of free thought, however, it is only in our era these ideas have become a little bit more than mere speculation. Contents 1 Introduction 3 1.1 Introduction . .3 1.2 Purpose ..............................................4 1.3 Outline of the Thesis . .4 1.4 Author's contribution . .4 2 Background 5 2.1 DefiningETI ...........................................5 2.2 The Fermi Paradox . .5 2.3 Solutions to the Fermi Paradox . .6 2.3.1 They exist and they are (were) here . .6 2.3.2 They exist but we have not yet established contact . .7 2.3.3 They do not exist . .9 2.4 The Drake Equation . 10 2.4.1 Two Examples . 10 2.4.2 Alternative Form . 11 2.5 Figure of Merits . 11 2.6 SETI Surveys . 13 2.7 The Kardashev Scale . 14 3 Theory 15 3.1 The Poisson Process . 15 3.1.1 The Nonhomogeneous Poisson Process . 15 3.1.2 A Birth and Death Process . 16 3.1.3 A Statistical Drake Equation . 17 3.2 Bayesian Analysis . 18 3.2.1 The Likelihood: Two Special Cases . 19 3.2.2 The Prior Distribution . 20 3.2.3 The Posterior Distributions . 20 3.3 Elements from Radio Astronomy . 21 3.3.1 Isotropic and Directional Antennas . 21 3.3.2 The Radiometer Equation . 21 3.3.3 Doppler Drift . 22 3.4 Galactic and Equatorial Coordinates . 22 4 Simulation overview 24 4.1 Description of the Simulation Algorithm . 24 4.2 Submodels............................................. 27 4.2.1 Galactic Geometry . 27 4.2.2 Radiated Power . 27 4.2.2.1 The PPO(I-III) Models . 27 4.2.2.2 The SPO(KI-KIII) Models . 28 4.2.3 Transmitting Frequency . 29 4.3 Filtering Conditions . 31 4.3.1 Causal Contact . 31 4.3.2 Sky Coverage . 31 4.3.2.1 All-Sky Surveys . 31 1 4.3.2.2 Targeted Searches . 32 4.3.3 Signal-to-Noise Ratio . 32 4.3.4 Frequency Coverage . 33 4.4 Boundaries . 33 4.4.1 The Birth Rate Parameter . 33 4.4.2 The Lifetime Parameter . 33 4.4.3 Sampling Domain . 34 5 Results 36 5.1 Initial Results . 36 5.1.1 Two Important Distributions . 36 5.1.2 The Significance of the Lower Cutoff . 36 5.2 Submodel Results . 37 5.2.1 Varying Galactic Geometry . 39 5.2.2 Varying Radiated Power . 40 5.2.2.1 SPO Models . 40 5.2.2.2 PPO Models . 41 5.2.3 Varying Transmitting Frequency . 42 5.2.4 Constraints on the Fermi Paradox . 42 5.3 Additional Results . 47 5.3.1 Mean Minimum Distance . 47 5.3.2 Relation between Population Parameters . 47 5.3.3 Future Limits . 47 6 Discussion and Conclusion 50 6.1 Discussion . 50 6.2 Conclusions . 52 6.2.1 Limitations of the Thesis . 53 6.2.2 Current and Future Research . 53 6.2.3 Is SETI Meaningful? . 54 7 Acknowledgements 55 Chapter 1 Introduction 1.1 Introduction The Kepler space telescope and other observatories have discovered 4003 exoplanets to date1. Approxi- mately 1-2 % of them are Earth-sized planets (0:5R⊕ ≤ R ≤ 2R⊕) orbiting in the habitable zone of their star (Exoplanetarchive.ipac.caltech.edu, 2019). Extrapolations of the planetary data further suggest that there could be 40 billion habitable worlds in the Milky Way Galaxy (Petigura et al. 2013). In addition building blocks of life (such as aromatic hydrocarbons, isopropyl cyanide, and amino acids) have been detected in comets, meteorites, and in the interstellar medium (e.g. Belloche, 2014; Glavin et al. 2010). By the Copernican principle, this should imply the existence of life, and possibly, intelligent life elsewhere in the galaxy. Early probabilistic estimates suggested that the Milky Way harbors between a thousand and a million extraterrestrial intelligent civilizations (ETIs) (e.g. Shklovski & Sagan, 1966; Drake, 1993). Other estimates with only conservative assumptions show, however, that a single technological civiliza- tion, capable of interstellar travel, should be able to spread all over the Milky Way within just tens of millions of years, a minuscule fraction.