Analysis of an Interstellar Communications Link Why SETI is probably almost certainly never going to find anything James Nagel, PhD December, 2016

Overview SETI = Search for Extraterrestrial Intelligence Radio-frequency (RF) transmissions have the power to travel across interstellar distances and form communication links How feasible is this, really?

Understanding Radio Pt Imagine a point source of light that continually radiates energy equally well in all directions This is called an isotropic radiator Pt = Transmitted power Pt

Understanding Radio Pt Pr A Now place a rectangular aperture far away. How much power flows through this aperture? Pr = Received power Pt Pr A

Understanding Radio Pt Pr A What happens if the light source is directive? Energy radiates more in some directions and less in others We call this directive gain Pt Pr A

Understanding Radio Pt Pr A Power captured by the receiver increases in proportion with the directive gain Pt Pr A

Understanding Radio Pt Pr A The product of Pt times Gt is call the equivalent isotropic radiated power (EIRP) Pt Pr A

Understanding Radio Pt Pr Ae In practice, the receiver isn’t a perfect aperture, but some physical object that interacts with light All receivers have an equivalent effective area Pt Pr Ae

Understanding Radio Pr Ae Pn Meanwhile there’s random radio noise coming in from all over the universe All radio receivers have some net noise power Pn Pr Ae Pn

Understanding Radio Pr Ae Pn Define signal-to-noise ratio (SNR) as the received power from the source divided by noise power Pr Ae Pn

Shannon-Hartley Theorem Given a band-limited channel (bandwidth BW) with some signal and noise, there is a maximum capacity at which reliable communication can occur Capacity = Error-free bits per second (bps)

Proxima Centauri The nearest neighboring star to us is 4.25 light years away. What would it take to build a communication link?

Fun Facts The Alpha Centauri system consists of THREE stars Alpha Centauri A Alpha Centauri B Proxima Centauri (red dwarf) Proxima is orbited by an Earth-sized planet, Proxima-B, within the habitable zone A B Proxima

Step 1: Pick a wavelength Higher frequencies are better because they provide higher gain Earth’s atmosphere grows opaque around 2-3 cm (f = 10 GHz) http://imgur.com/gallery/YGgY0

Step 2: Build the antennas Largest fully-steerable radio telescope in the world is the Green Bank Telescope in West Virginia Bigger ones exist, but they are not fully-steerable Diameter = 100 m Assume perfect aperture efficiency Total effective area Ae ≈ 8000 m2

Step 3: Pick an output power The Arecibo message in 1977 had a total transmit power of 1.0 MW Typical for high-powered radar Roughly the total output of a single coal-fired power plant

Step 4: Calculate Noise Power When doing radio astronomy, the dominant source of radio noise is the cosmic microwave background (CMB) Johnson-Nyquist noise Surface temperate of a typical red dwarf star is about 3000 K We can reduce noise by reducing bandwidth, but this reduces our channel capacity

Step 5: “Hello, World” Crunch the numbers: Total received power = 6 x 10-17 W Total noise power at 1 kHz BW = 4 x 10-17 W Signal to noise ratio = about 1ish Channel capacity = 1000 bits per second About the same as dial-up internet

Non-cooperative Link What happens if the aliens aren’t specifically cooperating with us? We need to get their attention. Hydrogen does a lot of neat stuff around 1.4-1.6 GHz. Alien astronomers are bound to be sniffing around this bandwidth, right?

“Hello, Aliens” Key assumptions: You already know which star has aliens on it The aliens have a vibrant radio astronomy program The aliens are listening on the right channel The aliens are pointing their telescope near our sector of the sky The aliens will recognize an unnatural signal when they see it Alien atmosphere has similar windows Let SNR ≈ 10 --- That will definitely turn some heads! Let BW = 100 Hz (not natural at all!)

Pay Attention to Me, World! Crunch the numbers. How far away can I conceivably catch ET’s attention? Our sun’s equivalent noise temperature = 5000 K Blast 1.0 MW of power continuously Be generous and assume alien telescope is 10 times bigger Solve for distance:

Pay Attention to Me, World! Crunch the numbers. How far away can I conceivably catch ET’s attention? Our sun’s equivalent noise temperature = 5000 K Blast 1.0 MW of power continuously Be generous and assume alien telescope is 10 times bigger Solve for distance: R = 2 light years … 

Ambassador Hitler From the movie Contact, we learn that the 1936 Olympic games were the first signals to penetrate deep space Transmit antenna would have been omnidirectional Gt = 5-10 at most Frequency = 40 MHz Just enough to break the ionosphere Power = 100 kW ? Bandwidth = 5 MHz ?

“Sieg Heil, World” Let’s be super generous and grant the aliens a full SQUARE KILOMETER of receiver area. Let SNR = 0.1 barely enough to turn some heads Solve for maximum distance

“Sieg Heil, World” R = 320 AU  Let’s be super generous and grant the aliens a full SQUARE KILOMETER of receiver area. Let SNR = 0.1 barely enough to turn some heads R = 320 AU  Distance to Pluto = 50 AU

Once Per Lifetime Link 50 years 50 more years Human beings only live about 100 years. The only interesting people worth talking to are thus 50 ly away. Hello, World! 50 years What’s up? 50 more years

100,000 Light Years! 500 Light Years!

Local Stars Worth Talking To Stars visible to naked eye within 50 ly There are about 1500 stars within 50 ly Most are brown dwarfs and probably won’t have aliens

Local Stars Worth Talking To Stars visible to naked eye within 50 ly Contact requires that you deliberately beam many megawatts of energy at someone continuously for a long time Receive telescope must also deliberately look at the source and at the proper bandwidth

Someone Listen to Me, Dammit! I want everyone to know that I’m here. Broadcast equally in all directions (G = 1) Blast 2.0 GW of power continuously peak power output of Hoover dam Give aliens a square-kilometer receiver BW = 100 Hz Hydrogen times pi: f = 4.71 GHz Let SNR = 1.0

Someone Listen to Me, Dammit! I want everyone to know that I’m here. Total Distance = 16 light years

Thoughts about SETI SETI continues to scan the sky for ET signals Unspoken assumption of SETI is that ET will deliberately beam gigawatts of power at us on a continuous basis Aliens cannot possibly know that we are here in the first place “Stray” signal detection is out of the question Allen Telescope Array