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

2. 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?

3. 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

4. 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

5. 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

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

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

8. 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

9. 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

10. 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

11. 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)

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

13. 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

14. 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)

15. 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

16. 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

17. 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

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

19. 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 GHz.
Alien astronomers are bound to be sniffing around this bandwidth, right?

20. “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 ≈ That will definitely turn some heads!
Let BW = 100 Hz (not natural at all!)

21. 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:

22. 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 … 

23. 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 ?

24. “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

25. “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

26. 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

27. 100,000 Light Years!
500 Light Years!

28. 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

29. 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

30. 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

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

32. 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