It is well known that seti@home, and actually most other SETI projects
on-going, are currently focusing on detecting a 'beacon' signal from an ETI,
containing a message deliberately aimed and intended for us.
In this posting, I want to show that it is very unlikely (less than 0.001%
chance ) to find a beacon at the "water-hole" (1.42GHz), knowing what we
know now about Drake's formula's variables.
Moreover, I'll show that even if we would detect such a signal, we would
currently discard it as being 'noise' or RFI, simply because it does not
repeat at the exact rate as Arecibo is pointing at the same point in the
sky.
Also, I'll show that it is about 1000 times (1%) more likely to find a
beacon in the optical spectrum (OSETI), but that the really interesting
beacons are likely to be found between 50GHz and 5000GHz, and are likely to
come from 1000-10KLYs distance. They are most likely pulsed (not continuous)
to save energy.
--------------------------
Beacons could be anywhere in the spectrum, so seti pioneers had to guess
where the most likely beacons would be. Too low a frequency (<1GHz), and
cyclotron radiation from the galaxy would make interstellar communications
hard. Too high (>20GHz), and our atmosphere starts absorbing so much that we
surely would not detect any beacons even if they would be there, and also
our technology is not so advanced above 10GHz.
Between 1 and 10GHz is nice and quiet, so SETI could be done easily there.
This is still a very wide spectrum, so seti pioneers focused in on a smaller
spectrum, called the "water-hole", because that is where there are some
absorption line of H2O (water), which is (as far as we know) crucial to the
development of life. Seems indeed a good choice. The frequency range
(between the two absorption lines) is between 1.40 and 1.42 GHz. Indeed, if
ET would set-up a microwave beacon, and their life-form is water-based as
ours, this seems indeed a preferred frequency to set-up a beacon.
Let's look at what our chances are of detecting a beacon at 1.42 GHz.
Here goes.
First requirement (for us to detect a beacon) is that somebody actually has
a beacon aimed at us now.
Imagine an ET civilization somewhere in our galaxy, with technology at least
as advanced as ours.
Lets assume that they have been listening and searching (as we do now), for
signs of intelligent life beyond their own planet. Maybe they listened to
noise for 100 years. There comes a point (I have to assume), that somebody
would propose to set-up a beacon to let nearby starsystems know that they
are not alone. It would be reasonable to assume that the decision to start
transmitting signals is a touch one. There will (for one) be many people
(creatures..) who will object out of fear that the universe might be full of
dangers that are unknown. Maybe the Bork really exist. We don't know.
Also, beacons cost money (or the equivalent of that for ET). They cost
real-estate (space) and they cost energy. Either way, it is going to be a
matter of probability. Maybe 10% of intelligent civilizations decide to
set-up a sustained beacon. Others won't. Or if it is very easy (low cost) to
set-up a beacon, the probability might actually go up (to 50%?).
So, with our current seti@home project, we are listening for the fraction of
civilizations who set-up a beacon program.
Here is the second requirement for us to detect a ETI beacon : ET must have
a dedicated (transmitting almost constantly), widespread (covering many
stars), and sustained (over many years and possibly centuries or millennia)
beacon program running. Otherwise, we will NOT detect them.
This requirement is derived from Drake's formula (with rather optimistic
settings of its variables), which essentially states that the number of
civilizations in the galaxy is approximately equal to the number of years
that a average civilization exists. Read 'exist' as a beacon program, and
thus if an ET beacon program would run for 1000 years, then there would be
1000 civilizations like that in the galaxy today. That means that the neares
t such civilization would be about 4000LYs away (1 is 100Million stars is
currently equipped with a beacon). That also means that each such
civilization needs to target 100Million stars simultaneously with their
beacon program, or else we still will not even find a single beacon anywhere
here on earth (or at least the probability is way below 50%).
The galaxy might be deprived of beacons, even if it is filled with life....!
Third requirement is that we listen at the right frequency.
Now here its gets even more interesting.
----
Phase I
Lets assume that ET first starts a moderate program to target the nearby
stars, and they transmit in the water-hole, just as we hoped they would.
That is, they transmit a signal around 1.42 GHz, to a couple (10) of nearby
stars in the 10LYs around them. Lets for now assume that they use a
Arecibo-like transmitting antenna. At that distance, at 1.4GHz, the
transmitters will use about 1KW/star for a continuous narrowband signal of
1Hz (requires some calculations with the seti@home FAQ formula's) to drop a
moderate (10db) SNR into a similar (Arecibo) receiver at 10LYs away.
That project thus uses about 10KW continuously. So far so good.
Now, targeting 10 stars at 10LYs is not really putting many bags on the dike
(sorry; Dutch expression). In terms of us (on earth) detecting such a
civilization, we would need to be one of the very lucky 10. Out of
100billion stars in the galaxy.
---
Phase II :
So, after a while, we hope that ET will upgrade their program to cover 1000
stars (radius of about 100LYs) continuously. Here are the costs : First of
all, to extend the range to 100LYs, energy costs of a continuous beacon
would go up to about 100kW/star. This is because power needs to go up with
R^2. For 1000 stars this is 100MW continuously. That is a small power plant
continuously running only for that program. For a whimsical 1Hz signal for
each star. This MUST be too much energy for any civilization to spend on a
ET beacon program (which will not bear results for at least 1000years).
And they only target 1000 stars with this program.
Very interesting note : This signal IS the one that we are currently looking
for : continuously present, Doppler-compensated (targeted at us), and
narrowband. However, this simple calculation shows that it is unlikely that
ETI will afford to generate such a continuous beacon for more than the stars
in a 100LY radius. For a considerable period of time. At least not at 1.42
GHz.
ET's engineers will get to work to save energy :
(1) instead of continuous signal, they can send 1bit (in 1Hz) signals
every 1000sec or so. Savings : factor 1000. Means that the beacon is now
'pulsed' with slow pulses of 1sec/1Hz (1bit) each, one every 1000sec. This
also means that we (at the receiver) will NOT see it repeat if we
arbitrarily look at the transmitter for 25sec or so.
Essentially, a good measure of the cost of a beacon (or the cost of
interstellar communication in general) is energy per bit, not watt/target.
Energy per bit for 1.42 GHz for Arecibo-style antenna targeting 100LYs would
be about 100kJ/bit.
(2) Use a large antenna. Antenna amplification goes up with r^2. Since we
were already have a r=100m (Arecibo size) transmitting antenna, which
transmits to many stars simultaneously, an considerably larger one must
cause some objections with the locals. Lets use this only as a last resort..
So, if there IS a beacon at 1.42 GHz, it will likely come from less than
100LYs, and it will likely be 'pulsed' to save energy.
Another interesting note : We will currently NOT detect such a pulsed signal
as a valid beacon, even if it is strong enough. We only look for 'almost'
continuous signals. We discard non-repeating signals (in seti@home), and a
signal that is 'on' only 1/1000 of the time will currently certainly be
considered non-repeating.
So, ET has the program running, targeting 1000 stars within a 100LY range,
and they made it 1/1000'th pulsed (1 1-bit pulse every 1000sec) and it thus
costs 1000*(100kW/1000)=100kW, which they can afford.
Still, only 1000 stars are targeted, and only 100LYs radius are covered.
There is only a low probability that we (on earth) would detect this system.
If the average beacon civilization is (as we estimated before) in one out of
100Million stars around us, there is only a 0.001% chance of detecting this
beacon.
-----
Next (phase III) ET gets again a factor 1000 more serious : Target 1million
stars. Radius 1000LYs.
For 1000LYs, cost/bit goes up from 100kJ/bit to 10MJ/bit. Again the R^2
factor..
Energy usage (even for a 1/1000 pulsed beacon) would go up to 1M * 10MJ/1000
= 10GW.
That is massive energy usage. Unlikely to sustain for 1000years or more
(which is what we need).
So a bright ET engineer comes up with a good solution : Lets go optical !
With ns laser pulses, you can achieve lower energy cost.
Ballpark estimates : Cost/bit : Get 10 photons (in 1ns or so) into a 10meter
telescope at 1000LYs : transmit around 20AU around a target star, at near
infrared (1um) would cost only 10kJ/bit/star.
Instead of the 10MJ/bit of the 1.42 GHz beacon !
That is a factor 1000 improvement in energy cost. Hard to negotiate with
that !!
And the transmitter would only be a moderate (5meter?) telescope...
Program seems very feasible. To target the 1Million stars in a 1000LYs
radius would cost
1M*10kJ= 1GJ/bit. For a 1/1000 pulsed signal (1 1-ns pulse every 1000sec)
this would cost ET about 1MW of energy. Better than the 10GW for the 1.42GHz
beacon !!!
So this (phase III) program would be optical, 1 ns(or shorter) pulses,
dropping 10photons in a 10meter target dish. OSETI is looking for this, but
the important thing is that if ET is between 100LYs and 1000LYs away, a
optical beacon is about 1000 times more likely than a 1.42Ghz beacon.
Probability with Drake's formula again :
1M stars covered in a galaxy where 1/100M stars has a beacon program, this
means 1% chance of finding a optical beacon (up till 1000LYs away). Chances
of finding a 1.42GHz beacon up till 1000LYs away deminishes to about 0,001%.
Incidentally, the same probability as finding a 1.42GHz beacon up till
100LYs...
-----
Now phase IV. ET is deadly serious now. Maybe they didn't find anyone in
1000LYs (waited 2000years). Or they found some neighbors, and were encourage
to check-out the 'city' in which they live...
So ET starts phase IV of their beacon program : target 1Billion stars. Range
is about 10kLYs. They are now targeting more than just a few percent of the
entire galaxy.
What are the logistics ? Gonna be enormous, but any technology assumed
available, Energy is the main problem with 1Billion stars to target.
Optical was 100kJ/bit/star for 1000LYs distance. That does not change much
with 10kLYs distance, since the 'antenna' (the transmitting telescope)
determines which area of the target star system is covered. We assume that
ET will target an area with a radius of about 20AU around each star system,
which, at 10kLYs, can be obtained with a transmitting telescope of about
50m...
Quite feasible for an advanced civilization, so optical beacon still costs
100kJ/bit/star.
With 1Billion stars to cover, this is 1*10^14J/bit. For a 1/1000 pulsed
laser (1 pulse per 1000sec), this means power usage of the system will be
about 10GW. That is the power output of the largest power-plant on earth.
So for sure that for phase IV of this beacon project, ET engineers are
asked to think about power saving again.
This time, I think they will come up with the optimal frequency :
In the microwave spectrum, you can increase antenna amplification by
increasing the frequency. Actually, power output goes up with f^2 if you
increase frequency f.
This should drive the frequency of beacons UP.
There is also a point where the antenna amplification becomes so large that
that the targeted beam starts to illuminate less than 20AU around a target
star. At that point, it would not make sense to increase antenna
amplification, since that would only start to rule-out interesting areas
around a star that might harbor a planet with intelligent life on it.
However, this point is not reached well before the quantum limit is hit :
In the optical spectrum (around f = 10^15 Hz) the energy of one quanta
(E=h*f) starts to determine the energy needed to transfer one bit of
information. This means that from optical, it should drive the frequency
DOWN, so that no energy per bit is wasted on 'bits' (quanta).
The 'optimal' frequency; that is, the frequency where the cost/bit of
interstellar communication is minimized, depends on the size of the
receiving and transmitting antenna size, but considering the previous two
effects (drive up from microwave, and drive down from visible light) is
between 500 and 5,000GHz.
In that range, the cost/bit is between 50 and 500J/bit. Depending on the
transmitting/receiving antenna's. At 500J/bit a 1/1000 beacon (1 pulse per
1000sec), targeting 1billion stars at max range of 10kLYs would cost
1*10^9*(500/1000)= 500MW of energy.
That (500J/bit/star) is be affordable, and certainly is a lot better than
the 100kJ/bit for optical beacons, or the astronomical MJ/bit/star of a
1.42GHz beacon.
Actually, the lowest energy/bit is theoretically (disregarding real-estate
taken by antenna's) at about 50GHz. At that point, the cosmic background
radiation (2.7K) has the same energy as the quanta at that frequency. Beyond
that (50GHz), energy/bit would only increase. Incidentally, 50GHz also
collides with a very strong O2 absorption line, which makes it impossible
for us to actually observe any outer-space 50GHz signals. Still O2 is very
indicative of life (at least on earth), so it is an interesting frequency to
observe.
Probability : again, if 1 out of 100M stars has a beacon-bearing
civilization, and every civilization builds up to a level IV program
(transmitting to 1 Billion other stars), then we should have about 10 such
beacons in the skies at this time.
Unfortunately, we need a space-based antenna to receive signals in the
extremely interesting frequency-range of 50GHz-1000GHz, the frequency range
where these interstellar communication signals are lowest cost...
Tell me if you want to know more...