1 kW (SETI) Signals AT 100 L.Y.

9008-003

9008-003a

The graph 9006-020 illustrates communications out to 100 light years.  This range encompasses a large number of candidate star systems believed to be capable of supporting life.  The graph shows the received signal levels for three different types of 1 kW beacon.  For the purposes of this model, the transmitter powers are assumed to be confined to a 1 Hz bandwidth.  The received signal and Planck radiation is plotted on a spectral density basis, i.e., W/m².Hz.   This makes it easy to adjust the calculated results to accommodate other bandwidths.

As with the 10 L.Y. model, quantum shot noise dominates the noise-floor of the optical systems, so that whatever the electrical output bandwidth of the receivers, and to a large extent the bandwidth of any optical pre-filter, the noise- floor is set by the local oscillator level and the noise associated with the arrival of the signal photons.

The noise temperature of the microwave system includes the effect of the 2.7 K cosmic background radiation.  The Planck radiation curve at these frequencies also shows the effect of excess radio noise and is represented by part of a Planck curve corresponding to a star with increased surface brightness, i.e., at some frequencies the effective surface temperature > 100,000 K.  However, this noise isn't "seen" because the kT noise-floor of the receiver predominates.

9008-003b

The 656 nm visible transmitter would appear as a +28 Magnitude star, so it would be very dim.  It would only just be detectable by the new Hubble and Keck telescopes if background starlight could be eliminated.   The alien star appears as a +7 Magnitude body, and since the naked eye can see out to +6 Magnitude, this star would not be visible to the naked eye.

Since signal and Planck spectral densities scale with the square of the distance, the spectral energy densities and Signal-To-Noise Ratios (SNRs) at 100 L.Y. are two orders of magnitude (20 dB) smaller than for 10 L.Y.  The SNR in this model for the microwave system is essentially 0 dB, while the CO₂ and 656 nm optical systems yield 2 dB and 14 dB, respectively.

Again, as for the 656 nm 10 L.Y. model, it is not out of the question for an advanced alien culture to be able to build lasers and telescopes that can put out Continuous Wave (C.W.) powers of >> 1 MW.   Hence, an SNR of 14 dB re 1 Hz bandwidth represents a grossly conservative view of what might be possible.  It may indeed be feasible to produce SNRs > 70 dB re 1 Hz.  This would take a transmitter power of nearly 1 GW.  Since alien laser transmitters might be solar or nuclear pumped, this may not present much of a technological problem.

Copyright (c), 1996