1 kW (SETI) Signals At 10 L.Y.

9008-002

9008-002a

The graph 9006-019 illustrates communications out to our nearest start systems at about 10 L.Y. distance.  This puts us into the range of several star systems that are candidates for supporting life.  Tau Ceti is a G-type star, like our Sun, and is at a range of 11.9 light years.  The graph shows the received signal levels for three different types of 1 kW beacon which have their transmitter powers confined to a 1 Hz bandwidth.  The received signal and Planck radiation is plotted on a spectral density basis, i.e., W/m².Hz.

Clearly, quantum shot noise dominates the noise-floor of the optical system, so that whatever the electrical output bandwidth of the receiver, 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 increased 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.

9008-002b

The 656 nm visible transmitter would appear as a +23 Magnitude star, so it would be very dim.  It would only just be detectable photographically by the largest telescopes if background starlight could be eliminated.  The alien star appears as a +2 Magnitude body, and since the naked eye can see out to +6 Magnitude, this star would be readily visible in the dark sky.

The important factor here is not what a wide-band detector or the eye sees with its 100 nm (70 THz) bandpass, but what a narrow-band optical receiver sees.  If this graph was replotted on an Intensity basis, i.e., W/m², in a 70 THz bandwidth, the optical transmitters would be obliterated by the Planck radiation and the photodetector shot-noise it produces.  The Signal-To-Noise Ratio (SNR) of the 656 nm system is 34 dB.  This is 14 dB greater than available from the microwave system.  The huge Effective Isotropic Radiated Power (EIRP) of 2.3 x 10¹⁸ W more than overcomes the increase in Planck radiation at these frequencies.  Even the infrared CO₂ transmitter shows a small SNR advantage over its microwave counterpart.  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 34 dB re 1 Hz bandwidth represents a grossly conservative view of what might be possible.  It may indeed be feasible to produce SNRs > 90 dB re 1 Hz.

Copyright (c), 1996