1 kW (SETI) Signals AT 1000 L.Y.
The final graph 9006-021 in this sequence illustrates communications out to 1000 light years. This range encompasses over 1 million stars. 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 and 100 L.Y. models, 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.
The 656 nm visible transmitter would appear as a +33 Magnitude star, so it would be so dim that it could not be detectable by any conventional (incoherent) telescope, even if background starlight could be eliminated. The alien star appears as a +12 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 1000 L.Y. are four orders of magnitude (40 dB) smaller than for 10 L.Y. The SNR in this model for the microwave system is essentially -20 dB, while the CO2 and 656 nm optical systems yield -18 dB and -6 dB, respectively. These signals would not be detectable in this bandwidth without signal integration.
Again, as for the 656 nm 10 and 100 L.Y. models, it is not out of the question for an advanced alien civilization to be able to build lasers and telescopes that can put out Continuous Wave (C.W.) powers of >> 1 MW. Hence, an SNR of -6 dB re 1 Hz bandwidth represents a grossly conservative view of what might be possible. It may indeed be feasible to produce SNRs > 50 dB re 1 Hz. As with the 10 and 100 L.Y. models, this would take a transmitter power of nearly 1 GW.
Copyright (c), 1996