Messaging with Cost-Optimized Interstellar Beacons

On Earth, how would we build galactic-scale beacons to attract the attention of extraterrestrials, as some have suggested we should do? From the point of view of expense to a builder on Earth, experience shows an optimum trade-off. This emerges by minimizing the cost of producing a desired power density at long range, which determines the maximum range of detectability of a transmitted signal. We derive general relations for cost-optimal aperture and power. For linear dependence of capital cost on transmitter power and antenna area, minimum capital cost occurs when the cost is equally divided between antenna gain and radiated power. For nonlinear power-law dependence, a similar simple division occurs. This is validated in cost data for many systems; industry uses this cost optimum as a rule of thumb. Costs of pulsed cost-efficient transmitters are estimated from these relations by using current cost parameters ($/W, $/sq m) as a basis. We show the scaling and give examples of such beacons. Galactic-scale beacons can be built for a few billion dollars with our present technology. Such beacons have narrow "searchlight" beams and short "dwell times" when the beacon would be seen by an alien observer in their sky. More-powerful beacons are more efficient and have economies of scale: cost scales only linearly with range R, not as R(exp 2), so number of stars radiated to increases as the square of cost. On a cost basis, they will likely transmit at higher microwave frequencies, -10 GHz. The natural corridor to broadcast is along the galactic radius or along the local spiral galactic arm we are in. A companion paper asks "If someone like us were to produce a beacon, how should we look for it?"