Messaging with Cost Optimized Interstellar Beacons

Abstract

This paper considers galactic scale Beacons from the point of view of expense to a builder on Earth. For fixed power density in the far field, what is the cost-optimum interstellar Beacon system? Experience shows an optimum tradeoff, depending on transmission frequency and on antenna size and power. This emerges by minimizing the cost of producing a desired effective isotropic radiated power, which in turn 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 non-linear 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 using current cost parameters ($/W, $/m2) as a basis. Galactic-scale Beacons demand effective isotropic radiated power >1017 W, emitted powers are >1 GW, with antenna areas > km2. We show the scaling and give examples of such Beacons. Thrifty beacon systems would be large and costly, have narrow searchlight beams and short dwell times when the Beacon would be seen by an alien oberver at target areas in the sky. They may revisit an area infrequently and will likely transmit at higher microwave frequencies, ~10 GHz. The natural corridor to broadcast is along the galactic spiral radius or along the spiral galactic arm we are in. Our second paper argues that nearly all SETI searches to date had little chance of seeing such Beacons.