Scintillation-induced intermittency in SETI

We use scattering theory, simulations, and empirical constraints on interstellar scintillations to discuss the intermittency of radio signals from extraterrestrial intelligence (ETI). The number of ETI sources in the Galaxy has a direct influence on the expected dynamic range of fluxes in a survey, through inverse square-law effects and, equally importantly, by the number of independent statistical trials made on modulations caused by interstellar scintillations. We demonstrate that scintillations are very likely to allow initial detections of narrowband signals, while making redetections extremely improbable, a result that follows from the skewed, exponential distribution of the modulation. This conclusion holds for relatively distant sources but does not apply to radio SETI toward nearby stars (less than or similar to 100 pc). Recent SETI has found nonrepeating, narrowband events that are largely unexplained. We consider three models in order to assess these events and to analyze large surveys in general: (model I) radiometer noise fluctuations; (model II) a population of constant Galactic sources that undergo deep fading and amplification due to interstellar scintillation, consistent with ETI transmissions; and (model III) real, transient signals (or hardware errors) of either terrestrial or extraterrestrial origin. We derive likelihood and Bayesian tests of the models for individual events and globally on entire surveys. Applying them to The Planetary Society/Harvard META data, we find that models II and III are both highly preferred to model I, but that models II and III are about equally likely. In the context of model II, the likelihood analysis indicates that candidate events above threshold (similar to 32 sigma) are combinations of large amplitude noise fluctuations and scintillation gains, making it highly probable that events seen once will only very rarely be seen again. Ruling out model II in favor of model III is difficult-to do so, many more reobservations (e.g., thousands) are needed than were conducted in META (hundreds) or the reobservation threshold must be much lower than was used in META. We cannot, therefore, rule out the possibility that META events are real, intrinsically steady ETI signals. Our formalism can be used to analyze any SETI program. We estimate the number of reobservations required to rule out model II in favor of model III, taking into account that reobservations made promptly sample the same scintillation gain as in the original detection, while delayed reobservations sample a decorrelated scintillation modulation. The required number is a strong function of the thresholds used in the original survey and in reobservations. We assess optimal methods for applying statistical tests in future SETI programs that use multiple site and multiple beam observations as well as single site observations. We recommend that results be recorded on many more events than have been made to date. In particular, we suggest that surveys use thresholds that are far below the false-alarm threshold that is usually set to yield a small number of noise-induced ''detections'' in a massive survey. Instead, large numbers of events should be recorded in order to (1) demonstrate that background noise conforms to the distribution expected for it; and (2) investigate departures from the expected noise distribution as due to interference or to celestial signals. In this way, celestial signals can be investigated at levels much smaller than the false-alarm threshold. The threshold level for archiving candidate intensities and their corresponding sky positions is best defined in terms of the recording and computational technology that is available at a cost commensurate with other survey costs.