Signal coverage approach to the detection probability of hypothetical extraterrestrial emitters in the Milky Way

The lack of evidence for the existence of extraterrestrial life, even the simplest forms of animal life, makes it is difficult to decide whether the search for extraterrestrial intelligence (SETI) is more a high-risk, high-payoff endeavor than a futile attempt. Here we insist that even if extraterrestrial civilizations do exist and communicate, the likelihood of detecting their signals crucially depends on whether the Earth lies within a region of the galaxy covered by such signals. By considering possible populations of independent emitters in the galaxy, we build a statistical model of the domain covered by hypothetical extraterrestrial signals to derive the detection probability that the Earth is within such a domain. We show that for general distributions of the signal longevity and directionality, the mean number of detectable emitters is less than one even for detection probabilities as large as 50%, regardless of the number of emitters in the galaxy.