Against the Use of Power Law Luminosity Functions for ET Beacons

Abstract

Not infrequently it is suggested that the luminosity function (the distribution of the space densities of objects as a function of their luminosities) of extraterrestrial transmitters can plausibly be modeled as a power law, L^-α, of the luminosity L (Drake 1973; Gulkis 1985; Lampton 2002). This assertion is usually motivated by analogy to the luminosity function for stars in the solar vicinity, which can be (very) roughly modeled as such a power law Fig. 1, data from Mihalas and Binney (1981). The argument then continues that if the power law is sufficiently flat (α < 1.5), then a flux limited sample of transmitters will be dominated by the most luminous, since their relative scarcity is more than made up by the much larger volume in which they can be detected. This is an extreme example of the infamous Malmquist bias (Mihalas & Binney 1981). It is then concluded that if the distribution of ET transmitters were to have such a flat distribution, then the seemingly obvious SETI search strategy of starting with the nearest stars and working outward would be incorrect, and, since we do not know the value of α it makes sense to “hedge” our bets by performing all-sky SETI searches even if such searches are much less sensitive.