摘要：We model the settlement of the Galaxy by space-faring civilizations in order to address issues related to the Fermi Paradox. We are motivated to explore the problem in a way that avoids assumptions about the agency (i.e., questions of intent and motivation) of any exo-civilization seeking to settle other planetary systems. We begin by considering the speed of an advancing settlement front to determine if the Galaxy can become inhabited with space-faring civilizations on timescales shorter than its age. Our models for the front speed include the directed settlement of nearby settleable systems through the launching of probes with a finite velocity and range. We also include the effect of stellar motions on the long-term behavior of the settlement front which adds a diffusive component to its advance. As part of our model we also consider that only a fraction, f, of planets will have conditions amenable to settlement by the space-faring civilization. The results of these models demonstrate that the Milky Way can be readily filled-in with settled stellar systems under conservative assumptions about interstellar spacecraft velocities and launch rates. We then move on to consider the question of the Galactic steady state achieved in terms of the fraction X of settled planets. We do this by considering the effect of finite settlement civilization lifetimes on the steady states. We find a range of parameters for which 0<X<1, i.e., the Galaxy supports a population of interstellar space-faring civilizations even though some settleable systems are uninhabited. In addition we find that statistical fluctuations can produce local overabundances of settleable worlds. These generate long-lived clusters of settled systems immersed in large regions that remain unsettled. Both results point to ways in which Earth might remain unvisited in the midst of an inhabited galaxy. Finally we consider how our results can be combined with the finite horizon for evidence of previous settlements in Earth’s geologic record. Using our steady-state model we constrain the probabilities for an Earth visit by a settling civilization before a given time horizon. These results break the link between Hart’s famous “Fact A” (no interstellar visitors on Earth now) and the conclusion that humans must, therefore, be the only technological civilization in the Galaxy. Explicitly, our solutions admit situations where our current circumstances are consistent with an otherwise settled, steady-state galaxy.
