ASYMPTOTICS AND STAR FORMATION

Star formation is a process that spans many decades in length and time scales. As a consequence, asymptotic methods of the variety pioneered by C. C. Lin and other applied mathematicians can be used to great effect at various stages of the problem. In this lecture, we give an overview of the complete problem in the case of the formation of single stars of sunlike masses, and we highlight a few of the mathematical solutions made possible by an application of asymptotic techniques and ideas — the formation of molecular cloud cores; the gravitational collapse of self-similar, magnetized, rotating toroids; the dissipation by magnetic reconnection of the trapped interstellar flux brought in by gravitational collapse that would otherwise have prevented the formation of circumstellar disks; and the jets and outflows that result when the accreting circumstellar disk interacts with the magnetosphere of the newly formed star. We end by indicating where additional progress requires a better understanding of the role of turbulence, another subject where astronomers of the future can look to the work of C. C. Lin for guidance.