ThebDistribution and the Velocity Structure of Absorption Peaks in the Lyα Forest

A theory is developed which relates the observed b-parameter of a Lyman-alphaabsorption line to the velocity-curvature of the corresponding peak in theoptical depth fluctuation. Its relation to the traditional interpretation of bas the thermal broadening width is discussed. It is demonstrated that,independent of the details of the cosmological model, the differential bdistribution has a high b asymptote of $dN/db \propto b^{-m}$, where $m \geq5$, when we make the reasonable assumption that low-curvature fluctuations arestatistically favored over high-curvature ones. There in general always existabsorption lines much broader than the thermal width. We then develop a linearperturbative analysis of the optical depth fluctuation, which yields asingle-parameter prediction for the full b distribution: in addition toexhibiting the general high velocity tail, it explains the observed sharp low bcut-off. The dependence of the b distribution on cosmological parameters, suchas $\Omega$ and the power spectrum, and reionization history as well asobservation/simulation resolution is derived and discussed.Comment: 18 pages, Latex with aaspp4.sty, submitted to Ap