The b distribution and the velocity structure of absorption peaks in the Lyα forest

A theory is developed that relates the observed b parameter of a Ly alpha absorption line to the velocity curvature of the corresponding peak in the optical depth fluctuation. Its relation to the traditional interpretation of b as the thermal broadening width is discussed. It is demonstrated that, independent of the details of the cosmological model, the differential b distribution has a high-b asymptote of dN/db proportional to b(-m), where m greater than or equal to 5, when we make the reasonable assumption that low-curvature fluctuations are statistically favored over high-curvature ones. There in general always exist lines much broader than the thermal width. We develop a linear perturbative analysis of the optical depth fluctuation, which yields a single-parameter prediction for the full b distribution. In addition to exhibiting the high-velocity tail, it qualitatively explains the observed sharp low-b cutoff-a simple reflection of the fact that high-curvature fluctuations are relatively rare. Although the existence of the high-b asymptote, which is independent of the validity of the linear expansion, is consistent with the observed b distribution, a detailed comparison of the linear prediction with six observational data sets indicates that higher order corrections are not negligible. The perturbative analysis nonetheless offers valuable insights into the dependence of the b distribution on cosmological parameters such as Omega and the power spectrum. A key parameter is the effective smoothing scale of the optical depth fluctuation, which is in turn determined by three scales: the thermal broadening width, the baryon smoothing scale (approximately the Jeans scale), and the observation/simulation resolution. The first two are determined by reionization history, but are comparable in general, whereas the third varies by about an order of magnitude in current hydrodynamic simulations. Studies with non-resolution-dominated b distributions can be used to probe the reionization history of the universe.