Equilibrium slab models of Lyman-alpha clouds

Abstract

We model the Lyα clouds as slabs of hydrogen with an ionizing extragalactic radiation field incident from both sides. In general, the equilibrium configuration of a slab at redshift z <~ 5 is determined by a balance of the gas pressure, gravity (including the effects of a dark matter halo), and the pressure exerted by the inter-galactic medium, P_ext_. These models have been used to make predictions of the number of slabs as a function of the neutral hydrogen column density, N_H_. A break in the curve is predicted at the transition between regimes where gravity and pressure are the dominant confining forces, with a less rapid decrease at larger NH. The transition from optically thin to optically thick slabs leads to a gap in the distribution, whose location is governed largely by the spectrum of ionizing radiation. Observations provide us with the distribution of N_H_ at z ~ 2.5, from the Lyα forest through the damped Lyα clouds. Recent HST data also provide a rough count of forest clouds at present and an indication of the rate of evolution. We define the parameters ζ ~ (1 + z)^j^ and P_ext_ ~ (1 + z)^P^, representing the time-dependent ionization rate and external pressure. Comparisons with various observations are used to constrain these parameters- assuming that the population of clouds is described by a power-law distribution of total column densities (1) The best fit is provided by P_ext_/k = 366 cm^-3^ K near z ~ 2.5, based on the current observed value of the relative number of damped and forest clouds. If damped systems are undercounted due to dust obscuration, a smaller value of P_ext_/k will result. (2) At z ~ 2.5 the number of Lyα forest clouds is observed to decrease rapidly, with the number dN/dz ~ (1 + z)^2.4^. This constrains the clouds to be pressure confined at that time, since gravity-confined clouds would evolve too slowly. (3) The large number of observed low z forest clouds (slower evolution since z ~ 2.5) requires a large value of P_ext_/k and j ~> 3. Gravity confinement may lead to evolution that is too slow, unless j <~ 0 or unless the gravity-confined clouds are mixed with some more rapidly evolving pressure-confined clouds. Combining the various arguments we find the best model has P_ext_/k ~ 1 cm^-3^ K and ζ ~ 10^-14^ s^-1^ at present. Much smaller values of the pressure seem unlikely. There are certain parallels between lines of sight through the outer HI disk of spiral galaxy with increasing radius, and the progression from damped, to Lyman limit, to forest clouds. We discuss briefly the possibility that at least some of the observed low z forest clouds may be a separate population associated with galaxies, as suggested by the observations of Bahcall et al. This population could dominate the forest at present if the dark matter attached to galaxies should lead to gravity confinement for this disk population, while the isolated clouds remain pressure confined. The formalism developed in this paper will allow a more detailed study. We also discuss a more general parameter study of the equilibrium configuration of slabs, including mock gravity and Lyα photon trapping. Although mock gravity on dust does not impact the analysis of Lyα clouds at z <~ 5, it may affect early growth of small scale structure at higher z.