## Lyman Alpha Forest II December 8, 2008

Posted by keithkchan in Cosmology.

I continue my discussion on Lyman alpha forest.

Lyman alpha forest is one of the few tools that enables us to probe the structure at $z$~3, and it is still relatively linear.   As you may recall, the observed spectrum from the quasar is very choppy, so it is not surprising that one can only extract the information statistically. It turns out to be useful to regard the whole spectrum as a continuum rather than a background plus absorption lines.

One of the reason that Lyman alpha forest is useful as the IGM satisfies some simple relation.  For IGM, the UV background photoionization and the adiabatic cooling are approximately in equilibrium, so $n_{HI}\Gamma=\alpha_{Rec}n_en_p$, where $n_{HI}$, $n_e$  and $n_p$ are the hydrogen, electron and proton number densities respectively. $\Gamma$ is the photoionization coefficient, and $\alpha_{ \rm Rec }$ is the recombination coefficient. Also the temperature T of the gas  satisfies a power law $T=T_0 (\rho/\bar{\rho})$. The recombination coefficient can be approximated as $\alpha_{\rm Rec }\propto T^{-0.7}$ in the relevant temperature range. Using these relations and the fact that the optical depth $\tau$ is proportional to $n_{HI }$, one can derive

$\tau = A( \rho/ \bar{\rho} )^{\beta}$, where $\beta \approx 1.6$. The expression for A is complicated, and we don’t bother to write it down here.  This relation is called Fluctuating Gunn Peterson Approximation (FGPA). This simple relation turns out to be rather accurate although it has neglected the peculiar velocity, thermal broadening, and shock heating.  From the optical depth, one can get the flux $F = F_c e^{ -\tau }$. Flux is the important, as astronomers only measure fluxes. Therfore it is a central quantity in Lyman alpha forest measurement.

It is not surprising that one needs hydrodynamic simulations in order to capture the details of the forest accurately. A cheap way is to run a gravity only PM N-Body simulation and impose the FGPA.

From Lyman alpha forest, researchers have managed to crank the underlying matter power spectrum, and tested the Gaussian initial conditions. I may talk about more constrints  we may get out from Lyman alpha forest.