Lyman forest

The spectra of high redshift galaxies suffer of a drop in flux below Ly$\alpha$ at $\lambda=1216$Å and a further decline below Ly$\beta$, at $\lambda=1026$Å. These drops are attributed to absorbing neutral hydrogen clouds at different redshifts between the source and the observer, forming the so-called Lyman forest in the spectra of high redshift objects.

Oke & Korycansky (1982), studying a sample of high redshift QSOs, defined two depression factors, $D_A$ and $D_B$, characterizing the amount of absorption between Ly$\alpha$ and Ly$\beta$ and between Ly$\beta$ and the Lyman limit respectively: $D_A = 1 - f_{\rm obs}(\lambda)/f_{\rm int}(\lambda)$, where $f_{\rm obs}(\lambda)$ and $f_{\rm int}(\lambda)$ are the observed and intrinsic fluxes per unit wavelength in the QSO restframe. $D_B$ is defined in the same way as$D_A$. We adopted the estimates given by Madau (1995) for the attenuation of the continuum due to line blanketing as a function of redshift. He found the flux decrements averaged over all the lines of sight to be

$$\left<D_A\right> = 1 - \frac{1}{\Delta \lambda_A}\int_{1050(1+z_{\rm em})}^{1170(1+......ac{\lambda_{\rm obs}}{\lambda_\alpha}\right)^{3.46}\right]\,d\lambda_{\rm obs}$$ (2)

$$\left<D_B\right> = 1 - \frac{1}{\Delta \lambda_B}\int_{920(1+z_{\rm em})}^{1015(1+z......{\lambda_{\rm obs}}{\lambda_j}\right)^{3.46} \right] \,d\lambda_{\rm obs} \: ,$$ (3)

where $\Delta\lambda_A=120(1+z_{\rm em})$Å and $\Delta\lambda_B=95(1+z_{\rm em})$Å. The coefficient $A_2$ relative to the Ly$\alpha$ forest contribution is equal to $3.6\times10^{-3}$. The main contribution to $\left<D_B\right>$, representing the flux decrement caused by all Lyman series lines, belongs to Ly$\beta$, Ly$\gamma$ ($\lambda=973$Å) and Ly$\delta$ ($\lambda=950$Å), whose coefficients are $A_3=1.7\times 10^{-3}$, $A_4=1.2\times 10^{-3}$ and $A_5=9.3\times 10^{-4}$. Figure 5 shows the depression factors $D_A$ and $D_B$ as computed from equations 2 and 3. The fact that$D_B>D_A$ implies that Ly$\beta$ and higher order lines contribute significantly to line blanketing. We have applied Madau's prescriptions to compute the opacity of IGM through the mean factors $\left<D_A\right>$ and $\left<D_B\right>$, whereas we approximated the Lyman continuum absorption setting $f_{\rm obs}(\lambda)=0$ for both observed and synthetic SEDs below $\lambda_{\rm L}$, where $\lambda_{\rm L}=912$Å is the Lyman limit.

Figure:The depression factors $D_A$ and $D_B$ as function of redshift, computed by means of equations 2 and 3 prescribed by Madau (1995).

2000-12-10