Large gaps in Ly$\balpha$ forests
due to fluctuations in line distribution

(This appendix was not part of the original paper by A.V. Raveendran and is included here just for illustrative purposes.)

Spectroscopic observations of bright quasars show that the mean number density of Lyα forest lines, which satisfy certain criteria, evolves like dN/dz = A(1 + z)γ, where A and γ are two constants. Given the above intrinsic line distribution we examine the probability of finding large gaps in the Lyα forests. We concentrate here only on the statistics and neglect all observational complications such as the line blending effect (see Ostriker, Bajtlik & Duncan 1988).

Suppose we have observed a Lyα forest between redshifts z1 and z2 and found N - 1 lines. For high-redshift quasars z2 is usually the emission redshift zem and z1 is set to (λLyβ/λLyα)(1 + zem) = 0.844(1 + zem) to avoid contamination by Lyβ lines. We want to know whether the largest gaps observed in the forest are significantly inconsistent with the above line distribution. To do this we introduce a new variable x:

x = $\displaystyle {(1+z)^{\gamma+1}-(1+z_1)^{\gamma+1} \over (1+z_2)^{\gamma+1}-(1+z_1)^{\gamma+1}}$. (4)
x varies from 0 to 1. We then have dN/dx = λ, where λ is the mean number of lines between z1 and z2 and is given by

λ≡$\displaystyle {A[(1+z_2)^{\gamma+1}-(1+z_1)^{\gamma+1}]\over\gamma+1}$. (5)
This means that the Lyα forest lines are uniformly distributed in x. The probability of finding N - 1 lines between z1 and z2, PN-1, is assumed to be the Poisson distribution.
Figure: P( > xgap) as a function of xgap for, from left to right, N = 160, 150, 140, 110, 100, 90, 50, 45 and 40.
\begin{figure} \vspace{11pc} \end{figure}


Subsections