= Solution
The <quasar proximity effect> is weaker <Lyman-alpha forest> absorption near a <quasar>'s emission redshift. Extra photons from the <quasar> increase the <photoionization rate> and reduce the neutral fraction without necessarily reducing the total gas density.
For isotropic <specific intensity> $J_\nu$ and a steady, isotropically radiating <quasar> with <spectral luminosity> $L_\nu$, the background and local rates are
$$
\Gamma_{\rm bg}=4\pi\int_{\nu_0}^\infty\frac{J_\nu\sigma_\nu}{h\nu}\,d\nu,\qquad\Gamma_Q(r)=\int_{\nu_0}^\infty\frac{L_\nu\sigma_\nu}{4\pi r^2h\nu}\,d\nu.
$$
Here $r$ is a proper separation small enough that attenuation and expansion across it can initially be neglected, and $\sigma_\nu$ is the hydrogen photoionization cross-section. At fixed density and temperature, <photoionization equilibrium> makes the neutral <column density>, and hence a given line's <optical depth>, scale as
$$
\boxed{\frac{\tau(r)}{\tau_{\rm field}}\simeq\frac{\Gamma_{\rm bg}}{\Gamma_{\rm bg}+\Gamma_Q(r)}.}
$$
The observed <quasar> luminosity supplies $\Gamma_Q(r)$; the distance at which the absorption changes significantly estimates where $\Gamma_Q\sim\Gamma_{\rm bg}$. Adopting a background spectral shape then converts the inferred rate to its <specific intensity>, often quoted near the hydrogen <ionization energy> threshold.
Important uncertainties include an enhanced gas <density contrast> around the host, the unobserved ionizing spectrum, anisotropic emission, source lifetime and variability, the systemic redshift and continuum placement, attenuation between source and absorber, and fluctuations between <lines of sight>. Higher gas density enhances recombination and can partially hide the effect, biasing a simple background estimate upward. https://arxiv.org/abs/0801.1767[Dall'Aglio, Wisotzki and Worseck's 2008 measurements] illustrate the observed sightline scatter and the roles of variability and clustering.
Back to article page
