Gravitational lensing as signal and noise in Lyman-α forest measurements

In Lyman-alpha forest measurements it is generally assumed that quasars are mere background light sources which are uncorrelated with the forest. Gravitational lensing of the quasars violates this assumption. This effect leads to a measurement bias, but more interestingly it provides a valuable signal. The lensing signal can be extracted by correlating quasar magnitudes with the flux-power spectrum and with the flux decrement. These correlations will be challenging to measure but their detection provides a direct measure of how features in the Lyman-alpha forest trace the underlying mass density field. Observing them will test the fundamental hypothesis that fluctuations in the forest are predominantly driven by fluctuations in mass, rather than in the ionizing background, helium reionization, or winds. We discuss ways to disentangle the lensing signal from other sources of such correlations, including dust, continuum, and background residuals. The lensing-induced measurement bias arises from sample selection: one preferentially collects spectra of magnified quasars which are behind overdense regions. This measurement bias is similar to 0.1-1% for the flux-power spectrum, optical depth, and the flux probability distribution. Since the effect is systematic, quantities such as the amplitude of the flux-power spectrum averaged across scales should be interpreted with care.