Background power subtraction in Lyα forest

When measuring the one-dimensional (1D) power spectrum of the Lyman-α (Lyα) forest, it is common to measure the power spectrum in the flux fluctuations redward of the Lyα emission of quasars, and to subtract this power from the measurements of the Lyα flux power spectrum. This removes the excess power present in the Lyα forest, which is believed to be dominated by metal absorption of low-redshift metals uncorrelated with the neutral hydrogen absorbtion in Lyα. In this paper we note that, assuming the contaminants are additive in the optical depth, the correction contains a second-order term. We estimate the magnitude of this term for two currently published measurements of the 1D Lyα flux power spectrum and show that it is negligible for the current generation of measurements. However, future measurements must take this effect into account when the error bars improve by a factor of 2 or more.