Background power subtraction in Lyman-alpha forest

When measuring the one-dimensional power spectrum of the Ly$\alpha$ forest, it is common to measure the power spectrum in flux fluctuations red-ward of the Ly$\alpha$ emission of quasars and subtract this power from the measurements of the Ly$\alpha$ flux power spectrum. This removes excess power present in the Ly$\alpha$ forest which is believed to be dominated by metal absorption by the low-redshift metals uncorrelated with the neutral hydrogen aborbing in Ly$\alpha$. In this brief report we note that, assuming the contaminants are additive in optical depth, the correction contains a second order term. We estimate the magnitude of this term for two currently published measurements of the 1D Ly$\alpha$ flux power spectrum and show that it is negligible for the current generation of measurements. However, future measurements will have to take this into account when errorbars improve by a factor of two or more.