The bias of weighted dark matter haloes from peak theory

We give an analytical form for the weighted correlation function of peaks in a Gaussian random field. In a cosmological context, this approach strictly describes the formation bias and is the main result here. Nevertheless, we show its validity and applicability to the evolved cosmological density field and halo field, using Gaussian random field realizations and dark matter N-body numerical simulations. Using this result from peak theory, we compute the bias of peaks (and dark matter haloes) and show that it reproduces results from the simulations at the {{O}}(10 per cent) level. Our analytical formula for the bias predicts a scale-dependent bias with two characteristics: a broad-band shape which, however, is most affected by the choice of weighting scheme and evolution bias, and a more robust, narrow feature localized at the baryon acoustic oscillation (BAO) scale, an effect that is confirmed in simulations. This scale-dependent bias smooths the BAO feature but, conveniently, does not move it. We provide a simple analytic formula to describe this effect. We envision that our analytic solution will be of use for galaxy surveys that exploit galaxy clustering.