Systematic effects in the sound horizon scale measurements

We investigate three potential sources of bias in distance estimations made assuming that a very simple estimator of the baryon acoustic oscillation (BAO) scale provides a standard ruler. These are the effects of the non-linear evolution of structure, scale-dependent bias and errors in the survey window function estimation. The simple estimator used is the peak of the smoothed correlation function, which provides a variance in the BAO scale that is close to optimal, if appropriate low-pass filtering is applied to the density field. While maximum-likelihood estimators can eliminate biases if the form of the systematic error is fully modeled, we estimate the potential effects of un- or mis-modelled systematic errors. Non-linear structure growth using the Smith et al. (2003) prescription biases the acoustic scale by <0.3% at z>1 under the correlation-function estimator. The biases due to representative but simplistic models of scale-dependent galaxy bias are below 1% at z>1 for bias behaviour in the realms suggested by halo model calculations, which is expected to be below statistical errors for a 1000 sq.degs. spectroscopic survey. The distance bias due to a survey window function errors is given in a simple closed form and it is shown it has to be kept below 2% not to bias acoustic scale more than 1% at z=1, although the actual tolerance can be larger depending upon galaxy bias. These biases are comparable to statistical errors for ambitious surveys if no correction is made for them. We show that RMS photometric zero-point errors (at limiting magnitude 25 mag) below 0.14 mag and 0.01 mag for redshift z=1 (red galaxies) and z=3 (Lyman-break galaxies), respectively, are required in order to keep the distance estimator bias below 1%.