Robustness of Baryon Acoustic Oscillations Measurements with Photometric Redshift Uncertainties

Abstract

We investigate the robustness of baryon acoustic oscillations (BAO) measurements with a photometric galaxy sample using mock galaxy catalogs with various sizes of photometric redshift (photo-$z$) uncertainties. We first investigate the robustness of BAO measurements, assuming we have a perfect knowledge of photo-$z$ uncertainties. We find that the BAO shift parameter $\alpha$ can be constrained in an unbiased manner for various sizes of photometric redshift uncertainties at $z=0.251$, $0.617$, and $1.03$ as long as the number density of galaxies is high. A sparse galaxy sample causes additional noise in the covariance matrix calculation and it can bias the constraint on $\alpha$. Next, we investigate the scenario where incorrect photometric redshift uncertainties are assumed in the fitting model and find that underestimating the photo-$z$ uncertainty leads to a degradation in the constraining power on $\alpha$. In addition, we investigate BAO measurements with a cross-correlation signal between a spec-$z$ sample and a photo-$z$ sample. We find BAO constraints are unbiased and slightly tighter than the auto-correlation signal of a photo-$z$ sample. We also quantify the constraining power on $\Omega_{\rm m0}$ assuming the LSST-like covariance and find that the 95\% confidence level is $\sigma(\Omega_{\rm m0})\sim0.03$-$0.05$ corresponding to the photo-$z$ uncertainties of 1\% to 3\% respectively. Finally, we examine whether the skewness in the photometric redshift can bias the constraint on $\alpha$ and confirm that the constraint on $\alpha$ is unbiased even if we use a fitting model assuming a Gaussian photo-$z$ uncertainty.Comment: 10 pages, 11 figures, 3 table