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We investigate the robustness of baryon acoustic oscillations (BAO)measurements with a photometric galaxy sample using mock galaxy catalogues withvarious sizes of photometric redshift (photo-$z$) uncertainties. We firstconduct the robustness of BAO measurements, assuming we have a perfectknowledge of photo-$z$ uncertainties. We find that the BAO shift parameter$\alpha$ can be constrained in an unbiased manner even for 3% photometricredshift uncertainties up to $z\sim 1$. For instance, $\alpha=1.006 \pm 0.078$with 95% confidence level is obtained from 3% photo-$z$ uncertainty data at$z=1.03$ using the sample of $M_* \ge 10^{10.25} M_{\odot}/h^2$. We also findthat a sparse galaxy sample, e.g. $<2\times10^{-4}$ [$h$ Mpc$^{-1}]^3$ causesadditional noise in the covariance matrix calculation and can bias theconstraint on $\alpha$. Following this, we look into the scenario whereincorrect photometric redshift uncertainties are assumed in the fitting model.We find that underestimating the photo-$z$ uncertainty leads to a degradationin the constraining power on $\alpha$. However, the constrained value of$\alpha$ is not biased. We also quantify the constraining power on $\Omega_{\rmm0}$ assuming the LSST-like covariance and find that the 95% confidence levelis $\sigma(\Omega_{\rm m0})\sim0.03$-$0.05$ corresponding to the photo-$z$uncertainties of 1% to 3% respectively. Finally, we examine whether theskewness in the photometric redshift can bias the constraint on $\alpha$ andconfirm that the constraint on $\alpha$ is unbiased, even assuming a Gaussianphoto-$z$ uncertainty in our model.

Robustness of Baryon Acoustic Oscillations Measurements with Photometric Redshift Uncertainties