The three-dimensional correlation function offers an effective way to summarize the correlation of the large-scale structure even for imaging galaxy surveys. We have applied the projected three-dimensional correlation function, ${\xi }_{\mathrm{p}}$ to measure the baryonic acoustic oscillations (BAO) scale on the first-three years Dark Energy Survey data. The sample consists of about 7 million galaxies in the redshift range $0.6<z_{\mathrm{p}}<1.1$ over a footprint of $4108{\mathrm{deg}}^2$. Our theory modeling includes the impact of realistic true redshift distributions beyond Gaussian photo-$z$ approximation. ${\xi }_{\mathrm{p}}$ is obtained by projecting the three-dimensional correlation to the transverse direction. To increase the signal-to-noise of the measurements, we have considered a Gaussian stacking window function in place of the commonly used top-hat. ${\xi }_{\mathrm{p}}$ is sensitive to $D_{\mathrm{M}}(z_{\mathrm{eff}})/r_{\mathrm{s}}$, the ratio between the comoving angular diameter distance and the sound horizon. Using the full sample, $D_{\mathrm{M}}(z_{\mathrm{eff}})/r_{\mathrm{s}}$ is constrained to be $19.00\pm 0.67$ (top-hat) and $19.15\pm 0.58$ (Gaussian) at $z_{\mathrm{eff}}=0.835$. The constraint is weaker than the angular correlation $w$ constraint ($18.84\pm 0.50$), and we trace this to the fact that the BAO signals are heterogeneous across redshift. While ${\xi }_{\mathrm{p}}$ responds to the heterogeneous signals by enlarging the error bar, $w$ can still give a tight bound on $D_{\mathrm{M}}/r_{\mathrm{s}}$ in this case. When a homogeneous BAO-signal subsample in the range $0.7<z_{\mathrm{p}}<1.0$ ($z_{\mathrm{eff}}=0.845$) is considered, ${\xi }_{\mathrm{p}}$ yields $19.80\pm 0.67$ (top-hat) and $19.84\pm 0.53$ (Gaussian). The latter is mildly stronger than the $w$ constraint ($19.86\pm 0.55$). We find that the ${\xi }_{\mathrm{p}}$ results are more sensitive to photo-$z$ errors than $w$ because ${\xi }_{\mathrm{p}}$ keeps the three-dimensional clustering information causing it to be more prone to photo-$z$ noise. The Gaussian window gives more robust results than the top-hat as the former is designed to suppress the low signal modes. ${\xi }_{\mathrm{p}}$ and the angular statistics such as $w$ have their own pros and cons, and they serve an important crosscheck with each other.

• Received 13 October 2022
• Accepted 21 November 2022

DOI:https://doi.org/10.1103/PhysRevD.106.123502