Dark Energy Survey Year 3 results: Measurement of the baryon acoustic oscillations with three-dimensional clustering

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, ${\ensuremath{\xi}}_{\mathrm{p}}$ 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 $4108\text{ }\text{ }{\mathrm{deg}}^{2}$. Our theory modeling includes the impact of realistic true redshift distributions beyond Gaussian photo-$z$ approximation. ${\ensuremath{\xi}}_{\mathrm{p}}$ 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. ${\ensuremath{\xi}}_{\mathrm{p}}$ 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 $19.00\ifmmode\pm\else\textpm\fi{}0.67$ (top-hat) and $19.15\ifmmode\pm\else\textpm\fi{}0.58$ (Gaussian) at ${z}_{\mathrm{eff}}=0.835$. The constraint is weaker than the angular correlation $w$ constraint ($18.84\ifmmode\pm\else\textpm\fi{}0.50$), and we trace this to the fact that the BAO signals are heterogeneous across redshift. While ${\ensuremath{\xi}}_{\mathrm{p}}$ 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, ${\ensuremath{\xi}}_{\mathrm{p}}$ yields $19.80\ifmmode\pm\else\textpm\fi{}0.67$ (top-hat) and $19.84\ifmmode\pm\else\textpm\fi{}0.53$ (Gaussian). The latter is mildly stronger than the $w$ constraint ($19.86\ifmmode\pm\else\textpm\fi{}0.55$). We find that the ${\ensuremath{\xi}}_{\mathrm{p}}$ results are more sensitive to photo-$z$ errors than $w$ because ${\ensuremath{\xi}}_{\mathrm{p}}$ 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. ${\ensuremath{\xi}}_{\mathrm{p}}$ and the angular statistics such as $w$ have their own pros and cons, and they serve an important crosscheck with each other.

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