# Optimized Clustering Estimators for BAO Measurements Accounting for Significant Redshift Uncertainty

## TL;DR

This paper develops an optimized clustering statistic for BAO measurements in galaxy samples with significant redshift uncertainty, demonstrating near-optimal results using simulations and providing a method for improved distance measurements in photometric surveys.

## Contribution

The paper introduces a new optimized clustering estimator tailored for high redshift uncertainty, validated with extensive simulations, enhancing BAO analysis in photometric galaxy surveys.

## Key findings

- Clustering along the LOS is nearly evenly spread in observed space for high redshift uncertainty.
- Projected separation clustering captures nearly all BAO information for $\sigma_z extgreater= 0.02(1+z)$.
- Predicted 5% distance measurement accuracy for DES Y1 using the new method.

## Abstract

We determine an optimized clustering statistic to be used for galaxy samples with significant redshift uncertainty, such as those that rely on photometric redshifts. To do so, we study the baryon acoustic oscillation (BAO) information content as a function of the orientation of galaxy clustering modes with respect to their angle to the line-of-sight (LOS). The clustering along the LOS, as observed in a redshift-space with significant redshift uncertainty, has contributions from clustering modes with a range of orientations with respect to the true LOS. For redshift uncertainty $\sigma_z \geq 0.02(1+z)$ we find that while the BAO information is confined to transverse clustering modes in the true space, it is spread nearly evenly in the observed space. Thus, measuring clustering in terms of the projected separation (regardless of the LOS) is an efficient and nearly lossless compression of the signal for $\sigma_z \geq 0.02(1+z)$. For reduced redshift uncertainty, a more careful consideration is required. We then use more than 1700 realizations (combining two separate sets) of galaxy simulations mimicking the Dark Energy Survey Year 1 sample to validate our analytic results and optimized analysis procedure. We find that using the correlation function binned in projected separation, we can achieve uncertainties that are within 10 per cent of those predicted by Fisher matrix forecasts. We predict that DES Y1 should achieve a 5 per cent distance measurement using our optimized methods. We expect the results presented here to be important for any future BAO measurements made using photometric redshift data.