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