Estimating the Correlation Length r_0 from the Number of Galaxy Pairs with Similar Redshifts

Abstract

We discuss methods that can be used to estimate the spatial correlation length r_0 of galaxy samples from the observed number of pairs with similar redshifts. The standard method is unnecessarily noisy and can be compromised by errors in the assumed selection function. We present three alternatives, one less noisy, one that responds differently to systematic errors, the third insensitive to the selection function, and quantify their performance by applying them to a cosmological N-body simulation and to the Lyman-break survey of galaxies at redshift z~3. Researchers adopting the standard method could easily conclude that the Lyman-break galaxy comoving correlation length was r_0 \~ 11 Mpc/h, several times larger than the correct value. The use of our proposed methods would make this error impossible, except in the small sample limit. When N_gal<~20, major errors in estimates of r_0 occur alarmingly often.