Estimating the Galaxy Correlation Lengthr0from the Number of Galaxy Pairs with Similar Redshifts

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 h -1 Mpc, 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.