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

We discuss methods that can be used to estimate the spatial correlationlength r_0 of galaxy samples from the observed number of pairs with similarredshifts. The standard method is unnecessarily noisy and can be compromised byerrors in the assumed selection function. We present three alternatives, oneless noisy, one that responds differently to systematic errors, the thirdinsensitive to the selection function, and quantify their performance byapplying them to a cosmological N-body simulation and to the Lyman-break surveyof galaxies at redshift z~3. Researchers adopting the standard method couldeasily 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 ourproposed methods would make this error impossible, except in the small samplelimit. When N_gal<~20, major errors in estimates of r_0 occur alarmingly often.Comment: 19 pages, accepted for publication in the Ap