ESTIMATING THE GALAXY CORRELATION LENGTH r0 FROM THE NUMBER OF GALAXY PAIRS WITH SIMILAR REDSHIFTS

We discuss methods that can be used to estimate the spatial correlation length r0 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 Lymanbreak survey of galaxies at redshift z ∼ 3. Researchers adopting the standard method could easily conclude that the Lyman-break galaxy comoving correlation length was r0 ∼ 11h −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 Ngal < ∼ 20, major errors in estimates of r0 occur alarmingly often. Subject headings: galaxies: high-redshift — large-scale structure of universe — methods: statistical