Toward an Improved Analytical Description of Lagrangian Bias

We carry out a detailed numerical investigation of the spatial correlationfunction of the initial positions of cosmological dark matter halos. In thisLagrangian coordinate system, which is especially useful for analytic studiesof cosmological feedback, we are able to construct cross-correlation functionsof objects with varying masses and formation redshifts and compare them with avariety of analytical approaches. For the case in which both formationredshifts are equal, we find good agreement between our numerical results andthe bivariate model of Scannapieco & Barkana (2002; SB02) at all masses,redshifts, and separations, while the model of Porciani et al. (1998) does wellfor all parameters except for objects with different masses at smallseparations. We find that the standard mapping between Lagrangian and Eulerianbias performs well for rare objects at all separations, but fails if theobjects are highly-nonlinear (low-sigma) peaks. In the Lagrangian case in whichthe formation redshifts differ, the SB02 model does well for all separationsand combinations of masses, apart from a discrepancy at small separations insituations in which the smaller object is formed earlier and the differencebetween redshifts or masses is large. As this same limitation arises in thestandard approach to the single-point progenitor distribution developed byLacey & Cole (1993), we conclude that a more complete understanding of theprogenitor distribution is the most important outstanding issue in the analyticmodeling of Lagrangian bias.Comment: 22 pages, 8 figures, ApJ, in pres