Bias deconstructed: unravelling the scale dependence of halo bias using real-space measurements

We explore the scale dependence of halo bias using real-space cross-correlation measurements in N-body simulations and in PINOCCHIO, an algorithm based on Lagrangian Perturbation Theory. Recent work has shown how to interpret such real-space measurements in terms of k-dependent bias in Fourier space, and how to remove the k-dependence to reconstruct the k-independent peak-background split halo bias parameters. We compare our reconstruction of the linear bias, which requires no free parameters, with previous estimates from N-body simulations which were obtained directly in Fourier space at large scales, and find very good agreement. Our reconstruction of the quadratic bias is similarly parameter-free, although in this case there are no previous Fourier space measurements to compare with. Our analysis of N-body simulations explicitly tests the predictions of the excursion set peaks (ESP) formalism of Paranjape et al. for the scale dependence of bias; we find that the ESP predictions accurately describe our measurements. In addition, our measurements in PINOCCHIO serve as a useful, successful consistency check between PINOCCHIO and N-body simulations that is not accessible to traditional measurements.