Lagrangian Perturbation Theory for Biased Tracers: Significance of the Number Conservation

Abstract

The Lagrangian perturbation theory provides a simple yet powerful way of computing the nonlinear matter power spectrum, and it has been applied to biased tracers such as halos and galaxies. The number conservation of matter particles allows a simple relation between the fluctuations at the initial and the late times, which is essential in deriving the exact expression for the nonlinear matter power spectrum. Here we investigate the significance of the number conservation in the Lagrangian perturbation theory for biased tracers. We use $N$-body simulations to test the significance of number conservation by tracing dark matter halo samples in time. For the mass bin sample $\Delta \log M_h(h^{-1}{M}_{\odot })=0.5$ at $z\simeq 3$, the theoretical predictions for the halos overestimates the power spectrum at $z=0$ by a factor of three, while the simulation results match the theoretical predictions if the number conservation of halos is imposed in the simulations throughout the evolution. Starting with a halo sample at $z=0$ as another test, we trace back in time the particles that belong to the halos at~$z=0$ and use their center-of-mass positions as halo positions at $z>0$. The halo power spectra at $z>0$ from the simulations agree with the theoretical predictions of the Lagrangian perturbation theory. This numerical experiment proves that the number conservation is crucial in the Lagrangian perturbation theory predictions. We discuss the implications for various applications of the Lagrangian perturbation theory for biased tracers.

8 pages, 3 figures, accepted for publication in ApJ

References in corpus (12)

• Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space
• The Evolution of Galaxy Number Density at z < 8 and its Implications
• Blinded challenge for precision cosmology with large-scale structure: results from effective field theory for the redshift-space galaxy power spectrum
• Nonlinear Perturbation Theory Integrated with Nonlocal Bias, Redshift-space Distortions, and Primordial Non-Gaussianity
• Redshift-Space Distortions in Lagrangian Perturbation Theory
• Consistent Modeling of Velocity Statistics and Redshift-Space Distortions in One-Loop Perturbation Theory
• Calibrating the Baryon Oscillation Ruler for Matter and Halos
• The Gaussian streaming model and Lagrangian effective field theory
• Baryon acoustic signature in the clustering of density maxima
• Lagrangian perturbation theory at one loop order: successes, failures, and improvements
• An $n$-th order Lagrangian Forward Model for Large-Scale Structure
• Large-scale structure perturbation theory without losing stream crossing