Effective window function for Lagrangian halos

2015/11/30 by Kwan Chuen Chan, Ravi K. Sheth, Roman Scoccimarro +1 · 20 citations
Mathematics · Physics and Astronomy · #Astrophysics #Astrophysics and Cosmic Phenomena #Convolution (computer science) #Correlation function (quantum field theory) #Cosmology #Cosmology and Gravitation Theories #Dark energy #Excursion #Function (biology) #Galaxies: Formation, Evolution, Phenomena #Galaxy #Gaussian #Halo #Halo effect #Mathematics #Matter power spectrum #Physics #Quantum mechanics #Spectral density #Statistical physics #Statistics #Window function #astro-ph.CO

paper · pdf · doi:10.1103/physrevd.96.103543

published in Physical review. D/Physical review. D. 96(10) (American Physical Society) · 15 pages, 14 figures, matched the published version, discussion and presentation significantly improved, conclusions unchanged

arxiv created 2017/11/23 · openalex publication_date 2017/11/27 · arxiv updated 2017/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The window function for protohalos in Lagrangian space is often assumed to be a top hat in real space. We measure this profile directly and find that it is more extended than a top hat but less extended than a Gaussian; its shape is well described by rounding the edges of the top hat by convolution with a Gaussian that has a scale length about 5 times smaller. This effective window W_eff is particularly simple in Fourier space, and has an analytic form in real space. Together with the excursion set bias parameters, W_eff describes the scale-dependence of the Lagrangian halo-matter cross correlation up to kR_Lag\ensuremath∼10, where R_Lag is the Lagrangian size of the protohalo. Moreover, with this W_eff, all the spectral moments of the power spectrum are finite, allowing a straightforward estimate of the excursion set peak mass function. This estimate requires a prescription of the critical overdensity enclosed within a protohalo if it is to collapse, which we calibrate from simulations. We find that the resulting estimate of halo abundances is only accurate to about 20%, and we discuss why: a top hat in ``infall time'' towards the protohalo center need not correspond to a top hat in the initial spatial distribution, so models in which infall rather than smoothed overdensity is the relevant variable may be more accurate.

Citations

• Excursion set peaks: a self-consistent model of dark halo abundances and clustering
• Bias deconstructed: unravelling the scale dependence of halo bias using real-space measurements
• Lagrangian bias in the local bias model
• Redshift space correlations and scale-dependent stochastic biasing of density peaks
• Testing tidal-torque theory - II. Alignment of inertia and shear and the characteristics of protohaloes
• Halo Assembly Bias in Hierarchical Structure Formation
• One step beyond: the excursion set approach with correlated steps
• Toward a Halo Mass Function for Precision Cosmology: The Limits of Universality