BAO Damping and Reconstruction

Cheng Zhao 2015.04.16

Baryon Acoustic Oscillations (BAO) Standard Ruler (100 Mpc/h) • Density fluctuation + pressure → sound wave

https://www.sdss3.org/surveys/boss.php

Daniel Eiensentein

BAO Damping Physical Interpretation • Advancing scale of nonlinear gravitational collapse: • Bulk flow • Supercluster formation • Halo formation (subdominant) • Redshift space distortion (RSD) • Kaiser effect • Finger of God (FoG)

de Lapparent V. et al, 1986 Hamilton 1998

BAO Damping Linear @ z = 49 Simulation @ z = 0 2-point correlation function Power spectra

Eisenstein et al., 2007

BAO Damping Modeling of Power Spectrum 𝑃 𝑘 = 𝑃 𝑙𝑖𝑛 𝑘 − 𝐴 𝑘 𝑃 𝑙𝑖𝑛 𝑛𝑤 𝑘 exp − 𝑘 2 Σ 2 𝑛𝑙 2

BAO Damping Modeling of Power Spectrum 𝑃(𝑘)/𝑃 𝑛𝑤 𝑘 𝑃 𝑙𝑖𝑛 (𝑘/𝛼) = 𝐴(𝑘)𝑃 𝑙𝑖𝑛 𝑛𝑤 (𝑘/𝛼) 𝐴 𝑘 = 𝑎 0 𝑘 𝑎 1 𝐶 𝑘 = 𝑐 0 𝑘 𝑐 1 − 1 exp(− 𝑘 2 Σ 2 𝑛𝑙 2 ) + 1 𝐶(𝑘) Fitting parameters: {𝛼, Σ 𝑛𝑙 , 𝑎 0 , 𝑎 1 , 𝑐 0 , 𝑐 1 }

BAO Damping

Prada et al., 2014

BAO Damping Perturbation Theory: 𝛼 𝑧 − 1 ≈ 0.3716

Σ 𝑛𝑙 = 2 𝐷 𝑧 𝐷 0 1/2 1 3𝜋 2 𝑃 𝑙𝑖𝑛 𝑘 𝑑𝑘

BAO Damping Open symbols: dispersion of dark matter pair separation at BAO scales.

BAO Reconstruction Linear Theory Undo the motion of galaxies.

• Compute the density field 𝛿 • Gaussian filter (to filter out small scale modes) • Predict the linear-theory motion 𝒒 : 𝛻 ∙ 𝒒 = −𝛿 • • Move the particles by −𝒒 FoG compression: move all cluster particles to the center of mass of the cluster

BAO Reconstruction Linear Theory Linear @ z = 49 Simulation @ z = 0 20Mpc/h filter / Without FoG comp.

10Mpc/h filter / With FoG comp.

Eisenstein et al., 2007

BAO Reconstruction Zel’dovich Approximation