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The Detection of the Imprint of Filaments on Cosmic Microwave Background Lensing

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The Detection of the Imprint of Filaments on Cosmic Microwave Background Lensing LETTERS https://doi.org/10.1038/s41550-018-0426-z The detection of the imprint of filaments on cosmic microwave background lensing Siyu He 1,2,3*, Shadab Alam4,5, Simone Ferraro6,7, Yen-Chi Chen8 and Shirley Ho1,2,3,6 Galaxy redshift surveys, such as the 2-Degree-Field Survey where n is the angular position, Πf(,nz ) is the angular posi- 1 2 (2dF) , Sloan Digital Sky Survey (SDSS) , 6-Degree-Field Survey tion of the closest point to n on the nearest filament and ρf (,nz ) 3 4 (6dF) , Galaxy And Mass Assembly survey (GAMA) and VIMOS is the uncertainty of the filament at Πf(,nz ). Using the inten- Public Extragalactic Redshift Survey (VIPERS)5, have shown that sity map at each redshift bin, we construct the filament intensity the spatial distribution of matter forms a rich web, known as the overdensity map via cosmic web6. Most galaxy survey analyses measure the ampli- tude of galaxy clustering as a function of scale, ignoring informa- In(,zz)d −Ī In(,zz)dΩ d tion beyond a small number of summary statistics. Because the ∫∫n δf()n = , Ī = , (2) matter density field becomes highly non-Gaussian as structure Ī ∫ dΩn evolves under gravity, we expect other statistical descriptions of the field to provide us with additional information. One way to study the non-Gaussianity is to study filaments, which evolve where Ωn is the solid angle at n. non-linearly from the initial density fluctuations produced in the In this work, we use the CMB lensing convergence map (pub- primordial Universe. In our study, we report the detection of lens- licly available at http://pla.esac.esa.int/pla/#cosmology) from the ing of the cosmic microwave background (CMB) by filaments, Planck22 satellite experiment. The Planck mission has reconstructed and we apply a null test to confirm our detection. Furthermore, the lensing potential of the CMB from a foreground-cleaned map we propose a phenomenological model to interpret the detected synthesized from the Planck 2015 full-mission frequency maps signal, and we measure how filaments trace the matter distribu- using the SMICA code23. The lensing convergence is defined in tion on large scales through filament bias, which we measure to terms of the lensing potential ϕ as be around 1.5. Our study provides new scope to understand the environmental dependence of galaxy formation. In the future, the 1 2 κϕ()nn=∇ () (3) joint analysis of lensing and Sunyaev–Zel’dovich observations 2 n might reveal the properties of ‘missing baryons’, the vast major- ity of the gas that resides in the intergalactic medium, which has We measure the cross angular power spectrum (the angular so far evaded most observations. power spectrum of the cross-correlation) of CMB lensing conver- Cross-correlations of CMB lensing with tracers of large-scale structure gence and filaments κf using standard techniques (see ‘Estimator’ Cl have been widely studied7–17. In our study, we detect the imprint of fila- in Methods section). We compute the error for each power spec- ments on CMB lensing by cross-correlating filaments with the CMB lens- trum by jackknife resampling the observed area into 77 equally ing convergence (κ) map. We use a filament intensity map derived from weighted regions (see Supplementary Section 1 and Supplementary the Cosmic Web Reconstruction filament catalogue18 (publicly available at Fig. 2) that comprise the CMASS galaxy survey from where the fila- https://sites.google.com/site/yenchicr/catalogue) from the SDSS2 Baryon ments are detected. Oscillations Spectroscopic Survey19 Data Release 12 (DR 12)20. The fila- We construct a phenomenological model to describe the cross- ment finder (see Methods section) partitions the Universe from z = 0.005 correlation of filaments and the CMB lensing convergence field. to z =​ 0.700 into slices with Δ z =​ 0.005. In our study, we use the filaments Instead of modelling the filament profile on small scales24–26, our from z = 0.450 to z =​ 0.700 that are detected from the CMASS galaxy sur- model studies how filaments trace matter distribution on large vey (a galaxy sample from SDSS that targets high redshift). Filaments are scales through the use of the filament bias. We assume a Λ CDM found in each redshift bin as the density ridge of the smoothed galaxy cosmology with Planck parameters from the 2013 release27, where 21 density field , and the filament uncertainty, which describes the uncer- Ωm = 0.315, h = 0.673, σ8 = 0.829 and ns =​ 0.9603. In a spatially flat tainty of the filament position, is also calculated (see Methods). The fila- Friedmann–Robertson–Walker universe described by general rela- ment intensity, illustrated in Supplementary Fig. 1, is defined as tivity, the convergence field is 2 1 ∥−nnΠf(,z)∥ χCMB χχ()−χ In(, z) = exp− (1) CMB 2 2 κρ()nG=π4 N0 (1 + zn)(δχm ,)dχ (4) 2(ρ nz,) ̄∫0 2(πρf nz,) f χCMB 1Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, USA. 2McWilliams Center for Cosmology, Carnegie Mellon University, Pittsburgh, PA, USA. 3Lawrence Berkeley National Laboratory, Berkeley, CA, USA. 4Institute for Astronomy, University of Edinburgh, Edinburgh, UK. 5Royal Observatory, Blackford Hill, Edinburgh, UK. 6Berkeley Center for Cosmological Physics, University of California, Berkeley, CA, USA. 7Miller Institute for Basic Research in Science, University of California, Berkeley, CA, USA. 8Department of Statistics, University of Washington, Seattle, WA, USA. *e-mail: [email protected] NatURE AstRONOMY | VOL 2 | MAY 2018 | 401–406 | www.nature.com/natureastronomy 401 © 2018 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. © 2018 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. LETTERS NATURE ASTRONOMY 54 where χ is the comoving radial distance, z is the redshift observed Mean at radial distance, GN is Newton’s gravitational constant, ρ0̄ is the 300 Median 48 present-day mean density of the Universe, and χCMB is the comoving 42 distance to the CMB. On a linear scale, we assume that filaments 250 36 trace the matter as δf = bfδm, where bf is defined as the large-scale 200 filament bias. 30 On a large scale, we expect the filament overdensity δf to be 150 24 related to the matter fluctuations through a linear filament bias bf: 18 100 Filament length (Mpc) 12 δδff()nb= fz()m(,nz)dz (5) ∫ 50 6 where f(z) is the mean redshift distribution of the filament intensity, 0 0 0.45 0.50 0.55 0.60 0.65 defined as Redshift (z) Fig. 1 | The filament length as a function of redshift. The orange (red) Fz() 1 fz()==,(Fz) In(,z)dΩn (6) crosses are the mean (median) of the filament length in each redshift bin, Fz()dz Δz ∫ ∫ where the error bars come from the standard error of the mean (median). The large difference in the mean and the median values implies that the filament length distribution is not Gaussian. The background mesh where In(, z) is the filament intensity defined in equation (1) and plot shows the 2D histogram of the number of filaments as a function of Δ z is the width of a redshift slice. In cross-correlation, on scales the redshift and the filament length. The magnitude of the histogram is smaller than the typical filament length, using filaments introduces represented by the colour bar on the right. additional smoothing compared with the true matter density. We model the smoothing as follows: the filaments have typical length, and we lose all small-scale information about fluctuations along the To check the validity of our model, we also compare the results filament; therefore, we take the corresponding filament power spec- to simulations. The excellent agreement that we find in simulations trum to be exponentially suppressed below the filament scale k|| ≈ 1/ provides an important consistency check. The theoretical predic- κf (filament length) in Fourier space. Similarly, any matter in between tion for Cℓ is shown in equation (7). The matter–filament correla- mf filaments is either assigned to a filament or eliminated from the tion Cℓ is defined as catalogue (in underdense regions). For this reason we also intro- duce a suppression in power in the direction perpendicular to the z mf 2 Hz() −2 ℓ filaments, with suppression scale k⊥. We use two ways to model k⊥. Czd fz() ()zP , z (9) ℓ = ∫ χ mf The detailed models are shown later in the paper. Using the Limber z1 c χ()z approximation28 and the smoothing scale for small scales, the fila- ment–convergence cross-correlation can be written as By taking the parameters that are slowly varying compared with f2(z), we get 2 z κf 3H0 Ωm,0 2 −2 ℓ C d(zW zf)(zz)()(1 zP) ,(z 7) 2 ℓ =+2 ∫ χ mf 3(HWzz)(1 ) 2c z1 χ()z κf 0 Ωm,0 + mf C = C (10) ℓℓ2(cH z) ()z where Wz()=−χ()z 1 χ is the CMB lensing kernel, ℓ is the ()χCMB For the filament catalogue, the effective redshift, defined as the angular scale in spherical harmonics and Pmf is modelled as weighted mean redshift of filament intensity, is 0.56. This approx- imation is not perfect, leading to a systematic bias in the predic- 1 22 κf −∕(ckkos()ϕϕ⊥∣()zk)(−∕sin( )(kz∣ )) tion for Cℓ . We propose an estimator for this systematic bias in Pkmf(,zb) = d(ϕ fmPkm ,)ze (8) 2π ∫ Supplementary Section 2 (ref. 14). As shown in Supplementary Fig. 4, the systematic bias is less than 5%. Thus, the approximation only mf where Pmm is the matter power spectrum. Sub- and superscript ref- causes a negligible bias.
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