Beyond the standard Baryon Acoustic Oscillation measurement Florian Beutler 20 April, 2018
Outline of the talk BOSS DR12 BAO measurement. First Measurement of Neutrinos in the BAO Spectrum. A complete FFT-based decomposition formalism for the redshift-space bispectrum. Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 2
The BOSS galaxy survey Third version of the Sloan Digital Sky Survey (SDSS-III). Spectroscopic survey optimised for the measurement of Baryon Acoustic Oscillations (BAO). The galaxy sample includes 1 100 000 galaxy redshifts in the range 0 . 2 < z < 0 . 75. The effective volume is ∼ 6 Gpc 3 . 1000 fibres/redshifts per pointing. The final data release (DR12) covers about 10 000 deg 2 . SDSS now moved on to eBOSS (see Hector’s talk). Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 3
Baryon Acoustic Oscillations Baryon and photon perturbations in the radiation dominated era follow ¨ δ b γ − c 2 s ∇ 2 δ b γ = ∇ 2 Φ + with δ b γ = A cos ( kr s + ϕ ) . Preferred distance scale between galaxies. Can be used as a standard ruler using the CMB calibration. Can be separated from the broadband signal. Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 4
BOSS & BAO 0.2 < z < 0.5 1.08 1.08 1.06 1.06 1.04 1.04 (k) smooth 1.02 1.02 1 1 P(k)/P 0.98 0.98 0.96 0.96 0.94 0.94 pre-recon post-recon 0.92 0.92 0.4 < z < 0.6 1.08 1.08 1.06 1.06 1.04 1.04 (k) D A ∼ 1 . 5 % smooth 1.02 1.02 1 1 P(k)/P 0.98 0.98 H ∼ 2 . 5 % 0.96 0.96 0.94 0.94 [ ] 1 / 3 ∼ 0 . 9 % pre-recon post-recon 0.92 0.92 D 2 D V ∝ A / H 1.08 0.5 < z < 0.75 1.08 1.06 1.06 1.04 1.04 (k) smooth 1.02 1.02 1 1 P(k)/P 0.98 0.98 0.96 0.96 0.94 0.94 pre-recon post-recon 0.92 0.92 0.05 0.1 0.15 0.2 0.25 0.3 0.3 0.05 0.1 0.15 0.2 0.25 0.3 -1 -1 k [h Mpc ] k [h Mpc ] Beutler et al. (2017) Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 5
Fitting the BAO Start with linear P ( k ) and separate the broadband shape, P sm ( k ) , and the BAO feature O lin ( k ) . Include a damping of the BAO feature: [ nl / 2 ] 1 + ( O lin ( k /α ) − 1 ) e − k 2 Σ 2 P sm , lin ( k ) = P sm ( k ) Add broadband nuisance terms A ( k ) = a 1 k + a 2 + a 3 k + a 4 k 2 + a 5 k 3 P fit ( k ) = B 2 P sm , lin ( k /α ) + A ( k ) Marginalize to get L ( α ) . Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 6
correlation function – power spectrum Alam et al. (2016) Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 7
Future of galaxy surveys 1.1 MGS BOSS Ly 1.08 WiggleZ 1.06 1.04 (z) 1.02 Planck V 1 (z)/D 0.98 V D BOSS 0.96 0.94 6dFGS 0.92 0.9 0 0.5 1 1.5 2 2.5 3 3.5 redshift z Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 8
Future of galaxy surveys 1.1 MGS BOSS Ly 1.08 WiggleZ 1.06 DESI (2019) 1.04 (z) 1.02 Planck V 1 (z)/D 0.98 V D BOSS Euclid (start 2021) 0.96 0.94 6dFGS 0.92 0.9 0 0.5 1 1.5 2 2.5 3 3.5 redshift z Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 9
First Measurement of Neutrinos in the BAO Spectrum D. Baumann, F. Beutler, R. Flauger, D. Green, M. Vargas-Magana, A. Slosar, B. Wallisch & C. Yeche (2018) Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 10
Neutrinos in the BAO Spectrum The main effect of neutrinos is to increase the damping of the damping of the spectrum (degenerate with helium fraction). D. Baumann, D. Green & B. Wallisch (2017) Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 11
Neutrinos in the BAO Spectrum The oscillation have been imprinted during radiation domination ¨ δ b γ − c 2 s ∇ 2 δ b γ = ∇ 2 Φ with solutions ( Φ sourced by γ , DM, baryons + ν ) δ b γ = A cos ( kr s )+ δ B sin ( kr s ) = A cos ( kr s + ϕ ) The gravitational sources on the right only impact A , but they cannot change the phase (Bashinsky & Seljak 2003, Baumann et al. 2015). Any fluctuation in the grav. potential which travels faster than the baryon-photon plasma can generate a phase shift (free streaming neutrinos c ν > c γ ). Planck allowed the first detection of the phase shift in the CMB with N eff = 2 . 8 + 1 . 1 − 0 . 4 (Follin et al. 2015). The phase is immune to the effects of nonlinear evolution (Baumann, Green & Zaldarriaga 2017) Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 12
Neutrinos in the BAO Spectrum The oscillation have been imprinted during radiation domination ¨ δ b γ − c 2 s ∇ 2 δ b γ = ∇ 2 Φ with solutions ( Φ sourced by γ , DM, baryons + ν ) δ b γ = A cos ( kr s ) + δ B sin ( kr s ) = A cos ( kr s + ϕ ) The gravitational sources on the right only impact A , but they cannot change the phase (Bashinsky & Seljak 2003, Baumann et al. 2015). Any fluctuation in the grav. potential which travels faster than the baryon-photon plasma can generate a phase shift (free streaming neutrinos c ν > c γ ). Planck allowed the first detection of the phase shift in the CMB with N eff = 2 . 8 + 1 . 1 − 0 . 4 (Follin et al. 2015). The phase is immune to the effects of nonlinear evolution (Baumann, Green & Zaldarriaga 2017) Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 13
Neutrinos in the BAO Spectrum Free-streaming neutrinos overtake the photons, and pull them ahead of the sound horizon. D. Eisenstein, H.-J. Seo & M. White (2007) Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 14
Neutrinos in the BAO Spectrum s ) e − k 2 σ 2 O ( k ) = O lin ( k /α + ( β − 1 ) f ( k ) / r fid nl / 2 D. Baumann, F. Beutler, R. Flauger, D. Green, M. Vargas-Magana, A. Slosar, B. Wallisch & C. Yeche (2018) Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 15
Neutrinos in the BAO Spectrum s ) e − k 2 σ 2 O ( k ) = O lin ( k /α + ( β − 1 ) f ( k ) / r fid nl / 2 → This is a proof of principle for extracting information on light relics from galaxy clustering data. D. Baumann, F. Beutler, R. Flauger, D. Green, M. Vargas-Magana, A. Slosar, B. Wallisch & C. Yeche (2018) Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 16
Neutrinos in the BAO Spectrum D. Baumann, F. Beutler, R. Flauger, D. Green, M. Vargas-Magana, A. Slosar, B. Wallisch & C. Yeche (2018) Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 17
A complete FFT-based decomposition formalism for the redshift-space bispectrum N. Sugiyama, S. Saito, F. Beutler & H-J. Seo (2018) Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 18
New decomposition formalism for the bispectrum The estimator is based on the spherical harmonics expansion proposed in Sugiyama et al. (2017), Hand et al. (2017) ( ) ∑ � ℓ 1 ℓ 2 L B ℓ 1 ℓ 2 L ( k 1 , k 2 ) = H ℓ 1 ℓ 2 L m 1 m 2 M m 1 m 2 M ∫ d 2 ˆ ∫ d 2 ˆ × N ℓ 1 ℓ 2 L k 1 k 2 4 π y m 1 ∗ (ˆ 4 π y m 2 ∗ (ˆ k 1 ) k 2 ) ℓ 1 ℓ 2 I ∫ ( ) d 3 k 3 ⃗ k 1 + ⃗ k 2 + ⃗ ( 2 π ) 3 ( 2 π ) 3 δ D × k 3 × δ n ( ⃗ k 1 ) δ n ( ⃗ L ( ⃗ k 2 ) δ n M k 3 ) were y M ∗ -weighted density fluctuation L x ) ≡ y M ∗ δ n M L ( ⃗ (ˆ x ) δ n ( ⃗ x ) L ∫ d 3 x e − i ⃗ L ( ⃗ k · ⃗ δ n M x δ n M k ) = L ( ⃗ x ) √ and y m 4 π/ ( 2 ℓ + 1 ) Y m ℓ = ℓ . Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 19
Why using this formalism This decomposition compresses the data into 2D quantities B ℓ 1 ℓ 2 L ( k 1 , k 2 ) rather than 3D quantities like other decompositions B m ℓ ( k 1 , k 2 , k 3 ) . This reduces the size of the connected covariance matrix. This decomposition allows for a self consistent inclusion of the survey window function. The RSD information is clearly separated into the L multipoles. The complexity of our estimator is O (( 2 ℓ 1 + 1 ) N 2 b N log N ) . Only some multipoles are non-zero: (1) ℓ 1 > ℓ 2 (2) L = even (3) | ℓ 1 − ℓ 2 | ≤ L ≤ | ℓ 1 + ℓ 2 | and (4) ℓ 1 + ℓ 2 + L = even. Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 20
First detection of the anisotropic bispectrum N. Sugiyama, S. Saito, F. Beutler & H-J. Seo (2018) Florian Beutler Beyond the standard Baryon Acoustic Oscillation measurement 20 April, 2018 21
Recommend
More recommend
