Primordial and Doppler modulations with Planck Antony Lewis On behalf of the Planck collaboration

Transcription

1 Primordial and Doppler modulations with Planck Antony Lewis On behalf of the Planck collaboration

2 Outline Primordial modulations and power asymmetry τ NL trispectrum Kinematic Doppler dipoles Note: statistical anisotropy trispectrum T P(T Ω) is statistically anisotropic in direction Ω T P(T, Ω)dΩ is statistically isotropic and non-gaussian

3 Primordial curvature modulation: z=0 θ Mpc z~1000 Squeezed shape large-scale modulations

4 e.g. local NG Long + short modes: ζ 0 = ζ s + ζ l i.e. modulated ζ ζ s 1 + φ with φ = 6f NL 5 ζ l Large-scale modulations CMB bispectrum 6 5 f NLC L Tζ (C l2 + C l3 ) L l 3 l 2 CMB trispectrum 6 5 f NL 2 CL ζ ζ (C l1 + C l2 ) (C l3 + C l4 ) l 1 l 2 L l 3 l 4

5 Pearson, Lewis, Regan arxiv: Define τ NL trispectrum by (almost all S/N at L < 10, half in dipole) Note f O(10 3 ) τ NL 500 f = 6f NL 5 ζ l f = 6f NL 5 ζ l + χ Combined estimator for nearly scale-invariant modulation (optimal to percent level)

6 Just need to reconstruct f( n) to find its power spectrum QML estimator for f: Optimally filtered temperature Pipeline almost identical to CMB lensing, but with different weight functions. General anisotropy estimator is Mean field (estimate from sims) Hanson & Lewis 2009

7 Modulation mean field: mainly noise + mask 143x x217 Avoids uncertainty in noise modelling (mask is well known)

8 Kinematic dipole signal Modulation Illustrated for v c = 0.85 Aberration n n + ( n v) - just like a dipole lensing convergence Challinor & van Leeuwen 2002

9 known dipole amplitude and direction v c Modulation f = x coth x n v b ν n v Planck maps: 100 GHz 143 GHz 217 GHz 353 GHz 545 GHz 857 GHz Approx boost factor b ν = x coth x 2 /2 1 Map modulation amplitude 0.18% 0.24% 0.37% 0.64% 1.1% 1.7% Use 143, 217 only (with dust subtraction from 857) Note: SMICA maps are a complicated mixture; modulation effect not currently included in FFP6 sims

10 Dipole kinematic effect using appropriate quadratic estimators Note: not included in parameter analysis - bias due to aberration average over mask 0.25σ

11 143x217 modulation reconstruction (L 5) - map of estimated modulation field f Kinematics not subtracted Kinematics subtracted in mean field from sims

12 f Modulation pseudo-power spectrum Consistent with zero except for anomalous octopole

13 Anomalous signal seems to be mostly due to may be related to β (frequency dependence from dust?) Octopole signal varies between frequencies: (large auto-quadrupole expected from noise bias)

14 Planck τ NL trispectrum constraint L max = 2 L max = 10 Estimator result Gaussian simulations: Consistent with Gaussian null hypothesis (octopole has small weight) Note: signal most L<5 - small number of modes Skewed distribution Upper limits weaker than you might expect Conservative upper limit, allowing octopole to be physical using Bayesian posterior

15 Scale-dependent dipole modulation and power asymmetries Full analysis suggests no non-kinematic dipole power asymmetry Can also look for scale-dependent effect: filter range of scales used in quadratic estimator (new results, thanks Duncan)

16 Power modulation dipole amplitude for l l max WMAP 5 (Hanson & Lewis 2009) Planck 217x143 (kinematic subtracted) 1% 0.1% Modulation < 1% for l l max = 500 Modulation < 0.2% for l max =

17 Power dipole directions (l l max ) Kinematic subtracted Kinematics not subtracted (as in Doppler paper but here pure modulation estimator)

18 Power dipoles in Δl = 100 bands Kinematic subtracted Kinematics not subtracted

19 Conclusions 5σ detection of kinematic dipole effects in Planck maps Large-scale modulation power nearly consistent with zero after kinematic subtraction (foreground octopole?) Conservative limit τ NL < 2800 (95% CL) Power at l 400 consistent with WMAP and previous analyses (must be maps looks the same) Dipole power modulations at low L do not persist to high L after kinematic subtraction: f < 0.2% at l max = (but possible foreground issues, ongoing work..) Kinematic effects currently not included in Planck isotropy paper results, e.g. hemisphere and patch anisotropy constraints. Different model, mask, maps, filtering so not directly comparable; ongoing work

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21 l 1100 only

22 SMICA (sims subtract aberration but not modulation) Power in Δl = 100 bands Cumulative