Planck CMB Lensing

Julien CarronOn behalf of Planck’s collaboration

Several slides credit to Antony Lewis

CMB Lensing :

• 2 arcmin deflection of CMB photons on their path from last scattering surface to us by the large scale structure.

• Valuable cosmological signal in itself, that also correlates to large scale structure tracers.

• Very linear (z ~ 2), no intrinsic alignments, no photo-z’s to obtain…

• Lensing potential map always estimated from data via estimators quadratic in CMB data (Okamoto & Hu 2003)

T (n) (±293.0µK)

E(n) (±22.0µK)

B(n) (±2.0µK)

Noisefree, unlensed CMBs, 100 ` 2048

T (n) (±293.0µK)

E(n) (±22.0µK)

B(n) (±2.0µK)

Noisefree, lensed CMBs, 100 ` 2048

T (n) (±297.0µK)

E(n) (±41.0µK)

B(n) (±32.0µK)

Planck noise, unlensed CMBs, 100 ` 2048

T (n) (±297.0µK)

E(n) (±41.0µK)

B(n) (±32.0µK)

Planck noise, lensed CMBs, 100 ` 2048

Methodology

7

Quadratic estimators for a small anisotropy source :

Okamoto & Hu 2003,Hanson & Lewis 2012

Inverse filtering

�

�

First iteration of a vastly more sophisticated max. likelihood procedure, assuming Gaussian unlensed CMB fields. First step enough for Planck.

� ln p[�]

�(n) /Z

dn1,2

✓T

S +N

◆(n1)

�⇠TT (n1, n2)

��(n)

✓T

S +N

◆(n2)

→ Inverse variance filter input maps

→ estimate lensing potential

Filtering

Quadratic Estimator

Power Spectrum Estimation

Filtering

Quadratic Estimator

Data / Sims Data / Sims

Cross-correlation

ϕ Tracer

Filtering

Data / Sims

Filtering

Data / Sims

→ estimate lensing power spectrum.

Planck Lensing Pipeline:

Planck reconstruction noise levels

Planck potential maps are mostly noise. Minimum Variance reconstruction dominated by TT, TE.

S/N = 1

Lensing power spectrum

1.0 5.0 50.0

Planck 2015 ACT

SPTPOLARBEAR

Measurement significanceSPTPOL

�

detected at ~50σ.

CIB provides an independent,

high S/N probe of the lensing

potential.

Cross-correlation with the infrared background

Useful for lensing B-modes, CMB delensing…

CIB(@545GHz)⇥ �

detected at ~10σ.

0

1

2

3

0 500 1000 1500 2000

CBB

` B[10�

6µK

2]

`B

CIB

�TT

�MV

Lensing B-modes

·B

�0.5

0

0.5

1

1.5

2

10 30 50 70 90

L3C

T�

L[10�

2µK]

L

�MV

ISW-lensing at 3σ

Lensing bispectrum

Null tests

14

• Must control a variety of large biases and sources of anisotropy.

« Mean fields »: mask, noise, beams… Mostly large scales. Subtracted using MCs.

Spectrum biases

�2

�1

0

1

2

10 100 500 1000

L

TE ⇥ TE(⇥1) TE ⇥ TE(⇥1)

10 100 500 1000

L

EB ⇥ EB(⇥0.15) EB ⇥ EB(⇥0.15)

10 100 500 1000

L

TB ⇥ TB(⇥0.05) TB ⇥ TB(⇥0.05)

10 100 500 1000

L

EE ⇥ EE(⇥0.5) EE ⇥ EE(⇥0.5)�2

�1

0

1

2Half � ring(⇥200)Half � ring(⇥200) Half �mission(⇥100)Half �mission(⇥100) MV ⇥ MV (⇥15) MV ⇥ MV (⇥15) TT ⇥ TT (⇥15) TT ⇥ TT (⇥15)

[L(L

+1)]2C

L/2⇡[⇥

107]

Curl Curl

CurlCurlCurlCurl

Conservative likelihood uses 40 ≤ L ≤ 400

2015 Null tests

TT Curl

Stable to foregroundsPrel

imina

ryCurl feature seen in all relevant frequency channels, and component separation methods.

• First step of the pipeline requires

• So far, Planck lensing filtering always knew about the mask, but used a constant noise matrix N.

Improving the polarisation analysis

(S +N)�1

0

@TQU

1

A

• Planck noise maps have a huge dynamical range. • We are improving our estimators

using noise variance maps.

log

Improving the polarisation analysis

rad

Homogeneous filtering

Preliminary

Improving the polarisation analysisInhomogeneous filtering

rad

Preliminary

Improving the polarisation analysisPr

elim

inar

y

Prel

imin

ary

DC ��

L

E= C��

L +N0,L +X

L0

N1,LL0C��L0

| {z }N1,L

C��L = (�LL0 +N1LL0)�1

⇣C ��

L0 �N0L0

⌘

• First internal determination of N1

N1 bias

• So far Planck always subtracted a fiducial N1 bias.

• We are now testing N1 deconvolution:(but 2015 likelihood uses full result and recalculates N1 in parameter space)

Dev

iatio

ns w

.r.t.

FFP9

inpu

t sp

ectru

m

Cur

l spe

ctru

m

N1 deconvolution

• Consistent reconstruction (and curl). • Slight improvements in covariance matrix. • (but no expected gain in S/N)

Prelim

inary

23

- New release of CMB lensing products by the end of year.

- Have interest in a particular product or a variant thereof ?

- New maps and simulations reducing map-level systematics.

- Better characterisation of foreground and contaminations - Investigations of null test failures.

- More optimal weighting of polarization improving S/N; improvements from more optimal estimators.

What to expect from Planck lensing ?

Talk to us !

CITA – ICAT

UNIVERSITÀ DEGLI STUDIDI MILANO

ABabcdfghiejkl