The small scale power asymmetryin the cosmic microwave background

Samuel Flender

University of Helsinki

September 3, 2013

[Flender, Hotchkiss, arXiv:1307.6069 (2013),accepted for publication in JCAP]

1

Motivation

I There is a hemispherical power asymmetry in the CMB onthe large scales (` = 2− 600).

I There is no asymmetry on the small scales(` = 601− 2048).

2

The hemispherical power asymmetry: overview

I Eriksen et al, Hansen et al 2004:The hemisphere centred at (l , b) = (237◦,−20◦) has significantlymore power than the opposite one, in the multipole range` = 2− 40.

I Gordon et al 2007: Asymmetry fits a dipolar modulation,

δT = δTiso(1 + Ap · n) (1)

I Eriksen, Hansen et al 2009: Asymmetry persists up to `max = 600

3

The hemispherical power asymmetry: overview

I Planck 2013:I Confirmation of the asymmetry up to ` = 600I Asymmetry can be seen up to much higher multipoles

010

0020

0040

0050

00

Positive directionNegative direction

0.07

0 400 800 1200 1600 2000

ℓ(ℓ+1)C

ℓ/2π

[ µK

2]

ℓ

∆C

ℓ/C

ℓ

Figure: Asymmetry along (l , b) = (224◦, 0◦) (Planck 2013 XXIII)

4

Question

I How much new information about the asymmetry comes from thehigh multipoles ` = 601− 2048 alone?

5

Methodology

I Method: (based on Hansen et al (2009))I Calculate the local power in a disc of 90◦ diameter centred at

(l , b) = (224◦, 0◦) and opposite disc

I Calculate the relative power difference ∆` ≡C+`−C−

`

C+`

between the

two discsI CMB data: Planck’s SMICA mapI Mask:

I SMICA confidence mask (89%)I ‘M74’ (74%)

I We apply the same method to 1000 random realisations of the CMB.

Figure: SMICA map with SMICA mask (left) and M74 mask (right) applied. 6

Results

∆` ≡C+` −C

−`

C+`

0 200 400 600 800 1000 1200 1400 1600 1800 2000−30

−20

−10

0

10

20

30

ℓ

∆ℓ[%

]

smica mask

M74 mask

Figure: ∆` along (l , b) = (224◦, 0◦) in the SMICA map with SMICA mask (red)and M74 mask (blue) applied. The red and blue bands are the 1σ-regions fromthe corresponding values found in 1000 simulations.

7

Results

∆` ≡C+` −C

−`

C+`

0 200 400 600 800 1000 1200 1400 1600 1800 2000−30

−20

−10

0

10

20

30

ℓ

∆ℓ[%

]

smica mask

M74 mask

∆̄ll ≡1

599

600∑

`=2

∆` ∆̄hl ≡1

1448

2048∑

`=601

∆`

8

Results

I Low multipoles (` = 2− 600):I ∆̄ll = 6.62% (3σ) with the SMICA maskI ∆̄ll = 6.90% (2.5σ) with the M74 maskI consistent with previous results.

9

Results

I High multipoles (` = 601− 2048):I ∆̄hl = 7.01% (6.5σ) (p ∼ 10−10 !) with SMICA maskI ∆̄hl = 4.23% (3.6σ) with the M74 mask

0 1 2 3 4 5 6 7 8

0

20

40

60

80

100

120

140

∆̄hl [ %]

−6 −4 −2 0 2 4 6

0

20

40

60

80

100

120

140

160

180

∆̄hl [ %]

Figure: Distribution of ∆̄hl values in the simulations with SMICA

mask (left) and M74 (right) applied. The red line indicates the valuein the SMICA map.

10

Results

I However, in the calculation of the high-` we need to take intoaccount the following effects:

1. Relativistic power modulation2. Edge effects from the mask applied3. Inter-scale correlations

11

Relativistic power modulation

I The motion of our Galaxy causes a relativistic power modulation inthe direction of motion, (l , b) = (264◦, 48◦)

Figure: Direction of the CMB dipole (Planck XXVII)

I This contaminates the asymmetry along (l , b) = (224◦, 0◦)

I estimated contamination to our measure:

∆̄rel = 0.43%− 1.08% (2)

12

Edge effects

I After applying a mask, the cut sky map has sharp edgesI If one of the discs contains more edges, this creates an artificial

asymmetry.I This is clearly the case for the SMICA mask:

I We solve this by smoothing the mask with a Gaussian filter(FWHM = 10′) before applying it to the map.

13

Edge effects

0 200 400 600 800 1000 1200 1400 1600 1800 2000−30

−20

−10

0

10

20

30

ℓ

∆ℓ[%

]

smica mask

M74 mask

0 200 400 600 800 1000 1200 1400 1600 1800 2000−30

−20

−10

0

10

20

30

ℓ

∆ℓ[%

]

smoothed smica mask

smoothed M74 mask

14

Edge effects

I Before smoothing:I ∆̄hl = 7.01% (6.5σ) with SMICA maskI ∆̄hl = 4.23% (3.6σ) with M74 mask

I After smoothing:I ∆̄hl = 1.52% (4σ) with smoothed SMICA maskI ∆̄hl = 1.79% (4.1σ) with smoothed M74 mask

I After smoothing the SMICA mask, the significance dropsfrom 6.5σ to 4σ.

I Significant alignment between edges of the SMICA mask and theSMICA map.

I Edges in the SMICA mask are correlated with regions of high variancein the SMICA map.

15

Inter-scale correlations

I In the analysis of an incomplete sky large scale power gets weaklycorrelated with small scale power (Wandelt et al 2000)

I A part of the asymmetry on large scales gets imprinted into thesmall scales.

I We create to 1000 constrained simulations:

constraint : ∆̄ll ≥ ∆̄SMICAll = 6.9% (3)

16

Corrected results

0 1 2 3 4 5 6 7 8

0

20

40

60

80

100

120

140

∆̄hl [ %]

−6 −4 −2 0 2 4 6

0

20

40

60

80

100

120

140

160

180

∆̄hl [ %]

−1.5 −1 −0.5 0 0.5 1 1.5 2 2.5

0

50

100

150

200

250

300

∆̄hl [ %]

−1.5 −1 −0.5 0 0.5 1 1.5 2 2.5

0

50

100

150

200

250

∆̄hl [ %]

Figure: Results after corrections (left SMICA mask, right M74)

17

Corrected results

I After correcting for all systematic effects the significance of thesmall-scale asymmetry drops to the 1σ-level.

I There is no significant power asymmetry in the small scales /high multipoles (` = 601− 2048).

18

Implications for theoretical models

I Dipolar modulation δT = δTiso(1 + A(k) p · n)

I Constraint on the dipolar modulation amplitude:

A(k) < 0.0045 at k−1 ∼ 10 Mpc (95% C.L.) (4)

I Tighter than the quasar-constraint,|A(k)| < 0.012 at k−1 ∼ 10 Mpc (95% C.L.)

I A(k) must be running!Theoretical models that produce asymmetry on large scalesmust not produce asymmetry on small scales.

19

Thank you!

[Flender, Hotchkiss, arXiv:1307.6069 (2013),accepted for publication in JCAP]

20