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