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The Clipped Power Spectrum
Fergus SimpsonUniversity of Edinburgh
FS, James, Heavens, Heymans (2011 PRL)FS, Heavens, Heymans (arXiv:1306.6349)
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Outline
Introduction to Clipping Part I: The Clipped Bispectrum Part II: The Clipped Power Spectrum
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Outline
Introduction to Clipping Part I: The Clipped Bispectrum Part II: The Clipped Power Spectrum
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Ripples
Waves(hard)
(easy)
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…but also spatial dependence:
Accuracy of Perturbation TheoryNot only time dependence…
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Local Density Transformations
• Reduce nonlinear contributions by suppressing high density regions
Neyrinck et al (2009)
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Clipping
• Typically only 1% of the field is subject to clipping
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Outline
Introduction to Clipping Part I: The Clipped Bispectrum Part II: The Clipped Power Spectrum
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The Bispectrum
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The Clipped Bispectrum
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The Clipped Bispectrum
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The Clipped Bispectrum
FS, James, Heavens, Heymans PRL (2011)
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Part I Summary >104 times more triangles available after clipping
Enables precise determination of galaxy bias
BUT
Why does it work to such high k?
What about P(k)?
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Outline
Introduction to Clipping Part I: The Clipped Bispectrum Part II: The Clipped Power Spectrum
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The Power Spectrum
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The Clipped Power Spectrum
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The Clipped Power Spectrum
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δ (x)
δ (x) = δG +O(δG2 ) +O(δG
3 ) + δ X
Clipped Perturbation Theory
• Reduce contributions from by suppressing regions with large
δcδ c = δ c1δ c1 + δ c
2δ c2 + δ c
1δ c3 +K
δX
δc (x) = δ c1 + δ c
2 +δ c3 + δ c
X
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Clipping Part II: The Power Spectrum
Pc(k)=14
1+ erfδ0
2σ⎛⎝⎜
⎞⎠⎟
⎡⎣⎢
⎤⎦⎥2
P(k)+σ 2
Hn−12 δ0
2σ⎛⎝⎜
⎞⎠⎟
π2n n +1( )!n=1
∞
∑ e−δ02
σ 2 P̂*(n+1)(k)
Exact solution for a Gaussian Random Field δG:
Exact solution for δ2 :
Pc (k)= erf u0( )−
2πu0 e
−u02⎡
⎣⎢⎤⎦⎥2
P(k)+σ 2∑ K u0 =δ0 +σ
2
2σ 2
⎡
⎣⎢⎢
⎤
⎦⎥⎥
PC (k)=A11PL(k)+ A22P1Looπ(k)
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The Clipped Power Spectrum
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The Clipped Power Spectrum
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The Clipped Galaxy Power Spectrum
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Parameter Constraints
FS, Heavens, Heymans arXiv:1306.6349
Pc (10%)PLPc (5%)
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Part II: Summary Clipped power spectrum is analytically tractable
Higher order PT terms are suppressed
Nonlinear galaxy bias terms are suppressed
Well approximated by
Applying δmax allows kmax to be increased ~300 times more Fourier modes available
BUT what happens in redshift space?
PC (k)=A11PL(k)+ A22 P22(k)+ P13(k)[ ]