![Page 1: The Clipped Power Spectrum Fergus Simpson University of Edinburgh FS, James, Heavens, Heymans (2011 PRL) FS, Heavens, Heymans (arXiv:1306.6349)](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649d925503460f94a78451/html5/thumbnails/1.jpg)
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
![Page 3: The Clipped Power Spectrum Fergus Simpson University of Edinburgh FS, James, Heavens, Heymans (2011 PRL) FS, Heavens, Heymans (arXiv:1306.6349)](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649d925503460f94a78451/html5/thumbnails/3.jpg)
Outline
Introduction to Clipping
Part I: The Clipped Bispectrum
Part II: The Clipped Power Spectrum
![Page 4: The Clipped Power Spectrum Fergus Simpson University of Edinburgh FS, James, Heavens, Heymans (2011 PRL) FS, Heavens, Heymans (arXiv:1306.6349)](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649d925503460f94a78451/html5/thumbnails/4.jpg)
Ripples
Waves(hard)
(easy)
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…but also spatial dependence:
Accuracy of Perturbation Theory
Not 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
![Page 8: The Clipped Power Spectrum Fergus Simpson University of Edinburgh FS, James, Heavens, Heymans (2011 PRL) FS, Heavens, Heymans (arXiv:1306.6349)](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649d925503460f94a78451/html5/thumbnails/8.jpg)
Outline
Introduction to Clipping
Part I: The Clipped Bispectrum
Part II: The Clipped Power Spectrum
![Page 9: The Clipped Power Spectrum Fergus Simpson University of Edinburgh FS, James, Heavens, Heymans (2011 PRL) FS, Heavens, Heymans (arXiv:1306.6349)](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649d925503460f94a78451/html5/thumbnails/9.jpg)
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
![Page 15: The Clipped Power Spectrum Fergus Simpson University of Edinburgh FS, James, Heavens, Heymans (2011 PRL) FS, Heavens, Heymans (arXiv:1306.6349)](https://reader036.vdocuments.site/reader036/viewer/2022081603/56649d925503460f94a78451/html5/thumbnails/15.jpg)
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 c
1δ 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( )−
2π
u0 e−u02⎡
⎣⎢⎤
⎦⎥
2
P(k) +σ 2∑ K u0 =δ0 +σ 2
2σ 2
⎡
⎣⎢⎢
⎤
⎦⎥⎥
PC (k)=A11PL (k) + A22P1Loop(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)[ ]