the clipped power spectrum fergus simpson university of edinburgh fs, james, heavens, heymans (2011...
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The Clipped Power Spectrum
Fergus SimpsonUniversity of Edinburgh
FS, James, Heavens, Heymans (2011 PRL)FS, Heavens, Heymans (arXiv:1306.6349)
Outline
Introduction to Clipping
Part I: The Clipped Bispectrum
Part II: The Clipped Power Spectrum
Outline
Introduction to Clipping
Part I: The Clipped Bispectrum
Part II: The Clipped Power Spectrum
Ripples
Waves(hard)
(easy)
…but also spatial dependence:
Accuracy of Perturbation Theory
Not only time dependence…
Local Density Transformations
• Reduce nonlinear contributions by suppressing high density regions
Neyrinck et al (2009)
Clipping
• Typically only 1% of the field is subject to clipping
Outline
Introduction to Clipping
Part I: The Clipped Bispectrum
Part II: The Clipped Power Spectrum
The Bispectrum
The Clipped Bispectrum
The Clipped Bispectrum
The Clipped Bispectrum
FS, James, Heavens, Heymans PRL (2011)
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)?
Outline
Introduction to Clipping
Part I: The Clipped Bispectrum
Part II: The Clipped Power Spectrum
The Power Spectrum
The Clipped Power Spectrum
The Clipped Power Spectrum
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
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)
The Clipped Power Spectrum
The Clipped Power Spectrum
The Clipped Galaxy Power Spectrum
Parameter Constraints
FS, Heavens, Heymans arXiv:1306.6349
Pc (10%)PLPc (5%)
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)[ ]