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 TheoryNot 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 c1δ 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( )−

2πu0 e

−u02⎡

⎣⎢⎤⎦⎥2

P(k)+σ 2∑ K u0 =δ0 +σ

2

2σ 2

⎡

⎣⎢⎢

⎤

⎦⎥⎥

PC (k)=A11PL(k)+ A22P1Looπ(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)[ ]