### The Clipped Power Spectrum

The Clipped Power Spectrum
Fergus Simpson
University 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
(easy)
Waves
(hard)
Accuracy of Perturbation Theory
Not only time dependence…
…but also spatial 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?
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
Clipped Perturbation Theory
 ( x )   G O ( G ) O ( G )   X
2
3
• Reduce contributions from  by suppressing
regions with large  ( x )
X
 c ( x )   c   c  c   c
1
2
3
X
 c c   c  c   c  c   c  c  K
1
1
2
2
1
3
Clipping Part II: The Power Spectrum
 Exact solution for a Gaussian Random Field δG:
 0 
2
H n 1 

 2 
2

2
0


1
 0  
2
2
*( n  1 )
Pc ( k )  1  erf 
e  Pˆ
(k )
  P (k )   
n
 2  
4

2
n

1
!


n 1
 Exact solution for δ2 :
2
2
2

u 
2
Pc ( k )   erf u 0  
u0 e 0  P (k )    K




u0 

PC (k )  A11 PL (k )  A 22 P1Loop (k )
2
0   
2
2


The Clipped Power Spectrum
The Clipped Power Spectrum
The Clipped Galaxy Power Spectrum
Parameter Constraints
PL
Pc (10% )
Pc (5% )
FS, Heavens, Heymans arXiv:1306.6349
Part II: Summary
 Clipped power spectrum is analytically tractable
 Higher order PT terms are suppressed
 Nonlinear galaxy bias terms are suppressed
 Well approximated by
PC ( k )  A11 PL ( k )  A 22 P22 ( k )  P13 ( k ) 
 Applying δmax allows kmax to be increased
 ~300 times more Fourier modes available
 BUT what happens in redshift space?