Nonlinear biasing effect in threepoint statistics

1
Non-linear biasing effect in three-point
statistics

• Takahiro Nishimichi
• Department of Physics, The University of Tokyo
• Collaborators Yasushi Suto, Atsushi Taruya,
  Kazuhiro Yahata, Chiaki Hikage, Issha Kayo
  Yipeng Jing
• The 1st China-Japan-Korea Joint Workshop on
  Cosmology, Large Scale Structure and Galaxy
  Formation Numerical Simulations
• _at_Shanghai Nov. 10 - 13 2005

2
Table of Contents

• Motivation
• Related theories
• Our model
• N-body simulation
• Summary future plans

3
Motivation(1)

• Hierarchical model for 3pt statistics

• Real space

our interest

• Fourier space

• The distribution of galaxies does not trace the
  matter distribution.
• a local deterministic non-linear bias model

• Qgalaxy ? Qmatter but they are somehow related.

4
Motivation(2)

• Luminosity, morphology and color dependence
  disappears in 3pt amplitude.
• It implies that linear bias model is not
  sufficient and there exists some correlation
  between b1 and b2.

Kayo et al. PASJ 56(2004) 415
5
Related theories(1)

• MJW formalism

Mo Jing White MNRAS 284(1997) 189
Conditional MF
Unconditional MF

• excursion set theory
• spherical collapse ? the constant barrier
• ellipsoidal collapse ? the moving barrier

Bond et al. ApJ 379(1991) 440
Sheth Mo Tormen MNRAS 323(1999) 1
6
Related theories(2)

• Relation of Qmatter and Qhalo
• Assuming matter distribution has hierarchical
  connected moments
• They calculated connected moments of biased
  field.
• We obtain an expression of Qhalo from this.

Fry Gaztanaga. ApJ 413(1993) 447
(leading term)
7
Our model(1)

• This Work
• MJW formalism with Fry and Gaztanagas relation
• Qhalo as a function of Mhalo
• Qhalo as a function of b1
• Collapse model spherical and ellipsoidal barrier
  
• Cosmology SCDM and ?CDM
• Various formation time(redshift) zform
• How about the correlation between b1 and b2?

8
Our model(2)

• Qhalo, b1 and b2 as a function of mass
• Qhalo is not very sensitive to mass.
• Results are similar in spherical and SCDM cases.
• Now we can calculate the relation between b1 and
  b2.

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Our model(3)

• Qhalo and c2 b2/b1 as a function of b1
• Clear correlation between b1 and b2
• Qhalo is not sensitive to b1.
• Several effects
• Nonlinear growth?
• Redshift distortion?
• Survey shape effect?
• N-body simulation

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N-body Simulation

• 300h-1Mpc 100h-1Mpc box simulation by Jing
• Bispectrum
• 3pt CF
• We must consider some effects below
• Redshift-space distortion
• Nonlinearity
• Shape of survey volume

Jing MNRAS 335(2002) 89
Jing Suto ApJ 574(2002) 538
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Summary future plans

• With a simple analytic model we can explain the
  behavior of 3pt statistics seen in SDSS galaxies.
• N-body simulation
• Bispectrum
• 3pt-CF
• Comparison with observational data from SDSS
  galaxies
• Various effects should be examined.
• Redshift-space distortion
• Nonlinearity
• Survey shape effect