new approaches to modeling nonlinear structure formation
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New Approaches to Modeling Nonlinear Structure Formation
Nuala McCullaghJohns Hopkins University
Cosmology on the BeachCabo San Lucas, Mexico
January 13, 2014
In collaboration with:Alex Szalay and Mark Neyrinck
Outline
• Introduction• Modeling the correlation function• Beyond Gaussianity: log transform• Conclusions
z=0
z=1100
Modeling 2-point statistics: Linear Theory
Linear Theory:
Correlation Function:
Power Spectrum:
Overdensity:
Linear power spectrum
Linear correlation function
Modeling 2-point statistics: Systematics
π [M
pc/h
]
σ [Mpc/h]0 20-20
020
-20
Hawkins et al. (2002), astro-ph/02123752dFGRS: β=0.49±0.09
Nonlinearity
Redshift-space distortions
Galaxy bias
Image: Max Tegmark
Modeling 2-point statistics: SPTStandard Perturbation Theory: perturbative solution to the fluid equations in Fourier space:
Figure: Carlson, White, Padmanabhan, arXiv:0905.0497 (2009)
Linear2nd order3rd order
Modeling 2-point statistics: New Approach
• Structure of the Fourier space kernels suggests that in configuration space, the result may be simpler
• Terms beyond 2nd order may be simplified in configuration space compared to Fourier space
• Configuration space can be more easily extended to redshift space
Modeling 2-point statistics: New Approach
1st order Lagrangian perturbation theory (Zel’dovich approximation):
1LPT:
Poisson:
Expansion of the density in terms of linear quantities:
Modeling 2-point statistics: New Approach
Nonlinear correlation function:
McCullagh & Szalay. ApJ, 752, 21 (2012)
First nonlinear contribution to the correlation function in terms of initial quantities:
Where:
77 Indra simulationsT. Budavári, S. Cole, D. Crankshaw, L. Dobos, B. Falck, A. Jenkins, G. Lemson, M. Neyrinck, A. Szalay, and J. Wang
z=1.08 z=0.41
z=0.06 z=0.00
Line
of si
ght
Linear Nonlinear, z=0
Modeling 2-point statistics: New Approach
Zel’dovich model extended to redshift space:
Beyond Gaussianity: Log transform
A=log(1+δ(x))
McCullagh, Neyrinck, Szapudi, & Szalay. ApJL, 763, L14 (2013)
δ
log(1+δ)
Beyond Gaussianity: Log transformLinear Theory: 106.4 Mpc/hZel’dovich density: 105.8 Mpc/h -0.6 Mpc/hZel’dovich log-density: 106.1 Mpc/h -0.3 Mpc/h
McCullagh, Neyrinck, Szapudi, & Szalay. ApJL, 763, L14 (2013)
Conclusions & Future Directions• Extracting cosmological information from large-scale
structure requires accurate modeling of systematics• Modeling statistics in configuration space simplifies
higher-order corrections and extension to redshift space– Our approach should be extended to higher orders in LPT for
greater accuracy• Log-transform restores information to the 2-point
statistics– Possible improvements to BAO, redshift-space distortions, and
small-scale power spectrum– Must be demonstrated in real data in presence of discreteness
Thank you!
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