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New Approaches to Modeling Nonlinear Structure Formation

New Approaches to Modeling Nonlinear Structure Formation. Nuala McCullagh Johns Hopkins University Cosmology on the Beach Cabo San Lucas, Mexico January 13, 2014 In collaboration with: Alex Szalay and Mark Neyrinck. Outline. Introduction Modeling the correlation function

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New Approaches to Modeling Nonlinear Structure Formation

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  1. New Approaches to Modeling Nonlinear Structure Formation Nuala McCullagh Johns Hopkins University Cosmology on the Beach Cabo San Lucas, Mexico January 13, 2014 In collaboration with: Alex Szalayand Mark Neyrinck

  2. Outline • Introduction • Modeling the correlation function • Beyond Gaussianity: log transform • Conclusions

  3. z=1100 z=0

  4. Modeling 2-point statistics: Linear Theory Linear power spectrum Linear Theory: Overdensity: Correlation Function: Linear correlation function Power Spectrum:

  5. Modeling 2-point statistics: Systematics Hawkins et al. (2002), astro-ph/0212375 2dFGRS: β=0.49±0.09 20 Nonlinearity π [Mpc/h] 0 Galaxy bias -20 Redshift-space distortions -20 0 20 σ [Mpc/h] Image: Max Tegmark

  6. Modeling 2-point statistics: SPT Standard Perturbation Theory: perturbative solution to the fluid equations in Fourier space: Linear 2nd order 3rd order Figure: Carlson, White, Padmanabhan, arXiv:0905.0497 (2009)

  7. Modeling 2-point statistics: New Approach • Structure of the Fourier space kernels suggests that in configuration space, the result may be simpler • Terms beyond 2ndorder may be simplified in configuration space compared to Fourier space • Configuration space can be more easily extended to redshift space

  8. Modeling 2-point statistics: New Approach 1storder Lagrangian perturbation theory (Zel’dovich approximation): 1LPT: Poisson: Expansion of the density in terms of linear quantities:

  9. Modeling 2-point statistics: New Approach Nonlinear correlation function: First nonlinear contribution to the correlation function in terms of initial quantities: Where: McCullagh & Szalay.ApJ, 752, 21 (2012)

  10. z=0.41 z=1.08 z=0.06 z=0.00 77 Indra simulations T. Budavári, S. Cole, D. Crankshaw, L. Dobos, B. Falck, A. Jenkins, G. Lemson, M. Neyrinck, A. Szalay, and J. Wang

  11. Modeling 2-point statistics: New Approach Zel’dovich model extended to redshift space: Linear Nonlinear, z=0 Line of sight

  12. Beyond Gaussianity: Log transform δ log(1+δ) A=log(1+δ(x)) McCullagh, Neyrinck, Szapudi, & Szalay. ApJL, 763, L14 (2013) McCullagh, Neyrinck, Szapudi, & Szalay. ApJL, 763, L14 (2013)

  13. Beyond Gaussianity: Log transform Linear Theory: 106.4 Mpc/h Zel’dovich density: 105.8 Mpc/h -0.6 Mpc/h Zel’dovich log-density: 106.1 Mpc/h -0.3 Mpc/h McCullagh, Neyrinck, Szapudi, & Szalay. ApJL, 763, L14 (2013)

  14. 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

  15. Thank you!

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