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Probing cosmic structure formation in the wavelet representation

Probing cosmic structure formation in the wavelet representation. Li-Zhi Fang University of Arizona. IPAM, November 10, 2004. outline. introduction phenomenological hierarchical clustering models and scale-scale correlation intermittency and small scale problem of LCDM model

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Probing cosmic structure formation in the wavelet representation

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  1. Probing cosmic structure formation in the wavelet representation Li-Zhi Fang University of Arizona IPAM, November 10, 2004

  2. outline • introduction • phenomenological hierarchical clustering models and scale-scale correlation • intermittency and small scale problem of LCDM model • quasi-local evolution • summary

  3. cosmic random fields • density distribution • velocity field • temperature • entropy • …

  4. density distribution of hydrogen gas in the LCDM model Information of structures: position, scale dark matter baryon gas Feng,Shu, Zhang (2004)

  5. representations • x-representation f(x,t) • k(p)-representation f(k,t), f(p,t), • Wigner distribution function (WDF), Wigner representation W(x,k,t), W(x,p,t), phase-space behavior (position and scale) coherent structure phase-sensitive effects WDF is density matrix, not a linear transform of f(x,t).

  6. j=4 j=3 j=2 j=1 mode (j, l)

  7. space-scale decompositionby discrete wavelet mode WFCs (wavelet function coefficients) of mode (j, l) represents fluctuations on a length scale L/2j

  8. dynamical models of cosmic structure formation cosmological parameters, initial perturbations wavelet simulation sample wavelet N-body simulation hydrodynamic simulation pseudo-hydro simulation lognormal model predictions wavelet 1-D, 2-D, 3-D background radiation IGM, galaxies observational samples

  9. hierarchical clustering scale massive halo j j+1 j+2 small halos

  10. block model Cole, Kaiser (1988)

  11. branching model Pando, Lipa, Greiner, Fang (1998)

  12. The first and second orders statistical properties of the block model and branching model are the same if Pando, Lipa, Greiner, Fang (1998)

  13. scale-scale correlation block model branching model Pando, Lipa, Greiner, Fang (1998)

  14. Lu, Wolfe, Turnshek, sample of Ly-alpha absorption branching model Pando, Lipa, Greiner, Fang (1998)

  15. lognormalmodel Feng, Fang 2000

  16. APM-BGC galaxy sample mock samples Feng, Deng, Fang 2000

  17. problem of the LCDM model small scale powers reducing the power on small scales relative to the `standard' LCDM model is favored by the analysis of WMAP plus galaxy and Lyman-alpha forest data. It can also solve the halo concentration and substructure problems. Warm dark matter (WDM) models leads to exponential damping of linear power spectrum, and results in better agreement with observations

  18. intermittency The lognormal model of IGM (baryon gas) (x,t)Jeans is a Gaussian random field derived from the density contrast  DM of dark matter filtered on the Jeans scale. Bi, Davidsen 1997

  19. lognormal model at small scales Feng, Fang 2000

  20. lognormal field is intermittent structure function intermittent exponent A field is intermittent if Lognormal Field:

  21. structure function with DWT

  22. structure functions of Ly-alpha samples Samples: 28 Keck HIRES QSO spectra. redshift z from 2.19 – 4.11 Pando, Feng, Fang 2002

  23. Structure Functions of Ly-alpha transmission LCDM WDM mw =1000ev mw =800ev mw =600ev mw =300ev pseudo hydro simulation Pando, Feng, Jamkhedkar, Fang, 2002

  24. simulation box 6 Mpc/h 12 Mpc/h Feng, Pando, Fang 2003

  25. Fit Keck Data to j=10, 24 h-1 kpc j=11, 12 h-1 kpc Pando, Feng, Jamkhedkar, Fang, 2002

  26. Fit LCDM Data to j=11, 12 h-1 kpc j=10, 24 h-1 kpc Pando, Feng, Jamkhedkar, Fang, 2002

  27. Fit WDM 300 eV Data to j=10, 24 h-1 kpc j=11, 12 h-1 kpc Pando, Feng, Jamkhedkar, Fang, 2002

  28. quasi-local evolution of cosmic clustering in the wavelet representation

  29. Gaussian field in the DWT representation j l

  30. spatial localized correlation strong weak

  31. quasi-locality (second order) different physical position

  32. quasi-locality (higher order)

  33. quasi-locality of mass field inZeld’ovich approximation(weak linear regime) If the initial perturbations are Gaussian, the cosmic gravitation clustering in weakly nonlinear regime given by the Zeldovich approximation is quasi-localized in the DWT representation. Pando, Feng, Fang 2001

  34. second orderquasi-locality : Ly-alpha data Pando, Feng, Fang 2001

  35. second orderquasi-locality : Ly-alpha data Pando, Feng, Fang 2001

  36. Ly-alpha data: second order Pando, Feng, Fang 2001

  37. 4th order locality: Ly-alpha data Pando, Feng, Fang 2001

  38. halo model(highly nonlinear regime)

  39. Feng,Shu, Zhang (2004)

  40. halo model Xu, Fang, Wu 2000

  41. quasi-locality of mass field in halo model If the initial perturbations is Gaussian (no correlation between modes at different physical positions), the evolved field will also spatially weakly correlated. The nonlinear evolution of gravitational clustering has memory of the initial spatial correlations. Feng, Fang 2004

  42. N-body simulation samples Jing, Suto (2000), Jing (2001)

  43. N-body simulation sample (Jing, Suto 2002) One-point distribution of WFCs Feng, Fang 2004

  44. two-point correlation functions: N-body simulation sample (Jing, Suto 2002) Feng, Fang 2004

  45. Scale-scale correlation: N-body simulation sample (Jing, Suto 2002) Feng, Fang 2004

  46. DWT mode-mode correlations: N-body simulation sample (Jing, Suto 2002) Feng, Fang 2004

  47. Feng, Fang 2004

  48. Feng, Fang 2004

  49. galaxy sample: 2MASS XSC(Jarrett et al. 2000) 987,125 galaxies

  50. angular correlation functions: 2MASS data Guo, Chu, Fang 2004

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