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Understanding the Evolution of the Halo Mass Function: Key Insights and Implications

This study delves into the evolution of the Halo Mass Function (HMF) and its significance in cosmology. It explores how the distribution of halo masses influences our understanding of dark energy properties and the formation of quasars and the first stars. By utilizing advanced simulations and Particle-Mesh codes, the research presents a comprehensive analysis of halo masses across varying redshifts. It also discusses necessary corrections for finite box sizes and provides insights into the potential breaking of universality with the introduction of dark energy.

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Understanding the Evolution of the Halo Mass Function: Key Insights and Implications

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  1. Evolution of the Halo Mass Function Zarija Lukić (UIUC) Katrin Heitmann (LANL) Salman Habib (LANL) Sergei Bashinsky (LANL) Paul Ricker (UIUC) astro-ph/0702360

  2. Mass function • Distribution of masses in the Universe: bin all objects (halos) in mass bins – dn/dM • Or, presenting it in a redshift (+cosmology) independent way : where σ is the mass variance: ∞ ∫ σ2(M) = P(k) W2(k;M) k2 dk 0

  3. Why Bothering? • At low redshifts (z ≤ 2) is used for constraining the dark energy properties (Ωλ,w) • - At high redshift is used for quasar abundances & formation sites, reionization history and first stars studies • At high redshift (2006) data from different groups differ by a factor of few!

  4. Simulations • MC2: Particle-Mesh code, tested against other well known cosmo codes (Heitmann et al. 2005, 2007) • 2563 DM particles on 10243 grid • Large set of simulations (60) : 1) Different box sizes (4 – 256 Mpc/h) 2) Many realizations of the same box size • That enables us to : 1) Obtain excellent statistics 2) Probe large range of masses (107 – 1014 h-1 M☼) and redshifts (0 – 20).

  5. Visualization – 90 Mpchttp://tsoodzil.astro.uiuc/~zlukic/mc2_z=0.mov

  6. FOF mass correction Ncorr = N (1-N-0.6) (Warren et al.2006) - Very important for interpreting data!

  7. Results

  8. Universality?

  9. Extended Press-Schechter ∞ ∞ fbias-ps= fps(δc-δ(R), σ2-σ2(R)) -- Bond et al. 1991

  10. EPS correction

  11. Box-corrected MF

  12. Corollary • Need FOF number of particles correction, and to account for finite box correction, especially for high z • - Warren et al. fit gives prediction with 10% accuracy for a wide range of masses and redshifts (ST very good as well) • Good evidence for the universality in CDM phase • (z ≥ 5) • Possible breaking of universality with entrance of dark energy? • - For more check: astro-ph/0702360

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