Racah Institute of physics, Hebrew University (Jerusalem, Israel) Structure Formation in the Universe: Simulating Our Local Cosmic Neighborhood Yehuda Hoffman (HU) Formation of Local Universe University of kentucky (Apr 2008) Title: Structure Formation in the Universe: SImulating Our Local Cosmic Neighborhood The early universe was homogenous and isotropic down to small fluctuations of the order of 1.e-5 or smaller. Out of these primordial random perturbation field structure has evolved by means of gravitational instability. Gravity drives dark matter to collapse and virialize in bound clumps, known as dark matter halos, which further cluster to form the cosmic web made of clusters, filaments, sheets and voids. The baryonic matter, in the form of gas, responds to the gravitational pull of the dark matter and settles at the cores of the dark matter halos where it cools and forms stars, thereby forming the visible galaxies. Using the algorithm of constrained realizations of Gaussian random fields we simulate the formation of the local universe, including the Local Group that contain the Milky Way and the Andromeda galaxies. Yehuda Hoffman Racah Institute of physics, Hebrew University (Jerusalem, Israel) Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Cosmological Time Line Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008) Yehuda Hoffman (HU) Formation of Local Universe University of kentucky (Apr 2008)

Cosmic Microwave background: Temperature Fluctuations Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Detection of dark matter Gravitational Lensing Galaxy cluster Abell 1689 Distance 2 million Ly Gravitational lensing predicted by Einstein’s general relativity The gravitational mass exceeds the mass seen in light & X-ray =====> DARK MATTER Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Detection of dark energy Supernovae Type Ia Standard candles Observed magnitude vs redshift High redshift SN are fainter than expected in “standard” cosmologies Universe is currently accelerating =====> DARK ENERGY Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Content of the Universe Angular Power Spectrum Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

What have we learned from WMAP? ΛCDM standard model The Universe is flat - Euclidian geometry The mass-energy budget of the Universe: 4.5% ordinary matter (baryons) 23% non-baryonic unknown dark matter Dark matter is cold (100-27.5)% cosmological constant (Λ)? dark energy? All structure emerged from quantum fluctuations of the vacuum in the very early universe (≈10-30s after the Big Bang) Cocktail party remark: Everything has formed from nothing Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

τplanck=(Gh/c5)1/2≈10-44s Structure Formation Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Structure & Galaxy Formation Dark Matter dynamics: gravity - Newtonian, non-linear, non- dissipative Baryons dynamics: gravity, hydrodynamics, radiation physical processes: star formation, stellar feedback, cooling & heating ... (sub-grid) Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Initial Conditions Primordial perturbations constitute a Gaussian random field The power spectrum (shape & normalization) is determined from the CMB: (Δ T / T) ≈ 10-5 Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Prevailing idea: dark matter talks & baryons listen Dark matter clusters and forms bound objects (called DM halos) - GRAVITATIONAL INSTABILITY Baryons follows the gravitational pull of the dark matter Baryons cools radiatively, sinks to the bottom of the DM halos & form stars - GALAXY FORMATION Complex non-linear gravitational, hydrodynamical, radiative, star formation & stellar evolution processes determine the structural, dynamical, stellar & chemical properties of galaxies Massive numerical simulations are the main tool used to study these complex phenomena! Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

N-body simulations: gravity only Distribution of DM halos Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Conditional Luminosity Function: Φ(L|M)dL is the average # of galaxies in the range of L±dL/2 residing in a DM halo of mass M (van de Bosch et al 2007) Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Millennium Simulation: N-body + Semi-analytical Modeling DM Populating DM with galaxies: Identify DM halos Construct the merging history of each halo Apply simplified analytical recipes to model galaxy formation for each halo at any given time Form galaxies in the DM halos Millenium: Introduction: The Millennium Simulation The Millennium Run used more than 10 billion particles to trace the evolution of the matter distribution in a cubic region of the Universe over 2 billion light-years on a side. It kept busy the principal supercomputer at the Max Planck Society's Supercomputing Centre in Garching, Germany for more than a month. By applying sophisticated modelling techniques to the 25 Tbytes of stored output, Virgo scientists have been able to recreate evolutionary histories both for the 20 million or so galaxies which populate this enormous volume and for the supermassive black holes which occasionally power quasars at their hearts. By comparing such simulated data to large observational surveys, one can clarify the physical processes underlying the buildup of real galaxies and black holes. Pictures of the galaxy distributiontop The top row of the following pictures shows the galaxy distribution in the simulation, both on very large scales, and for a rich cluster of galaxies where one can see them individually. The top right panel hence represents the large-scale light distribution in the Universe. For comparison, the images in the lower row give the corresponding dark matter distributions. galaxies Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Constrained Simulations Initial conditions - Gaussian random fields Random realization - only power spectrum is assumed Constrained realizations of Gaussian random fields - construct random realizations which obey any number of (linear) imposed constraints (Hoffman & Ribak 1991) Use observations to impose the ‘observed universe’ on the initial conditions =====> Constrained Simulations (CSs) of the Local Universe Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

(~1000 cpu yrs) Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

LG: DM MW M31 M33 Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

MW: stars Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

M33: stars Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)

Constrained Simulations of the Local Universe Things we don’t know Galaxy formation Luminosity function Structural properties of galaxies Star formation & its feed back on galaxy formation Environmental dependance ... What have we learnt? How to make DM halos The distribution of dark matter The Local Universe appears to be typical - near field cosmology makes sense The LG in particular appears to be typical: environment, structure of MW & M31’s halo Constrained Simulations of the Local Universe Numerical laboratory for galaxy formation experiments, done under realistic conditions performing near field cosmology on the computer Yehuda Hoffman (HU) Formation of Local Universe University of Kentucky (Apr 2008)