XIIth School of Cosmology
 
September 15 - 20, 2014IESC, Cargèse
STRUCTURE FORMATION AFTER PLANCK
their impact in the study of galaxies and
Cosmology

Modeling the structure formation in their cosmic web

Christophe PICHON
Institut d'Astrophysique de Paris (IAP)

Abstract
Why simulate structure formation ?
  • to understand the effects of non-linear processes
  • to connect the early universe to statistical surveys at low redshifts
  • to validate upcoming instruments via mocks
  • to advance the field of High Performane Computing/ computationnal geometry
Purposes
  1. AB INITIO MODELING
- understand what matters: can we explain what we (think) we see?

Numerical simulations seek to contrain the nature of the dark matter and designs experiments for its direct detection. Numerical simulations also seek to explore the formation of galaxies including our own Galaxy. The fundamental equations governing the forces between particles and fields in this low-energy regime are fairly well known. They aim to explain cosmic objects we see around us, like galaxies and compact objects (e.g. supermassives black holes). Structure formation involves a complicated blend of gravity, hydrodynamics, nuclear and atomic physics, as well as magnetohydrodynamics and radiation physics. One challenge is  to separate the important from the unimportant, and to find some answers to the many questions that astrophysicists face in contemporary extragalactic astronomy.

For LSS:

  • expanding background: not everything collapses, but when it does gravity almost always win
  • expanding background: voids repel
  • tdyn~1/√ρ
  • Gaussian ICs: anisotropic collapse: formation of cosmic web
  1. STATISTICS
Concordant model intrinsically statistical: it can only be disproved statistically.

  • make (large) virtual data sets/ surveys
  • validate inverse methods
  • build realistic estimators/ model biases
  • estimate error bars/covariance matrices
  • validate perturbation theory
  • "bias theory (light does not trace DM)
  • "semi-analytic models;properly account for scale coupling/anisotropy
  • allow for visualisation of the effect of complex processes
  1. PROSPECTIVE FOR ASTROPHYSICS

- design new instrument: assume everything holds; how well can we measure things from a given incomplete survey?

LSS as probes of cosmology:

Carrying out high-resolution cosmological simulations of different dark energy cosmologies, including also non-standard theories of gravity (e.g. MG) and coupled dark matter-dark energy cosmologies, and to comparing them to the standard ΛCDM model allows us to explore the viability of these theories

LSS as environment for galaxies :

The basis of (dark matter) n-body simulation. Basic concepts of numerical simulations, continuous and discrete simulations.Discretization of ordinary differential equations, integration schemes of different order. N-body problems.
  • dynamics in a expanding universe
  • symplectic integrators
  • multi-scale dynamics
  • Multigrid Poisson solver
  • Cosmological initial conditions
  • Zoom simulations

Accounting for baryons :

  • Multi-scale hydro-dynamics
  • Optimal discretization of partial differential equations
  • Finite element and finite volume methods
  • Subgrid physics: effective laws
  • Inverse cascade
  • Feedback or not feedback?
  • ISM, ray tracing, dust, magnetic fields, cosmic rays,anisotropic diffusion etc.
  1. SIMULATION AS A BRANCH OF COMPUTATIONAL SCIENCE

Simulation techniques are used to study cosmic structure formation.In order to allow use of the full power of modern supercomputers, the community develops massive parallel simulation algorithms, and new methods for discretizing the Euler and Navier-Stokes equations,for example on a refining/moving mesh,and sub-grid techniques  that allow multi-physics.

  • Lattice methods
  • Adaptive mesh refinement and multi-grid methods
  • Shock preserving algorithms
  • Multi-timescales
  • Matrix solvers and FFT methods
  • Monte Carlo methods, Markov chains
  • Code validation (!)

Bibliography

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Program