nonlinear evolution of intergalactic medium IGM

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nonlinear evolution of intergalactic medium (IGM)
Taipei School/Workshop on Large Scale Structures
of the Universe National Center for
Theoretical Sciences ???????? May 28 June 2,
2007
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mass budget of Universe

• dark energy 70
• dark matter 26
• rest of ordinary matter (baryons and electrons)
  are 4
• 90 of baryon matter is gaseous
• stars and galaxies are only 0.5
• neutrinos are 0.3
• anti-matter 0

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parameters of WMAP III (2006)

• the clustering dynamics of cosmic baryon
• gas is governed by the gravity of underlying
• dark matter

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the dynamics of baryonic gas is governed by
the gravity of dark matter
similarity ?
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similarity is correct in linear evolution
Initial condition
growth mode
finial solution
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non-linear evolution

• the dynamics of baryonic gas is also
• governed by the gravity of dark matter

assumption igm-dm similarity mapping
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baryon fraction
If
We have
for all space.
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missing baryon in clusters
Ettori,(2003)
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Physics today Nov. 2006
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baryon matter-dark matter similarity does not
consistent with observations!
statistical decoupling betweenbaryon matter and
dark matterin nonlinear regime
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dynamical equation of collisionless dark
matter
phase space distribution f(t,x,p)
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dynamical equation of cosmic baryon fluid
hydrodynamic equations in expanding universe
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intersection of trajectories of particles
velocity field is multi-valued
Shandarin, Zeldovich(1989)
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velocity field of baryon fluid
shocks formed in IGM
Shandarin,Zeldovich(1989)
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Liu et al 2006
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growth mode of peculiar velocity is irrotational
Burgers equation
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Burgers equation

• considering growth mode, the dynamical
  equation of baryon matter is stochastic force
  driven Burgers' equation or KPZ equation

gravitational potential
velocity potential
Jeans diffusion
Berera, Fang, PRL (1994) Jeans, MNRAS
(1999) Matarrese, Mohayaee, MNRAS (2002)
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Burgers fluid and shocks
t 0.0, 0.2, 0.6, 1.0, 1.4, 2.0
1-dimension Burgers equation
Initial condition
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shocks
He, Feng, Fang, 2004
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Burgers equation Schrodinger
equation of quantum mechanics
Hopf-Cole transformation
gravitational potential (random)
is the wavefunction of a particle in a random
potential.
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Solutions of Schrodinger equation
path integral
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statistics of IGM field
lognormal statistics
Lognormal model of Ly-alpha forests of Quasars
absortion spectrum
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lognormal distributions
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Ly-alpha absorption spectrum (Gunn-Peterson
effect)
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intermittence
random variables
random variable
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intermittence of Ly-alpha transmitted flux
Jamkhedkar, Zhan, Fang, (2000) Feng, Pando,
Fang, (2003) Pando, Feng, Fang, (2004).
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stock market
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Burgers turbulence
turbulence in imcompressible fluid vorticity

Burgers turbulence of baryon matter shocks

• Reynolds number

Correlation length of random gravitational field
Jeans smoothing length
R gt 1 turbelence
scaling
Polyakov, PRE, (1995) Boldyrev, Linde, Polyakov,
PRL, (2004)
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scaling
Kim, He, Pando, Feng, Fang(2005)
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statistical decoupling of passive substance
from underlying mass field
fluorescent dye in turbulence (Nature, 2000)
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fully developed turbulence
Kolmogorov's turbulence

homogeneous and isotropic
in scale-free range, dimension analysis yields
scaling relation
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whether the cosmic baryon fluid follows the
scaling of fully developed turbulence ?
scale free, homogeneous and isotropic
evolution

cosmic baryon matter compressible fluid,
irrotational
-

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universal properties of fully developed
turbulence intermittency
structure function
Kolmogorov scaling (1941)
lognormal model (Kolmogorov, 1962)
mulifractal model (Parisi, Frisch, 1985)
She-Leveque formula (1994) log-Poisson model
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hierarchical cascade log-Poisson process
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meaning of gamma
From
we have
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hierarchical structure
\beta hierarchical structure
He, Liu, Feng, Shu, Fang, PRL, (2006)
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He, Liu, Feng, Shu, Fang, PRL, (2006)
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high order moment
Liu, Fang, 2007
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scale-scale correlation
Liu, Fang, 2007
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scale free initial perturbations
linear growth (scaling)
non-linear regime, fully developed
Burgers turbulence (statistical quasi-
equilibrium state)
thermal equilibrium
gas in halos
virialized halos
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• application
• turbulent broadening
• non-Gaussianity of
• CMB polarization maps
• 21 cm maps
• .

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turbulent broadening
Liu, Jamkhadkar, Zheng, Feng, Fang 2006
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CMB polarization
CMB polarization is due to the scattering of CMB
photons along the line of sight

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Burgers turbulence scenario of the evolution of
cosmic baryon gas linear regime
non-linear regime (Burgers
turbulence) thermal
equilibrium gas in halos
virialized halos