The appropriate perturbation equations in this limit are easily derived for a background FLRW expanding model, assuming a metric of the form
where andThe governing equations in the Newtonian limit are the hydrodynamic conservation equations,
the geodesic equations for collisionless dust or dark matter (in comoving coordinates), Poisson’s equation for the gravitational potential, and the Friedman equation for the cosmological scale factor, HereAn alternative total energy conservative form of the hydrodynamics equations that allows high resolution Godunov-type shock capturing techniques is
with the corresponding particle and gravity equations whereA fairly complete chemical network system useful for primordial gas phase compositions, including hydrogen molecules, consists of the following collisional, photoionization, and photodissociation chains
![]() |
|||
(1) |
![]() |
![]() |
![]() |
(2) |
![]() |
![]() |
![]() |
(3) |
![]() |
![]() |
![]() |
(4) |
![]() |
![]() |
![]() |
(5) |
![]() |
![]() |
![]() |
(6) |
![]() |
![]() |
![]() |
![]() ![]() |
|||
(7) |
![]() |
![]() |
![]() |
(8) |
![]() |
![]() |
![]() |
(9) |
![]() |
![]() |
![]() |
(10) |
![]() |
![]() |
![]() |
(11) |
![]() |
![]() |
![]() |
(12) |
![]() |
![]() |
![]() |
(13) |
![]() |
![]() |
![]() |
(14) |
![]() |
![]() |
![]() |
(15) |
![]() |
![]() |
![]() |
(16) |
![]() |
![]() |
![]() |
(17) |
![]() |
![]() |
![]() |
(18) |
![]() |
![]() |
![]() |
(19) |
![]() |
![]() |
![]() |
![]() |
|||
(20) |
![]() |
![]() |
![]() |
(21) |
![]() |
![]() |
![]() |
(22) |
![]() |
![]() |
![]() |
![]() |
|||
(23) |
![]() |
![]() |
![]() |
(24) |
![]() |
![]() |
![]() |
(25) |
![]() |
![]() |
![]() |
(26) |
![]() |
![]() |
![]() |
(27) |
![]() |
![]() |
![]() |
For a comprehensive description of the
chemistry and explicit formulas modeling the kinetic and cooling
rates relevant for cosmological calculations, the reader is
referred to
[92, 144, 54, 1, 21
]
. This reactive network is by no means complete, and in fact,
ignores important coolants and contaminants (e.g.,
,
, and their intermediary products
[151, 78, 48]) expected to form through non-equilibrium reactions at low
temperatures and high densities. Although it is certainly
possible to include even in three dimensional simulations, the
inclusion of more complex reactants demands either more
computational resources (to resolve both the chemistry and
cooling scales) or an increasing reliance on equilibrium
assumptions which can be very inaccurate.
It is beyond the scope of this review to
discuss algorithmic details of the different methods and their
strengths and weaknesses. Instead, the reader is referred
to
[103, 77
]
for thorough comparisons of various numerical methods applied to
problems of structure formation. Kang et al.
[103]
compare (by binning data at different resolutions) the
statistical performance of five codes (three Eulerian and two
SPH) on the problem of an evolving CDM Universe on large scales
using the same initial data. The results indicate that global
averages of physical attributes converge in rebinned data, but
that some uncertainties remain at small levels. Frenk et
al.
[77]
compare twelve Lagrangian and Eulerian hydrodynamics codes to
resolve the formation of a single X-ray cluster in a CDM
Universe. The study finds generally good agreement for both
dynamical and thermodynamical quantities, but also shows
significant differences in the X-ray luminosity, a quantity that
is especially sensitive to resolution
[17]
.
The standard Zel’dovich solution [165, 68] is commonly used to generate initial conditions satisfying observed or theoretical power spectra of matter density fluctuations. Comoving physical displacements and velocities of the collisionless dark matter particles are set according to the power spectrum realization
where the complex phases are chosen from a gaussian random field,Overdensity peaks can be filtered on specified spatial or mass scales by Gaussian smoothing the random density field [27]
on a comoving scaleBertschinger [44] has provided a useful and publicly available package of programs called COSMICS for computing transfer functions, CMB anisotropies, and gaussian random initial conditions for numerical structure formation calculations. The package solves the coupled linearized Einstein, Boltzman, and fluid equations for scalar metric perturbations, photons, neutrinos, baryons, and collisionless dark matter in a background isotropic Universe. It also generates constrained or unconstrained matter distributions over arbitrarily specifiable spatial or mass scales.
![]() |
http://www.livingreviews.org/lrr-2001-2 | © Max Planck Society and
the author(s)
Problems/comments to |