E^2(z) (k=0)

Convective Derivative

Contuity Equation

Euler Equation

Poisson Equation

At early times or small fluctuations

Eulerian vs Lagrangian

Comoving Gradient

Growth of structures when delta is small

EdS

Linear Growth Factor D(a)

Form of D

Potential Evolution

ZA

ZA comoving position

Initial Displacement Field

EdS radius growth of sphere at mean density

Radius of slightly overdense sphere

Linear sol to radius of overdense sphere

Mean vs overdense sphere

Overdensity linear approx

Overdensity Values

Virial Theorem

Virial radius for Spherical Tophat

Mass of virialised Perturbation

Value of Delta_c

Gaussian Random Field

Average of the Gaussian Random Field

Vairance of Gaussian Random Field

Usual Power Spectrum and Inflation Prediction

Meszaros Effect

Linear power spectrum

Smoothed overdensity field (variance on a certain scale)

What is filtered by the smoothing?

Ergodic principle

Characteristic comoving scale of dark matter halo definition

Characteristic radius for k^n power spectrum

When is sigma_8 evaluated

Rstar Mstar relation, Mstar definition

Behaviour of characteristic halo mass

Local gradient of CDM power spectrum

Halo mass function and cumulative mass function

Press-Schechter ansatz

Peak height

PS mass function behaviours

Dynamical timescale

Dynamical timescale formula

Relaxation timescale

Relaxation timescale formula

Singular Isothermal Sphere grav potential

SIS velocity dispersion

Hernquist model grav potential

SIS density

Hernquist Density

Navarro, Frenk and White (NFW)

Jean Length

Jeans Length Formula

Adiabatic Sound Speed

gamma for monoatomic ideal

Jeans Mass (If greater, Collapse)

Temperature- DM velocity dispersion relation for isothermal sphere in hydrostatic equilibrium

Virial Temperature

Spherical top hat definition of halo

Cooling time

Specific thermal energy

Emissivity (Power radiated per unit volume)

Cooling time with cooling function

Cooling to dynamical time relations

Cooling radius

When the virial radius is the cooling one

How do DM haloes acquire spin ang mom?

Time evolution of ang mom of proto-halo region, EdS case

Spatial evolution of ang mom of proto-halo

Halo spin parameter

Typical halo spin param

Exponential surface density of disks

Halo vs disk

Isothermal halo disk central surface density

Isothermal halo disk central length scale

Model ISM

Kennicut-Schmidt Law

Parameters of KS law

Feedback processes

Galactic wind speed due to supernovae

Parameters of wind speed

Galaxy velocity dispersion-Halo mass relation

Hot clusters thermal emission

X-ray luminosity-mass

Real LM relation