Definitions and Explanations Flashcards
galaxies appear to be
clustered
evidence of galaxy clustering
projected distribution of galaxies in the sky
redshift surveys.
Redshift survey
reveals patterns in the galaxy distribution i.e. clusters, sheets and voids.
peculiar motion
is caused by galaxy clusters’ gravitational interaction with the other cluster members.
Superclusters
galaxy clusters are themselves clustered and are organised into larger-scale structures
luminosity indicators
RR Lyrae stars and Cepheid variable stars
Hubble’s constant measures
the expansion rate of the Universe
The standard model for the origin and evolution of the Universe is called
the Hot Big Bang model
Cosmological Principle
The universe is homogeneous and isotropic:
universe homogeneous = no matter where you are in it
universe isotropic = no matter what direction you look in
Galaxies can be thought of as
local disturbances in an otherwise perfectly homogeneous and isotropic Universe.
The scale factor measures
the characteristic size of the Universe at time t.
the proper distance
Is the physical distance between two objects in the Universe.
the co-moving separation
is the separation of two objects in a coordinate system that expands along with the expansion of space-time.
a(t) is not a constant in
time, but is a constant in space at any given time.
Hubble time, τ
sets the timescale for the expansion of the Universe
Hubble time : t(0) < τ is when
including the effects of gravity
gives an age of the universe smaller than the hubble time
number of things in defence of homogeneity and isotropy
- The Hubble-Lemaitre Law
- The cosmic microwave background radiation
- Primordial nucleosynthesis
- The age of the universe
Statement of Olber’s Paradox
‘why is the sky dark at night’
if the Universe is infinite in extent and eternal, with stars roughly uniformly distributed throughout space. Every line of sight will intercept a star, so that the whole night sky should be as bright as the surface of a star.
Resolution of Olber’s Paradox
- Stars have finite lifetimes
- The speed of light is finite
- The universe has a finite age.
Hubble-lemaitre law is a natural consequence of
the cosmological principle
The Friedmann equation describes
how gravity acts against the expansion of the Universe
the constant k defines
the geometry or curvature of the Universe, it determines how a(t) evolves with time
three classes of solutions depending on values of k:
k > 0: the universe is closed, with positive curvature
k < 0: the universe is open, with negative curvature
k = 0: the universe is flat, with zero curvature
p(c) is
the density required to just close the Universe
If p > p(c) the universe recollapses
if p < p(c) the universe expands indefinitely
density parameter has three classes of solutions:
Ω > 1 implies Universe is closed
Ω < 1 implies Universe is open
Ω = 1 implies Universe is flat
Although Ω can change with time it can be shown that
its state of being closed, open or flat cannot change
the mass continuity equation tells us
that in a steady state, the rate at which mass enters a system is equal to the rate at which mass leaves the system
in a matter-dominated universe p ~
in a radiation-dominated universe p ~
p ~ 1/a^3
p ~ 1/a^4
the mass continuity equation has three resulting solutions:
k < 0: a(dot) -> c√-k - open universe
k > 0: a(dot) = 0 at some critical radius a(c), and a collapse phase starts after a = a(c) - closed universe
k = 0: a(dot) -> 0 at t -> ∞ - flat universe
temporal behaviour of the scale factor is given by
a(t) ∝ t^2/η
a(t) ∝ { t^2/3 matter-dominated
{ t^1/2 radiation-dominated
the effect of the pressure term P is to
slow down the expansion
Galaxy rotation curves
the observed rotation velocities are greater than those expected from the gravitational influence of the luminous stars alone,
Indicating the presence of a dark matter halo surrounding the galaxy
virial theorem assumes
galaxies can be seen as being in a fluid in hydrostatic equilibrium
other methods for identifying dark matter
- gravitational lensing
- nucleosynthesis
- studying the pattern of temperature variations in the CMBR
for any η of interest Ω ->
1 as z -> ∞ in the Early Universe
in the case where Ω(0) < 1
we can expect a fast decrease from Ω = 1 to Ω -> 0.
Hence any value of Ω(0) which is not ~1 or ~0 would place us at a very special time.
Dark matter candidates
Baryonic:
1. Gas clumps in galaxy halos and clusters
2. MACHOS
3. Low surface brightness galaxies
Non-Baryonic:
1. WIMPs
2. Primordial black holes
hot dark matter
non-baryonic dark matter was moving relativistically at the time of decoupling from baryonic matter
cold dark matter
non-baryonic dark matter was moving non-relativistically at decoupling.
Jeans mass
how much mass can you have in a given volume of space before it starts to collapse under its own weight
Gravitational collapse will occur when
the characteristic length L of the perturbation is larger than Jean’s length λ(J).
stable oscillations
If M < M(J) or L < L(J)
Jeans instability is not
fast enough to create large-scale structures
c^2(s) = γp^(γ-1)
γ is the ratio of specific heats
such that γ = 5/3 for adiabatic process
and γ = 4/3 for isothermal process
Hubble flow
Will produce time-independent coefficients in the density equation
The exponential law is replaced by a power law
Jeans mass still persists allowing for an expanding universe
Fragmentation less plausible as an explanation for the observed mass distribution
open universe
universe expands forever
closed universe
the universe will stop expanding and will then contract
flat universe
the expansion will slow down unit it stops at t -> ∞
newtonian cosmology
the study of the evolution of the Universe using only Newton’s law to describe gravity
matter dominated
corresponds to the epoch where the evolution of the Universe is dominated by ‘matter’, i.e. non relativistic particles exerting negligible pressure
radiated-dominated
corresponds to the epoch where the evolution of the Universe is dominated by relativistic particles exerting a non-negligible pressure
graph of how d(diam) varies with redshift z
see notes
How the viral theorem can lead to infer the existence of dark matter
Measure o(vr) and the effective radius of the cluster to obtain an estimate of gravitating matter in the cluster
On comparison there is a discrepancy between the measurements and theory invokes the existence of dark matter
Luminosity distance
The distance to the object implied by the observed flux
Angular diameter distance
Is the distance implied by the small angle approximation
If γ < 4/3
Jeans mass decreases with increasing density
Isothermal collapse
If γ = 5/3
An adiabatic process and therefore jeans mass increases with density
Gravitational collapse halts.
