Section 1-2 Flashcards
The universe we see and measure is
inhomogeneous and anisotropic on almost every scale
The spatial distribution of galaxies is not
uniform
galaxies appear to be clustered
We see evidence of galaxy clustering in the
projected distribution of galaxies on the sky
Hubble - Lemaitre’s law says that
distant galaxies recede from us with speeds that increase linearly with distance
Redshift survey
accurate maps of the galaxy distribution on large scales using the measured redshift to indicate the relative separation of galaxies
Redshift surveys reveal
patterns in the galaxy distribution that we see galaxy clusters, sheets and filamentary structure, and voids
A feature that suggests the universe is not homogeneous or isotropic
The Sloan Great Wall
On small scales galaxies are grouped together in
clusters
Within galaxy clusters, galaxies may have a peculiar motion, or speed, that differs slightly from
their recession velocity given by the Hubble-Lemaitre law.
The peculiar motion is caused by
their gravitational interaction with the other cluster members. The effects of this are most pronounced for galaxies that are reasonably close and have therefore relatively low recession velocities.
The distribution of galaxy clusters is
non-uniform
Galaxy clusters are themselves
clustered
Superclusters
Galaxy clusters that are organised into larger-scale structures
The two most commonly used variable star distance indicators are
RR Lyrae Stars and Cepheid variable Stars
For the closest galaxies the Hubble-Lemaitre expansion law is
distorted by peculiar motions due to the pull of nearby galaxies.
Hubble’s constant measures
the expansion rate of the Universe
Hubble reached the wrong expansion rate due to underestimating the distances to his calibrating galaxies.
Hubble’s constant value is widely accepted as
70kms^-1 Mpc^-1
The standard model for the origin and evolution of the Universe is called the
Hot Big Bang
The Universe began
13.7 billion years ago and has been expanding ever since
The Cosmological Principle
The Universe is homogenous (no matter where you are in it) and isotropic (no matter what direction). The universe looks the same.
The Cosmological Principle states there are no
‘special places’ in the Universe such as a centre or an edge.
Only space between _ is expanding
galaxies
Gravitationally bound systems do not
expand
The sizes of galaxies themselves
do not change, only the distances between them
Galaxies can be thought of as local disturbances in an
otherwise perfectly homogenous and isotropic universe.
cosmic scale factor a(t)
a dimension-less number that can describe the size of the evolution of the Universe
a(t) measures the
characteristic size of the Universe at time t. More specifically, it allows one to determine by how far galaxies have been carried apart by the expansion of the underlying space.
The present day factor of the scale factor is
a(t₀) = a₀
The proper distance between two galaxies at time t is their
actual seperation
co - moving separation of two galaxies
is their separation expressed in terms of a coordinate system which expands along the background space.
Galaxies co-moving separation is
not changed
Cosmological redshifts are not
due to the motions of distant objects, but are the result of the stretching of the wavelength of their light as it propagates through expanding space.
Hubble’s constant measures the rate of change of the
scale factor a(t): it is not a constant in time, but a constant in space at any given time
Hubble time
τ, is a timescale for the expansion of the Universe. This simple treatment ignores the effect of gravity, which will slow down the expansion so that H(t) was larger in the past.
proper distance formula
r(t) = a(t) x s
how does the expansion of the universe affect the wavelength of light emitted by a distant object
the wavelength is stretched by the expansion of the universe
redshift formula
z = (λobs - λem) / λem
Hubble-Lemaitre law formula
Vrec = Ho * d
Hubble-Lamaitre law distorted by peculiar motions
Vobs = Ho * d + Vpec
λobs / λem =
a₀ / a(t)
1 + z =
a₀ / a(t)
v = dr/dt =
d/dt (as) = ȧ*s = ȧ/a * (as) = ȧ/a * r
H(t) =
ȧ/a
present day value of Hubble constant formula
Ho = (ȧ/a)t=to
age of the universe
τ = 9.8h⁻¹ x10⁹ yr
luminosity distance
d²lum ≡ L/S
accounting for redshift
=>
dlum = a₀r₀ (1+z)
relating angular and luminosity distances via
ddiam = a₀r₀ / 1+z = dlum / (1+z)²
what is used to estimate luminosity distances
the 3-band near-infrared photometry of 2MASS
4 things that support a homogeneous and isotropic universe
1) Hubble-Lemaitre law has been verified over a large range of scales and its accuracy supports
2) The CMBR is isotropic to a very high accuracy, and it has a very large energy density
Standard hot Big Bang models naturally incorporate the CMBR
3) By adjusting only the baryon density, given the standard model for expansion, one obtains an accurate prediction for the abundances of several light elements and their isotopes which is in agreement
4) All measurements give consistent values for the age of the universe of 13.7x10^9 y
The number of objects observed from any given point within a solid angle at radii smaller than r is
N = no 4/3πr³*Ω/4π
The number of objects of a given luminosity L and a flux larger than F is
N(>F) = const*no L³/² F-³/²Ω
If not all galaxies have same luminosity L N(>F) =
constnoF-³/²Ω 0 ∫∞ f(L)L³/²dL
we obtain the number of object of a given luminosity L and an apparent magnitude smaller than m
logN(< m) = const + 3/5 m+logΩ
Robertson - Walker metric
ds² = -c²dt² + a²(t) [(dr²/1-kr²) + r²(d² + sin²θ d²ϕ)]
The total number of sources out to some distance ro is,
N(ro) = n(to)ao³ 0 ∫ ro (r²dr/√1-kr²)
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, then 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, and can’t fill their portion of space with light forever
- The speed of light is finite, so only stars within a finite distance can be observed, i.e. the light from the most distant sources has not had time to reach us,
- Above all, the Universe almost certainly has a finite age.
dlum derivation
photons lose energy ∝ (1+z)
photons arrive less frequently, also ∝ (1+z)
S = L/a0^2r0^2(1+a)^2
dlum = a0r0(1+z)
ddiam derivation
ddiam = l/sinθ = l/θ
l = ds = r0a(te)dθ
dθ = 1/r0a(te) = 1(1+z)/a0r0
dlum/(1+z^2) = a0/1+z
graph for d diam
see notes
