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A3 Cosmology > Part1 - Appearance of the Universe > Flashcards

Part1 - Appearance of the Universe Flashcards

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1
Q

on almost every scale, the universe is

A

inhomogeneous and anisotropic

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2
Q

As we survey the local Universe, we see that the spatial distribution of galaxies is

A

not uniform ie galaxies appear to be clustered.

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3
Q

The APM Galaxy Survey

A

contains positions, magnitudes, sizes and shapes for
about 3 million galaxies selected from UKST survey plates which were scanned using
the APM Facility.

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4
Q

Edwin Hubble plotted…

A

the observed (radial) velocities of nearby galaxies, deduced from the Doppler shift of their spectral lines, against their distances, derived
from Cepheid variables within the galaxies.

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5
Q

doppler shift of a spectral line

A

z = λo-λe/λe

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6
Q

By assuming that the observed Doppler shift was related to the velocity of the galaxy by v = cz, where c is the speed of light, Hubble found that

A

the galaxies were nearly all moving away from us (they were redshifted) and that their recession velocities, vrec, were approximately proportional to their distances, d, so that
vrec = H0d

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7
Q

Hubble-Lemaître’s law says that distant galaxies recede from us with

A

speeds that
increase linearly with distance – the first indication of an expanding Universe

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8
Q

Hubble constant is usually measured in units of

A

kms-1 Mpc-1

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9
Q

redshift survey

A

accurate maps of the galaxy distribution on large scales using measured redshift values to indicate the relative separation of galaxies

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10
Q

redshift surveys reveal

A

patterns in the galaxy distribution. In particular we see:
galaxy clusters
sheets and filamentary structure
voids

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11
Q

problem with results for redshift surveys

A

see lots of features which suggest universe is not homogeneous or isotropic
eg sloan great wall

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12
Q

sloan great wall

A

This shows a recession velocity range of about 30,000 km s−1 which corresponds to a size of about 430 Mpc.

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13
Q

Cosmologists use various different statistical methods to quantify the
degree of structure and clustering in redshift surveys. When applied to the most recent
redshift surveys they show

A

On scales larger than about 30 000 km s−1
the Universe
begins to look uniform and homogeneous.

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14
Q

on small scales, galaxies

A

are grouped together in clusters (10-1000 members)

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15
Q

within galaxy clusters, galaxies may have

A

a large peculiar motion, or speed, that differs slightly from their recession velocity given by the Hubble-Lemaître law.

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16
Q

peculiar motion is cause by

A

gravitational interaction with the other cluster members.

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17
Q

peculiar motion is most pronounced

A

for galaxies that are reasonably close, and have therefore
relatively low recession velocities.

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18
Q

superclsuters

A

The distribution of galaxy clusters is also non-uniform. Galaxy clusters are themselves clustered, and are organised into larger-scale structures which we refer to as
superclusters

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19
Q

If we know the luminosity of a star and measure its flux at Earth, we can

A

estimate its distance because the flux drops off as the inverse-square of the distance.

can express this in distance modulus formula

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20
Q

luminosity indicators

A

Certain variable stars provide us with an estimate of M, so these distance indicators are basically luminosity indicators.
eg: RR Lyrae stars, and Cepheid variable stars.

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21
Q

For the closest galaxies the Hubble-Lemaître expansion law is distorted by

A

peculiar motions due to the pull of nearby galaxies

vobs=H0d+vpec

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22
Q

typical magnitudes for vpec

A

300 kms-1

although in rich clusters some
galaxy peculiar motions may be as much as several thousand km s−1

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23
Q

when can we ignore the effects of peculiar motion

A

on large enough scales

note if vpec=300, H0=71, for d>100, vpec is less than 5% of H0d

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24
Q

We can expect that Hubble-Lemaître’s law will hold to within

A

a few percent provided we are not considering galaxies in our immediate neighbourhood, where peculiar velocities significantly affect the observed recession velocities

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25
If we want to measure the distance to nearby galaxies
we cannot rely on using Hubble-Lemaître’s law to do so, i.e., we need to use galaxy distance indicators independent of redshift.
26
Cosmological distance ladder
shows how different overlapping measuring techniques allow us to measure distances out to Gpc scales.
27
why was Hubble wrong
measured within distance, where peculiar velocities are dominant and he was not measuring the true cosmological expansion velocity. Grossly underestimated the distances to his calibrating galaxies, partly due to using the wrong absolute magnitude for Cepheid variables, making the wrong correction for extinction, and misclassifying as Cepheids objects which were not Cepheids at all
28
why is it common to write H0=100h
so that uncertainty over the value of H0 could be recast as uncertainty over the value of the dimensionless number h
29
why did launch of hubble space telescope help with disagreements of H0
Cepheids became directly observable within nearby clusters. This allowed the direct calibration of secondary distance indicators, and provided a link to more distant clusters
30
The standard model for the origin and evolution of the Universe is called
the hot big bang model
31
Although the Universe is evolving over time, it is assumed that at any time t and on large enough scales,
the Universe is homogeneous and isotropic
32
homogeneous universe
universe looks the same no matter where you are in it
33
isotropic universe
universe looks same no matter what direction you look in
34
cosmological principle
no ‘special places’ in the Universe, such as a centre or an edge.
35
underlying structure in universe is assumed to satisfy cos princ on all scales so
galaxies can be thought of as local disturbances in an otherwise perfectly homogeneous and isotropic Universe.
36
The evolution of the Universe can then be described by
the size of a dimensionless number which we call the cosmic scale factor and is usually written a(t).
37
the scale factor measures the
characteristic size of the Universe at time t
38
by convention, values of cosmological quantities at the present time are denoted
subscript 0
39
proper distance between two galaxies at t
actual separation
40
co-moving separation
separation expressed in terms on a coordinate system which expands along with the background space co-moving separation is not changed by the expansion of the Universe
41
The wavelength of light emitted by a distant object will be
stretched by the expansion of the Universe. The redshift of light from a distant object can be interpreted in terms of the amount by which the Universe has expanded since the light from the object was emitted
42
proper velocity
rate of change of proper distance (v=dr/dt=d/dt(as)=adot s = a./a r which is hubbles law)
43
In a homogeneously and isotropically expanding universe, an observer in any galaxy would observe
neighbouring galaxies to obey the Hubble-Lemaître law and have proper velocities proportional to their proper distances.
44
Hubble's constant measures
the rate of change of the scale factor a(t): it is not a constant in time, but is a constant in space at any given time.
45
To find the age of the universe, we define it by the condition that
a(t) → 0 at time t = 0, so that it is the time in the past when the proper distance between galaxies tended to zero The Big Bang occurred at time t = 0.
46
We can estimate the time elapsed since the Big Bang by the following simple argument
If we assume a constant expansion rate, so that H(t) = H0 for all t, then v=H0r =r/t so t=H0^-1
47
hubble time
sets a timescale for the expansion of the Universe.
48
what is missing in simple argument for estimating time since Big Bang
the effect of gravity, which will slow down the expansion so that H(t) was larger in the past. Therefore, including the effects of gravity should give an age of the Universe which is smaller than the Hubble time: t0 < τ .
49
We can learn about how far away objects are by considering
their apparent sizes and how bright they are
50
the luminosity distance of an object realtes
flux observed to distance
51
luminosity distance
the distance the object appears to have when assuming the inverse square relationship holds
52
luminosity distance is not physical distance to the object because
in the real Universe, the inverse square law does not hold
53
breaking of the inverse square will happen if
the universe is not flat and because the universe is expanding
54
luminosity
energy emitted per solid angle per second
55
why is luminosity total power divided by 4pi
because there are 4pi steradians of solid angle in the whole sky
56
radiation flux density, s
energy received per unit area per second
57
luminosity distance relationship
dlum^2=L/S
58
in a static, non-expanding universe, S=
L/d^2phys
59
space is expanding so need to take into account
redshift
60
two effects due to expansion
photons lose energy prop to (1+z) so have less energy on arrival photons arrive less frequently - also prop to 1+Z
61
received flux and luminosity distance with redshift taken into account
S=L/a0^2r0^2(1+z)^2 dlum = a0r0(1+z)
62
distant objects appear to be further away than they really are because of
the effect of cosmological redshift reducing their apparent luminosity, with dlum > dphys for z>>1
63
effect of dlum>dphys is exacerbated if the universe is not flat because
luminosity distance being enhanced for hyperbolic geometries, or suppressed for spherical geometries.
64
issue with assuming bolometric luminosity
detectors are sensitive to only a range of wavelengths, they have a limited bandwidth. Redshift of light due to cosmological expansion means that a detector detects light emitted in a different part of the spectrum for distant objects in comparison to nearby objects, introducing a bias into measurements
65
luminosity distance depends on
the cosmology, and whether the universe is flat or not. So could be used to tell us which cosmological model describes our Universe.
66
the angular diameter distance is a measure of
how large an object appears to be.
67
As with luminosity distance, angular diameter distance is well-defined for
euclidean geometries (universe with no curvature)
68
assuming an object lies perpendicular to the line of sight and has physical extent l, its angular distance is
ddiam = l/sin theta = l/theta
69
physical size of the object will be related by
l=r0 a(te) theta where te is the time the light from the object was emitted
70
we observe an angular size, theta=
l/ro a(te) = l(1+z)/a0r0
71
If we consider objects with fixed physical size l, the earlier we consider them...
the larger a comoving size they have
72
the Universe is expanding so very distant objects now were closer to us in the past and therefore
looked larger when they emitted the light we currently observe.
73
In resolving distant objects with physical extent,what does the luminosity distance effect do?
dims the radiation and the angular diameter distance effect causes the light to be spread over a larger angular area.
74
For objects with z ≈ 1, physical size appears to be
minimised so we can use high-redshift objects in an attempt to probe the cosmological model.
75
The 3-band near-infrared photometry of the 2MASS survey has been used to estimate luminosity distances to galaxies. Since the broad-band integrated flux is strongly correlated with distance to the object...
a qualitative view of the 3D galaxy distribution is created
76
evidence for the cosmological principle
Hubble law CMBR Primordial nucleosynthesis age of the universe
77
how does hubble law support CP
verified over a large range of scales and its accuracy supports homogeneous isotropic cosmologies
78
how does CMBR support CP
CMBR is isotropic to a very high accuracy and it has a very large energy density standard hot big bang models naturally incorporate CMBR
79
how does primordial nucleosynthesis support CP
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 with their observed values
80
how does the age of the universe support CP
all measurements give consistent values for the age of the Universe which supports the model of a homogeneous and isotropic universe
81
galaxy number counts - start point
non-expanding universe with no curvature and homogeneous, isotropic distribution of matter with number density n0
82
galaxy number count expression does not take into account
the cosmological redshift nor galaxy evolution
83
differential galaxy number count - starting point
Robertson-Walker metric - non-flat, expanding space time in spherical coords
84
when do we see a departure form the euclidean method
faint magnitudes and high redshifts
85
differential galaxy number counts could be used to determine which model the Unievrse adheres to but
galaxy evolution means that luminosity is time dependent and difficult to deconvolve the effects of evolution from the effects of expansion
86
resolution of Olbers' paradox
stars have finite lifetimes speed of light finite so only stars within a finite distance can be observed universe has a finite age
87

A3 Cosmology (4 decks)

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