Seb Oliver

1
Distant Universe

• Seb Oliver
• Lecture 7 8 Classic Cosmological Tests

2
Main Topics

• Standard Hot Big Bang Model
• Classical Observational Cosmology
• Galaxy Evolution
• The Hunt for the First Galaxies
• Background Light
• Structure Formation

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Classical Observational Cosmology

• Observable Parameters
• Distances
• Classical Tests
• The microwave background and Primordial
  Abundances

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Classic Cosmological Tests

• Hubble Diagram
• Number Counts
• Tolman Test
• Angular-Diameter Distance Test
• Age of the Universe
• The microwave Background and Primordial
  Abundances

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Hubble Diagram
Ideally choose a standard candle, i.e. a class of
object whose Luminosities do not change over
cosmological time
Predict f(z) from DL in cosmological model
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Hubble Diagram Plots
Same information can be plotted in a variety of
ways
Measure Dl from ratio of flux to Luminosity
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Luminosities z
My luminosity is 1000
My luminosity is 100
My luminosity is 10
zz3
z0
zz2
zz1
How to measure luminosity?
Standard candles?
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Hubble Diagram

• Not possible to find a class of fixed luminosity
  object
• Usually choose a class whose luminosity in the
  local Universe depends in a known way on a
  limited number of other parameters

• So measuring a1,etc. give L
• The stronger the correlation with a and smaller
  the dispersion the better

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Hubble Diagram
Measurement of a reduces the spread in standard
candle luminosities, but a residual dispersion re
mains
Local calibration
L(a)
Uncertainty in L, knowing a
Uncertainty in L
s
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What makes a good candle?

• Small range of luminosities
• High Luminosities
• Few calibration parameters
• Low dispersion of calibration relation
• Doesnt evolve

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Hubble Diagram

• Cephid variables a is period
• Spiral galaxies a is rotational velocity
• Elliptical galaxies a is velocity dispersion
• Brightest Cluster Galaxy (BCG) a is cluster
  X-ray temperature
• Super Novae Ia a is time-constant of light curve

See. The Cosmological Distance Ladder
(Rowan-Robinson) or 5.3, 5.4 5.5 Cosmological
Physics Peacock
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Supernovae Hubble Diagram
We will discuss this on Friday
13
Supernovae Hubble Diagram
We will discuss this on Friday
14
Number Counts
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Euclidean Number Counts
Assume a class of objects with L which with a
sensitivity f are visible to a distance r
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Euclidean Number Counts
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Cosmological Number counts
Assume co-moving density is constant
Co-moving volume element (all-sky)
Co-moving volume
since we know
we can deduce N(f)
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Cosmological Number counts
Number density of sources
Assume co-moving density is constant
Proper volume element
since we know
we can deduce N(f)
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Measuring Number Counts
N (f2)
time since begin of Universe
N (f1)
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Number Counts
Perform a surveys often at different deeper flux
limits
All matter-dominated, P0 models have
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Olbers Paradox again

• Another statement of Olbers paradox says that
  the Sky should be infinitely bright as in an
  infinite Universe

(4p converts from surface brightness to flux over
whole sky, f max is brightest object in the sky)
True in a Euclidean Universe, but not in other
cosmological models with
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Tolman Test
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Surface Brightness
Surface brightness is flux per unit solid angle
Independent of cosmology!
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Surface Brightness / Tolman Test
Gregory D. Wirth ltwirth_at_uvastro.phys.uvic.cagt Last
modified Sat Apr 19 131318 1997
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Angular-Diameter Distance Test
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Angular Diameter Distance Test

• Virtually identical to the Hubble diagram
• Except instead of flux the observed parameter is
  angular diameter of object
• Instead of luminosity the true quantity is
  length, so a standard rod rather than standard
  candle is required

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What makes a good rod?

• Small range of sizes
• Sizes at frequencies that are observable with
  high resolution
• Large sizes!
• Few calibration parameters
• Low dispersion of calibration relation
• Doesnt evolve

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Angular-Diameter Distance Test
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Angular - Diameter test
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Angular - Diameter Distance test
Using Clusters
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Angular - Diameter Distance Test
Using Radio galaxies
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Angular - Diameter Distance Test
Using Radio galaxies
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Age of the Universe
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Age of the Universe
Different models give different ages e.g. for
matter dominated
luckily
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Age of the Universe
empty
half way between
critical

• Age can be measure by
• Age of globular clusters
• age of Universe gt age of stars
• Nuclear Cosmo-chronology
• Age of Universe gt age of chemicals

e.g. Peacock Chapter 5.
36
Cosmic Microwave Background and Nucleosynthesis
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Nucleosynthesis
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Summary

• Black-body CMBR and nucleosynthesis confirm big
  picture but dont constrain models
• Hubble Diagram assumes Luminosity of standard
  candle does not depend on redshift
• Number counts diagram assumes co-moving number
  density of sources is constant
• Angular-diameter distance assumes rods dont
  change length (plus large scatter)
• Age of the Universe assumes we can measure the
  age accurately