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Observational Cosmology 4. Cosmological Distance
Scale
The distance scale path has been a long and
tortuous one, but with the imminent launch of HST
there seems good reason to believe that the end
is finally in sight.    Marc Aaronson
(1950-1987) 1985 Pierce Prize Lecture).
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4.1 Distance Indicators

• Distance Indicators

• Measurement of distance is very important in
  cosmology
• However measurement of distance is very
  difficult in cosmology
• Use a Distance Ladder from our local
  neighbourhood to cosmological distances

• Primary Distance Indicators ? direct distance
  measurement (in our own Galaxy)
• Secondary Distance Indicators ? Rely on primary
  indicators to measure more distant object. 
• Rely on Primary Indicators to calibrate secondary
  indicators!

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4.1 Distance Indicators

• Distance Indicators

• Primary Distance Indicators
• Radar Echo
• Parallax 
• Moving Cluster Method
• Main-Sequence Fitting 
• Spectroscopic Parallax
• RR-Lyrae stars
• Cepheid Variables
• Galactic Kinematics

• Secondary Distance Indicators
• Tully-Fisher Relation
• Fundamental Plane
• Supernovae
• Sunyaev-Zeldovich Effect
• HII Regions
• Globular Clusters
• Brightest Cluster Member
• Gravitationally Lensed QSOs
• Surface Brightness Fluctuations

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4.2 Primary Distance Indicators

• Primary Distance Indicators

Primary Distance Indicators

• Radar Echo
• Parallax 
• Moving Cluster Method
• Main-Sequence Fitting 
• Spectroscopic Parallax
• RR-Lyrae stars
• Cepheid Variables
• Galactic Kinematics

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4.2 Primary Distance Indicators

• Radar Echo

• Within Solar System, distances measured, with
  great accuracy, by using radar echo
• (radio signals bounced off planets).
• Only useful out to a distance of 10 AU beyond
  which, the radio echo is too faint to detect.

1 AU 149,597,870,691 m
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4.2 Primary Distance Indicators

• Trigonometric Parallax

• Observe a star six months apart,(opposite sides
  of Sun)
• Nearby stars will shift against background star
  field
• Measure that shift. Define parallax angle as
  half this shift

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4.2 Primary Distance Indicators

• Trigonometric Parallax

• Observe a star six months apart,(opposite sides
  of Sun)
• Nearby stars will shift against background star
  field
• Measure that shift. Define parallax angle as
  half this shift

Define a parsec (pc) which is simply 1 pc
206265 AU 3.26ly.  A parsec is the distance to a
star which has a parallax angle of 1"
Nearest star - Proxima Centauri is at 4.3 light
years 1.3 pc ? parallax 0.8" Smallest parallax
angles currently measurable 0.001" ? 1000
parsecs ? parallax is a distance measure for
the local solar neighborhood.
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4.2 Primary Distance Indicators

• Trigonometric Parallax

• The Hipparcos Space Astrometry Mission
• Precise measurement of the positions, parallaxes
  and proper motions of the stars.
• Mission Goals
• - measure astrometric parameters 120 000 primary
  programme stars to precision of 0.002
• - measure astrometric and two-colour photometric
  properties of 400 000 additional stars (Tycho
  Expt.)
• Launched by Ariane, in August 1989,
• 3 year mission terminated August 1993.
• Final Hipparcos Catalogue
• 120 000 stars
• Limiting Magnitude V12.4mag
• complete fro V7.3-9mag
• Astrometry Accuracy 0.001
• Parallax Accuracy 0.002

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4.2 Primary Distance Indicators

• Trigonometric Parallax

• GAIA MISSION (ESA launch 2010 - lifetime 5
  years)
• Measure positions, distances, space motions,
  characteristics of one billion stars in our
  Galaxy.
• Provide detailed 3-d distributions space
  motions of all stars, complete to V20 mag to
  lt10-6.
• Create a 3-D map of Galaxy.

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4.2 Primary Distance Indicators

• Secular Parallax

• Used to measure distance to stars, assumed to be
  approximately the same distance from the Earth.
• Mean motion of the Solar system is 20 km/s
  relative to the average of nearby stars
• corresponding relative proper motion, dq/dt away
  from point of sky the Solar System is moving
  toward.
• This point is known as the apex
• For anangle q to the apex, the proper motion
  dq/dt will have a mean component ? sin(q)
  (perpendicular to vsun )
• Plot dq/dt - sin(q) ? slope m

green stars show a small mean distance red stars
show a large mean distance
http//www.astro.ucla.edu/wright/distance.htm
Statistical Parallax
If stars have measured radial velocities, ?
scatter in proper motions dq/dt can be used to
determine the mean distance.
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4.2 Primary Distance Indicators

• Moving Cluster Method

Observe cluster some years apart ? proper motion m
Radial Velocity (km/s) vR from spectral lines
Stars in cluster move on parallel paths ?
perceptively appear to move towards common
convergence point (Imagine train tracks or
telegraph poles disappearing into the
distance) Distance to convergence point is given
by q
Main method for measuring distance to Hyades
Cluster 200 Stars (Moving Cluster Method ?
45.7 pc). One of the first rungs on the
Cosmological Distance Ladder c.1920 40 pc (130
ly) c.1960 46 pc (150 ly) (due to
inconsistency with nearby star HRD) Hipparcos
parallax measurement 46.3pc (151ly) for the
Hyades distance.
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4.2 Primary Distance Indicators

• Moving Cluster Method

Ursa Major Moving Cluster 60 stars 23.9pc
(78ly) Scorpius-Centaurus cluster 100 stars
172pc (560ly) Pleiades by Van Leeuwen at 126
pc, 410 ly)

• Hipparcos 3D structure of the Hyades as seen
  from the Sun in Galactic coordinates.
• X-Y diagram looking down the X-axis towards
  the centre of the Hyades.
• Note Larger spheres closer stars
• Hyades rotates around the Galactic Z-axis.
• Circle is the tidal radius of 10 pc
• Yellow stars are members of Eggen's moving group
  (not members of Hyades).
• Time steps are 50.000 years. (Perryman et al. )

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4.2 Primary Distance Indicators

• Standard Rulers and Candles

• To measure greater distances (gt10-20kpc -
  cosmological distances)
• ? Require some standard population of objects
• e.g., objects of
• the same size (standard ruler)
• or
• the same luminosity (standard candle)
• and
• high luminosity

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4.2 Primary Distance Indicators

• Main sequence Fitting

Einar Hertzsprung Henry Norris Russell Plot
stars as function of luminosity temperature ?
H-R diagram Normal stars fall on a single track ?
Main Sequence
Observe distant cluster of stars, Apparent
magnitudes, m, of the stars form a track parallel
to Main Sequence ? correctly choosing the
distance, convert to absolute magnitudes, M, that
fall on standard Main Sequence.

• Useful out to few 10s kpc (main sequence stars
  become too dim)
• used to calibrate clusters with Hyades

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4.2 Primary Distance Indicators

• Spectroscopic Parallax

Information from Stellar Spectra

• Spectral Type ? Surface Temperature - OBAFGKM
  RNS
• O stars - HeI, HeII
• B Stars - He
• A Stars - H
• F-G Stars - Metals
• K-M Stars - Molecular Lines

• Surface Gravity ? Higher pressure in atmosphere ?
  line broadening, less ionization - Class I(low)
  -VI (high)
• Class I - Supergiants
• Class III - Giants
• Class V - Dwarfs
• Class VI - white Dwarfs

Temperature from spectral type, surface gravity
from luminosity class ? mass and luminosity.
Measure flux ? Distance from inverse square Law
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4.2 Primary Distance Indicators
Cepheid variable stars - very luminous yellow
giant or supergiant stars. Regular pulsation -
varying in brightness with periods ranging from 1
to 70 days. Star in late evolutionary stage,
imbalance between gravitation and outward
pressure ?pulsation Radius and Temperature change
by 10 and 20. Spectral type from F-G

• Cepheid Variables

• Henrietta S. Leavitt (1868 - 1921) - study of
  1777 variable stars in the Magellanic Clouds.
• c.1912 - determined periods 25 Cepheid variables
  in the SMC ? Period-Luminosity relation
• Brighter Cepheid Stars Longer Pulsation
  Periods
• Found in open clusters (distances known by
  comparison with nearby clusters). ? Can
  independently calibrate these Cepheids

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4.2 Primary Distance Indicators

• Cepheid Variables

Prior to HST, Cepheids only visible out to 5Mpc
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4.2 Primary Distance Indicators
Stellar pulsation ? transient phenomenon Pulsating
stars occupy instability strip vertical strip
on H-R diagram.  Evolving stars begin to pulsate
? enter instability strip. Leave instability
strip ? cease oscillations upon leaving.  

• RR Lyrae Variables

Type Period Pop Pulsation
LPV 100-700d I, II radial
Classical Cepheids-S 1-6 I radial
Classical Cepheids-L 7-50d I radial
W Virginis (PII Ceph) 2-45d II radial
RR Lyrae 1-24hr II radial
ß Cephei stars 3-7hr I radial/non radial
d Scuti stars 1-3hr I radial/non radial
ZZ Ceti stars 1-20min I non radial

• RR-Lyrae stars
• Old population II stars that have used up their
  main supply of hydrogen fuel
• Relationship between absolute magnitude and
  metallicity (Van de Bergh 1995)
• Mv (0.15 0.01) Fe/H 1.01
• Common in globular clusters major ? rung up in
  the distance ladder
• Low luminosities, ? only measure distance to
  M31

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4.3 Secondary Distance Indicators

• Secondary Distance Indicators

Secondary Distance Indicators

• Tully-Fisher Relation
• Fundamental Plane
• Supernovae
• Sunyaev-Zeldovich Effect
• HII Regions
• Globular Clusters
• Brightest Cluster Member
• Gravitationally Lensed QSOs
• Surface Brightness Fluctuations

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4.3 Secondary Distance Indicators

• Globular Clusters

• Main Sequence Fitting
• H-R diagram for Globular clusters is different to
  open Clusters (PII objects!)
• Cannot use M-S fitting for observed Main Sequence
  Stars
• Use Theoretical HR isochrones to predict Main
  Sequence ? distance
• Alternatively use horizontal branch fitting

• Angular Size
• Make assumption that all globular clusters same
  diameter D
• Distance to cluster, d, is given by angualr size
  qD/d

Distance range of GCLF method is limited by
distance at which peak Mo is detectable, 50 Mpc
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4.3 Secondary Distance Indicators

• Tully Fisher Relationship

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4.3 Secondary Distance Indicators

• Tully Fisher Relationship

Tully and Fischer (1977) Observations with I ?
45o a 6.250.3 b 3.5 0.3,
Knowing M ?
? Problems with Tully-Fisher Relation

• TF depends on waveband
• Relation is steeper by a factor of two in the IR
  band than the blue band. (Correction requires
  more accurate measure of M/L ratio for disk
  galaxies)

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4.3 Secondary Distance Indicators

• D-s Relationship

• Elliptical Galaxies ? Cannot use Tully Fisher
  Relation
• Little rotation
• little Hydrogen (no 21cm)

Faber-Jackson (1976) Elliptical Galaxies L?s4
L Luminosity s central velocity dispersion
Large Scatter ? constrain with extra parameters?
Define a plane in parameter space
Faber-Jackson Law
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4.3 Secondary Distance Indicators
Any 2 parameters ? scatter (induced by 3rd
parameter)

• D-s Relationship

• Combine parameters
• Constrain scatter
• Fundamental Plane

Instead of Io, ro Use Diameter of aperture, Dn,
Dn - aperture size required to reach surface
Brightness B20.75mag arcsec2

• Advantages
• Elliptical Galaxies - bright ? measure large
  distances
• Strongly Clustered ? large ensembles
• Old stellar populations ? low dust extinction

• Disadvantages
• Sensitive to residual star formation
• Distribution of intrinsic shapes, rotation,
  presence of disks
• No local bright examples for calibration

• Usually used for RELATIVE DISTANCES and
  calibrate using other methods

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4.3 Secondary Distance Indicators

• Surface Brightness Fluctuations

SBF method Measure fluctuation in brightness
across the face of elliptical galaxies
Fluctuations - due to counting statistics of
individual stars in each resolution element
(Tonry Schneider 1988)
Can use out to 70 Mpc with HST
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4.3 Secondary Distance Indicators

• Brightest Cluster Members

• Assume
• Galaxy clusters are similar
• Brightest cluster members similar brightness
  cD galaxies

• Calibration
• Close clusters
• 10 close galaxy clusters
• brightest cluster member MV 22.82?0.61

• Advantage
• Can be used to probe large distances

• Disadvantage
• Evolution galaxy cannibalism
• Large scatter in brightest galaxy
• Use 2nd, 3rd brightest
• Use N average brightest N galaxies.

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4.3 Secondary Distance Indicators

• Supernova Ia Measurements

(similarly applied to novae)
SN1994D in NGC4526
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4.3 Secondary Distance Indicators

• Supernova Ia Measurements

• Supernova Ia
• Found in Ellipticals and Spirals (SNII only
  spirals)
• Progenitor star identical
• Characteristic light curve fast rise, rapid
  fall,
• Exponential decay with half-Life of 60 d.
• (from radioactive decay Ni56 ? Co56 ? Fe56)
• Maximum Light is the same for all SNIa !!

Supernovae luminosities ? entire galaxy1010Lo
(1012Lo in neutrinos)
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4.3 Secondary Distance Indicators

• Supernova Ia Measurements

Lightcurves of 18 SN Ia z lt 01 (Hamuy et al )
Supernovae distances good out to gt 1000Mpc ?
Probe the visible Universe !
after correction of systematic effects and time
dilatation (Kim et al., 1997).
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4.3 Secondary Distance Indicators

• Gravitational Lens Time Delays

• Light from lensed QSO at distance D, travel
  different distances given by DDcos(q) -
  Dcos(f)
• Measure path length difference by looking for
  time-shifted correlated variability in the
  multiple images

source - lens - observer is perfectly aligned ?
Einstein Ring source is offset ? various multiple
images Can be used to great distances

• Uncertainties
• Time delay (can be gt 1 year!) and seperation of
  the images
• Geometry of the lens and its mass
• Relative distances of lens and background sources

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4.3 Secondary Distance Indicators

• Gravitational Lens Time Delays

• Light from the source S is deflected by the
  angle a when it arrives at the plane of the lens
  L, finally reaches an observer's telescope O.
• Observer sees an image of the source at the
  angular distance h from the optical axis
• Without the lens, she would see the source at the
  angular distance b from the optical axis.
• The distances between the observer and the
  source, the observer and the source, and the lens
  and the source are D1, D2, and D3, respectively.

http//leo.astronomy.cz/grlens/grl0.html
Small angles approximation Assume angles b, h,
and deflection angle a are ltlt1 ? tanqq Weak
field approximation Assume light passes through
a weak field with the absolute value of the
perculiar velocities of components and Gltltc2
For perfectly aligned lens and source (b0) -
two images at same distance from lens h1 h2 e
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4.4 The Distance Ladder

• The Distance Ladder

The Distance Ladder
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4.4 The Distance Ladder

• The Distance Ladder

Comparison eight main methods used to find the
distance to the Virgo cluster.
Method Distance Mpc
1 Cepheids 14.9?1.2
2 Novae 21.1 ?3.9
3 Planetary Nebula 15.4 ?1.1
4 Globular Cluster 18.8 ?3.8
5 Surface Brightness 15.9 ?0.9
6 Tully Fisher 15.8 ?1.5
7 Faber Jackson 16.8 ?2.4
8 Type Ia Supernova 19.4 ?5.0
Jacoby etal 1992, PASP, 104, 599
HST Measures distance to Virgo (Nature 2002)
D17.1 1.8Mpc
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4.4 The Distance Ladder

• The Distance Ladder

Supernova (1-1000Mpc)
Hubble Sphere (3000Mpc)
1000Mpc
Tully Fisher (0.5-00Mpc)
100Mpc
Coma (100Mpc)
10Mpc
Virgo (10Mpc)
Cepheid Variables (1kpc-30Mpc)
1Mpc
M31 (0.5Mpc)
RR Lyrae (5-10kpc)
100kpc
LMC (100kpc)
Spectroscopic Parallax (0.05-10kpc)
10kpc
Galactic Centre (10kpc)
Parallax (0.002-0.5kpc)
1kpc
RADAR Reflection (0-10AU)
Pleides Cluster (100pc)
Proxima Centauri (1pc)
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4.5 The Hubble Key Project

• The Hubble Key Project

The Hubble Key Project
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4.5 The Hubble Key Project

• To the Hubble Flow

• The Hubble Constant
• Probably the most important parameter in
  astronomy
• The Holy Grail of cosmology
• Sets the fundamental scale for all cosmological
  distances

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4.5 The Hubble Key Project

• To the Hubble Flow

• To measure Ho require
• Distance
• Redshift

Cosmological Redshift - The Hubble Flow - due to
expansion of the Universe
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4.5 The Hubble Key Project

• Hubble Key Project

• Observations with HST to determine the value of
  the Hubble Constant to high accuracy
• Use Cepheids as primary distance calibrator
• Calibrate secondary indicators
• Tully Fisher
• Type Ia Supernovae
• Surface Brightness Fluctuations
• Faber - Jackson Dn-s relation
• Comparison of Systematic errors
• Hubble Constant to an accuracy of ?10

• Cepheids in nearby galaxies within 12 million
  light-years.
• Not yet reached the Hubble flow
• Need Cepheids in galaxies at least 30 million
  light-years away
• Hubble Space Telescope observations of Cepheids
  in M100.
• Calibrate the distance scale

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4.5 The Hubble Key Project

• Hubble Key Project

H0 75 ? 10 kmsMpc
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4.5 The Hubble Key Project

• Combination of Secondary Methods

• Biggest Uncertainty
• zero point of Cepheid Scale (distance to LMC)

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4.6 Summary

• Summary

• There are many many different distance
  indicators
• Primary Distance Indicators ? direct distance
  measurement (in our own Galaxy)
• Secondary Distance Indicators ? Rely on primary
  indicators to measure more distant object. 
• Rely on Primary Indicators to calibrate
  secondary indicators
• Create a Distance Ladder where each step is
  calibrated by the steps before them
• Systematic Errors Propagate!
• Hubble Key Project - Many different methods
  (calibrated by Cepheids)
• Accurate determination of Hubble Constant to 10

Is the Ho controversy over ?
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4.6 Summary

• Summary

?
Observational Cosmology 4. Cosmological Distance
Scale
Observational Cosmology 5. Observational Tools
?