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2017/5/22
Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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). 1
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
4.2: Primary Distance Indicators
Primary Distance Indicators
Primary Distance Indicators
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Radar Echo
Parallax
Moving Cluster Method
Main-Sequence Fitting
Spectroscopic Parallax
RR-Lyrae stars
Cepheid Variables
Galactic Kinematics
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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
d  c t
2
1 AU = 149,597,870,691 m
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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
QuickTime™ and a
Animation decompressor
are needed to see this picture.
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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
d
d
1 AU
1 radian =
57.3o
1 AU
1
 AU
tan prads p
p

= 206265"
d
1
206265
AU 
AU
prads
p
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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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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 V=12.4mag
•complete fro V=7.3-9mag
•Astrometry Accuracy 0.001”
•Parallax Accuracy 0.002”
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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 V=20 mag to <10-6”.
• Create a 3-D map of Galaxy.
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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
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
http://www.astro.ucla.edu/~wright/distance.htm
For anangle
The mean distance of the stars is

v sun
4.16
d

pc
m m(" / yr)
4.16 for Solar motion in au/yr.
green stars show a small mean distance
red stars show a large mean distance
Statistical Parallax
If stars have measured radial velocities,
 scatter in proper motions
dq/dt can be used to determine the mean distance.
v
d  Ýr
q
v r in pc/s
Ýin rad/s
q
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
4.2: Primary Distance Indicators
Moving Cluster Method
vC
vr
Observe cluster some years apart  proper motion m
Radial Velocity (km/s) vR from spectral lines
Tangential Velocity (km/s)
vT  4.74m d
q
vt
d
q
m (“/yr)
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

vT  vC sin q 
vR
 d 
v R  vC cosq 
4.74m tan 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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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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)
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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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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
4.2: Primary Distance Indicators
Standard Rulers and Candles
To measure greater distances (>10-20kpc - 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
can calculate
L
• Flux (S) from luminosity, (L)
S
• Calculate distance (DL)
4DL2
• Measuring redshift (z)
•  Cosmological parameters Ho, Wm,o, WL,o


M  2.5lg( L /L0 ) 
m  2.5lg( S /S0 )
dL  10

(mM )
5
 DL 
L
4 S
DISTANCE
MODULUS
 dL 
 M  m  5lg 
  m  M  5lg dL ,Mpc  25
10 pc 
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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.
AGB
Red Giant
Branch
Turn
off

m  M  5lg dL,Mpc  25
Magnitude (more -ve)
Get Distance from the distance modulus
near stars
m-M
far stars
WHITE DWARF
 temperature
• Useful out to ~few 10s kpc (main sequence stars become too dim)
• used to calibrate clusters with Hyades
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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
L  4T 4 R 2
• Class III - Giants
• Class V - Dwarfs
L  M  ( ~ 3  4)
• Class VI - white Dwarfs
g
GM
R2
Temperature from spectral type, surface gravity from luminosity class  mass and luminosity.
Measure flux  Distance from inverse square Law

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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
4.2: Primary Distance Indicators
Cepheid Variables
•
•
•
•
Cosmological Distance Scale
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
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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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
4.2: Primary Distance Indicators
Cepheid Variables
2 types of Classical Cepheids
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M v  2.76lg Pd 1.0  4.16
Distance Modulus
m  M  5lg dL,Mpc  25
Prior to HST, Cepheids only visible out to ~ 5Mpc
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
4.2: Primary Distance Indicators
RR Lyrae Variables
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.
Type
Period
Pop
Pulsation
LPV*
100-700d
I, II
radial
Classical Cepheids-S
1-6
I
radial
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
Classical Cepheids-L
• 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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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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 ~
 Distance to cluster, d, is given by angualr size q=D/d
D
Globular Cluster Luminosity Function (GCLF) (similarly for PN)
Use Number density of globular clusters as function of magnitude M
 (M)  Ce
(M M * )2
2
2
Peak in luminosity function occurs at same luminosity (magnitude)
Number density of globular clusters as function
of magnitude M for Virgo giant ellipticals
Distance range of GCLF method is limited by distance at which peak Mo is detectable, ~ 50 Mpc
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
4.3: Secondary Distance Indicators
Tully Fisher Relationship
Centrifugal
Redshift
v R2 GM
 2
R
R
Gravitational
Assume same mass/light ratio for all spirals
 M /L
Assume same surface brightness for all spirals

  L / R2
v R4
L   2 2  v R4
 G

Flux
 L 
CvR4 
In Magnitudes M  M o  2.5lg   M o  2.5lg 

Lo 
 Lo 
n


More practically
Blueshift
M  10lg( v R )  C
W o 
M  alg   b
sin i 
Wo = spread in velocities
i = inclination to line of sight of galaxy
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
4.3: Secondary Distance Indicators
Tully Fisher Relationship
Tully and Fischer (1977): Observations with I  45o
a = 6.25±0.3
b = 3.5 ± 0.3,


M  2.5lg( L /L0 ) 
m  2.5lg( S /S0 )
Tully-Fisher
Fornax & Virgo Members
Bureau et al. 1996
Knowing
dL  10
W o 
M  alg  b
sin i 
M
(mM )
5
DISTANCE
MODULUS
 dL 

  m  M  5lg dL ,Mpc  25
M  m  5lg 
10 pc 
 Problems with Tully-Fisher Relation
• TF Depends on Galaxy Type
Mbol = -9.95 lgVR + 3.15
Mbol = -10.2 lgVR + 2.71
Mbol = -11.0 lgVR + 3.31
(Sa)
(Sb)
(Sc)
• 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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Cosmological Distance Scale
Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
4.3: Secondary Distance Indicators
D-Relationship
Elliptical Galaxies  Cannot use Tully Fisher Relation
• Little rotation
• little Hydrogen (no 21cm)
Faber-Jackson (1976): Elliptical Galaxies
L = Luminosity
 = central velocity dispersion
L4
Ellipticals
Lenticulars
M32 (companion to M31)
M B  19.38  0.07  (9.0  0.7)(lg   2.3)
M B  19.65  0.08  (8.4  0.8)(lg   2.3)

http://burro.astr.cwru.edu/Academics/Astr222/Galaxies/Elliptical/kinematics.html
Large Scatter  constrain with extra parameters Define a plane in parameter space
Faber-Jackson Law
Intensity profile (surface brightness)
(r1/4 De Vaucouleurs Law)
Virial Theorem
 m 2 

I
L
I
 Io ro2
1 GM
M
2
m




2 ro
ro

M
Mass/Light ratio
 M
L
1  4(1 ) (1 )
o
L
I(r)  Io e  (r /ro )1/ 4
Fundamental Plane
(Dressler et al. 1987)
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Cosmological Distance Scale
4.3: Secondary Distance Indicators
Any 2 parameters  scatter (induced by 3rd parameter)
I
I
D-Relationship
Combine parameters
Constrain scatter
 Fundamental Plane
Instead of Io, ro: Use Diameter of aperture, Dn,
Dn - aperture size required to reach surface Brightness ~ B=20.75mag 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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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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)
Consider 2 images taken by CCD to illustrate the SBF effect;
Represent 2 galaxies with one twice further away as the other
measure
the mean flux per pixel (surface brightness)
rms variation in flux between pixels.
m  NS
  NS 
1
d
N  d 2 
 of distance
m
is
independent

S  d2 

2

L
S

d
2
m 4d
Compare nearby dwarf galaxy, nearby giant galaxy, far giant galaxy
Choose distance such that flux is identical to nearby dwarf.
The distant giant galaxy has a much smoother image than nearby dwarf.’

Can use out to 70 Mpc with HST
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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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Cosmological Distance Scale
Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
4.3: Secondary Distance Indicators
Supernova Ia Measurements
(similarly applied to novae)
White dwarf pushed over Chandrasekhar limit by accretion begins
to collapse against the weight of gravity, but rather than
collapsing , material is ignited consuming the star in an an
explosion 10-100 times brighter than a Type II supernova
Supernova !
Type II (Hydrogen Lines)
Type I (no Hydrogen lines)
SN1994D in NGC4526
Massive star M>8Mo
Type Ib,c
(H poor massive Star M>8Mo)
Stellar wind or stolen by companion
Type Ia
(M~1.4Mo White Dwarf + companion)
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Cosmological Distance Scale
4.3: Secondary Distance Indicators
Supernova Ia Measurements
Supernovae: luminosities  entire galaxy~1010Lo
(1012Lo in neutrinos)
SN1994D in NGC4526 in Virgo Cluster (15Mpc)
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 !!
MB,max  18.33 5lg h100
L ~ 1010 Lo

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Cosmological Distance Scale
4.3: Secondary Distance Indicators
Supernova Ia Measurements
MB,max  18.33 5lg h100
L ~ 1010 Lo
Gibson et al. 2000 - Calibration of SNIa via Cepheids

lg H o  0.2M B ,max  0.720  0.459
m
B ,15,t
1.1 1.010  0.934
mB ,15,t 1.1
Lightcurves of 18 SN Ia z < 0:1 (Hamuy et al )
2

 28.653  0.042
mB ,15,t  mB,15  0.1E(B  V )
mB ,15  15 day decay rate

E(B  V )  total extinction (galactic

after correction of systematic effects
and time dilatation (Kim et al., 1997).
+ intrinsic)
Distance derived from Supernovae depends on extinction
Supernovae distances good out to > 1000Mpc
 Probe the visible Universe !
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Cosmological Distance Scale
4.3: Secondary Distance Indicators
Gravitational Lens Time Delays
q

http://spiff.rit.edu/classes/phys240/lectures/lens_results/lens_results.html
• Light from lensed QSO at distance D, travel different distances given by =[Dcos(q) - Dcos()]
• 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 > 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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Cosmological Distance Scale
Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
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 <<1  tanq~q
Weak field approximation
Assume light passes through a weak field with the absolute value of the perculiar velocities of components and G<<c 2
lens equation (relation between the angles b,
Where  is the Einstein Radius

h, a)
4GMD3
c 2 D1D2
Lens equation - 2 different solutions
corresponding to 2 images of the source:

D3 
2
b  h  a  h 
h
D1 

h 

1
b  b 2  4 2 
1/ 2
2


h 
b  b 2  4 2 
2
For perfectly aligned lens and source (b=0) - two images at same distance from lens
1/ 2

2
h1 = h2 = e
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
4.4: The Distance Ladder
The Distance Ladder
The Distance Ladder
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
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) D=17.1 ± 1.8Mpc
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Cosmological Distance Scale
Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
4.4: The Distance Ladder
The Distance Ladder
Supernova (1-1000Mpc)
Hubble Sphere (~3000Mpc)
1000Mpc
Tully Fisher (0.5-00Mpc)
100Mpc
10Mpc
Cepheid Variables (1kpc-30Mpc)
1Mpc
Coma (~100Mpc)
Virgo (~10Mpc)
M31 (~0.5Mpc)
RR Lyrae (5-10kpc)
100kpc LMC (~100kpc)
Spectroscopic Parallax (0.05-10kpc)
Parallax (0.002-0.5kpc)
RADAR Reflection (0-10AU)
10kpc Galactic Centre (~10kpc)
1kpc
Pleides Cluster (~100pc)
Proxima Centauri (~1pc)
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
4.5: The Hubble Key Project
The Hubble Key Project
The Hubble Key Project
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
4.5: The Hubble Key Project
cz  Hod
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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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
4.5: The Hubble Key Project
cz  H d
To the Hubble Flow
o
To measure Ho require
• Distance
• Redshift
Cosmological Redshift - The Hubble Flow - due to expansion of the Universe
Must correct for local motions / contaminations
1 z  (1 z)(1 vo /c  vG /c)

vo = radial velocity of observer
vG = radial velocity of galaxy
vo - Measured from CMB Dipole ~ 220kms-1
(Observational Cosmology 2.3)
vG - Contributions include Virgocentric infall, Great attractor etc…
Decompostion of velocity field (Mould et al. 2000, Tonry et al. 2000)
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
4.5: The Hubble Key Project
cz  Hod
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- 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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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
4.5: The Hubble Key Project
Hubble Key Project
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H0 = 75  10 km=s=Mpc
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Cosmological Distance Scale
4.5: The Hubble Key Project
Combination of Secondary Methods
Mould et al. 2000; Freedman et al. 2000
H0 = 716 km s-1 Mpc-1  t0 = 1.3  1010 yr
Biggest Uncertainty
• zero point of Cepheid Scale (distance to LMC)
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
4.6: Summary
Cosmological Distance Scale
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%
H0 = 716 km s-1 Mpc-1  t0 = 1.3  1010 yr
Is the Ho controversy over ?
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Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
4.6: Summary
Cosmological Distance Scale
Summary
Observational Cosmology
4. Cosmological Distance Scale
終
Observational Cosmology
5. Observational Tools
次：
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