Transcript Document
2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
Observational Cosmology: 4.
Cosmological Distance Scale
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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2020/4/26 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 Secondary Distance Indicators direct distance measurement (in our own Galaxy) Rely on primary indicators to measure more distant object.
Rely on Primary Indicators to calibrate secondary indicators!
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2020/4/26 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 3
2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
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 4
2020/4/26 Radar Echo Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
4.2: Primary Distance Indicators
• 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.
d
1 2
c
t
1 AU = 149,597,870,691 m
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2020/4/26 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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2020/4/26 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
tan
p rads
1
p AU p
1 AU
1 radian = 57.3
o = 206265"
d
1
p rads AU
206265
p
AU
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 Smallest parallax angles currently measurable ~ 0.001" parallax 0.8" 1000 parsecs parallax is a distance measure for the local solar neighborhood. 7
2020/4/26 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” 8
2020/4/26 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. 9
2020/4/26 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,
d
q
/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
d
q
/dt
Plot
d
q
/dt - sin(
q
)
slope
=
m will have a mean component
sin(
q
)
(perpendicular to
v sun
) The mean distance of the stars is
d
v sun
m
4.16
m
(" /
yr
)
pc
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
d
q
/dt
can be used to determine the mean distance.
d
v
q
r
v r
in pc/s
q
in rad/s
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2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
4.2: Primary Distance Indicators
Moving Cluster Method v C v r q v t
d
q Observe cluster some years apart proper motion m Radial Velocity (km/s)
v R
Tangential Velocity (km/s) from spectral lines
v T
4.74
m
d
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
v T v R
v C v C
sin cos
q q
d
4.74
v R
m
tan
q Main method for measuring distance to Hyades Cluster ~ 200 Stars (Moving Cluster Method One of the first “rungs” on the Cosmological Distance Ladder c.1920: 40 pc (130 ly) Hipparcos parallax measurement 46.3pc (151ly) for the Hyades distance. 45.7 pc).
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2020/4/26 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) ¿Ã ±³ QuickTime¢‚• ° ±‚ ¿ß«ÿ « ø‰«’¥œ¥Ÿ.
• 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. ) 12
2020/4/26 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 • • Flux (
S
) from luminosity, ( • Calculate distance (
D
• Measuring redshift (
z L
) )
L
Cosmological parameters )
H o , S
W
m,o ,
W L
,o
4
L
D L
2
m M
2.5lg(
2.5lg(
S
/
S
0
)
L
/
L
0
)
D L
L
4
S d L
10
(
m
5
M
M
m
5lg
d L
10
pc
DISTANCE MODULUS
m
M
5lg
d L
,
Mpc
25
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2020/4/26 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 Normal stars fall on a single track
Main Sequence
H-R diagram 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. Get Distance from the distance modulus
m
M
5lg
d L
,
Mpc
25
AGB Red Giant Branch near stars Turn off WHITE DWARF far stars m-M • • temperature Useful out to ~few 10s kpc (main sequence stars become too dim) used to calibrate clusters with Hyades 14
2020/4/26 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 • O stars - HeI, HeII • B Stars - He • A Stars - H Surface Temperature - OBAFGKM RNS • F-G Stars - Metals • K-M Stars - Molecular Lines •Surface Gravity Higher pressure in atmosphere • Class I - Supergiants • Class III - Giants • Class V - Dwarfs • Class VI - white Dwarfs line broadening, less ionization - Class I(low) -VI (high)
L L g
4
M
T
4
R
2
GM R
2 ( ~ 3 4) Temperature from spectral type, surface gravity from luminosity class Measure flux Distance from inverse square Law mass and luminosity. 15
2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
4.2: Primary Distance Indicators
Cepheid Variables 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 16
2020/4/26 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 ¿Ã ±³ QuickTime¢‚• ° ±‚ ¿ß«ÿ « ø‰«’¥œ¥Ÿ.
M v
2.76lg
P d
1.0
4.16
Distance Modulus
m
M
5lg
d L
,
Mpc
25 Prior to HST, Cepheids only visible out to ~ 5Mpc 17
2020/4/26 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 LPV* Classical Cepheids-S Classical Cepheids-L W Virginis (PII Ceph) RR Lyrae ß Cephei stars d Scuti stars ZZ Ceti stars Period Pop 100-700d I, II 1-6 7-50d 2-45d 1-24hr 3-7hr I I II II I 1-3hr 1-20min I I Pulsation radial radial radial radial radial radial/non radial radial/non radial 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]
• Common in globular clusters major • Low luminosities, ±
1.01
rung up in the distance ladder only measure distance to ~ M31 18
2020/4/26 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 19
2020/4/26 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!) 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 q
=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 M o is detectable, ~ 50 Mpc 20
2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
4.3: Secondary Distance Indicators
Tully Fisher Relationship Redshift Centrifugal
v R
2
R
GM R
2 Gravitational Flux Assume same mass/light ratio for all spirals
M
/
L
Assume same surface brightness for all spirals 4 In Magnitudes
L M
M o
v R
2
G
2.5lg
2
L L o
v R
4
M o
L
/
R
2 2.5lg
Cv R
4
L o
Blueshift n
M
10lg(
v R
)
More practically
M
a
lg
W o
sin
i
i W o
= spread in velocities = inclination to line of sight of galaxy
C b
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2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
4.3: Secondary Distance Indicators
Tully Fisher Relationship
M
b
Tully and Fischer (1977): Observations with I a = 6.25±0.3
b = 3.5 ± 0.3, Knowing
M
45 o
a
lg
W o
sin
i
DISTANCE MODULUS
m M
2.5lg(
2.5lg(
S
/
S
0
)
L
/
L
0
)
d L
10
(
m
5
M
)
M
m
5lg
d L
10
pc
m
M
5lg
d L
,
Mpc
25
Tully-Fisher Fornax & Virgo Members Bureau et al. 1996
Problems with Tully-Fisher Relation
• TF Depends on Galaxy Type
M bol M bol M bol = -9.95 lgV R = -10.2 lgV R = -11.0 lgV R + 3.15
+ 2.71
+ 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) 22
2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
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 Large Scatter Ellipticals Lenticulars L
M M B
constrain with extra parameters
B
4 19.38
19.65
0.07
(9.0
0.7)(lg 0.08
(8.4
M32 (companion to M31) 0.8)(lg 2.3) 2.3) Define a plane in parameter space Faber-Jackson Law Intensity profile (surface brightness) (r 1/4 De Vaucouleurs Law)
I
(
r
)
L
I I o e
(
r
/
r o
) 1/ 4
I o r o
2 Virial Theorem
m
2 Mass/Light ratio
L
1
M
M
L
4(1 )
I o
(1 ) 2 1
GM
m r o
2
M r o
Fundamental Plane (Dressler et al. 1987) 23
2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
4.3: Secondary Distance Indicators
D Relationship Any 2 parameters scatter (induced by 3rd parameter) Combine parameters Constrain scatter Fundamental Plane Instead of
I o , r o
: Use Diameter of aperture,
D n
,
D n
- aperture size required to reach surface Brightness ~
B=20.75mag arcsec 2
Advantages • Elliptical Galaxies - bright •Strongly Clustered • Old stellar populations measure large distances large ensembles 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 24
2020/4/26 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 Compare nearby dwarf galaxy, nearby giant galaxy, far giant galaxy Choose distance such that flux is identical to nearby dwarf. measure the mean flux per pixel (surface brightness) rms variation in flux between pixels.
m
N S NS
1
d N S
d
d
2 2 m
S
is independent of distance
m 2
L
4
d
2
d
Can use out to 70 Mpc with HST 25
2020/4/26 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 M V = 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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2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
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>8M o Type Ib,c (H poor massive Star M>8M o ) Stellar wind or stolen by companion Type Ia (M~1.4M
o White Dwarf + companion) 27
2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
4.3: Secondary Distance Indicators
Supernova Ia Measurements Supernovae: luminosities (10 12 L o in neutrinos) entire galaxy~10 10 L o
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 Ni 56 Co 56 Fe 56 ) • Maximum Light is the same for all SNIa !!
M B
,max
18.33
5lg
h
100
L
~ 10
10
L o
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2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
4.3: Secondary Distance Indicators
Supernova Ia Measurements
M B
,max
18.33
5lg
h
100
L
~ 10
10
L o
Lightcurves of 18 SN Ia z < 0:1 (Hamuy et al ) Gibson et al. 2000 - Calibration of SNIa via Cepheids lg
H o
0.2
M B
,max
m B
,15,
t
0.720
0.459
1.1
1.010
m B
,15,
t
1.1
2 0.934
28.653
0.042
m B
,15,
t
m B
,15
m B
,15 0.1
E
(
B
15 day decay rate
V
)
E
(
B
V
) total extinction (galactic + intrinsic) after correction of systematic effects and time dilatation (Kim et al., 1997).
Distance derived from Supernovae depends on extinction Supernovae distances good out to > 1000Mpc Probe the visible Universe !
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2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
4.3: Secondary Distance Indicators
Gravitational Lens Time Delays q • 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 source is offset various multiple images Can be used to great distances Einstein Ring 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 30
2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
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 tan q~q
Weak field approximation
Assume light passes through a weak field with the absolute value of the perculiar velocities of components and G<
b, h, a) b
h
a
D
3
D
1
h
2
h
Where is the Einstein Radius 4
GMD
3
c
2
D
1
D
2 Lens equation - 2 different solutions corresponding to 2 images of the source:
h
1
b
b
2 2 4 2 1/ 2
h
2
b
b
2 4 2 1/ 2 2 For perfectly aligned lens and source (
b=0
) - two images at same distance from lens
h1 = h2 = e
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2020/4/26 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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2020/4/26 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.
6 7 8 1 2 3 4 5 Method Cepheids Novae Planetary Nebula Globular Cluster Surface Brightness Tully Fisher Faber Jackson Type Ia Supernova Distance Mpc 14.9
1.2
21.1 3.9
15.4 1.1
18.8 3.8
15.9 0.9
15.8 1.5
16.8 2.4
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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2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
4.4: The Distance Ladder
The Distance Ladder Supernova (1-1000Mpc) Hubble Sphere (~3000Mpc) 1000Mpc Tully Fisher (0.5-00Mpc) 100Mpc Coma (~100Mpc) Cepheid Variables (1kpc-30Mpc) RR Lyrae (5-10kpc) Spectroscopic Parallax (0.05-10kpc) Parallax (0.002-0.5kpc) RADAR Reflection (0-10AU) 10Mpc Virgo (~10Mpc) 1Mpc M31 (~0.5Mpc) 100kpc LMC (~100kpc) 10kpc Galactic Centre (~10kpc) 1kpc Pleides Cluster (~100pc) Proxima Centauri (~1pc) 34
2020/4/26 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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2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
4.5: The Hubble Key Project
To the Hubble Flow
cz
H o d
The Hubble Constant • Probably the most important parameter in astronomy • The Holy Grail of cosmology • Sets the fundamental scale for all cosmological distances 36
2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
4.5: The Hubble Key Project
To the Hubble Flow To measure Ho require • Distance • Redshift Cosmological Redshift -
cz
H o d
The Hubble Flow - due to expansion of the Universe Must correct for local motions / contaminations 1
z
(1
z
)(1
v o
/
c
v G
/
c
)
v o -
Measured from CMB Dipole ~ 220kms -1 (Observational Cosmology 2.3)
v o v G
= radial velocity of observer = radial velocity of galaxy
v G -
Contributions include Virgocentric infall, Great attractor etc… Decompostion of velocity field (Mould et al. 2000, Tonry et al. 2000) 37
2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
4.5: The Hubble Key Project
Hubble Key Project
cz
H o d
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 D n 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 38
2020/4/26 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale
4.5: The Hubble Key Project
Hubble Key Project ¿Ã ±³ QuickTime¢‚• ° ±‚ ¿ß«ÿ « ø‰«’¥œ¥Ÿ.
H 0 =
75
10 km
=
s
=
Mpc
39
2020/4/26 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 H 0
= 71
6 km s
-1
Mpc
-1 t 0
= 1.3
10
10
yr
Biggest Uncertainty • zero point of Cepheid Scale (distance to LMC) 40
2020/4/26 Summary Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
4.6: Summary
Cosmological Distance Scale • 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% H 0
= 71
6 km s
-1
Mpc
-1 t 0
= 1.3
10
10
yr
Is the H
o
controversy over ?
41
2020/4/26 Summary Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004
4.6: Summary
Cosmological Distance Scale
Observational Cosmology 4. Cosmological Distance Scale
終
Observational Cosmology
次：
5. Observational Tools
42