2020125 Chris Pearson Observational Cosmology 4 Cosmological Distance

2020/12/5 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

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Distance Indicators Cosmological Distance Scale 4. 1: 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 PPrimary Distance Indicators direct distance measurement (in our own Galaxy) PSecondary Distance Indicators Rely on primary indicators to measure more distant object. Rely on Primary Indicators to calibrate secondary indicators! 2

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 1: 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

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 2: Primary Distance Indicators • • Radar Echo Parallax Moving Cluster Method Main-Sequence Fitting Spectroscopic Parallax RR-Lyrae stars Cepheid Variables Galactic Kinematics 4

2020/12/5 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 AU = 149, 597, 870, 691 m 5

2020/12/5 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 6

2020/12/5 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 p 1 AU 1 radian = 57. 3 o = 206265" Define a parsec (pc) which is simply 1 pc = 206265 AU =3. 26 ly. 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. 7

2020/12/5 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. 4 mag • complete fro V=7. 3 -9 mag • Astrometry Accuracy 0. 001” • Parallax Accuracy 0. 002” 8

2020/12/5 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

2020/12/5 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 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. 10

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 2: Primary Distance Indicators Moving Cluster Method v. C vr Observe cluster some years apart proper motion m Radial Velocity (km/s) v. R from spectral lines Tangential Velocity (km/s) 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 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. 3 pc (151 ly) for the Hyades distance. 11

2020/12/5 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. 9 pc (78 ly) Scorpius-Centaurus cluster: ~100 stars 172 pc (560 ly) Pleiades: ~ by Van Leeuwen at 126 pc, 410 ly) • Hipparcos 3 D 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

2020/12/5 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 -20 kpc - 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, (L) • Calculate distance (DL) • Measuring redshift (z) • Cosmological parameters Ho, Wm, o, WL, o DISTANCE MODULUS 13

2020/12/5 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 WHITE DWARF M ai n Magnitude (more -ve) Get Distance from the distance modulus near stars m-M far stars se qu e nc e temperature • Useful out to ~few 10 s kpc (main sequence stars become too dim) • used to calibrate clusters with Hyades 14

2020/12/5 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 - He. I, He. II • 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 15

2020/12/5 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

2020/12/5 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 Distance Modulus Prior to HST, Cepheids only visible out to ~ 5 Mpc 17

2020/12/5 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 -700 d I, II radial Classical Cepheids-S 1 -6 I radial 7 -50 d I radial W Virginis (PII Ceph) 2 -45 d II radial RR Lyrae 1 -24 hr II radial ß Cephei stars 3 -7 hr I radial/non radial d Scuti stars 1 -3 hr I radial/non radial ZZ Ceti stars 1 -20 min 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 ~ M 31 18

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 3: 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

2020/12/5 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 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 20

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 3: Secondary Distance Indicators Tully Fisher Relationship Centrifugal Redshift Gravitational Assume same mass/light ratio for all spirals Assume same surface brightness for all spirals Flux In Magnitudes Dn More practically Blueshift Wo = spread in velocities i = inclination to line of sight of galaxy 21

2020/12/5 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 45 o a = 6. 25± 0. 3 b = 3. 5 ± 0. 3, Tully-Fisher Fornax & Virgo Members Bureau et al. 1996 Knowing DISTANCE MODULUS M Problems with Tully-Fisher Relation • TF Depends on Galaxy Type Mbol = -9. 95 lg. VR + 3. 15 (Sa) Mbol = -10. 2 lg. VR + 2. 71 (Sb) Mbol = -11. 0 lg. VR + 3. 31 (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

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 3: Secondary Distance Indicators D-s Relationship Elliptical Galaxies Cannot use Tully Fisher Relation • Little rotation • little Hydrogen (no 21 cm) Faber-Jackson (1976): Elliptical Galaxies L = Luminosity s = central velocity dispersion L s 4 M 32 (companion to M 31) Ellipticals Lenticulars http: //burro. astr. cwru. edu/Academics/Astr 222/Galaxies/Elliptical/kinematics. html Large Scatter constrain with extra parameters Define a plane in parameter space Faber-Jackson Law Intensity profile (surface brightness) (r 1/4 De Vaucouleurs Law) Virial Theorem Mass/Light ratio Fundamental Plane (Dressler et al. 1987) 23

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 3: Secondary Distance Indicators Any 2 parameters scatter (induced by 3 rd parameter) I I D-s Relationship Combine parameters Constrain scatter Fundamental Plane Instead of Io, ro: Use Diameter of aperture, Dn - aperture size required to reach surface Brightness ~ B=20. 75 mag arcsec 2 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 24

2020/12/5 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. 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 25

2020/12/5 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 ~ c. D 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 2 nd, 3 rd brightest Use N average brightest N galaxies. 26

2020/12/5 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) SN 1994 D in NGC 4526 Massive star M>8 Mo Type Ib, c (H poor massive Star M>8 M o) Stellar wind or stolen by companion Type Ia (M~1. 4 Mo White Dwarf + companion) 27

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 3: Secondary Distance Indicators Supernova Ia Measurements Supernovae: luminosities entire galaxy~1010 Lo (1012 Lo in neutrinos) SN 1994 D in NGC 4526 in Virgo Cluster (15 Mpc) 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 !! 28

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 3: Secondary Distance Indicators Supernova Ia Measurements Gibson et al. 2000 - Calibration of SNIa via Cepheids Lightcurves of 18 SN Ia z < 0: 1 (Hamuy et al ) Distance derived from Supernovae depends on extinction after correction of systematic effects and time dilatation (Kim et al. , 1997). Supernovae distances good out to > 1000 Mpc Probe the visible Universe ! 29

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 3: Secondary Distance Indicators Gravitational Lens Time Delays q f http: //spiff. rit. edu/classes/phys 240/lectures/lens_results. html • Light from lensed QSO at distance D, travel different distances given by D=[Dcos(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 > 1 year!) and seperation of the images • Geometry of the lens and its mass • Relative distances of lens and background sources 30

2020/12/5 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, and the lens and the source are D 1, D 2, and D 3, respectively. http: //leo. astronomy. cz/grlens/grl 0. 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 Where b, h, a) e is the Einstein Radius Lens equation - 2 different solutions corresponding to 2 images of the source: For perfectly aligned lens and source (b=0) - two images at same distance from lens h 1 = h 2 = e 31

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 4: The Distance Ladder 32

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 4: 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. 8 Mpc 33

2020/12/5 Cosmological Distance Scale Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4. 4: The Distance Ladder Supernova (1 -1000 Mpc) Hubble Sphere (~3000 Mpc) 1000 Mpc Tully Fisher (0. 5 -00 Mpc) 100 Mpc 10 Mpc Cepheid Variables (1 kpc-30 Mpc) 1 Mpc Coma (~100 Mpc) Virgo (~10 Mpc) M 31 (~0. 5 Mpc) RR Lyrae (5 -10 kpc) 100 kpc LMC (~100 kpc) Spectroscopic Parallax (0. 05 -10 kpc) Parallax (0. 002 -0. 5 kpc) RADAR Reflection (0 -10 AU) 10 kpc Galactic Centre (~10 kpc) 1 kpc Pleides Cluster (~100 pc) Proxima Centauri (~1 pc) 34

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 5: The Hubble Key Project 35

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 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 36

2020/12/5 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 - The Hubble Flow - due to expansion of the Universe Must correct for local motions / contaminations vo = radial velocity of observer v. G = radial velocity of galaxy vo - Measured from CMB Dipole ~ 220 kms-1 (Observational Cosmology 2. 3) v. G - Contributions include Virgocentric infall, Great attractor etc… Decompostion of velocity field (Mould et al. 2000, Tonry et al. 2000) 37

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 5: The 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 M 100. § Calibrate the distance scale 38

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 Cosmological Distance Scale 4. 5: The Hubble Key Project H 0 = 75 10 km=s=Mpc 39

2020/12/5 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 1010 yr Biggest Uncertainty • zero point of Cepheid Scale (distance to LMC) 40

2020/12/5 Chris Pearson : Observational Cosmology 4: Cosmological Distance Scale - ISAS -2004 4. 6: Summary Cosmological Distance Scale Summary • There are 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 1010 yr Is the Ho controversy over ? 41

2020/12/5 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： 42