Observational Cosmology: 4. Cosmological Distance Scale

Transcription

1 Chris Pearson : Observational Cosmology 4: - ISAS Observational Cosmology: 4. 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 ( ) 1985 Pierce Prize Lecture). 1

2 Chris Pearson : Observational Cosmology 4: - ISAS Distance Indicators 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 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! 2

3 Chris Pearson : Observational Cosmology 4: - ISAS Distance Indicators 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

4 Chris Pearson : Observational Cosmology 4: - ISAS : 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

5 Chris Pearson : Observational Cosmology 4: - ISAS Radar Echo 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 Δt 1 AU = 149,597,870,691 m 5

6 Chris Pearson : Observational Cosmology 4: - ISAS Trigonometric Parallax 4.2: Primary Distance Indicators 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

7 Chris Pearson : Observational Cosmology 4: - ISAS Trigonometric Parallax 4.2: Primary Distance Indicators 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 = 1 AU tan p rads 1 p AU d p 1 AU 1 radian = 57.3 o = " d = 1 AU = p rads p AU Define a parsec (pc) which is simply 1 pc = 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. 7

8 Chris Pearson : Observational Cosmology 4: - ISAS Trigonometric Parallax 4.2: Primary Distance Indicators The Hipparcos Space Astrometry Mission Precise measurement of the positions, parallaxes and proper motions of the stars. Mission Goals - measure astrometric parameters primary programme stars to precision of measure astrometric and two-colour photometric properties of additional stars (Tycho Expt.) Launched by Ariane, in August 1989, ~3 year mission terminated August Final Hipparcos Catalogue stars Limiting Magnitude V=12.4mag complete fro V=7.3-9mag Astrometry Accuracy Parallax Accuracy

9 Chris Pearson : Observational Cosmology 4: - ISAS Trigonometric Parallax 4.2: Primary Distance Indicators GAIA MISSION (ESA launch 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

10 Chris Pearson : Observational Cosmology 4: - ISAS : 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, dθ/dt away from point of sky the Solar System is moving toward. This point is known as the apex For anangle θ to the apex, the proper motion dθ/dt will have a mean component sin(θ) (perpendicular to v sun ) Plot dθ/dt - sin(θ) slope = µ The mean distance of the stars is d = v sun µ = 4.16 µ("/ 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 dθ/dt can be used to determine the mean distance. d = Δv r θ Δv r in pc/s θ in rad/s 10

11 Chris Pearson : Observational Cosmology 4: - ISAS : Primary Distance Indicators Moving Cluster Method v C Observe cluster some years apart proper motion µ v r θ v t d θ Radial Velocity (km/s) v R from spectral lines Tangential Velocity (km/s) v T = 4.74µ d µ ( /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 θ v T = v C sinθ v R = v C cosθ d = v R 4.74µtanθ 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. 11

12 Chris Pearson : Observational Cosmology 4: - ISAS : 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 years. (Perryman et al. ) 12

13 Chris Pearson : Observational Cosmology 4: - ISAS : 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, (L) S = Calculate distance (D L ) Measuring redshift (z) Cosmological parameters H o, Ω m,o, Ω Λ,o m = 2.5lg(S /S 0 ) M = 2.5lg(L /L 0 ) (m M ) 5 d L =10 M = m 5lg d L 10pc L 4πD L 2 D L = L 4π S DISTANCE MODULUS m M = 5lg d L,Mpc

14 Chris Pearson : Observational Cosmology 4: - ISAS Main sequence Fitting 4.2: Primary Distance Indicators 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. Get Distance from the distance modulus m M = 5lgd L,Mpc + 25 Turn off AGB Main sequence Red Giant Branch Magnitude (more -ve) far stars near stars m-m WHITE DWARF temperature Useful out to ~few 10s kpc (main sequence stars become too dim) used to calibrate clusters with Hyades 14

15 Chris Pearson : Observational Cosmology 4: - ISAS Spectroscopic Parallax 4.2: Primary Distance Indicators 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 L = 4πσT 4 R 2 L M α (α ~ 3 4) g = GM R 2 Temperature from spectral type, surface gravity from luminosity class mass and luminosity. Measure flux Distance from inverse square Law 15

16 Chris Pearson : Observational Cosmology 4: - ISAS Cepheid Variables 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 Henrietta S. Leavitt ( ) - study of 1777 variable stars in the Magellanic Clouds. c 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

17 Chris Pearson : Observational Cosmology 4: - ISAS Cepheid Variables 4.2: Primary Distance Indicators 2 types of Classical Cepheids M v = ( 2.76lgP d 1.0) 4.16 Distance Modulus m M = 5lgd L,Mpc + 25 Prior to HST, Cepheids only visible out to ~ 5Mpc 17

18 Chris Pearson : Observational Cosmology 4: - ISAS RR Lyrae Variables 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. Type Period Pop Pulsation LPV* d 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 δ 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 18

19 Chris Pearson : Observational Cosmology 4: - ISAS : 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

20 Chris Pearson : Observational Cosmology 4: - ISAS Globular Clusters 4.3: Secondary Distance Indicators 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 θ=d/d Globular Cluster Luminosity Function (GCLF) (similarly for PN) Use Number density of globular clusters as function of magnitude M (M M * ) 2 2σ φ(m) = Ce 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

21 Chris Pearson : Observational Cosmology 4: - ISAS : Secondary Distance Indicators Tully Fisher Relationship Redshift Centrifugal v R 2 R = GM R 2 Assume same mass/light ratio for all spirals Gravitational l = M /L Flux Assume same surface brightness for all spirals L = 4 v R σ l 2 G v 4 2 R σ = L /R 2 In Magnitudes M = M o 2.5lg L = M o 2.5lg Cv 4 R L o L o Blueshift Δν More practically M = 10lg(v R ) + C M = alg W o b sini W o = spread in velocities i = inclination to line of sight of galaxy 21

22 Chris Pearson : Observational Cosmology 4: - ISAS : 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, Knowing M M = alg W o b sini DISTANCE MODULUS m = 2.5lg(S /S 0 ) M = 2.5lg(L /L 0 ) (m M ) 5 d L =10 M = m 5lg d L 10pc m M = 5lg d L,Mpc + 25 Tully-Fisher Fornax & Virgo Members Bureau et al Problems with Tully-Fisher Relation TF Depends on Galaxy Type M bol = lgv R M bol = lgv R M bol = lgv R (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

23 Chris Pearson : Observational Cosmology 4: - ISAS D-σ Relationship 4.3: Secondary Distance Indicators Faber-Jackson (1976): Elliptical Galaxies L σ 4 L = Luminosity σ = central velocity dispersion Elliptical Galaxies Cannot use Tully Fisher Relation Little rotation little Hydrogen (no 21cm) Ellipticals Lenticulars M32 (companion to M31) M B = ± 0.07 (9.0 ± 0.7)(lgσ 2.3) M B = ± 0.08 (8.4 ± 0.8)(lgσ 2.3) Large Scatter constrain with extra parameters Define a plane in parameter space Faber-Jackson Law I(r) = I o e (r /r o ) 1/ 4 Intensity profile (surface brightness) (r 1/4 De Vaucouleurs Law) Virial Theorem Mass/Light ratio mσ 2 = 1 GM 2 r o M L M α 2 L = I I o r o m σ 2 M r o L 1+α σ 4(1 α ) I o (1 α ) Fundamental Plane (Dressler et al. 1987) 23

24 Chris Pearson : Observational Cosmology 4: - ISAS : Secondary Distance Indicators D-σ Relationship Any 2 parameters scatter (induced by 3rd parameter) Ι Ι 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 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

25 Chris Pearson : Observational Cosmology 4: - ISAS : 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. σ = µ = NS NS 1 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. N d 2 S d 2 µ is independent of distance S = σ 2 µ = L 4πd 2 d Can use out to 70 Mpc with HST 25

26 Chris Pearson : Observational Cosmology 4: - ISAS : 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. 26

27 Chris Pearson : Observational Cosmology 4: - ISAS : 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 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

28 Chris Pearson : Observational Cosmology 4: - ISAS : Secondary Distance Indicators Supernova Ia Measurements Supernovae: luminosities entire galaxy~10 10 L o (10 12 L o 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 Ni 56 Co 56 Fe 56 ) Maximum Light is the same for all SNIa!! M B,max = lgh 100 { L ~ L o } 28

29 Chris Pearson : Observational Cosmology 4: - ISAS : Secondary Distance Indicators Supernova Ia Measurements M B,max = lgh 100 { L ~ L o } Gibson et al Calibration of SNIa via Cepheids Lightcurves of 18 SN Ia z < 0:1 (Hamuy et al ) ( ) ( Δm B,15,t 1.1) ± lgh o = 0.2 M B,max ± ( ) (( Δm B,15,t 1.1) ± 0.042) Δm B,15,t = Δm B, E(B V) Δm B,15 = 15 day decay rate E(B V ) = total extinction (galactic + intrinsic) Distance derived from Supernovae depends on extinction after correction of systematic effects and time dilatation (Kim et al., 1997). Supernovae distances good out to > 1000Mpc Probe the visible Universe! 29

30 Chris Pearson : Observational Cosmology 4: - ISAS : Secondary Distance Indicators Gravitational Lens Time Delays φ θ Light from lensed QSO at distance D, travel different distances given by Δ=[Dcos(θ) - Dcos(φ)] 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

31 Chris Pearson : Observational Cosmology 4: - ISAS : 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. Small angles approximation Assume angles b, h, and deflection angle a are <<1 tanθ θ 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, h, a) b = h a D 3 = h ε2 h D 1 Where ε is the Einstein Radius ε = 4GMD 3 c 2 D 1 D 2 Lens equation - 2 different solutions corresponding to 2 images of the source: h 1 = ( b + ( b 2 + 4ε 2 ) 1/ 2 ) 2 h 2 = ( b ( b 2 + 4ε 2 ) 1/ 2 ) 2 For perfectly aligned lens and source (b=0) - two images at same distance from lens h1 = h2 = e 31

32 Chris Pearson : Observational Cosmology 4: - ISAS The Distance Ladder 4.4: The Distance Ladder The Distance Ladder 32

33 Chris Pearson : Observational Cosmology 4: - ISAS : The Distance Ladder The Distance Ladder Comparison eight main methods used to find the distance to the Virgo cluster Method Cepheids Novae Planetary Nebula Globular Cluster Surface Brightness Tully Fisher Faber Jackson Type Ia Supernova Distance Mpc 14.9± ± ± ± ± ± ± ±5.0 Jacoby etal 1992, PASP, 104, 599 HST Measures distance to Virgo (Nature 2002) D=17.1 ± 1.8Mpc 33

34 Chris Pearson : Observational Cosmology 4: - ISAS The Distance Ladder 4.4: The Distance Ladder Supernova (1-1000Mpc) Tully Fisher (0.5-00Mpc) Hubble Sphere (~3000Mpc) 1000Mpc 100Mpc Coma (~100Mpc) Cepheid Variables (1kpc-30Mpc) 10Mpc Virgo (~10Mpc) RR Lyrae (5-10kpc) Spectroscopic Parallax ( kpc) 1Mpc 100kpc M31 (~0.5Mpc) LMC (~100kpc) Parallax ( kpc) 10kpc Galactic Centre (~10kpc) RADAR Reflection (0-10AU) 1kpc Pleides Cluster (~100pc) Proxima Centauri (~1pc) 34

35 Chris Pearson : Observational Cosmology 4: - ISAS The Hubble Key Project 4.5: The Hubble Key Project The Hubble Key Project 35

36 Chris Pearson : Observational Cosmology 4: - ISAS To the Hubble Flow 4.5: The Hubble Key Project 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

37 Chris Pearson : Observational Cosmology 4: - ISAS To the Hubble Flow 4.5: The Hubble Key Project cz = H o d 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 v o /c + v G /c) v o = radial velocity of observer v G = radial velocity of galaxy v o - Measured from CMB Dipole ~ 220kms -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

38 Chris Pearson : Observational Cosmology 4: - ISAS Hubble Key Project 4.5: The 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 -σ 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

39 Chris Pearson : Observational Cosmology 4: - ISAS Hubble Key Project 4.5: The Hubble Key Project H0 = 75 ± 10 km=s=mpc 39

40 Chris Pearson : Observational Cosmology 4: - ISAS : The Hubble Key Project Combination of Secondary Methods Mould et al. 2000; Freedman et al H 0 = 71±6 km s -1 Mpc -1 τ 0 = yr Biggest Uncertainty zero point of Cepheid Scale (distance to LMC) 40

41 Chris Pearson : Observational Cosmology 4: - ISAS Summary 4.6: 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% H 0 = 71±6 km s -1 Mpc -1 τ 0 = yr Is the H o controversy over? 41

42 Chris Pearson : Observational Cosmology 4: - ISAS Summary 4.6: Summary Observational Cosmology 4. Observational Cosmology 5. Observational Tools 42