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The Cosmological Distance Ladder - to redshift 1000

The Cosmological Distance Ladder - to redshift 1000. Michael Rowan-Robinson Imperial College. First steps on the distance ladder. Aristotle (384-322 BC) - estimated the size of the earth (+ Eratosthenes, Poseidonius, 10%). Hipparcos (2 nd C BC) - estimated distance of the moon

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The Cosmological Distance Ladder - to redshift 1000

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  1. The Cosmological Distance Ladder - to redshift 1000 Michael Rowan-Robinson Imperial College

  2. First steps on the distance ladder Aristotle (384-322 BC) - estimated the size of the earth (+ Eratosthenes, Poseidonius, 10%) Hipparcos (2nd C BC) - estimated distance of the moon (59 RE, cf modern value 60.3) RAS Presidential Address Aristotle, by Raphael

  3. The Copernican revolution Copernicus (1473-1543) - gave the correct relative distances of the sun and planets (to 5%) - absolute value not determined accurately till the 19th century RAS Presidential Address

  4. The first steps outside the solar system Bessel 1838 - discovered parallax of nearby star 61 Cyg, its change in apparent direction on the sky due to the earth’s orbit round the sun (the final proof of the Copernican system) RAS Presidential Address

  5. The key modern distance indicator – Cepheid variable stars Delta Cephei is the prototype of the Cepheid variable stars, massive stars which pulsate and vary their light output RAS Presidential Address

  6. Henrietta Leavitt’s breakthrough In 1912, Henrietta Leavitt, working at the Harvard Observatory, discovered from her studies of Cepheids in the Small Magellanic Cloud that the period of Cepheid variability was related to their lumininosity RAS Presidential Address

  7. The distances of the galaxies In 1924 Edwin Hubble used Leavitt’s discovery to estimate the distance of the Andromeda Nebula. It clearly lay far outside The Milky Way system. RAS Presidential Address

  8. The expansion of the universe • Three years later, in 1927, he announced, based on distances to 18 galaxies, that the more distant a galaxy, the faster it is moving away from us • velocity/distance = constant, Ho (the Hubble law) • This is just what would be expected in an expanding universe. • The Russian mathematician Alexandr Friedmann had shown (1922, 1924) that expanding universe models are what would be expected according to Einstein’s General Theory of Relativity, if the universe is • homogeneous (everyone sees the same picture) and • isotropic (the same in every direction). RAS Presidential Address

  9. The history of the Hubble constant Hubble’s estimate of the Ho, the Hubble constant, was 500 km/s/Mpc, which gave an age for the universe of only 2 billion years. This was soon shown to be shorter than the age of the earth. From 1927 to 2001 the value of the Hubble constant was a matter of fierce controversy. Sandage 1958 > RAS Presidential Address

  10. The cosmological distance ladder This was my 1985 summary of the cosmological distance ladder RAS Presidential Address

  11. The cosmological distance ladder In my monograph ‘The Cosmological Distance Ladder’ (Freeman 1985), I set out to understand the competing estimates of Ho (50 - Sandage and Tammann, 100 - de Vaucouleurs), and to reconcile the systematic differences in distance estimates from different methods. With an objective weighting scheme based on quoted errors, and with higher weight for purely geometrical distance methods, I concluded that there were systematic errors in the supernova method (too high distances) and in the Tully-Fisher and HII region methods (too low) and that best overall value for H0 was Ho = 67 +_ 12 km/s/Mpc RAS Presidential Address

  12. Implications of the Hubble constant Ho is (velocity/distance) so has the dimensions of (1/time). 1/Ho is the expansion age of the universe (how old the Universe would be if no forces acting) = 15.3 billion yrs For simplest model universe with only gravity acting, age of universe would be 10.2 billion years (gravity slows expansion) RAS Presidential Address

  13. The age of the universe We can use the colours and brightnesses of the stars in globular clusters to estimate the age of our Galaxy ~ 12 billion years Long-lived radioactive isotopes give a similar answer Allowing time for our Galaxy to form, the age of the universe is ~ 13 billion years Already a problem for L= 0 ? RAS Presidential Address

  14. The Hubble Space Telescope Key Program Following the first HST servicing mission, which fixed the telescope aberration, a large amount of HST observing time was dedicated to measuring Cepheids in distant galaxies, to try to measure the Hubble constant accurately, and to give the different distance methods a secure and consistent calibration. The Key Program soon split into two teams, one led by Wendy Freedman, Jeremy Mould and Rob Kennicutt, the other by Allan Sandage and Gustav Tammann. RAS Presidential Address

  15. Some of the galaxies studied by HST RAS Presidential Address

  16. HST Key Project strategy Kennicutt et al 1995 RAS Presidential Address

  17. The HST Key program final result (1) Ho = 72 +- 8 km/s/Mpc (Freedman et al 2001) logV RAS Presidential Address

  18. There is good consistency between the HST Key Program value of Ho and the age of the universe, provided we invoke Einstein’s Cosmological Constant, L (dark energy) Uncertainties in Ho are (1) distance of Large Magellanic Cloud, (2) the adopted Cepheid calibration, (3) corrections for dust extinction, (4) corrections for metallicity effects, (5) corrections for local flow Using the Freedman et al data, my own best estimates for these corrections, and the weighting scheme of CDL 1985, I concluded: Ho = 63 +- 6 (Rowan-Robinson 2000, astro-ph/0012026) Any room for doubt ? RAS Presidential Address

  19. mo = 18.5+-0.1 (d = 50 kpc, +-10%) - a fundamental limitation of local estimates of Ho perhaps Gaia will resolve this Distance of LMC RAS Presidential Address

  20. In 1998 two teams announced that using Type Ia supernovae as standard candles implied that L > 0 (Schmidt et al 1998, Garnevich et al 1998, Riess et al 1998, Perlmutter et al 1999) There were issues with (1) treatment of extinction by dust, (2) consistency of treatment of correlation of decline rate with luminosity (Liebundgut 2001, Rowan-Robinson 2002). I also raised two other issues: (3) inconsistencies with earlier supernova data, (4) inappropriate use of supernovae not observed before maximum Joint HST Key Project and SN team found Ho = 68 +- 5 (Gibson et al 1999) Type Ia supernova RAS Presidential Address

  21. data is clearly excellent, but this is not a geometric distance method new HST-ACS observations of Cepheids in galaxies with well-observed Type Ia supernovae gives Ho = 73 +- 6 (Riess et al 2005) - but based on LMC, with 10% distance uncertainty inconsistencies with earlier results can be attributed to photographic data issue of luminosity-decline rate relation addressed by Jha et al (2007) (see also new approach by Wang et al 2005, Nobili et al 2005) still some unresolved inconsistencies in derivation of extinction (can only be resolved by use of more photometric bands) supernova issues RAS Presidential Address

  22. Latest data from Riess et al (2007) - clear support for consensus L model (cf also Astier et al 2005, SN Legacy Survey) supernovae 2007 RAS Presidential Address

  23. HST key program found Ho = 72 +- 8 (Freedman et al 2001) WMAP (year 1) found Ho = 72 +- 5 (Spergel et al 2003) (year 3) Ho = 73 +- 3 (Spergel et al 2007) new HST-ACS observations of Cepheids in galaxies with well-observed Type Ia supernovae gives Ho = 73 +- 6 (Riess et al 2005) so have consensus for H0=73, Wm=0.25, WL=0.75, age of universe 13.7 billion years ? consensus ? RAS Presidential Address

  24. History of the universe RAS Presidential Address

  25. The HST Key program final result (2) • new study of Cepheid P-L • relation (Tammann et al 2003) • difference between P-L • relation in Galaxy and LMC • (Sandage et al 2005) • new calibration using • Baade-Wesselink method • (so no LMC distance error) • new discussion of • extinction in supernovae • Ho = 62 +- 5 km/s/Mpc • (Sandage et al 2007) Hubble diagram for 62 supernovae RAS Presidential Address

  26. other work on Ho • Feast review (2007, ‘From IRAS to Herschel/Planck’): • new HST Cepheid distances (Benedict et al 2007) • revised Hipparcos parallaxes (van Leeuwen et al 2007) • - revise Sandage’s Ho to 69.6 • NGC4258 Cepheids (Macri et al 2006), consistency with maser distance • gravitational lens time delay: 68+- 10 (Oguri 2007) • 72+-10 (Saha et al 2006) • Sunyaev-Zeldovich method for clusters: • 66+-14 (Jones et al 2005) • 76+-10 (Bonamente et al 05) RAS Presidential Address

  27. Boomerang and Maxima, for flat universe, H0 = 75+-10 (Jaffe et al 2001) WMAP first year results: 72 +- 5 (Spergel et al 2003) include also SLOAN large-scale structure data: 68 +- 10 (Tegmark et al 2004) include Sloan large-scale structure + baryonic acoustic oscillation data: 65 +- 4.5 (Eisenstein et al 2005), WMAP 3-year results: 73 +- 3 (Spergel et al 2007) with LSS, BAO 69-72 CMB fluctuations and Ho RAS Presidential Address

  28. Primordial density spectrum power-law assumption • Spergel et al (2004)show that with power-law spectrum, but no restriction to flat models, can get wide range of fits just to WMAP3 CMB data • can see that priors on Ho or assumption of flatness force us towards WL = 0.75 consensus model • however dropping assumption of power-law opens up possibilities even further (Blanchard et al 2003) RAS Presidential Address

  29. Blanchard et al (2003) model • Blanchard et al (2003) showed that if we relax the assumption of a power-law primordial density spectrum (to a broken power-law) we can fit the CMB fluctuation spectrum just as well as the consensus model with aL=0, W0=1 (Einstein de Sitter) model, provided Ho = 46 • can get consistency with large-scale structure data if Wn ~ 0.2 (mixed dark matter) • however, inconsistent with supernova data and H0=46 is 3-s from the direct estimates • Shafieloo and Souradeep (2007) deconvolve primordial density spectrum from CMB fluctuations and show L=0, W0=1, H0=50, model is actually better fit than consensus model RAS Presidential Address

  30. SDSS (Eistenstein et al 2005) and 2dFGRS (Cole et al 2005) have claimed to detect baryon acoustic oscillation (BAO) peak on scale ~ 150 Mpc in the galaxy correlation function Blanchard et al (2006) admit this is fatal for their L=0 model, if confirmed BAO plus CMB first Doppler peak is the ultimate geometrical measurement of Ho galaxy baryon acoustic peak RAS Presidential Address

  31. angular diameter distance test RAS Presidential Address courtesy: Paniez Paykari

  32. rph = R(tdec) cph (radius of particle horizon at decoupling) cph = A1/2 ∫01/Zdec {W0 x +Wr + WL x4-3(1+w) + (1-W0-Wr-WL)x2}-1/2 dx A = |(1-W0-Wr-WL)| if k=+1,-1, = 1 if k= 0 zdec ~ 1100, w =-1 radius of acoustic horizon racoust = rph/{3(1+3rb/4rg)}1/2 = rph/{3(1+1.25(Wbh2)/(W0h2)}1/2 Wbh2 ~ 0.022 (Doppler peak ratios+nucleosynthesis) angular radius of first Doppler peak qDoppler = racoust/Ddiam(zdec) angular radius of baryon acoustic peak qBAO ~ 150 (W0h2/0.25x0.732)-0.0853 Mpc/Ddiam(z) diameter distance Ddiam(z) = ct0 ro(z)/(A 1/2 (1+z)) ct0 = 9.8 h-1 Gyr ro (z) = sin c (z) for k = +1, = c (z) for k = 0, = sinh c (z) for k =-1 c (z) = A1/2 ∫11/(1+z) {W0 x +Wr + WL x4-3(1+w) + (1-W0-Wr-WL)x2}-1/2 dx some formulae RAS Presidential Address

  33. black curve: zero curvature solid curves: first Doppler peak for Ho = 73 (blue), 65 (red), 48 (green) dotted curves: baryon acoustic peak for same 3 cases C: consensus model E: Einstein de Sitter to z = 1100 RAS Presidential Address

  34. local direct estimates of H0 = 62-72 +- 10% CMB estimates = 65-73 +- 4% (generally assuming flat universe, power-law spectrum, negligible Wn, w=-1) baryonic acoustic peak plus CMB first Doppler peak is the ultimate geometrical measurement of Ho precision measurements of H0 (say to 1%) could tell us that we need new physics beyond Standard Model. * accurate distance to LMC (Gaia) * Baade-Wesselink methods for Cepheids and supernovae, * multi-l photometry to control extinction and metallicity conclusions RAS Presidential Address

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