Rowan-Robinson: Presidential Address Rowan-Robinson: Presidential Address

(a) (b) (c)

Climbing the cosmological distance ladder

In his Presidential Address for 2008, Michael Rowan-Robinson Abstract describes the steps taken to extend our knowledge of cosmological Humankind’s efforts to measure the distance – towards redshift 1000! distances of the planets, stars and are closely bound up with the ristotle (384–322 BC) was the first to motion of all stars on the sky due to the Earth’s evolution of our ideas about the universe estimate the size of the Earth, using the motion, a century earlier. we find ourselves in. This link stretches angle of the shadow of a pole at noon at from classical times to today, with the A very latest analysis of the fluctuations in a location 100 miles south of the equator. Era- Cepheids, M31 and the Hubble Law tosthenes and Poseidonius later used a similar The next crucial step on the distance ladder, the cosmic microwave background. method. All these estimates are within about still of prime importance today, was the dis- 10% of the modern value. In the 2nd century BC covery by Henrietta Leavitt in 1912, working Hipparcos used an eclipse method to estimate at the Harvard Observatory, that the periods Controversy over H0

the distance of the Moon and deduced a value of stars in the Small Magel- Hubbles’s estimate of H0 was 500 km/s/Mpc. –1 59 RE, compared to the modern value of 60.3 RE. lanic Cloud are related to their luminosity: the Now H0 has the dimensions of time and so Aristarcos tried to estimate the distance of the period–luminosity relation. In 1924 Edwin 1/H0 is the expansion age of the universe, the age Sun using an eclipse method, but was out by a Hubble used Leavitt’s discovery to estimate the the universe would have if no forces were acting.

factor of 20. The Greeks also gave us Euclidean distance of M31, the Andromeda Nebula. It Hubble’s value for H0 implied an age of the uni- geometry (Euclid 300 BC), the idea of absolute, clearly lay far outside our , verse of 2 billion years and it was soon realized uniform time (Aristotle), and the idea of an thus resolving the long-standing controversy this was shorter than the age of the Earth as infinite physical frame (the atomists, Epicurus). about the spiral nebulae and opening up the derived from radioactive isotopes. From 1927 Interestingly, and contrary to the picture held universe of galaxies. Three years later Hubble to 2001 the value of the Hubble constant was by medieval thinkers, Aristotle believed that the announced, based on the distances of 18 galax- a matter of fierce controversy. Baade pointed stars were at a range of distances. ies, that the more distant a galaxy, the faster it is out in 1952 that there were two different types A discovery of Copernicus (1473–1543) that is moving away from us (the Hubble Law): of Cepheid, so Hubble’s calibration had been

less well-known than his heliocentric system is velocity/distance = constant, H0 (1) incorrect. This reduced H0 to 200 km/s/Mpc. that he worked out, for the first time, the correct This is just what would be expected in an In 1958 Sandage recognized that objects that relative distances of the Sun and planets. His expanding universe. Aleksandr Friedmann Hubble had thought were the brightest stars in values were within 5% of the modern values. had shown in 1922 that expanding universe some of his galaxies were in fact H ii regions and The absolute scale of the solar system was not models are what would be expected according arrived at the first recognizably modern value of

determined accurately till the 19th century. to Einstein’s General Theory of Relativity, if H0 of 75 km/s/Mpc. During the 1970s there was The Copernican picture also immediately the universe is (a) homogeneous (everyone sees an acute disagreement between Sandage and

implied a much greater distance for the “immov- the same picture) and (b) isotropic (the universe Tammann, on the one hand, favouring H0 = 50, able” stars. Newton tried, unsuccessfully, to looks the same in every direction). and de Vaucouleurs, on the other, favouring estimate the distances of stars through their This unlikely assumption, the cosmological 100 km/s/Mpc. This disagreement stimulated brightness, but the first step on the distance principle, had been introduced by Einstein in me to write my monograph The Cosmologi- ladder outside the solar system was taken by 1917 when he derived a static model of the cal Distance Ladder (1985), in which I set Bessel in 1838 when he measured the parallax of universe in which gravity is balanced by a new out to review all aspects of the distance lad- 61 Cyg, its change in apparent direction on the force, the cosmological repulsion. Einstein’s der and to reconcile the systematic differences sky due to the Earth’s orbit round the Sun. This inspired guess that the universe must be very in distance estimates from different methods. was the final proof of the Copernican system. simple (homogeneous and isotropic) is con- With an objective weighting scheme based on Bradley had discovered aberration, the elliptical firmed to very high accuracy today. quoted errors, and with higher weight for purely

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(d) 1: Looking out from Earth into the universe. (a) The solar system: a Clementine image of Venus and the solar corona behind the Moon lit by earthshine (NASA/JPL/USGS). (b) The galaxy: the Milky Way seen above the dome of the Gemini North telescope on Hawaii, taken during commissioning of the laser guide star system (P Michaud/Gemini Observatory). (c) Other galaxies: M31, the in infrared, from the Spitzer Space Telescope (NASA/JPL-Caltech/P Barmby, Harvard-Smithsonian CfA). (d) The universe as a whole: fluctuations in the cosmic microwave background measured by the Wilkinson Microwave Anisotropy Probe satellite. (WMAP) Climbing the cosmological distance ladder

geometric distance methods (or those based on we shall see later, evidence from Type Ia super- impressive. A problem with the Gibson et al. theoretical arguments), I concluded that there novae presented in 1998 was already support- (2000) analysis was that it used photographic were systematic errors in the Type Ia supernova ing the idea of a positive cosmological constant. magnitudes for some of the older supernovae. method (too high distances) and in the Tully- But it was still of interest to see whether there Riess et al. (2005) used new HST–ACS observa- Fisher and H ii region methods (too low) and were any possible doubts about this HST Key tions of Cepheids in galaxies with well-observed

that the best overall value was Project value for H0. The uncertainties in this recent Type Ia supernovae and concluded that H0 = 67 ± 12 km/s/Mpc. value are (a) the distance of the Large Magel- H0 = 73 ± 6 km/s/Mpc. This analysis also dem- H0 = 67 would give an expansion age for the lanic Cloud, which remains uncertain by 10%, onstrated that some of the inconsistencies with universe of 15.3 billion years (Gyr). In the sim- (b) the adopted Cepheid calibration, based on earlier Type Ia supernovae can be attributed to

plest, Einstein de Sitter (Ωm = 1, Λ = 0) model, OGLE Cepheids, (c) corrections for the effects systematic errors in the photographic magni- with only gravity acting to slow the expansion, of dust extinction, (d) corrections for differ- tudes. The issue of the luminosity–decline rate the age of the universe would be 10.2 billion ences in metallicity between the LMC and the relation has been addressed by Jha et al. (2007) years. This could be compared with ages of the Cepheid host galaxies, (e) corrections for the and by Nobili et al. (2005) and Wang et al. oldest stars in globular clusters, between 10 local peculiar velocity flow. Using the Freedman (2006). There are still some unresolved incon- and 15 Gyr. Chaboyer et al. (1998) estimated et al. data, my own best estimates for these cor- sistencies in the derivation of extinction, which 12.6 ± 1.1 Gyr, and the age of the galaxy derived rections and the weighting scheme of The Cos- can only be resolved with the use of more photo- from radioactive isotope abundances was also mological Distance Ladder (1985), I concluded metric bands in future supernova studies. 10–15 Gyr. Was this already a headache for the (Rowan-Robinson 2000) A consensus? Einstein de Sitter model? H0 = 63 ± 6 km/s/Mpc. With the WMAP three-year results yielding HST Key Project Type Ia supernovae H0 = 73 ± 3 km/s/Mpc (Spergel et al. 2007), it Following the launch of the Hubble Space Tele- In 1998 two teams announced that using looks as though we have a consensus around

scope (HST) in 1990, and the subsequent repair Type Ia supernovae as standard candles out to H0 = 73 km/s/Mpc, Ωm = 0.25, ΩΛ = 0.75, and an mission, substantial amounts of HST time were significant redshifts (~0.5) implied that the cos- age of the universe 13.7 Gyr. However, in 2006 dedicated to measuring Cepheids in galaxies mological constant had to be greater than 0 Sandage et al. announced the results of their Λ out to distances of 20 Mpc, to try to measure (Riess et al. 1998, Perlmutter et al. 1999). There HST programme, with

the Hubble constant accurately and to give the were issues with (a) the treatment of extinction H0 = 62 ± 5 km/s/Mpc (3) different distance methods a secure and consist- by dust, and (b) the consistency of the assumed This was based on a new extensive study of ent calibration. The HST Key Project soon split correlation of the luminosity at maximum light the Cepheid period–luminosity relation (Tam- into two teams, one led by Wendy Freedman, with the exponential decline rate after maxi- mann et al. 2003), and recognition that there Jeremy Mould and Rob Kennicutt (Kennicutt mum raised by Liebundgut (2001), Rowan- is a difference between the P–L relation in the et al. 1995), and the other by Allan Sandage Robinson (2002). I also raised two other issues: galaxy and the LMC (Sandage et al. 2004). and Gustav Tammann. In 2001 Freedman et (c) inconsistencies with earlier Type Ia super- They used a new Cepheid calibration based on al. announced their final result nova data, (d) inappropriate use of supernovae the Baade–Wesselink expanding photosphere

H0 = 72 ± 8 km/s/Mpc (2) not observed before maximum light. A group method, so do not incur the uncertainty in the This, as we shall see, agreed extremely well which combined members of the high redshift LMC distance. And they give a new discussion with the first results from the WMAP CMB supernova team and the HST Key Project team of extinction in supernovae. In my view this is

mission (72 ± 5 km/s/Mpc, Spergel et al. 2003). announced a value for H0 from Type Ia super- an analysis that has to be taken very seriously. It gave an age of the universe for an Einstein de novae of 68 ± 5 km/s/Mpc (Gibson et al. 2000). I will discuss below whether this is inconsistent Sitter model of 9.1 Gyr, which meant that a posi- The supernova data is clearly excellent and with the WMAP CMB estimate. tive cosmological constant would be required the latest results (Astier et al. 2006, Riess et al. Mike Feast has presented a recent review of

for constancy with the age of the oldest stars. As 2007), reaching out to redshift 1.5, are extremely work on H0 (Feast 2007). New HST Cepheid

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Table 1: CMB fluctuation results forH 0 600 Data set assumptions/other data H0 reference 400 Boomerang, Maxima flat universe 75 ± 10 Jaffe et al. 2001 WMP first year  72 ± 5 Spergel et al. 2003 (km/s/Mpc) 0

H WMP first year + SLOAN LSS data 68 ± 10 Tegmark et al. 2004 200 WMP first year + BAO data 65 ± 4.5 Eisenstein et al. 2005 WMAP three-year data  73 ± 3 Spergel et al. 2007 1920 1940 1960 1980 2000 WMAP three-year data + LSS, BAO 69– 72 Spergel et al. 2007 date WMAP five-year data + LSS, BAO 70.1 ± 1.3 Komatsu et al. 2008

2: Estimated values of H0 from 1927–2001. (Copyright SAO) the distance to be estimated if the gas cloud is we can fit the CMB fluctuation spectrum just as

assumed to be spherical and smooth. well as the consensus model with an Ωm = 1, Λ = 0 4.6 Unfortunately both methods appear to have (Einstein de Sitter) model, provided H0=46. We irreducible systematic uncertainties. In the case can also get consistency with galaxy large- 4.4 of gravitationally lensed systems we have to scale structure data provided there are one 4.2 know the exact distribution of matter, including or more neutrinos with a mass of a few keV, B CM v 4.0 dark matter, in the foreground lensing galaxy. such that Ων ~ 0.2 (a mixed dark matter model).

log 3.8 In the case of the S–Z method we can not be However, this model is inconsistent with the sure that the gas clouds are spherical and there Type Ia supernova data and H = 46 is 3σ from 3.6 0 is a strong possibility that the gas is clumpy. the direct HST Key Project estimates. Recently c = 0.688±0.004 3.4 v Shafieloo and Souradeep (2007) have confirmed 14 15 16 17 18 19 CMB first Doppler peak and BAOs that the low-H , Einstein de Sitter model, is as mcorr 0 v Finally I want to discuss the distance method good a fit to the WMAP CMB fluctuation spec- 3: Hubble diagram for Type Ia supernovae. that takes us to a redshift of 1100, the angular trum as the consensus model if the primordial (From Sandage et al. 2006) scale of the first Doppler peak in the CMB fluc- density fluctuation spectrum is allowed to have tuations. If we think we know the physics of a free form. distances by Benedict et al. (2007) and the universe at the time of decoupling of matter So the CMB fluctuations do not on their own revised Hipparcos parallaxes result in a revi- from radiation (epoch of “recombination”), then determine H0. An important advance is the dis- sion of Sandage et al.’s H0 value from 62 to we know the sound speed in the universe at that covery of the baryon acoustic oscillation (BAO) 69.6 km/s/Mpc (van Leeuwen et al. 2007). The time and hence the linear scale of the acoustic feature in the power spectrum of galaxy den- Freedman et al. value is also increased. Macri horizon. This will translate to the angular scale sity fluctuations (Eisenstein et al. 2005, Cole et al. (2006) have shown that the Cepheid dis- of the largest structures in the CMB fluctuations, et al. 2005). This feature is essentially the same tance to NGC 4258 is consistent with a geo- the first Doppler peak, depending onH 0 and the acoustic horizon scale seen in the CMB fluctua- metrical estimate derived from maser emission. cosmological model. Analysis of the CMB fluc- tions, but now seen in galaxy redshift surveys

The latest H0 estimates from the gravitational tuations usually proceeds by fitting the whole at z ~ 0.35. At this epoch it has a linear scale of lens time-delay method are 68 ± 10 (Oguri CMB fluctuation spectrum, with some assump- about 150 Mpc. Blanchard et al. (2006) admit 2007), 72 ± 10 (Saha et al. 2006), and from tions about the primordial density fluctuation that this feature, if confirmed (it is between the Sunyaev–Zeldovich method for clusters spectrum (usually that it is a power-law, some- about 2 and 3σ significance at the moment), of galaxies are 66 ± 14 (Jones et al. 2005) and times with the further restriction that the power- would be fatal for their low-H0, Einstein de Sit- 76 ± 10 km/s/Mpc (Bonamente et al. 2006). law index has the Harrison–Zeldovich scale-free ter model. The combination of the CMB first The gravitational lens time-delay and Sunyaev– value n = –1), the spatial curvature (often taken Doppler peak and the baryon acoustic oscil- Zeldovich methods offered the prospect of to be zero) and requiring consistency with other lation peak is the ultimate geometric measure- completely independent geometrical methods astrophysical data (Type Ia supernovae, large- ment of H0. Using the WMAP five-year data which could be applied at high redshift, thereby scale structure). Results of some of these CMB combined with baryon acoustic oscillation and overcoming any uncertainty due to the peculiar analyses are summarized in table 1. Type Ia supernova data, Komatsu et al. (2008) velocities of local galaxies. The gravitational lens Spergel et al. (2003) show that with the assump- conclude that H0 = 70.1 ± 1.3 km/s/Mpc. time-delay method uses double images of quasars tion of a power-law spectrum, but no restriction Figure 4 shows the result of applying these two caused by gravitational lensing by an intervening to flat models, consistency with the WMAP tests as a pure diameter–distance test. The black galaxy. If the background quasar varies its light (year 1) fluctuation spectrum can be achieved line shows the locus of a zero-curvature universe. output, the two images will be seen to vary out with a wide range of cosmological models and The solid curves show the loci which give the of phase because of the different time it takes values for H0. Priors on H0 or the assumption of same observed angular scale for the first Doppler the light to arrive via the two different routes. flatness then force us to theΩ Λ = 0.75 consensus peak, for H0 = 73, 65 and 48 km/s/Mpc. We see The time delay can then be used to estimate the model. However, if we also drop the assumption that the H0 = 48 curve intersects the zero-cur- distance of the quasar. The Sunyaev–Zeldovich of a power-law primordial density fluctuation vature line at the Ωm = 1, Λ = 0 Einstein de Sitter method is based on the fact that very hot X-ray spectrum, which is not necessarily expected in a model, consistent with the Blanchard et al. (2003) emitting gas in rich clusters of galaxies inter- universe that has been through a series of phase and Shafieloo and Souradeep (2007) claims. acts with the photons of the cosmic microwave transitions, the possibilities are opened up even The broken curves show loci for the same background to produce either a brightening or further. Blanchard et al. (2003) showed that if three values of H0 for models that give the dimming at microwave wavelengths. A combi- we relax the assumption of a power-law to the same observed angular diameter for the baryon nation of the microwave and X-ray data allows simplest alternative, a broken power-law, then acoustic oscillation peak at z = 0.35. The H0 = 65

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1.0 Some formulae gal. peak z=0.35 flat (H=73) radius of particle horizon at decoupling r = R(t ) 0.8 ph dec χph (H=65) 1/2 1/Zdec 4–3(1+w) 2 –1/2 C ph = A Ω0 x + Ωr + Ω x + (1–Ω0 – Ωr – Ω )x } dx χ ∫0 { Λ Λ A = | (1 – Ω0 – Ωr – Ω )| if k = +1, –1, Λ = 1 if k = 0 0.6 CMB peak H=48 zdec ~ 1100, w = –1

Λ CMB peak H=73 radius of acoustic horizon Ω (H=48) 1/2 2 2 1/2 racoust = rph / {3 (1 + 3 b / 4 ) } = rph / {3 (1 + 1.25 (Ωb h ) / (Ω0 h ) } γ 2 ρ ρ 0.4 Ωb h ~ 0.022 (Doppler peak ratios + nucleosynthesis) angular radius of first Doppler peak = r / D (z ) θDoppler acoust diam dec 0.2 angular radius of baryon acoustic peak ~ 150 (Ω h2 / 0.25 × 0.732)–0.0853 Mpc/D (z) θBAO 0 diam diameter distance 1/2 0 E Ddiam(z) = ct0 ro(z) / {A (1 + z) } 0 0.2 0.4 0.6 0.8 1.0 ct = 9.8 h–1 Gyr Ω 0 m r (z) = sin (z) for k = +1, 4: Models with the same angular size CMB Doppler peak (solid blue, red o χ = (z) for k = 0, and green, for H0 = 73, 65, 48), and the BAO feature (broken curves). C χ marks the “consensus” model, E the Einstein de Sitter model. CMB data = sinh (z) for k = –1 alone cannot separate C and E, without prior knowledge of H or the shape 1/2 χ1/(1+z) 4–3(1+w) 2 –1/2 (z) = A {Ω0 x + Ωr + Ω x + (1 – Ω0 – Ωr – Ω ) x } dx of the spectrum of initial density fluctuations. The BAO feature can break χ ∫1 Λ Λ

this degeneracy, but models with H0 = 65–73 are permitted.

locus passes close where the corresponding atmosphere method for Cepheids and super­ References first Doppler peak locus intersects the zero- novae. For Cepheids this would reduce the Astier P et al. 2006 AA 447 31. Benedict G F et al. 2007 AJ 133 1810. curvature line. However, the H0 = 48 locus lies uncertainty in the absolute calibration. To gen- Blanchard A et al. 2003 AA 412 35. nowhere near the Einstein de Sitter model. The erate accurate atmospheric models for Type Ia Blanchard A et al. 2006 AA 449 925.

conclusion is that H0 = 65 is consistent with this supernovae is challenging, but would improve Bonamente M et al. 2006 ApJ 647 25. combined test, but H = 48 is ruled out. confidence in the method enormously and would Chaboyer B et al. 1998 ApJ 494 96. 0 Cole S et al. 2005 MNRAS 362 505. eliminate the need for ad hoc corrections for the Conclusions Eisenstein D J et al. 2005 ApJ 633 560. luminosity dependence on decline rate. Feast M 2007 From IRAS to Herschel/Planck: Local direct estimates of H are in the range (c) Use of multiwavelength photometry, espe- Cosmology with Infrared Surveys. ● 0 62–72 km/s/Mpc, with an uncertainty of 10%, cially in the infrared, to control extinction and Freedman W L et al. 2001 ApJ 553 47. Gibson B K et al. 2000 ApJ 529 723. and this is a big advance on the range 50–100 metallicity. Further work on estimating distances Jaffe A H et al. 2001 Phys.Rev.Lett. 86 3475. possible in the 1970s. My 1985 value of 67 still via Cepheids and supernovae really does not Jha S et al. 2007 ApJ 659 98. looks quite plausible. seem worthwhile without this development. Jones M E et al. 2005 MNRAS 357 518. The CMB fluctuation estimates ofH lie in the (d) Much better mapping of the local density Kennicutt R C et al. 1995 AJ 110 1476. ● 0 range 65–73 km/s/Mpc, depending on assump- field would be needed to reduce the uncertainty Komatsu E et al. 2008 ApJS astro-ph/0803.0547. Liebundgut B 2001 ARAA 39 67. tions made, with an uncertainty of 2%. in the peculiar velocities of galaxies. Macri L M et al. 2006 ApJ 652 1133. The angular scale of the baryonic acoustic In conclusion, progress in understanding the Nobili S et al. 2005 AA 437 789. ● oscillation peak, combined with the CMB first universe has always been strongly connected Oguri M 2007 ApJ 660 1. Doppler peak, is the ultimate geometrical meas- with our ability to measure distances. Today we Perlmutter S et al. 1999 ApJ 517 565. Riess A G et al. 1998 AJ 116 1009. urement of H0. have distance measurements to redshift 1100, Riess A G et al. 2005 ApJ 627 579 . It is still worthwhile to improve the direct the epoch when matter and radiation finally Riess A G et al. 2007 ApJ 659 98. ● Rowan-Robinson M 1985 The Cosmological Distance local estimates of H0. If an accuracy of, say, decoupled at the end of the hot Big Bang phase. 1%, could be achieved then there is the pros- Apparently we have reached a precision of 2% Ladder (W H Freeman, New York). Rowan-Robinson M 2000 astro-ph/001206. pect of learning about new physics beyond the in our measurements of the Hubble constant Rowan-Robinson M 2002 MNRAS 332 532 . standard model of particle physics, since tension and a consensus model of the universe with a Saha A et al. 2006 ApJS 165 108. between direct and CMB estimates would show dominant role for dark energy. Our inability Sandage A et al. 2004 AA 424 43. that the underlying assumptions being used in to provide a motivation for this dark energy Sandage A et al. 2006 ApJ 653 843. Shafieloo A and Souradeep T 2007 astro- CMB physics were incorrect. Such an accuracy remains troubling and we should remain open ph/0709.1944. could be achieved through: to the possibility of new physics beyond the Spergel D N et al. 2003 ApJS 148 175. (a) Direct parallax measurements of the distance standard model that might change our whole Spergel D N et al. 2007 ApJS 170 377. to the LMC, from the GAIA mission. This is picture of the universe. Tammann G A et al. 2003 AA 404 423. ● Tegmark M et al. 2004 ApJ 606 702. the main uncertainty in most current local esti- van Leeuwen F et al. 2007 MNRAS in press astro- mates, accounting for 10% uncertainty in H0. Michael Rowan-Robinson, President of the RAS ph/0705.1592. (b) Use of the Baade–Wesselink expanding 2006–2008; Imperial College, London. Wang L et al. 2006 ApJ 641 50.

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