the cosmological distance ladder - to redshift 1000 michael rowan-robinson imperial college

The Cosmological The Cosmological Distance Ladder - to Distance Ladder - to

redshift 1000redshift 1000

Michael Rowan-RobinsonMichael Rowan-Robinson

Imperial CollegeImperial College

Feb 8th 2008 RAS Presidential Address

First steps on the First steps on the distance ladderdistance ladder

Aristotle (384-322 BC)Aristotle (384-322 BC)

- estimated the size of the earth- estimated the size of the earth(+ Eratosthenes, Poseidonius, 10%)(+ Eratosthenes, Poseidonius, 10%)

Hipparcos (2Hipparcos (2ndnd C BC) C BC)

- estimated distance of the moon- estimated distance of the moon(59 R(59 REE, cf modern value 60.3), cf modern value 60.3)

Aristotle, by Raphael


The Copernican The Copernican revolutionrevolution

Copernicus (1473-Copernicus (1473-1543)1543)

- gave the - gave the correct relative correct relative distances of the distances of the sun and planets sun and planets (to 5%)(to 5%)

- absolute value - absolute value not not determined determined accurately accurately till the 19till the 19thth centurycentury


The first steps The first steps outside the solar outside the solar

systemsystem

Bessel 1838Bessel 1838

- discovered parallax of nearby star 61 Cyg, its change in - discovered parallax of nearby star 61 Cyg, its change in apparent direction on the sky due to the earth’s orbit round apparent direction on the sky due to the earth’s orbit round the sun (the final proof of the Copernican system)the sun (the final proof of the Copernican system)


The key modern distance The key modern distance indicator – Cepheid indicator – Cepheid

variable starsvariable stars

Delta Cephei is the prototype of theDelta Cephei is the prototype of theCepheid variable stars, massive starsCepheid variable stars, massive starswhich pulsate and vary their light outputwhich pulsate and vary their light output


Henrietta Leavitt’s Henrietta Leavitt’s breakthroughbreakthrough

In 1912, Henrietta Leavitt, workingIn 1912, Henrietta Leavitt, workingat the Harvard Observatory, discoveredat the Harvard Observatory, discoveredfrom her studies of Cepheids in the from her studies of Cepheids in the Small Magellanic Cloud that the periodSmall Magellanic Cloud that the periodof Cepheid variability was related toof Cepheid variability was related totheir lumininositytheir lumininosity


The distances of the The distances of the galaxiesgalaxies

In 1924 Edwin Hubble usedIn 1924 Edwin Hubble usedLeavitt’s discovery to estimateLeavitt’s discovery to estimatethe distance of the Andromedathe distance of the AndromedaNebula. It clearly lay far outsideNebula. It clearly lay far outsideThe Milky Way systemThe Milky Way system.


The expansion of the The expansion of the universeuniverse

Three years later, in 1927, he announced, based on Three years later, in 1927, he announced, based on distances to 18 galaxies, that the more distant a distances to 18 galaxies, that the more distant a galaxy, the faster it is moving away from usgalaxy, the faster it is moving away from us

velocity/distance = constant, Hvelocity/distance = constant, Ho o (the Hubble (the Hubble law)law)

This is just what would be expected in an expanding This is just what would be expected in an expanding universe.universe.

The Russian mathematician Alexandr Friedmann had shown The Russian mathematician Alexandr Friedmann had shown (1922, 1924) that expanding universe models are what (1922, 1924) that expanding universe models are what would be expected according to Einstein’s General would be expected according to Einstein’s General Theory of Relativity, if the universe isTheory of Relativity, if the universe is

(a)(a)homogeneous (everyone sees the same picture) and homogeneous (everyone sees the same picture) and (b)(b)isotropic (the same in every direction).isotropic (the same in every direction).


The history of the The history of the Hubble constantHubble constant

Hubble’s estimate of Hubble’s estimate of the Hthe Hoo, the Hubble , the Hubble constant, was 500 constant, was 500 km/s/Mpc, which gave an km/s/Mpc, which gave an age for the universe of age for the universe of only 2 billion years. only 2 billion years. This was soon shown to This was soon shown to be shorter than the age be shorter than the age of the earth. of the earth.

From 1927 to 2001 the From 1927 to 2001 the value of the Hubble value of the Hubble constant was a matter constant was a matter of fierce controversy.of fierce controversy.

Sandage 1958 >


The cosmological The cosmological distance ladderdistance ladder

This was my 1985This was my 1985 summary of thesummary of the cosmologicalcosmological distance ladderdistance ladder


The cosmological The cosmological distance ladderdistance ladder

In my monograph ‘The Cosmological Distance Ladder’ In my monograph ‘The Cosmological Distance Ladder’ (Freeman 1985), I set out to understand the (Freeman 1985), I set out to understand the competing estimates of Hcompeting estimates of Hoo (50 - Sandage and Tammann, 100 - de Vaucouleurs), (50 - Sandage and Tammann, 100 - de Vaucouleurs), and to reconcile the systematic differences in and to reconcile the systematic differences in distance estimates from different methods.distance estimates from different methods.

With an objective weighting scheme based on quoted With an objective weighting scheme based on quoted errors, and with higher weight for purely errors, and with higher weight for purely geometrical distance methods, I concluded that geometrical distance methods, I concluded that there were systematic errors in the supernova method there were systematic errors in the supernova method (too high distances) and in the Tully-Fisher and HII (too high distances) and in the Tully-Fisher and HII region methods (too low) and that best overall value region methods (too low) and that best overall value for Hfor H00 was was

HHo o = 67 +_ 12 km/s/Mpc= 67 +_ 12 km/s/Mpc


Implications of the Implications of the Hubble constantHubble constant

HHoo is (velocity/distance) so has the dimensions of (1/time). is (velocity/distance) so has the dimensions of (1/time).

1/H1/Hoo is the expansion age of the universe (how old the is the expansion age of the universe (how old the Universe would be if no forces acting) = 15.3 billion yrsUniverse would be if no forces acting) = 15.3 billion yrs

For simplest model universe with only gravity acting, age ofFor simplest model universe with only gravity acting, age ofuniverse would be 10.2 billion years (gravity slows expansion)universe would be 10.2 billion years (gravity slows expansion)


The age of the The age of the universeuniverse

We can use the colours andWe can use the colours andbrightnesses of the stars inbrightnesses of the stars inglobular clusters to estimateglobular clusters to estimatethe age of our Galaxythe age of our Galaxy ~ 12 billion years~ 12 billion years

Long-lived radioactive isotopesLong-lived radioactive isotopesgive a similar answergive a similar answer

Allowing time for our Galaxy toAllowing time for our Galaxy toform, the age of the universe isform, the age of the universe is ~ 13 billion years~ 13 billion years

Already a problem for Already a problem for = 0 ?= 0 ?


The Hubble Space The Hubble Space Telescope Key ProgramTelescope Key Program

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


Some of the galaxies Some of the galaxies studied by HSTstudied by HST


HST Key Project HST Key Project strategystrategy

Kennicutt et al 1995


The HST Key program The HST Key program final result (1)final result (1)

log V

HHoo = 72 +- 8 km/s/Mpc = 72 +- 8 km/s/Mpc

(Freedman et al 2001)(Freedman et al 2001)


Any room for doubt ?Any room for doubt ? There is good consistency between the HST Key Program value There is good consistency between the HST Key Program value

of Hof Hoo and the age of the universe, provided we invoke and the age of the universe, provided we invoke Einstein’s Cosmological Constant, Einstein’s Cosmological Constant, (dark energy) (dark energy)

Uncertainties in HUncertainties in Hoo are (1) distance of Large Magellanic are (1) distance of Large Magellanic Cloud, (2) the adopted Cepheid calibration, (3) corrections Cloud, (2) the adopted Cepheid calibration, (3) corrections for dust extinction, (4) corrections for metallicity for dust extinction, (4) corrections for metallicity effects, (5) corrections for local floweffects, (5) corrections for local flow

Using the Freedman et al data, my own best estimates for Using the Freedman et al data, my own best estimates for these corrections, and the weighting scheme of CDL 1985, I these corrections, and the weighting scheme of CDL 1985, I concluded:concluded:

HHoo = 63 +- 6 (Rowan-Robinson 2000, = 63 +- 6 (Rowan-Robinson 2000, astro-ph/0012026)astro-ph/0012026)


Distance Distance of LMCof LMC

oo = 18.5+-0.1 = 18.5+-0.1

(d = 50 kpc, +-(d = 50 kpc, +-10%)10%)

- a fundamental - a fundamental limitation of limitation of local estimates local estimates of Hof Hoo

perhaps Gaia will perhaps Gaia will resolve thisresolve this


Type Ia supernovaType Ia supernova In 1998 two teams announced that using Type Ia supernovae as In 1998 two teams announced that using Type Ia supernovae as

standard candles implied that standard candles implied that > 0 (Schmidt et al 1998, > 0 (Schmidt et al 1998, Garnevich et al 1998, Riess et al 1998, Perlmutter et al 1999)Garnevich et al 1998, Riess et al 1998, Perlmutter et al 1999)

There were issues with (1) treatment of extinction by dust, There were issues with (1) treatment of extinction by dust,

(2) consistency of treatment of correlation of decline rate (2) consistency of treatment of correlation of decline rate with luminosity (Liebundgut 2001, Rowan-Robinson 2002). with luminosity (Liebundgut 2001, Rowan-Robinson 2002).

I also raised two other issues: (3) inconsistencies with I also raised two other issues: (3) inconsistencies with earlier supernova data, earlier supernova data,

(4) inappropriate use of supernovae not observed before (4) inappropriate use of supernovae not observed before maximummaximum

Joint HST Key Project and SN team foundJoint HST Key Project and SN team found

HHoo = 68 +- 5 (Gibson et al 1999) = 68 +- 5 (Gibson et al 1999)


supernova issuessupernova issues

data is clearly excellent, but this is not a data is clearly excellent, but this is not a geometric distance methodgeometric distance method

new HST-ACS observations of Cepheids in galaxies new HST-ACS observations of Cepheids in galaxies with well-observed Type Ia supernovae gives Hwith well-observed Type Ia supernovae gives Hoo = 73 = 73 +- 6 (Riess et al 2005) - but based on LMC, with +- 6 (Riess et al 2005) - but based on LMC, with 10% distance uncertainty10% distance uncertainty

inconsistencies with earlier results can be inconsistencies with earlier results can be attributed to photographic data attributed to photographic data

issue of luminosity-decline rate relation issue of luminosity-decline rate relation addressed by Jha et al (2007) (see also new addressed by Jha et al (2007) (see also new approach by Wang et al 2005, Nobili et al 2005)approach by Wang et al 2005, Nobili et al 2005)

still some unresolved inconsistencies in still some unresolved inconsistencies in derivation of extinction (can only be resolved by derivation of extinction (can only be resolved by use of more photometric bands)use of more photometric bands)


supernovae 2007supernovae 2007

Latest data from Latest data from Riess et al (2007)Riess et al (2007)- clear support for- clear support forconsensus consensus model model

(cf also Astier et al (cf also Astier et al 2005, SN Legacy 2005, SN Legacy Survey)Survey)


consensus ?consensus ?

HST key program found HHST key program found Hoo = 72 +- 8 (Freedman et al = 72 +- 8 (Freedman et al 2001)2001)

WMAP (year 1) found HWMAP (year 1) found Hoo = 72 +- 5 (Spergel et al 2003) = 72 +- 5 (Spergel et al 2003)

(year 3) H(year 3) Hoo = 73 +- 3 (Spergel et al = 73 +- 3 (Spergel et al 2007)2007)

new HST-ACS observations of Cepheids in galaxies with new HST-ACS observations of Cepheids in galaxies with well-observed Type Ia supernovae gives Hwell-observed Type Ia supernovae gives Hoo = 73 +- 6 = 73 +- 6 (Riess et al 2005)(Riess et al 2005)

so have consensus for Hso have consensus for H00=73, =73, mm=0.25, =0.25, =0.75, age of =0.75, age of universe 13.7 billion years ? universe 13.7 billion years ?


History of the universeHistory of the universe


The HST Key program The HST Key program final result (2)final result (2)

• new study of Cepheid P-L new study of Cepheid P-L relation relation (Tammann et al 2003)(Tammann et al 2003)

• difference between P-L difference between P-L relation in Galaxy and LMC relation in Galaxy and LMC (Sandage et al 2005)(Sandage et al 2005)

• new calibration usingnew calibration usingBaade-Wesselink methodBaade-Wesselink method(so no LMC distance error)(so no LMC distance error)

• new discussion of new discussion of extinction in supernovaeextinction in supernovae

HHoo = 62 +- 5 km/s/Mpc = 62 +- 5 km/s/Mpc(Sandage et al 2007)(Sandage et al 2007)

Hubble diagram for 62 Hubble diagram for 62 supernovaesupernovae


other work on Hother work on Hoo

Feast review (2007, ‘From IRAS to Feast review (2007, ‘From IRAS to Herschel/Planck’):Herschel/Planck’):

• new HST Cepheid distances (Benedict et al new HST Cepheid distances (Benedict et al 2007)2007)• revised Hipparcos parallaxes (van Leeuwen revised Hipparcos parallaxes (van Leeuwen et al 2007)et al 2007)

- revise Sandage’s H- revise Sandage’s Hoo to 69.6 to 69.6• NGC4258 Cepheids (Macri et al 2006), NGC4258 Cepheids (Macri et al 2006), consistency with consistency with maser distancemaser distance• gravitational lens time delay: 68+- 10 gravitational lens time delay: 68+- 10 (Oguri 2007)(Oguri 2007)

72+-10 (Saha et al 72+-10 (Saha et al 2006)2006)• Sunyaev-Zeldovich method for clusters: Sunyaev-Zeldovich method for clusters:

66+-14 (Jones et al 66+-14 (Jones et al 2005) 2005)

76+-10 (Bonamente 76+-10 (Bonamente et al 05)et al 05)


CMB fluctuations and HCMB fluctuations and Hoo

Boomerang and Maxima, for flat universe, Boomerang and Maxima, for flat universe,

HH00 = 75+-10 (Jaffe et al 2001) = 75+-10 (Jaffe et al 2001)

WMAP first year results: 72 +- 5 (Spergel et al 2003) WMAP first year results: 72 +- 5 (Spergel et al 2003)

include also SLOAN large-scale structure data:include also SLOAN large-scale structure data: 68 +- 10 (Tegmark et al 2004)68 +- 10 (Tegmark et al 2004)

include Sloan large-scale structure + baryonic acoustic include Sloan large-scale structure + baryonic acoustic oscillation oscillation data:data: 65 +- 65 +- 4.5 (Eisenstein et al 2005), 4.5 (Eisenstein et al 2005),

WMAP 3-year results: 73 +- 3 (Spergel et al 2007)WMAP 3-year results: 73 +- 3 (Spergel et al 2007)with LSS, BAOwith LSS, BAO 69-72 69-72


Primordial density Primordial density spectrum spectrum

power-law assumptionpower-law assumption

• Spergel et al (2004) show show that with power-law that with power-law spectrum, but no restriction spectrum, but no restriction to flat models, can get wide to flat models, can get wide range of fits just to WMAP3 range of fits just to WMAP3 CMB dataCMB data

can see that priors on Hcan see that priors on Hoo or assumption of flatness or assumption of flatness force us towards force us towards = 0.75 = 0.75 consensus modelconsensus model

however dropping however dropping assumption assumption of power-law opens up of power-law opens up possibilities even further possibilities even further (Blanchard et al 2003) (Blanchard et al 2003)


Blanchard et al (2003) Blanchard et al (2003) modelmodel

• 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 a =0, 0=1 (Einstein de Sitter) model, provided Ho = 46

• can get consistency with large-scale structure data can get consistency with large-scale structure data if if ~ 0.2 (mixed dark matter) ~ 0.2 (mixed dark matter) • however, inconsistent with supernova data and Hhowever, inconsistent with supernova data and H00=46 =46 is 3-is 3- from the direct estimates from the direct estimates

• Shafieloo and Souradeep (2007) deconvolve primordial Shafieloo and Souradeep (2007) deconvolve primordial density spectrum from CMB fluctuations and show density spectrum from CMB fluctuations and show =0, 0=1, H0=50, model is actually better fit than

consensus model


galaxy baryon acoustic galaxy baryon acoustic peakpeak

SDSS (Eistenstein et al 2005) and SDSS (Eistenstein et al 2005) and 2dFGRS (Cole et al 2005) have claimed 2dFGRS (Cole et al 2005) have claimed to detect baryon acoustic oscillation to detect baryon acoustic oscillation (BAO) peak on scale ~ 150 Mpc in the (BAO) peak on scale ~ 150 Mpc in the galaxy correlation functiongalaxy correlation function

Blanchard et al (2006) admit this is Blanchard et al (2006) admit this is fatal for their fatal for their =0 model, if confirmed=0 model, if confirmed

BAO plus CMB first Doppler peak is the BAO plus CMB first Doppler peak is the ultimate geometrical measurement of Hultimate geometrical measurement of Hoo


angular diameter distance angular diameter distance testtest

courtesy: Paniez Paykari


some formulaesome formulae

rrphph = R(t = R(tdecdec) ) phph (radius of particle horizon at decoupling) (radius of particle horizon at decoupling)

phph = A = A1/21/2 ∫ ∫001/Zdec1/Zdec { {00 x + x +rr + + x x4-3(1+w)4-3(1+w) + (1- + (1-00--rr--)x)x22}}-1/2-1/2 dx dx

A = |(1-A = |(1-00--rr--)| if k=+1,-1,)| if k=+1,-1, = 1 if k= 0= 1 if k= 0

zzdecdec ~ 1100, w =-1 ~ 1100, w =-1

radius of acoustic horizonradius of acoustic horizon

rracoustacoust = r = rphph/{3(1+3/{3(1+3bb/4/4)}1/2 = r)}1/2 = rphph/{3(1+1.25(/{3(1+1.25(bbhh22)/()/(00hh22)}1/2)}1/2

bbhh22 ~ 0.022 (Doppler peak ratios+nucleosynthesis) ~ 0.022 (Doppler peak ratios+nucleosynthesis)

angular radius of first Doppler peakangular radius of first Doppler peak

DopplerDoppler = r = racoustacoust/D/Ddiamdiam(z(zdecdec))

angular radius of baryon acoustic peakangular radius of baryon acoustic peak

BAOBAO ~ 150 ( ~ 150 (00hh22/0.25x0.73/0.25x0.7322))-0.0853-0.0853 Mpc/D Mpc/Ddiamdiam(z)(z)

diameter distancediameter distance

DDdiamdiam(z) = c(z) = c00 r roo(z)/(A (z)/(A 1/21/2 (1+z)) (1+z))

cc00 = 9.8 h = 9.8 h-1-1 Gyr Gyr

rroo (z) = sin (z) = sin (z) for k = +1, = (z) for k = +1, = (z) for k = 0, = sinh(z) for k = 0, = sinh (z) for k =-1 (z) for k =-1

(z) = A(z) = A1/21/2 ∫ ∫111/(1+z)1/(1+z) { {00 x + x +rr + + x x4-3(1+w)4-3(1+w) + (1- + (1-00--rr--)x)x22}}-1/2-1/2 dx dx


to z = to z = 11001100

black curve: zero black curve: zero curvaturecurvature

solid curves: first solid curves: first Doppler peak for HDoppler peak for Hoo = = 73 (blue), 73 (blue), 65 (red), 48 (green)65 (red), 48 (green)

dotted curves: baryon dotted curves: baryon acoustic peak for acoustic peak for same 3 casessame 3 cases

C: consensus modelC: consensus model

E: Einstein de Sitter E: Einstein de Sitter


conclusionsconclusions

local direct estimates of Hlocal direct estimates of H00 = 62-72 +- 10% = 62-72 +- 10% CMB estimates = 65-73 +- 4% (generally assuming flat CMB estimates = 65-73 +- 4% (generally assuming flat

universe, power-law spectrum, negligible universe, power-law spectrum, negligible , w=-1), w=-1)

baryonic acoustic peak plus CMB first Doppler peak is baryonic acoustic peak plus CMB first Doppler peak is the ultimate geometrical measurement of Hthe ultimate geometrical measurement of Hoo

precision measurements of Hprecision measurements of H00 (say to 1%) could tell (say to 1%) could tell us that we need new physics beyond Standard Model. us that we need new physics beyond Standard Model. * accurate distance to LMC (Gaia)* accurate distance to LMC (Gaia)* Baade-Wesselink methods for Cepheids and supernovae, * Baade-Wesselink methods for Cepheids and supernovae, * multi-* multi- photometry to control extinction and photometry to control extinction and metallicitymetallicity

the cosmological distance ladder - to redshift 1000 michael rowan-robinson imperial college

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