Download The Cosmological Distance Ladder

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 (2nd C BC)
- estimated distance of the moon
(59 RE, cf modern value 60.3)
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Aristotle, by Raphael
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
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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)
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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
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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
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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.
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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
(a) homogeneous (everyone sees the same picture) and
(b) isotropic (the same in every direction).
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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.
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Sandage 1958 >
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The cosmological distance
ladder
This was my 1985
summary of the
cosmological
distance ladder
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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
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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)
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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 ?
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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.
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Some of the galaxies studied
by HST
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HST Key Project strategy
Kennicutt
et al 1995
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The HST Key program final
result (1)
Ho = 72 +- 8 km/s/Mpc
(Freedman et al 2001)
log V
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Any room for doubt ?

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)
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Distance of
LMC

mo = 18.5+-0.1
(d = 50 kpc, +-10%)
- a fundamental limitation
of local estimates of Ho
perhaps Gaia will resolve
this
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Type Ia supernova

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)
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supernova issues





data is clearly excellent, but this is not a geometric distance
method
new HST-ACS observations of Cepheids in galaxies with wellobserved 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)
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supernovae 2007

Latest data from Riess
et al (2007)
- clear support for
consensus L model
(cf also Astier et al 2005,
SN Legacy Survey)
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consensus ?


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 wellobserved 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 ?
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History of the universe
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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)
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Hubble diagram for 62 supernovae
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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)
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CMB fluctuations and Ho

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:
with LSS, BAO
73 +- 3 (Spergel et al 2007)
69-72
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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)

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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 a
L=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
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galaxy baryon acoustic peak

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
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angular diameter distance test
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courtesy: Paniez Paykari
some formulae
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
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to z = 1100

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
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conclusions

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
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