andrew connolly university of...
TRANSCRIPT
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Cosmology and Surveys Andrew Connolly
University of Washington
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What occupies your time when you’re not on a telecon…? • LSST
– Transient detection – Simulations of the LSST
• Photometric redshifts – Galaxy evolution – Large scale structure – Filter designs
• Scalable science – Machine learning applications – Data access and visualization – Google Sky
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Dinoj Surendran, Mark SubbaRao
The evolution of data
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Structure of the lectures
1. Evolution of Cosmogony through Surveys – How has our understanding of cosmology evolved with
time and how do surveys drive this understanding
2. What can we look forward to – In the era of survey astronomy what can we expect over
the next decade
3. Statistics and Cosmology – How can we scale the science (and statistics) we want to
undertake to the petascale surveys coming on line this decade
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A decade of surveys
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Last scattering Structure formation
Growth of structure in the universe
10-43 s 4x108 yrs 4x105 yrs 13.6 Gyrs
Inflation First stars
Radio, 21cm, Infrared, Optical-UV
Credit: WMAP
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What are we trying to learn?
We live in an isotropic and homogeneous universe (averaged over large scales)
€
H 2(t) ≡ 1adadt
⎛
⎝ ⎜
⎞
⎠ ⎟ 2
=8π3
⎛
⎝ ⎜
⎞
⎠ ⎟ Gρ(t) −
ka2(t)
Goal is to measure the scale factor: a(t) or H(t)
Scale factor
Hubble parameter Density
Curvature (-1,0,+1)
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In its more observer friendly form
€
H 2(z)H02 =Ωr,0(1+ z)4 +Ωm,0(1+ z)3 +ΩΛ,0 + 1−Ω0( )(1+ z)2
Where density is in terms of the critical density – five Hydrogen atoms per cubic meter
€
ρcrit ≡3H0
2
8πG=1.03 ×10−29grams/cm3
€
ΩX ,0 = ρX (t0) /ρcrit
€
H0 = 70.4−1.4+1.3 km /s /Mpc
€
H 2(z)H02 =Ωr,0(1+ z)4 +Ωm,0(1+ z)3 +ΩDE ,0 exp 3 (1+ w(z))d ln(1+ z)∫[ ] + 1−Ω0( ) 1+ z( )2
Equation of state parameter
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To accomplish this we require redshift and distance
€
ds2 = c 2dt 2 − a2(t) dr2 + Sk2(r) dθ 2 + sin2θ dφ 2{ }[ ]
€
cdt = a dr ⇒ r =cdta∫ = c da
a2H(a)= −c dz
H(z)∫∫
€
1+ z =λ(t2)λ(t1)
=a(t2)a(t1)
Redshift
FRW Metric
Comoving distance €
Sk (r) = sinh(r), r, sin(r) k = −1, 0, 1
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Surveys don’t need to be large
Hubble and Humason 1931
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Evolution of a(t) through surveys
Res
earc
h tim
e
WMAP Team
Open
Flat
Closed
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Cosmology circa 1990
€
H 2(a)H02 =Ωr,0(1+ z)4 +Ωm,0(1+ z)3 + 1−Ω0( )(1+ z)2
Measuring H0 and q0 were the primary goals
€
q0 = −˙ ̇ a a˙ a 2
Theoretical preference for Ω0=1 from inflation
Observational preference for Ω0=0.1 -- 0.3
€
H0 =˙ a 0a0
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Observational drivers
Koo 1990
Deep imaging data from CCDs and photographic plates
Open universe preferred for number counts and cluster abundances
Convolved with number, and luminosity evolution made interpretation complex
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Observational drivers
Too much large scale power
Efstathiou et al 1990
Evidence for Λ
Observations of too much large scale power
Suggests need for dynamically important energy density at late times
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Type Ia supernovae – High-z supernova factory – Supernova Cosmology Project – SNe at z~0.5 are ~0.25 mag
fainter than in an open Universe with same value of Ωm
– Breakthrough because of the volume of the survey (guarantee follow-up of supernova candidates)
– Enabled by large format CCDs
Cosmology circa 2000
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Cosmology circa 2000
€
H 2(z)H02 =Ωr,0(1+ z)4 +Ωm,0(1+ z)3 +ΩΛ + 1−Ω0( )(1+ z)2
No longer about geometry it is now about the equation of state of the energy density (w)
Introduction of precision cosmology (systematics are now a critical issue) and the age of Dark Energy
€
Ω(z) = Ωi,0z3(1+wi )
i∑
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Evolution of a(t) through surveys
WMAP Team
Open
Flat
Closed
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Surveys still don’t need to be large
Perlmutter et al 1999
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Cosmology circa 2010
Decade of CMB measurements: Boomerang, Maxima discover the first peak in the CMB power spectrum
WMAP makes exquisite measurements of multiple peaks
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Cosmology circa 2010
!
H 2(z)H02 ="m (1+ z)3 +"DE exp 3 (1+ w(z))d ln(1+ z)#[ ] + 1$"m $"DE( ) 1+ z( )2
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Cosmology circa 2010
WMAP Team
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Cosmology circa 2010
€
w(a) = w0 + wa (1− a)
Sullivan et al 2011
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What are we measuring?
Gravitational weak lensing Angular diameter distance Growth of structure
Supernovae Luminosity distance
Baryon Acoustic oscillations Angular diameter distance
Clusters of galaxies Volume element Growth of structure
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Luminosity Distance
€
dL = Sk (r)(1+ z)
€
f =L
4πdL2 ≡
L4πSk (r)
2(1+ z)2
For a bolometric source, luminosity distance relates the flux and luminosity assuming luminosity is emitted into solid angle dΩ and observed by a detector of a given area
1+z terms arise due to time dilation and redshifting of the photons
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We rarely measure bolometric measures
Blanton and Roweis 2007
K-corrections
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Standard Candles as distance indicators
€
mi −M j = 5log[H0dL (z,Ω,w(z))]− 5logH0 +Kij (z) + Ai +C
Measurement of the distance modulus Combines luminosity distance, H0, K-corrections, extinction, calibration of the photometric properies
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Angular Diameter Distance
θ D r =0
r =r
€
dA ≡Dθ
= a(t)Sk (r) =Sk (r)1+ z
Distance at which a source of proper size D subtends an angle θ
€
dA =dL1+ z( )2
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Standard rulers from the CMB onwards Baryon acoustic oscillations
Coupling between gas and photons in early universe causes perturbations in gas to oscillate as sound waves (travelling 57% of c)
Decoupling causes sound speed to plummet and waves stall at a radius of ~150Mpc
Overdensities imprinted on these scales
RS~150 Mpc
Eisenstein et al 2005
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Evolution of the growth factor
Expansion and growth of perturbations compete (expansion retards the exponential growth of overdensities)
€
˙ ̇ g + 2H ˙ g = 3ΩmH02
2a3 g
Albrecht et al 2005
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What should we take away?
• Introduced the multiple ways we will measure cosmological parameters in the next generation of surveys
• Seen how these measures will be dominated by calibration and systematics – Extinction (internal and Galactic) – Photometric zeropoints – Knowing the system response of the experiment
• Question becomes, what surveys do we need to characterize cosmology and how will we control their errors
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Much of the progress in cosmology has been driven by surveys
Tyson 2010
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Surveys are not always what they seem…
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Goals of the SDSS (1992)
• Large Scale Structure (5 pages) – Topology – Two point correlation function
• Clusters of galaxies (7 pages) – Topology – Cluster counts
• Galaxies (25 pages) – Luminosity functions, Low Surface Brightness Galaxies,
Morphological properties • QSOs (11 pages)
– QSO selection, high redshift clustering, • Stars (5 pages)
– Halo stars, variables, proper motions, supernovae
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SDSS Impact in terms of citation • “Cosmological parameters from SDSS and WMAP”
Tegmark et al 2004 1769 citations
• “Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies” Eisenstein et al 2005 1414 citations
• “The Three-Dimensional Power Spectrum of Galaxies from the Sloan Digital Sky Survey” Tegmark et al 2004 912 citations
• “The Origin of the Mass-Metallicity Relation: Insights from 53,000 Star-forming Galaxies in the Sloan Digital Sky Survey” Tremonti et al 2004 856 citations
• “Composite Quasar Spectra from the Sloan Digital Sky Survey” Vanden Berk et al 2001 619 citations
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What drives survey design
• Statistical uncertainties – Shot noise: drives large n – Sample variance: drives large V
• Systematic errors – Absolute calibration: drives multiple visits (photometricity) – Relative calibration: drives offset pointings (reproducability)
• Analysis efficiency – Large n: drives compute resources – Complexity is the real challenge
• Theoretical considerations – Simulations exceed the volumes of galaxy
surveys and have all of the same computational challenges