Age Crisis (~1995) HLecture 9 Observational Cosmology ...
Transcript of Age Crisis (~1995) HLecture 9 Observational Cosmology ...
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AS 4022 Cosmology
Lecture 9
Observational Cosmology
Discovery of “Dark Energy”
AS 4022 Cosmology
Age Crisis (~1995)
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H0 t0 =dx
x ΩM x 3 +ΩΛ + (1−Ω0) x2
1
∞
∫
observations : H0 = 72 ± 8 km s−1 Mpc−1
t0 ≥14 ± 2 Gyr old globular clusters H0 t0 ≥1.0 ± 0.15
H0 t0 =23
for ΩM ,ΩΛ( ) = (1,0)
Globular clusters older than the Universe ?Inconsistent with critical-density matter-only model :
Strong theoretical prejudice for inflation.Doubts about stellar evolution therory (e.g. convection).
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Ω0 =1( )
AS 4022 Cosmology
Deceleration parameter
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q ≡ −˙ ̇ R R˙ R 2
= −˙ ̇ R
R H 2
q0 ≡ −˙ ̇ R R˙ R 2
0
= −˙ ̇ R
R H 2
0
a(t) ≡ R(t)R0
=1+ H0 t − t0( ) − q0
2H0
2 t − t0( )2+ ...
˙ a = H a ˙ ̇ a = −q H 2a
Dimensionless measure of the
deceleration of the Universe
q0 > 0 => deceleration
q0 = 0 => coasting at constant velocity
q0 < 0 => acceleration
t - t0
R
q0 > 0
q0 < 0
AS 4022 Cosmology
Deceleration parameter
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q ≡ −˙ ̇ R R˙ R 2
= −˙ ̇ R
R H 2 q0 ≡ −˙ ̇ R R˙ R 2
0
= −˙ ̇ R
R H 2
0
Friedmann momentum equation :
˙ ̇ R = − 4π G3
ρ +3 pc 2
R +
Λ3
R
˙ ̇ R H0
2R= −
4π G3H0
2 ρ 1+ 3w( ) +Λ
3H02
ρ, p > 0 decelerate, Λ > 0 accelerates
Equation of state : p = wi ρi c 2
i∑
wR =13
wM = 0 wΛ = −1
q0 = −˙ ̇ R
R H 2
0
=1+ 3 wi
2
Ωi
i∑ =ΩR +
ΩM
2−ΩΛ €
ΩM€
ΩΛ
€
Ω= 1€
0
€
+1/ 2€
q0 = −1/ 2
t - t0
R
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DecelerationParameter
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q0 ≡ −˙ ̇ R R˙ R 2
0
=ΩM
2−ΩΛ
Measure q0 via :
1 . DA(z)
( e.g. radio jet lengths )
2. DL(z)
( curvature of Hubble Diagram )
+1
0
q0 = -1
acceleration
deceleration
Matter decelerates
Vacuum (Dark) Energyaccelerates
Critical density matter-only --> q0=1/2.
AS 4022 Cosmology
Observable Distances
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angular diameter distance :
θ = lDA
DA =r0
(1+ z )=
c zH0
1− q0 + 32
z + ...
luminosity distance :
F = L4π DL
2 DL = r0 (1+ z ) =c zH0
1+1− q0
2z + ...
deceleration parameter :
q0 =ΩM
2−ΩΛ
Verify these low-z expansions.
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AS 4022 Cosmology
1993 - Angular Size of Radio Jets
Deceleration
as expected for
But, are radio jets
standard rods ?
Kellerman 1993
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for ΩΛ = 0
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q0 ~ +0.5
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(ΩM ,ΩΛ ) =(1,0)
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ΩM€
ΩΛ
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θ =l
DA(z )
AS 4022 Cosmology
Kellerman 1993
1993 - Angular Size of Radio Jets
Deceleration
as expected for
But, are radio jets
standard rods ?
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θ =l
DA(z )
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q0 ~ +0.5
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(ΩM ,ΩΛ ) =(1,0)
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(ΩM ,ΩΛ ) =(0.3,0.7)
Also compatible withConcordance Model.
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ΩM€
ΩΛ
AS 4022 Cosmology
Angular Diameter Distance
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ΩM€
ΩΛ
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DA (z) =lθ
Similar redshift dependence.
AS 4022 Cosmology
Angular Diameter Distance
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ΩM€
ΩΛ
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DA (z) =lθ
Change jet length, closer still.
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Hubble Diagram
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m = M + 5 log DL (z)Mpc
+ 25
+ A + K(z)m = apparent magM = absolute magA = extinction (dust in galaxies)K(z) = K correction( accounts for redshift of spectrarelative to observed bandpass )
DL(z) =c zH0
1+1− q0
2z + ...
slope = +5
vertical shift --> H0
curvature --> q0
log ( c z )
app
aren
t m
ag
deceleration( q0 > 0 )
acceleration( q0 < 0 )
faint
bright
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Finding faint Supernovae
Observe 106 galaxies.
Again, 3 weeks later.
Find “new stars”.
Measure lightcurves.
Take spectra.
( Only rare Type IaSupernovae work ).
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AS 4022 Cosmology
Hi-Z Supernova Spectra
SN II --- hydrogen lines
(collapse and rebound ofthe core of a massive star)
SN I --- no hydrogen lines
(no H-rich envelopesurrounding the core)
SN Ia --- best knownstandard candles
(implosion of 1.4 Msunwhite dwarf, probably dueto accretion in a mass-transfer binary system).
HαHβ
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Calibrating“StandardBombs”
1. Brighter onesdecline more slowly.
2. Time runs slowerby factor (1+z).
AFTER correcting:Constant peak brightness
MB = -19.7
Observed peak magnitude:m = M + 5 log (d/Mpc) + 25gives the distance! Time ==>
Abs
olut
e m
agni
tude
M B
==>
AS 4022 Cosmology
SN Ia at z ~ 0.8are ~25% fainterthan expected
Acceleration ( ! ? )
1. Bad Observations?
-- 2 independent teams agree
1. Dust ?
-- corrected using reddening
2. Stellar populations ?
-- earlier generation of stars
-- lower metalicity
3. Lensing?
-- some brighter, some fainter
-- effect small at z ~ 0.8
Reiss et al. 1998
Perlmutter et al. 1998
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1998cosmologyrevolution
Acceleration ( ! ? )
matter-only modelsruled out
cosmological constantΛ > 0
“Dark Energy”
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if Ω0 =ΩM +ΩΛ =1 then ΩM ~ 0.3 ΩΛ ~ 0.7
AS 4022 Cosmology
HST Supernova SurveysHST surveys to find SN Ia beyond z = 1Tonry et al. 2004.
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25 HST SN 1a beyond z = 1Reiss et al. 2007.
SNAP = SuperNova Acceleration Probe
1.5m wide-angle multi-colour spacetelescope --- 1000 SN 1a
(Not Yet Funded)
Most distant SupernovaSN 2007ff z =1.75