Lecture 9
Observational Cosmology
Discovery of “Dark Energy”
AS 4022 Cosmology Age Crisis (~1995) ∞ dx H t = 0 0 ∫ 3 2 1 x ΩM x + ΩΛ + (1− Ω0) x observations : −1 −1 H0 = 72 ± 8 km s Mpc
t0 ≥14 ± 2 Gyr old globular clusters
H0 t0 ≥1.0 ± 0.15 Globular clusters older than the Universe ? Inconsistent with critical-density matter-only model : 2 H0 t0 = for (ΩM ,ΩΛ ) = (1,0) 3
Strong theoretical prejudice for inflation. (Ω0 =1) Doubts about stellar evolution therory (e.g. convection).
€ AS 4022 Cosmology € Deceleration parameter q0 < 0
R Dimensionless measure of the deceleration of the Universe q > 0 R˙˙ R R˙˙ 0 q ≡ − = − R˙ 2 R H 2 R˙˙ R R˙˙ t - t q ≡ − = − 0 0 ˙ 2 2 R 0 R H 0
R(t) q0 2 2 a(t) ≡ =1+ H0 (t − t0) − H0 (t − t0) + ... R0 2 a˙ = H a a˙˙ = −q H 2a
q0 > 0 => deceleration
q0 = 0 => coasting at constant velocity € q0 < 0 => acceleration
AS 4022 Cosmology Deceleration parameter
R˙˙ R R˙˙ R˙˙ R R˙˙ R q ≡ − = − q ≡ − = − ˙ 2 2 0 ˙ 2 2 R R H R 0 R H 0 Friedmann momentum equation : t - t 4π G 3 p Λ 0 R˙˙ = − ρ + R + R 3 c 2 3 q0 = −1/ 2 R˙˙ 4π G Λ ΩΛ 2 = − 2 ρ(1+ 3w) + 2 0 H0 R 3H0 3H0 ρ, p > 0 decelerate, Λ > 0 accelerates +1/ 2 2 Equation of state : p = ∑wi ρi c € i Ω € € M 1 w = w = 0 w = −1 R M Λ Ω = 1 3 € ˙˙ R 1+ 3 wi ΩM q0 = − 2 = ∑ Ωi = ΩR + − ΩΛ R H 0 i 2 2 €
AS 4022 Cosmology €
€ Deceleration Parameter q = -1 ˙˙ 0 R R ΩM q0 ≡ − = − ΩΛ R˙ 2 2 0 acceleration Matter decelerates 0 Vacuum (Dark) Energy accelerates deceleration €
Measure q0 via : +1 1 . DA(z) ( e.g. radio jet lengths )
2. DL(z) ( curvature of Hubble Diagram )
Critical density matter-only --> q0=1/2. AS 4022 Cosmology Observable Distances
angular diameter distance :
l r0 c z q0 + 3 θ = DA = = 1− z + ... DA (1+ z) H0 2 luminosity distance :
L c z 1− q0 F = 2 DL = r0 (1+ z ) = 1+ z + ... 4π DL H0 2 deceleration parameter :
ΩM q0 = − ΩΛ 2 Verify these low-z expansions.
€
AS 4022 Cosmology 1993 - Angular Size of Radio Jets
Kellerman 1993 for Ω = 0 l Λ θ = DA(z) € Deceleration
€ q0 ~ +0.5 as expected for
(ΩM ,ΩΛ ) =(1,0) € But, are radio jets standard rods ? € ΩΛ
ΩM AS 4022 Cosmology €
€ 1993 - Angular Size of Radio Jets
l Kellerman 1993 θ = DA(z)
Deceleration
€ q0 ~ +0.5 as expected for
(ΩM ,ΩΛ ) =(1,0) € But, are radio jets standard rods ? Also compatible with € ΩΛ Concordance Model.
(ΩM ,ΩΛ ) =(0.3,0.7) ΩM AS 4022 Cosmology €
€ € Angular Diameter Distance l D (z) = A θ ΩΛ
ΩM € €
€
Similar redshift dependence.
AS 4022 Cosmology Angular Diameter Distance l D (z) = A θ ΩΛ
ΩM € €
€
Change jet length, closer still.
AS 4022 Cosmology Hubble Diagram
faint D (z) m = M + 5 log L + 25 acceleration ( q < 0 ) Mpc 0 + A + K(z) mag m = apparent mag M = absolute mag deceleration ( q0 > 0 )
A = extinction (dust in galaxies) apparent K(z) = K correction
( accounts for redshift of spectra bright log ( c z ) relative to observed bandpass )
c z 1− q0 slope = +5 DL(z) = 1+ z + ... H0 2 vertical shift --> H0
curvature --> q0 AS 4022 Cosmology € Finding faint Supernovae
Observe 106 galaxies. Again, 3 weeks later. Find “new stars”. Measure lightcurves. Take spectra.
( Only rare Type Ia Supernovae work ).
AS 4022 Cosmology Hi-Z Supernova Spectra Hβ Hα
SN II --- hydrogen lines (collapse and rebound of the core of a massive star)
SN I --- no hydrogen lines (no H-rich envelope surrounding the core)
SN Ia --- best known standard candles (implosion of 1.4 Msun white dwarf, probably due to accretion in a mass- transfer binary system).
AS 4022 Cosmology Calibrating “Standard Bombs” ==> B 1. Brighter ones M decline more slowly. 2. Time runs slower by factor (1+z). magnitude AFTER correcting: Constant peak brightness M = -19.7 B Absolute
Observed peak magnitude: m = M + 5 log (d/Mpc) + 25 gives the distance! Time ==> AS 4022 Cosmology SN Ia at z ~ 0.8 are ~25% fainter than 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? Reiss et al. 1998 -- some brighter, some fainter Perlmutter et al. 1998 -- effect small at z ~ 0.8
AS 4022 Cosmology 1998 cosmology revolution
Acceleration ( ! ? ) matter-only models ruled out cosmological constant Λ > 0 “Dark Energy”
if Ω0 = ΩM + ΩΛ =1
then ΩM ~ 0.3 ΩΛ ~ 0.7
AS 4022 Cosmology € HST Supernova Surveys Tonry et al. 2004. HST surveys to find SN Ia beyond z = 1
AS 4022 Cosmology 25 HST SN 1a beyond z = 1
Most distant Supernova Reiss et al. 2007. SN 2007ff z =1.75
SNAP = SuperNova Acceleration Probe 1.5m wide-angle multi-colour space telescope --- 1000 SN 1a (Not Yet Funded) AS 4022 Cosmology