Cosmology 566: Class 2 Age Constraints, Density of the Universe

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Cosmology 566 Class 2Age Constraints, Density
of the Universe
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4. Hubble Age.cont..
Flat matter dominated
Recall
Flat rad. dominated
Plug in Numbers
H-19.77 h-1 Gyr
Hence for hgt.63 t0 lt 10 Gyr (flat, matter
dominated)
Note for open matter dominated universe
(with W gt0.2) t lt .8 H-1 lt12.4 Gyr for
flat, universe with with Wx 0.7 t 0.96 H-1
lt 14.9 Gyr
(Prove)
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A Lower Limit on the Age of the Universe Dating
Globular Cluster Stars
Theorem tuniverse gt tgalaxy
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• Globular Cluster Ages and Cosmology A Brief
  History
• Globular Cluster Dating A Primer
• New results abundances and distances
• Constraints on Equation of State

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A Brief History

• 1800 tstars 10,000 yrs
• 1900 tstars 100 Myr
• 1945 tstars 10 Gyr
• 1980s toldest stars 16-20 Gyr

To be compared with Hubble age for a flat
matter dominated universe t 2/3H-1 6.6
(h-1) Gyr
The first modern era evidence for dark energy?
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Stellar Dating
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Globular Cluster Colour Magnitude Diagram
Main Sequence lifetime L Mstar3 T M/L T M-2
Hydrostatic equilibrium
(An eq. at the basis of most astrophysics)
Mstar
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But..
UNCERTAINTIES!
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Observational Uncertainties!
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Theoretical Uncertainties!
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Theoretical Uncertainties!
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i.e..
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Isochrone Fitting
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Isochrone Fitting
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Age Determination Techniques

• D Magnitude (TO - HB) -- vertical method
• D Colour (TO - RGB) -- horizontal method
• Isochrone Fitting

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DColour Age Determinations

• Difference in colour between the main sequence
  turn-off and the base of the RGB
• Used to determine ages of globular clusters
• Well defined observational quantity -- gives
  precise relative ages
• Difficult to calibrate theoretically as a result
  should only be used to determine relative ages of
  clusters with similar heavy element abundances
• Comparisons between different clusters have found
  that all metal-poor clusters (Fe/H lt -1.7) have
  the same age, but an age spread of a few Gys
  appears among the more metal-rich clusters

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DMagnitude Ages

• Difference in magnitude between the main sequence
  turn-off or the SGB and the HB
• turn-off/SGB magnitude as a function of age
  determined from theoretical isochrones
• Absolute magnitude of the HB determined using a
  variety of methods
• Stellar evolution models
• Baade-Wesselink and infared flux method
• Statistical parallax
• RR Lyr stars in the LMC
• Main sequence fitting to GCs
• White dwarf fitting to GCs
• Parallax of field HB stars
• Astrometric (GC proper motion dispersion vs.
  radial velocity dispersion)

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HB calibration

• Express HB magnitude calibration in terms of RR
  Lyr magnitude typically it has been assumed that
  Mv(RR) is a linear function of metallicity
• Mv(RR) a Fe/H b
• Slope a affects relative ages for clusters of
  different metallicities
• Zero-point b affects the absolute ages
• Recent theoretical HB calculations find that the
  HB magnitude also depends on the HB type of the
  cluster (Demarque et al. 2000)
• Observations by Lee Carny (1999) and Clement
  and Shelton (1999) have also suggested that
  clusters with equal metallicities have different
  RR Lyr magnitudes
• For now, best to use the DMagnitude method for
  clusters with similar HB types

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Absolute GC Ages

• Interested in the oldest clusters -- select a
  sample of metal-poor (Fe/H lt -1.6) blue HB
  clusters
• Minimize theoretical errors by using the best
  understood age determination method -- the
  absolute magnitude of the main sequence turn-off
• Need to know distance (absolute magnitude of the
  RR Lyr stars)
• Calibrate RR Lyrae magnitude using metal-poor
  objects

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Ages of the Oldest Globular Clusters

• Critically examine the age determination processs
  and evaluate possible sources of error using a
  Monte Carlo simulation, in which the following
  variables used to determine the absolute age of
  the oldest globular clusters are varied within
  their known uncertainties
• Abundance of heavy elements, including oxygen
• Nuclear reaction rates
• Opacities
• Mixing length
• Surface boundary conditions
• Diffusion coefficients
• Colour transformation table
• Helium abundance

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New Analyses
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Oxygen Abundances at Fe/H -1.9

• Assume O/Fe 0.2 to 0.7 (flat distribution)

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Effect of Oxygen Abundance on the Derived Age
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Atomic Diffusion

• Helioseimology clearly shows that diffusion
  occurs in the Sun
• Fe abundance observations in NGC 6397 show that
  diffusion is not occuring in the outer layers of
  metal-poor stars
• As far as ages are concerned, inhibiting
  diffusion in the outer layers of a star is
  similar to reducing the diffusion coefficients by
  50
• Uncertainty in the diffusion coefficient
  calculations estimated to be G30
• For the Monte Carlo, multiply the nominal
  diffusion coefficients by 0.2 to 0.8
  (flat distribution)

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High Redshift Deutrium abundances and BBN suggest
YPRIMORDIAL 0.245
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Mv(RR) Determinations

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Use Mv(RR) 0.47 (0.13, -0.10)
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Absolute Age
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The Minimum Age of the Universe

• Mean age of 17 metal-poor (Fe/H lt -1.6) GC
  with blue HBs determined using the set of MC
  isochrones and Mv(RR) 0.47 (0.13, -0.10) mag
• tGC 12.5 Gyr
• One sided 95 CL lower limit of 10.2 Gyr
• To determine the age of the universe, one must
  add to this age the amount of time which passed
  between the big bang and the formation of the
  oldest GCs in the Milky Way

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Formation Time of GCs
Lower Limit important -recent studies Lyman a
systems z lt 5 (z lt6) Fortunately age of universe
insensitive to cosmological Uncertainties for Z
gt3-4
Recall
tgc gt 0.8 Gyr
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Constraints on Cosmology

• At the 95 CL, the oldest globular clusters have
  an age of 10.2 Gyr, so the age of the universe
  
• t0 gt 11 Gyr (95 CL)
• Hence
• Hoto gt 0.79 (95 CL) (H70)
• Hoto gt 0.91 (68 CL) (H70)
• Note Best fit age to 13.3 Gyr

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Now, use equation, for z0 to determine Hubble
age for flat universes with varying equation of
state, and compare to Globular cluster lower limit
Definitive evidence for dark energy if the
Universe is flat!
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H0 70
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H0 63
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Note

• SENSITIVE DEPENDENCE ON H
• NON-TRIVIAL LIMITS ON Wmatter!
• BEST FIT 13.3 Gyr.
• An Wm 0.3, WL 0.7 universe has Hoto 0.96
  which implies to 13.2 Gyr for h0.7!

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Comparison to Other Ages

• White dwarf cooling curves determine the age of
  the oldest stars in the thin disk to be 9 - 12
  Gyr, while my MSTO age for the oldest stars in
  the thin disk is 10 Gyr
• Deep HST observations found a white dwarf
  sequence in M4 by Richer et al. 1997 that the
  faintest white dwarfs observed were 9 Gyr
  old
• Observations of 232Th (half-life 14 Gyr) and 238U
  (half-life 4.5 Gyr) by Cayrel et al. (2001) in a
  very metal-poor field star yielded a radioactive
  decay age for this star of 12.5 3 Gyr
• Observations of detached ecliping double lined
  spectroscpic binaries allow one to determine the
  mass of the individual stars (Pacyñski 1996,
  BC,LMK 2002)

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Age-Mass Relation?
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Preliminary.. Single star.. Uncertainties?
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Preliminary.. Single star.. Uncertainties?
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Preliminary.. Single star.. Uncertainties?
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Recent result
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Direct Parallaxes to Globular Clusters
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Conclusion..Ages
Comparison of Hubble Age and GC age -A Flat
matter dominated Universe is ruled
out. -Either (a) Open Universe (b) Flat
with wlt0 component.
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II. Density of the Universe
Problem Telescopes measure light, not mass!
Mean (Optical) Luminosity
In galaxies
Clearly a lower limit.. What about the rest?
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Keplers Discovery
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Newtons Law of Gravity

• Brahe
• Kepler..
• Newton Fma, av2/r, v21/r

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Newtons Law of Gravity

• Brahe
• Kepler..
• Newton Fma, av2/r, v21/r

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Weighing the Sun!!!
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A little bit of Luck
What if dust component ?1/r2
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If it works. Copy it!
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Every Galaxy!!!
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Every Galaxy!!!
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Isothermal Spheres A Cultural Aside
Assume v isotropic, independent of radius, ie
ltv2gt T
Collisionless No interactions
Hydrostatic Equilibrium
Solve as r-gtinfinity
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How Much Dark Matter is out there?

• Local mass estimates i.e. clusters
• global mass estimates
• Large scale structure
• Distance-redshift relation
• Direct measures of geometry

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Weighing Clusters of Galaxies
X-Ray Clusters Top of the Cosmic Food Chain
Large Clusters of Galaxies, containing 100s of
galaxies. -The largest bound clumps in the
Universe. Tens of millions of light years across.
- anything that can fall into them, will -good
probes of total matter density?
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Largest clusters galaxies a small contamination,
most of the mass of these systems is in HOT GAS!
T107K
X-Rays!
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Assume in Hydrostatic Equilibrium (uniform,
spherical)
Pressure lt-gtGrav
(T,R) -gt (Mgas,Mtot)
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(SZE indep estimate of Mgas
)
If Mgas MB (a reasonable assumption) then
DARK MATTER IS NON-BARYONIC!
Note ?m lt 1 !!!!!!!!!!!
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Gravitational Lensing
Invert!
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Mtot comparable with X-Ray data
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Large Scale Structure Formation A Primer

• Primordial Fluctuations

Scale independent
Scale invariant n1 (isotropy and BHs)
But observed fluctuations Gravity Plus equation
of state
Large k -gt small wavelength
rad
Comes inside causal horizon sooner i.e. during
radiation domination..
matter
?
aeq
Damped
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keq
k
Problem calculate zeq if Wm0.3 and Wrad10-4
today
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Generally Define Shape Factor, G Naively, G
Wh However, considering effect of baryons on
overall density, and allowing for effects of
curvature, or other, Non-clustered forms of
energy G W0h exp -WB(12h1/2/W) (Peacock
and Dodds 94 sugiyama 95) Allowing for
primordial density perturbations with n?1 G W0h
exp -WB(12h1/2/W) 0.28 (1/n -1) (Liddle
et al, 96)
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.25lt?mhlt.35
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Liddle et al, 96 found
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Late time Evolution of Large Scale Structure
In a flat, matter dominated universe, ?? a(t)
for all scales inside the horizon.
Hence, large scale structure does not stop
forming.
Hence there should be many more large scale
galaxy clusters today than there were at higher
redshift
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?mlt. 5 ?
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Results

• Dark Matter dominates all large scale structure
• It is probably non-baryonic
• THERE IS NOT ENOUGH DARK MATTER TO MAKE THE
  UNIVERSE FLAT

QUESTIONS?

• What IS the Dark Matter?
• What about a flat universe?

Stay tuned
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The most important equation in Cosmology?
Distance -redshift relation This provides
dynamical information on the matter content and
equation of state of the Universe.. (cf-age
redshift relationdescribed earlier)
Problem 5
Define comoving distance interval R0dr (where
dr is the coordinate distance interval and R0 is
the scale factor today). Show
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Operational Distances
Luminosity Distance (Hubble Constant, SN..)
Angular Diameter Distance (Angular Size, Grav.
Lensing)
Proper Distance (Grav Lensing)
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Probes of Eq. Of State
Gravitational Lensing Statistics.. Integrate
Probabilities over Some Distance.. Galaxy Number
vs. redshift dN/dz sensitive to distance
redshift relation more on both of these
later