2. Cosmologia Despues de WMAP

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2. Cosmologia Despues de WMAP
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Menu du Jour

• Historia del descubrimiento del CMB
• Fisica del CMB
• - Radiacion de Cuerpo negro T2.73 K
• - Dipolo (Doppler)
• - Fluctuaciones
• - Espectro de Potencia Angular
• 3. Observaciones
• - COBE y WMAP
• 4. Corroboracion del dipolo velocidades
  peculiares
• 5. Parametros cosmologicos lo que sabemos hoy

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See cmb.pdf in Cosmology 2
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T 2.73 K
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CMB Dipole
DT 3.358 mK
V_sun w.r.t CMB 369 km/s towards l264o , b48o
Motion of the Local Group V 627 km/s
towards l 276o b 30o
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Removing the Galactic Contamination see
QuickTime movie mw in cosmology2
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WMAP CMB Fluctuations
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Qualitative Description of the CMB Power Spectrum

• As long as matter is ionized, baryons and photons
  are coupled via
• Thomson scattering we refer to a
  photon-baryon fluid
• Photons provide the pressure of the fluid, while
  baryons provide
• the mass density, i.e. the inertia.
• Gravity tries to compress the fluid, while
  pressure resists it
• acoustic oscillations are set.
• The Universe reaches the epoch of recombination
  with density
• fluctuations (of amplitude of 1 part in
  100,000).
• Acoustic oscillations take place within the
  potential wells of the
• density fluctuations the compression phase of
  the oscillation
• produces a slight enhancement in temperature of
  the fluid,
• the rarefaction phase produces temperature
  decrement.
• As the Universe recombines, the coupling between
  baryons and
• photons ceases, and the two components
  separate. The photon
• fluid ceases to oscillate and the temperature
  fluctuations freeze
• at the epoch of last scattering.
• The physical scale of the fluctuations at that
  epoch translates into
• an angle, as seen from our vantage point at
  z0 the larger the physical
• scale, the larger the angle.

Visit the website of Wayne Hu
http//background.uchicago.edu/whu
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Qualitative Description of the CMB Power Spectrum

• The map of CMB
• T fluctuations is
• analyzed in terms
• of its spherical
• harmonics.
• The eigennumber l
• is inversely prop.
• to the angular scale
• a 100o / l

• A fluctuation of
• comoving physical
• size l Mpc at the
• epoch of recombination
• subtends an angle
• a 17 l
• in the sky at the
• present time.

Image credit W. Hu
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Qualitative Description of the CMB Power Spectrum
At any given time before recombination, the
largest l possible for an acoustic mode is that
which the sound speed can travel in the Hubble
time

• At recombination (z1000), the Hubble
• radius is about 370,000 l.y., which
• translates into a comoving distance of
• 100 Mpc, i.e. an angle a 1700, or
• half a degree.

The acoustic mode that had time to compress (?
heat) the fluid for the first time at z1000
should thus have an angular size of half a
degree. Frozen by decoupling, that
mode should appear as a peak at
l 100/a 200
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Qualitative Description of the CMB Power Spectrum
By analogous logic, the next acoustic mode should
correspond to an oscillation that had time
to compress and expand once its angular scale
should thus be half that of the fundamental
mode. The second mode is a rarefaction mode.
The third mode is one that went through the
cycle compression-rarefaction-compression in one
Hubble time its angular scale is 1/3 that of the
fundamental mode and it is caught at z1000 near
max compression. And so on.
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Dependence of power spectrum on W
The position ( l number) of the peaks of the
power spectrum is strongly dependent on the
curvature of space. The identification of the
first acoustic peak indicated that the Universe
is spatially FLAT.
Display curvature2 Quick Time Movie in cosmology2
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Information in the Other Acoustic Peaks
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Variations in the CMB Power Spectrum
Varying h between 0.35 and 0.7 h2Wb 0.0125 is
fixed
Varying Wb between 0.01 and 0.10 h 0.5 is
fixed
Increasing the baryon density increases the
density of the coupled photon-baryon fluid,
altering the balance between pressure and gravity
in the fuid. Compression modes (peaks 1 and 3)
are enhanced with respect to rarefaction modes
(peak 2). ? the relative height of contiguous
peaks yields Wb
Credit Martin White
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Varying L between 0 and 0.9 h2Wb 0.0125 and
h0.5 are fixed
Time variation of the CMB power spectrum between
a(t)1/2000 and a(t)1 (now)
The angle subtended by a given physical size at
last scattering (i.e. a given mode) decreases as
the Universe expands, shifting the peaks to the
right (high l, small angle).
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CMB Power Spectrum according to WMAP
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See CMB_to_now QuickTime movie in Cosmology 2
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See WMPA_params_taple.pdf in Cosmology 2
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As for SN type Ia
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The Sunyaev-Zeldovich Effect
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Recovering the LG motion from Galaxy Surveys

• The Luminosity-Linewidth relation
• Its Calibration and the Determination of Ho
• Convergence Depth of the Local Universe
• The Local Group reflex motion

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Measurement of a velocity Width
1. Get good image of galaxy, measure PA,
position slit
2. Pick spectral line, measure peak l along
slit
3. Center kinematically
4. Fold about kinematical center
5. Correct for disk inclination, using
isophotal ellipticity
Outer slope
6. You now have a rotation curve.
Pick a parametric model and fit it.
E.g.
Inner scale length
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TF Relation Data
h H/100
Direct slope is 7.6 Inverse slope is 7.8
SCI cluster Sc sample
which is similar to the explicit theory-derived
dependence a 3
I band, 24 clusters, 782 galaxies
Giovanelli et al. 1997
a
Where L a (rot. vel.)
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Measuring the Hubble Constant
A TF template relation is derived independently
on the value of Ho . It can be derived for,
or averaged over, a large number of galaxies,
regions or environments. When calibrators are
included, the Hubble constant can be gauged over
the volume sampled by the template. From a
selected sample of Cepheid Calibrators, Giovanel
li et al. (1997) obtain H_not 69/-6
(km/s)/Mpc averaged over a volume of cz 9500
km/s radius. The HST key-project team Sakai et
al 2000 gets 71/-4/-7
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TF and the Peculiar Velocity Field

• Given a TF template relation, the peculiar
  velocity of a galaxy can be derived from its
  offset Dm from that template, via
• For a TF scatter of 0.35 mag, the error on the
  peculiar velocity of a single galaxy is typically
  (0.15-0.20) cz
• For clusters, the error can be reduced by a
  factor if N galaxies per cluster are
  observed

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No local Hubble Bubble
Zehavi et al. (1999) Local Hubble bubble
within cz 7500 km/s ? Giovanelli et al. (1999)
No local Hubble Bubble to cz 15000 km/s
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Convergence Depth
Given a field of density fluctuations d(r) ,
an observer at r0 will have a peculiar velocity
where W is W_mass
The contribution to by fluctuations in
the shell , asymptotically tends
to zero as
The cumulative by all
fluctuations Within R thus exhibits the
behavior
If the observer is the LG, the asymptotic
matches the CMB dipole
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The Peculiar Velocity Field to cz6500 km/s
SFI Haynes et al 2000a,b
Peculiar Velocities in the LG reference frame
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The Peculiar Velocity Field to cz6500 km/s
SFI Haynes et al 2000a,b
Peculiar Velocities in the CMB
reference frame
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The Dipole of the Peculiar Velocity Field
The reflex motion of the LG, w.r.t. field
galaxies in shells of progressively increasing
radius, shows convergence with the CMB
dipole, both in amplitude and direction, near cz
5000 km/s. Giovanelli et al. 1998
Giovanelli et al. 2000
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Verrazzano Bias
Pacific Ocean

• Map by Gerolamo da Verrazzano (1529)

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The Dipole of the Peculiar Velocity Field
Convergence to the CMB dipole is confirmed by
the LG motion w.r.t. a set of 79 clusters out
to cz 20,000 km/s
Giovanelli et al 1999 Dale et al. 1999
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