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2. Cosmologia Despues de WMAP. Menu du Jour. Historia del descubrimiento del CMB Fisica del CMB - Radiacion de Cuerpo negro T=2.73 K - Dipolo (Doppler) - Fluctuaciones - Espectro de Potencia Angular 3. Observaciones - COBE y WMAP

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Menu du Jour

  • Historia del descubrimiento del CMB
  • Fisica del CMB
  • - Radiacion de Cuerpo negro T=2.73 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

CMB Dipole

DT = 3.358 mK

V_sun w.r.t CMB:

369 km/s towards

l=264o , b=+48o

Motion of the Local Group:

V = 627 km/s towards

l = 276o b= +30o


Removing the Galactic Contamination:

see QuickTime movie mw in cosmology2


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 z=0: the larger the physical
  • scale, the larger the angle.

[Visit the website of Wayne Hu:]


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


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 (z~1000), 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 z~1000 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


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


The third mode is one that went

through the cycle:


in one Hubble time; its angular scale

is 1/3 that of the fundamental mode

and it is caught at z~1000 near max


And so on.


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


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


Varying L between 0 and 0.9

h2Wb = 0.0125 and h=0.5 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).


CMB Power Spectrum

according to WMAP


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
measurement of a velocity width
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


5. Correct for disk

inclination, using

isophotal ellipticity

Outer slope

6. You now have a

rotation curve.

Pick a parametric

model and fit it.


Inner scale length

tf relation data
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 dependencea = 3

I band, 24 clusters, 782 galaxies

[Giovanelli et al. 1997]


[WhereL a (rot. vel.) ]

measuring the hubble constant
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


From a selected sample of Cepheid


Giovanelli 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

tf and the peculiar velocity field
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
no local hubble bubble
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

convergence depth
Convergence Depth

Given a field of density fluctuations d(r) , an

observer at r=0 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

the peculiar velocity field to cz 6500 km s
The Peculiar Velocity Field to cz=6500 km/s

SFI [Haynes et al 2000a,b]

Peculiar Velocities in the

LG reference frame

the peculiar velocity field to cz 6500 km s1
The Peculiar Velocity Field to cz=6500 km/s

SFI [Haynes et al 2000a,b]

Peculiar Velocities in the CMB

reference frame

the dipole of the peculiar velocity field
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]

verrazzano bias

Pacific Ocean

Verrazzano Bias

Map by Gerolamo da Verrazzano (1529)

the dipole of the peculiar velocity field1
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]