2. Cosmologia Despues de WMAP

Historia del descubrimiento del CMB Fisica del CMB - Radiacion de Cuerpo negro T=2.73 K - Dipolo (Doppler) - Fluctuaciones - Espectro de Potencia Angular3. Observaciones - COBE y WMAP4. Corroboracion del dipolo: velocidades peculiares5. Parametros cosmologicos: lo que sabemos hoy

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See cmb.pdf in Cosmology 2

T = 2.73 K

CMB DipoleDT = 3.358 mKV_sun w.r.t CMB:

369 km/s towardsl=264o , b=+48oMotion of the Local Group:

V = 627 km/s towards l = 276o b= +30o

Removing the Galactic Contamination:

see QuickTime movie mw in cosmology2

WMAP: CMB Fluctuations

Qualitative Description of the CMB Power SpectrumAs long as matter is ionized, baryons and photons are coupled via Thomson scattering: we refer to a photon-baryon fluidPhotons 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: http://background.uchicago.edu/~whu]

Image credit: W. HuThe 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 / lA 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.Qualitative Description of the CMB Power Spectrum

Qualitative Description of the CMB Power SpectrumAt any given time before recombination,the largest l possible for an acoustic mode is that which the sound speed cantravel in the Hubble timeAt 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, orhalf a degree. The acoustic mode that had time tocompress ( heat) the fluid for thefirst time at z~1000 should thus havean angular size of half a degree.

Frozen by decoupling, that modeshould appear as a peak at l = 100/a ~ 200

Qualitative Description of the CMB Power SpectrumBy analogous logic, the nextacoustic mode should correspondto an oscillation that had time tocompress and expand once: itsangular scale should thus be halfthat of the fundamental mode.The second mode is a rarefactionmode.The third mode is one that wentthrough the cycle:compression-rarefaction-compressionin one Hubble time; its angular scaleis 1/3 that of the fundamental modeand it is caught at z~1000 near maxcompression.

And so on.

Display curvature2 Quick Time Movie in cosmology2Dependence of power spectrum on WThe position ( l number) of the peaks of the power spectrumis strongly dependent on the curvature of space.

The identification of the first acoustic peak indicated thatthe Universe is spatially FLAT.

Information in the Other Acoustic Peaks

Varying h between 0.35 and 0.7h2Wb = 0.0125 is fixedVariations in the CMB Power SpectrumVarying Wb between 0.01 and 0.10h = 0.5 is fixedCredit: Martin WhiteIncreasing the baryon density increases the densityof the coupled photon-baryon fluid, altering thebalance between pressure and gravity in the fuid.Compression modes (peaks 1 and 3) are enhancedwith respect to rarefaction modes (peak 2). the relative height of contiguous peaks yields Wb

Varying L between 0 and 0.9h2Wb = 0.0125 and h=0.5 are fixedTime variation of the CMB power spectrumbetween a(t)=1/2000 and a(t)=1 (now)The angle subtended by a given physical sizeat last scattering (i.e. a given mode) decreasesas the Universe expands, shifting the peaks tothe right (high l, small angle).

CMB Power Spectrumaccording to WMAP

See CMB_to_now QuickTime movie in Cosmology 2

See WMPA_params_taple.pdf in Cosmology 2

As for SN type Ia

The Sunyaev-Zeldovich Effect

Recovering the LG motion from Galaxy SurveysThe 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 Width1. Get good image of galaxy, measure PA, position slit2. Pick spectral line, measure peak l along slit3. Center kinematically 4. Fold about kinematical center5. Correct for disk inclination, using isophotal ellipticity6. You now have a rotation curve. Pick a parametric model and fit it. E.g.Inner scale lengthOuter slope

TF Relation: DataSCI : cluster Sc sampleI band, 24 clusters, 782 galaxies[Giovanelli et al. 1997]Direct slope is 7.6Inverse slope is 7.8which is similar to the explicittheory-derived dependence a = 3[Where L a (rot. vel.) ]ah= H/100

Measuring the Hubble ConstantA 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,Giovanelli et al. (1997) obtain

H_not = 69+/-6 (km/s)/Mpc

averaged over a volume ofcz = 9500 km/s radius.

The HST key-project team[Sakai et al 2000] gets 71+/-4+/-7

TF and the Peculiar Velocity FieldGiven 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) czFor clusters, the error can be reduced by a factor if N galaxies per cluster are observed

No local Hubble BubbleZehavi 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 DepthGiven a field of density fluctuations d(r) , anobserver at r=0 will have a peculiar velocity:where W is W_massThe contribution to by fluctuationsin the shell , asymptoticallytends to zero as The cumulative by all fluctuationsWithin 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/sSFI [Haynes et al 2000a,b] Peculiar Velocities in theLG reference frame

The Peculiar Velocity Field to cz=6500 km/sSFI [Haynes et al 2000a,b] Peculiar Velocities in the CMBreference frame

The Dipole of the Peculiar Velocity FieldThe 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 BiasMap by Gerolamo da Verrazzano (1529)Pacific Ocean

The Dipole of the Peculiar Velocity FieldConvergence to the CMB dipole is confirmed by the LG motion w.r.t.a set of 79 clusters out tocz ~ 20,000 km/s [Giovanelli et al 1999 ;Dale et al. 1999]