WMAP Density fluctuations at t = 79,000 yr he Growth of Structure Read [CO 0.2] 1.0000 1.0001 0.0001 10 4 Early U. contained condensations of many different sizes. Current large-scale structure t = t 0 = 1.7 Gyr 1 Log M Jeans Oscillates [CO Fig. 0.7] Log time he Simplest Picture of Galaxy Formation and Why It Fails (chapter title from Longair, Galaxy Formation ) Will a condensation collapse? he Jeans criterion: Mass = M emp = Density = o (see [CO Sect. 12.2 and pg. 1250] Unstable to collapse if 2 2K < -U Pressure < Gravity Mk GM m H 5 5k M G m H / 2 2 4 o 4 M o 1/ 2 Log M Jeans Oscillates Jeans mass M J [CO Fig. 0.7] Log time 1
How fast will it collapse? In a static medium (e.g. star formation): Perturbation analysis shows Expanding U. density = See [CO pg. 1249] M < M J / exp(-ir/ -it ) Oscillations M > M J / exp(-ir/ + Kt ) Exponential growth In an expanding medium (e.g. the universe): Outside the perturbation (flat universe): (Friedman Eqn) Mass Perturbation = M emp = Density = o 2 Rad. Matter Inside the perturbation (closed mini-universe): log Slow Growth log t Radiation era: 4 1/ 2 0 R( t) R( t) t Matter era: 0 R( t) 2 / R( t) t 2/ he Simplest Picture of Galaxy Formation and Why It Fails Cosmic Microwave Background is smooth to a few parts in 10 5 / ~ 10-4 Yet high contrast structures (QSOs, galaxies) by z ~ 6. / >> 1 Blue = 0 o K Red = 4 o K Adiabatic perturbations grow as / t 2/ R(t) 1/(1+z) Expect only QSO ( 1 z) CMB 1100 10 0.01 1 4 z 7 QSO CMB So where did galaxies and clusters come from? Blue = 2.724 o K Red = 2.72 o K Dipole Anistropy ~ 1 part in 00 After removing dipole Red blue = 0.0002 o K ~ 1 part in 10 4 2
In an expanding universe, will a cloud collapse? he Jeans criterion Version 2: Collapse if 2K < -U Radiation era c vs R( t) b R( t) M J, b 1 2 GM 2 M vs 2 5 4 4 2 2 GM G 4 / 4 2 vs G 5 5 5 2 / M 5v 2 b s 2 4 b 4G v M J, b const. b s / 2 After decoupling v s b M J, b 5k m 0 = [CO eq. 0.27] b H / 2 v s = sound speed 0 Log M Jeans,b 2K < -U Pressure support < gravity Radiation pressure keeps these clouds fluffed up. Oscillates Log [CO Fig. 0.7] Log time Radiation pressure has disappeared. Clouds now collapse. Q.When do oscillations start? When Particle horizon = M 2K < -U Pressure support < gravity Before decoupling: Particle Horizon d h = 2ct R(t) 2-2 Size scale for mass M (radiation era) Radiation pressure keeps these clouds fluffed up. Radiation pressure has disappeared. Clouds now collapse. d h Proper distance containing mass M = (M b / b ) 1/ M b 1/ R(t) M b 1/ -1 Mass for which = d h M b - R t /2 M b -/2 (radiation era) (matter era) Log M Jeans,b [CO Fig. 0.7] Oscillates Log Log time
Log M Jeans d h he Rest of the Story: Log / Baryons 10 15 M sun 10 17 M sun Log time Mass for which = d h M - (rad. era) M -/2 (matter era) At t decoupling this mass was ~ 10 16 M M > 10 16 M continued growth M < 10 16 M oscillations once mass scale comes into particle horizon. Log / Log time Dark Matter Log time Baryons Silk Damping But Dark Matter not subject to all this. Does not feel radiation pressure. Just collapses away Baryons fall into Dark Matter potential wells as soon as decoupling removes photon pressure support. Log / Log time DM Baryons Photons decoupling d h Log M Jeans Log time CMB Fluctuations = snapshot of oscillations at t decoupling DM Log / Baryons Photons Log time 4
(predicted) Average (/) 2 size scale (deg) Fourier analyze WMAP image: Measures Power for each size scale. = Power for each mass scale M. What is measured? Average (/) 2 size scale (predicted) (deg) Fourier analyze WMAP image: Measures Power for each size scale. = Power for each mass scale M. he Fourier ransform (sort of) a n2 (n) 5
(predicted) Average (/) 2 size scale (deg) Fourier analyze WMAP image: Measures Power for each size scale. = Power for each mass scale M. But why more power for some mass scales than others? (predicted) 1 st rarefaction Average (/) 2 size scale 1 st compression 2 nd compression (deg) Fourier analyze WMAP image: Measures Power for each size scale. = Power for each mass scale M. But why more power for some mass scales than others? All blobs of same mass M oscillate synchronously. Peaks are for mass scales that are either fully compressed or fully rarified. (/ ) Dark Matter (/ ) Baryons Baryons: Shorter spatial wavelengths oscillate with higher time frequency 6
(predicted) 1 st rarefaction Average (/) 2 size scale 1 st compression 2 nd compression (deg) First peak: Size of acoustic horizon r = v s (t t Horizon ) = c t = linear size of perturbation = r/(d) = sin(d), d, sinh(d) l peak = 220/ tot 1/2 ( l = multipole ) Measured l peak tot = 1.02.02 Positive Curvature (K > 0) Negative Curvature (K < 0) Flat (K = 0) Boomerang balloon flight (1999) Mapped Cosmic Background Radiation with far higher angular resolution than previously available. Launch near Mt. Erebus in Antarctica Boomerang 7
Position of 1 st peak measures curvature = 1.0 0.7 0.0 All models: b =.04, m =.2 First peak: Size of acoustic horizon r = v s (t t Horizon ) = c t = linear size of perturbation = r/(d) = sin(d), d, sinh(d) l peak = 220/ tot 1/2 ( l = multipole ) Measured l peak tot = 1.02.02 [CO fig 0.17] he Concordance Cosmology (or CDM) ype Ia Supernovae as standard candles accelerating expansion q o = m /2 - CMB anisotropy total = m + Can solve for m, Another independent measure: Rate of galaxy cluster evolution = Cosmological Constant m = matter density/critical density [CO 0.22] 8