The Simplest Picture of Galaxy Formation and Why It Fails (chapter title from Longair, Galaxy Formation ) Read [CO 30.2]

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1 (chapter title from Longair, Galaxy Formation ) Read [CO 0.] Will a condensation collapse? he Jeans criterion: (see [CO Sect. 1. and pg. 150] How fast will it collapse? In a static medium (e.g. star formation): Perturation analysis shows ass emp Density ρ o λ Unstale to collapse if K < -U k G < µ m H 5 λ 4 5 k πλ ρ > o Gµ m H / 4πρ Jeans mass J o 1/ < J δρ/ρ exp(-ir/λ -iωt ) Oscillations > J δρ/ρ exp(-ir/λ + Kt ) Exponential growth In an expanding medium (e.g. the universe): Outside the perturation (flat universe): Inside the perturation (closed mini-universe): Slow growth / Radiation era atter era Will a condensation collapse? he Jeans criterion Version : Collapse if K < -U Radiation era c vs ρ R( t) ρ R( t) J, 1 G vs < 5 λ G G vs < 5 λ 5 4 / 5vs λ 4πρ > 4πGρ / 5 4πρvs > 4 π 1/ 4 ( 4 / ) πλ ρ 4 πgλ ρ λ 5 ( Gρ ) / After decoupling v s ρ J, 5k µ m 0 ρ 0 [CO eq. 0.7] (almost) H / Before decoupling Particle Horizon d h ct R(t) - Log Jeans [CO Fig. 0.7] Collapses Oscillates (radiation era) Proper distance containing mass l (/ρ) 1/ 1/ R(t) 1/ -1 ass for which l d h - t / (radiation era) -/ (matter era) d h Collapses

2 Cosmic icrowave Background is smooth to a few parts in 10 5 δρ/ρ ~ 10-4 Yet high contrast structures (QSOs, galaxies) y z ~ 6. δρ/ρ >> 1 Blue 0 o K Red 4 o K Adiaatic perturations grow as δρ/ρ t / R(t) 1/(1+z) Expect only δρ ρ QSO ( 1+ z) CB δρ ( 1 ) 4 + z 7 QSO ρ CB So where did galaxies and clusters come from? Blue.74 o K Red.7 o K Dipole Anistropy ~ 1 part in 00 After removing dipole Red lue o K ~ 1 part in 10 5 he Solution: Dark atter Decoupling Particle Horizon d h ct R(t) - Proper distance containing mass l (/ρ) 1/ 1/ R(t) 1/ -1 ass for which l d h - t / At t CB this mass was ~ > continued growth < oscillations once mass scale comes into particle horizon. + Silk damping Photons drag aryons out of density condensations, up until time of decoupling. But Dark atter not suject to all this. Just keeps collapsing fall into Dark atter potential wells as soon as decoupling removes photon pressure support. Log Jeans Log δρ /ρ d h Log δρ /ρ Log δρ /ρ Dark atter Decoupling sun sun Silk Damping D Photons

3 Hot vs. Cold Dark atter Perturations Power spectrum of fluctuations P(k) k n where P δρ /ρ and k wave numer π/l Inflation predicts n 1 scale invariant : δρ /ρ always has same value when perturation enters horizon. Predicts δρ /ρ -/ l - HD perturations with wavelengths shorter than horizon are lost relativistic particles free stream out of smaller condensations D until particles ecome non-relativistic at ~ 10 5 K smallest condensations have ~ 10 1 sun CD perturations survive at all scales some attenuation at shorter wavelengths ut most power still at shorter wavelength N-ody simulations CD Start with perturation spectrum at time of decoupling Follow perturations into highly non-linear regime. Standard CD SDC, replaced y ΛCD model CD HD HD models ecome too highly clustered over oserved lifetime of galaxies

4 he Expanding Universe In proper coordinates In co-moving coordinates CD structure-formation models Reproduce oserved filamentary structure Weinerg et al. astro-ph/97081

5 ore CD Simulations (Frenk 1991, Physica Scripta 6, 70) Large Cluster Disk Galaxy Halo Small Group Violent assemly Steady growth W, 1 z.5 flat rotation curves reproduced z 1.0 z 0.0