1The Deep Inner Meaning of Hwk. Problem 30.4• Fixed energy density.• Same effect as large value of cosmological constant.• Exponential expansion until universe falls into true lowest energy state.• Then, reheating.• Vacuum energy density (latent heat) gets converted back to radiation energy.False vacuum: u = 1098J m-3Î heat Î particles“The Ultimate Free Lunch”Energy density = u ∝ R0Total E ∝ uR3∝ R3What is Dark Matter?Candidates• Cold dark matter• “cold” means v << c• Leading candidate: Weakly Interacting Massive Particles (WIMPs)• Hot dark matter• “hot” means v ~ c• Leading candidate: neutrinos• Baryonic dark matter• Black dwarfs, black holes, failed stars, etc.• Massive Compact Halo Objects (MACHOs)• General Relativity is wrong• MOND• Other alternate theories of gravityCO 2ndedpp. 896-898pp. 1232-12332MOdified Newtonian Dynamics (MOND)• Invented as ad-hoc explanation of flat rotation curves for galaxiesSuppose that Fgravfalls off slower than r -2• Originally not relativistically covariant • But there is now a version that does this• Cannot also explain temperature, density structure of galaxy clusters.• Dark matter simultaneously explains:• Flat rotation curves• Gravitational lensing results• Structure formation (coming attraction)We don’t want to trade it in for something that only explains one of these.Existence of Dark Matter: Blue = Total Mass Distribution (deduced from gravitational lensing). Red = Hot Gas Distribution (deduced from X-ray emission). Collision between 2 galaxy clusters. Normal matter (gas) loses energy in collisions. Dark Matter particles do not.movie1 movie23Baryonic Dark Matter• Candidates include black holes, neutron stars, brown dwarfs, cool white dwarfs, etc.• Use gravitational lensing to search for MACHOS• variability timescale t ~ 0.2 (M/Msun)1/2(D/10kpc)1/2(v /200 km/s)-1yr• cross section is Einstein radius•θE= (M/Msun)1/2(D/10 kpc)1/2mas• ==> if entire mass of MW is in Machos, still need to observe 106sources to find one microlensed background source at any given time.• Using LMC, SMC stars as background sources• LMC at 50 kpc, but MW halo goes to 200 kpcOrbiting MACHO crosses our line-of-sight.Gravitational lensing causes brightening.LargeMagellanicCloud• Two major searchesMACHO teamEROS Time (days) ÎFlux Î45• Macho Result: • MACHO Project: • 5.7 yrs, 11.9 million stars• 13-17 microlensed events• 2-4 expected from known stellar populations•EROS• 3 events towards LMC, 1 towards SMC• Fraction of MW halo in < 1 Msundark objects is < 20-40%.• Detected objects interpreted as white dwarfs• > 10 times more than expected from IMF• should be 6-10x more mass in gas than in white dwarfs ==> halo mass budget exceeded. • Alternative explanations require much less total mass. (<10% of halo) – LMC self-lensing often suggested• MW halo mostly dark matter, not baryons• But massive black holes still possible •~105Msunor so • primordial?Outof
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