0.5 % Stars and other visible stuff!Ay 127!The Contents of the Universe"Supernovae alone ⇒ Accelerating expansion ⇒ Λ > 0 CMB alone ⇒ Flat universe ⇒ Λ > 0 Any two of SN, CMB, LSS ⇒ Dark energy ~70% Also in agreement with the age estimates (globular clusters, nucleocosmochronology, white dwarfs)!Today’s Best Guess Universe € t0= 13.82 ± 0.05 GyrAge: Best fit CMB model - consistent with ages of oldest stars € H0= 69 km s-1 Mpc-1Hubble constant: CMB + HST Key Project to measure Cepheid distances € Ωbaryon= 0.04Density of ordinary matter: CMB + comparison of nucleosynthesis with Lyman-a forest deuterium measurement € Ωmatter= 0.31Density of all forms of matter: Cluster dark matter estimate CMB power spectrum € ΩΛ= 0.69Cosmological constant: Supernova data, CMB evidence for a flat universe plus a low matter densityTotal matter/energy density: Ω0,tot ≈ 1.00"Matter density: Ω0,m ≈ 0.31"Baryon density: Ω0,b ≈ 0.045"Luminous baryon density: Ω0,lum ≈ 0.005"Since: Ω0,tot > Ω0,m > Ω0,b > Ω0,lum "There is baryonic dark matter!There is non-baryonic dark matter!There is dark energy!at z ~ 0, in critical density units, assuming h ≈ 0.7 !The Component Densities"From local dynamics and LSS, and consistent with SNe, CMB!From CMB, and!consistent with SNe, LSS!From cosmic nucleosynthesis,!and independently from CMB!From the census of luminous matter (stars, gas)!The Luminosity Density"Integrate galaxy luminosity function (obtained from large redshift surveys) to obtain the mean luminosity density at z ~ 0!SDSS, r band: ρL = (1.8 ± 0.2) 108 h70 L/Mpc3!2dFGRS, b band: ρL = (1.4 ± 0.2) 108 h70 L/Mpc3!Luminosity To Mass"Typical (M/L) ratios in the B band along the Hubble sequence, within the luminous portions of galaxies, are ~ 4 - 5 M/L!This includes some dark matter - for pure stellar populations, (M/L) ratios should be slightly lower. ISM adds ~ 10%.!Note that in the B band, (M/L) ratios are very sensitive to any recent star formation, and to dust extinction. !The Local Mass Density of the Luminous Matter in Galaxies"ρlum = ρL  〈M/L〉  〈1 + fgas〉 ≈ (7 ± 2) 108 h70 M/Mpc3!ρlum ≈ (4.7 ± 1.3) 10-32 h70 g cm-3!Recall that ρ0,crit = 3H02/(8πG) = 0.921 10 -29 h702 g cm-3!Thus, Ω0,lum ≈ (0.0051 ± 0.0015) h70-1!All of the visible matter amounts to only half a percent of the total mass/energy content of the universe!!(Interestingly, this may be comparable to the contribution from the massive cosmological neutrinos…)!Baryon Density From Cosmic Nucleosynthesis"It is measured in two completely independent ways:"The Total Baryon Density"1. The cosmic nucleosynthesis:!• It occurs in the first few minutes after the Big Bang!• Reaction rates are ~ ρbaryon2, so the residual abundances of D, He, and Li are very sensitive to ρbaryon (especially for D)!• Measured in spectra of distant QSOs (actually Lyα forest clouds), low metallicity starforming dwarfs, halo stars, etc.!Results give:!2. Analysis of CMB fluctuations:!Results give:!! ! Thus, Ω0,b ≈ (0.045 ± 0.002) h70-2"€ Ωbaryonsh2= 0.021 → 0.025€ Ωbaryonsh2= 0.024 ± 0.001The Baryonic Dark Matter!(or just “missing”, not necessarily “dark”?)"• MAssive Compact Halo Objects (MACHOs)"– Very low mass stars, white dwarfs, neutron stars, black holes (produced post-nucleosynthesis, from baryons), brown dwarfs, interstellar comets, slushballs…!• Cold molecular (H2) gas clouds"– Would have to be compact, dense, low volume fill factor!– Very hard to detect!!• Warm/hot gas, bound to galaxy groups!– Leftover gas from IGM, never collapsed to galaxies!– Virial temperatures ~ 105 - 106 K, corresponding to the velocity dispersions ~ 300 km/s!– Very hard to detect! (ISM opaque to FUV/soft-X)!So, where are 90% of baryons hiding? Some possibilities:!The best bet?!This hypothetical Baryon reservoir would have Virial temps. of ~ 105 - 106 K, where the peak emission is in FUV/soft-X, which is effectively absorbed by the ISM in our Galaxy, and is thus essentially impossible to detect in emission …!Missing Baryons in Warm/Hot IGM?"However, it might have been detected in absorption in the UV (HST and FUSE) and X-Rays (Chandra), using O VI, O VII, and O VIII lines!Discovered by Zwicky in 1937, by comparing the visible mass in galaxies in the Coma cluster (estimated M* ~ 1013 M), with the virial mass estimates (Mvir ~ 51014 M)!The Non-Baryonic Dark Matter"Confirmed by the modern measurements of galaxy dynamics, X-ray gas analysis, and masses derived from gravitational lensing!Virial Masses of Clusters:!Virial Theorem for a test particle (a galaxy, or a proton), moving in a cluster potential well:!Ek = Ep / 2  mg σ2 / 2 = G mg Mcl / (2 Rcl)!where σ is the velocity dispersion!Thus the cluster mass is: Mcl = σ2 Rcl / G"Typical values for clusters:!σ ~ 500 - 1500 km/s!Rcl ~ 3 - 5 Mpc!Thus, typical cluster masses are Mcl ~ 1014 - 1015 M"The typical cluster luminosities (~ 100 - 1000 galaxies) are Lcl ~ 1012 L, and thus (M/L) ~ 200 - 500 in solar units" Lots of dark matter!"• Note that for a proton moving in the cluster potential well with a σ ~ 103 km/s, Ek = mp σ2 / 2 = 5 k T / 2 ~ few keV, and T ~ few 107 °K  X-ray gas!• Hydrostatic equilibrium requires:!M(r) = - kT/µmHG (d ln ρ /d ln r) r"• If the cluster is ~ spherically symmetric this can be derived from X-ray intensity and spectral observations!• Typical cluster mass components from X-rays:!Masses of Clusters From X-ray Gas!Coma cluster!Hydra cluster!Total mass: 1014 to 1015 M!Luminous mass: ~5%!Gaseous mass: ~ 10%!Dark matter: ~85%!Galaxy number"density"Light"Shear map"Mass"Cluster Abell 2218"Squires et al. 1996!Cluster Masses From Gravitational Lensing!Strong lensing constraints:!A370! M ~ 5x1013h-1 M!M/L ~ 270h!A2390! M ~ 8x1013h-1 M !M/L ~ 240h!MS2137! M ~ 3x1013h-1 M !M/L ~ 500h!A2218! M ~ 1.4x1014h-1! M!M/L ~ 360h!Weak lensing constraints (a subset):!MS1224!!M/L ~ 800h!A1689! ! M/L ~ 400h!CL1455!!M/L ~ 520h!A2218! ! M/L ~ 310h!CL0016!!M/L ~ 180h!A851! ! M/L ~ 200h!A2163! ! M/L ~ 300h!Clusters of galaxies imply Ωdm ~ 0.1 – 0.3!Lots of dark matter in clusters, in a broad agreement with virial mass estimates !The “Bullet” Clusters"Baryonic Mass Fraction in Clusters!• We can measure the baryonic