WEIGHING THE UNIVERSE Neta A. Bahcall Princeton University

Why Weigh Universe? How much matter in Universe? Is there Dark-Matter? Where is it located? Is there Non-baryonic (‘exotic’) dark-matter? What is it? [Baryon limit is ~4-5% of critical-density.] Most fundamental cosmological parameter  Cosmology; Evolution of Universe; Age of Universe; Galaxy Formation; Gravity

Mass Density of Universe How much? How distributed? Mass-to-Light Function Baryon Fraction Cluster Abundance and Evolution Other Large-Scale Structure Obs.  All yield m ~ 0.25  Mass ~ Light (on large scales)

Mass-Density (Units) m = 1 is the critical density  ‘Flat’ Universe Critical mass-density (= density needed to halt the Universe expansion): critical = 3Ho2/8G ~10-29g/cm3 ~ 6 p/m3 m = m/crit m = 1 is the critical density  ‘Flat’ Universe  b(baryons)(observed) ~ 0.04 [Mpc = 106pc; 1pc ~ 3 ly; Mo=2E33g]

Flat Rotation Curves M ~ v2R ~ R M/L ~ R [GMm/R2~mv2/R] Kaptyen (Local) 1920’s Zwicky (Clusters) 1930s Rubin (Galaxies) 1970s ( M/L ~ R ) M ~ v2R ~ R M/L ~ R [GMm/R2~mv2/R]

Mass-to-Light Method m = m/critical  <M/L>cl Luniv(Lo/Vol) = m(Mo/Vol)  Weigh cluster mass, Mcl (<R~1Mpc) <M/L>cl = 300h m = m/critical  m ~ 0.2 +-0.05

Weighing Clusters Motion of galaxies [MR ~ v2R] 3 Basic Methods Motion of galaxies [MR ~ v2R]  Temperature of hot gas [MR~TR]  Gravitational lensing [MR]

Mass-to-Light Function (Bahcall, Lubin & Dorman ‘95; Bahcall and Fan ‘98) SDSS Ωm=0.2

Theory vs. Observations (Bahcall, Yu, et al ‘01)

Cluster M/Li(R) Profile (SDSS, weak lensing 2x104 clusters N= 3 to 220 (Sheldon etal 2008) Flat >~ 1Mpc M ~ L X=R(vir)

M/Li(r=22Mpc) vs. Mcl (SDSS; Sheldon etal ‘08) Flat M/L on large scales; SAME for ALL clusters!

M/L Function: Conclusions  M/L Function Flattens on Large Scales:  M ~ L (on large scales) reaching the end of Dark-Matter  Total Mass-Density of Universe:  m = 0.2 +- 0.05

Baryons in Clusters [Stars and Gas]  Ωb/Ωm(cl)  Mb/Mtot(cl) = 0.13 (gas) + 0.03 (stars) = 0.16 (h=0.7) Ωb(BBN; CMB) = 0.042 (h=0.7) Ωm = Ωb/(Ωb/Ωm) = 0.26+-0.04  0.24 +- 0.04 corrected for gas outflow

Baryon Fraction vs. Scale ( 0.18) (Bahcall & Martin ‘07)

m from Baryon-Fraction b/m = 0.18 +- 0.02 h=0.7 (Clusters; CMB) b = 0.042 +- 0.004 (BBN; CMB)  m = 0.24 +- 0.04

Weighing the Universe  M/L Function m= 0.2 +- 0.05  Baryon Fraction 0.24 +- 0.04  Cluster Abundance 0.2 +- 0.05 and Evolution [8 = 0.9 +- 0.1] Supernovae Ia + Flat 0.25 +- 0.05 CMB + LSS + h + Flat 0.24 +- 0.04  m ≈ 0.23 +- 0.05  4% Baryons + ~20% Dark Matter Mass ~ Light (R >~ 1Mpc)

Cosmic Acceleration: Supernovae

Cosmic Acceleraion: Supernovae (‘07)

Cosmic Microwave Background (WMAP)

CMB Spectrum

Space Curvature

The Cosmic Triangle m +  + k = 1 Mass Density: m = 0.25 (Friedmann’s eq.) Mass Density: m = 0.25 Dark Energy:  = 0.75 Space Curvature: k = 0

Mass-density, Curvature, Expansion H2(t) = 8G(m + )/3 - k/a2(t) k = 0 Flat geometry (no curvature) 1 Closed (positivly curved space) -1 Open (negatively curved space) /H2  m + + k = 1 Friedmann Eq.   m ~ a-3  ~ constant (IF Cosmological Constant)

Cosmic Triangle  Mass Density of Universe: 25% Critical  Universe will expand forever Dark Energy in Universe: 75%  Universe expansion accelerates Universe Space Curvature: 0  Universe ‘Flat’

Fate of Universe  Universe Will Become:  Larger  Sparser  Darker  Colder

The Cosmic Triangle

Hot Gas in Clusters (X-Rays; S-Z) (Carlstrom etal)

Mass Density of Universe How much? How distributed? Mass-to-Light Function Baryon Fraction Cluster Abundance and Evolution Other Large-Scale Structure Obs.  All yield m ~ 0.25  Mass ~ Light (on large scales)

Mass-to-Light Function M/L(R) How does M/L depend on scale? How and where is the mass distributed? How use it to weigh Universe? <M/L>rep Luniv(Lo/Vol) = m(Mo/Vol) Determine M, <M/L> of clusters, SCs, LSS  <M/L> rep [≈ 300h ]  m ~ 0.2 +-0.05

Cluster (M/L)200 versus M200 M/L~M0.33+-0.02 M/L ~ M0.33+-0.02

M/L Function: Conclusions M/L Function Flattens on Large Scales  M ~ L (reaching end of Dark-Matter) Dark Matter located mostly in large galactic halos 100s Kpc) Group/Clusters: made up of Sp+E mix (+their DM halos); no significant additional DM Cluster M/L increases slightly with M (mergers?) Rich clusters M/LB is ‘Anti-biased’ (M/LB>mean) Asymptotic Cluster M/Li(22Mpc) is same for ALL Groups and Clusters, 362+-54h ! Mass-Density of Univers: m = 0.2 +- 0.03

III. Cluster Abundance and Evolution  Powerful method to determine m and 8 8 = Amplitude of mass fluctuations (initial ‘seeds’) ncl (z~0)  8 m0.6 ~ 0.35 ncl (hi z)  Breaks degeneracy  m=0.2+-0.05 and 8=0.9+-0.1  8 (galaxies)(obs) ~ 0.9 If Mass ~ Light (on large scale)  8(m)~ 0.9

Cluster Mass-Function (SDSS) (Bahcall, Dong, et al ‘02) Best-fit MF: m=0.2 and 8=0.9

m - 8 constraints from MF: m = 0.2 and 8 = 0.9

m - 8 constraints from SDSS cluster MF [Bahcall etal ‘03 Rozo etal ’09]

Cluster Abundance Evolution  8 (Bahcall & Bode)

Cosmological Constraints (Bahcall & Bode) (from Low and Hi redshift cluster abundance) Low z Hi z

Cosmic Acceleration: Supernovae (ESSENCE ‘08)

Cosmological Constraints Supernovae, CMB, Clusters

CMB Spectrum (Seivers etal ’09)

SDSS Clusters (Rozo etal ‘09)

Mass-to-Light Function (Bahcall, Lubin & Dorman ‘95; Bahcall and Fan ‘98) 1. M/L flattens on large-scales: M ~ L. End of Dark Matter. 2. Sp + E produce M/L of groups, clusters; Clusters have no excess DM ! 3. Most of the DM is in huge halos around galaxies (few-100 Kpc)