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 m ~ 0.25 Mass ~ Light (on large scales) Mass-Density (Units) Critical mass-density (= density needed to

halt the Universe expansion): 2 2 critical critical = 3Hoo /8G -29g/cm3 3 ~ 6 p/m3 3 ~10-29 = /

mm = mm/crit crit mm = 1 is the critical density Flat Universe bb(baryons)(observed)

(baryons)(observed) ~ 0.04 [Mpc = 1066pc; 1pc ~ 3 ly; Moo=2E33g] Flat Rotation Curves M/L Kaptyen (Local) 1920s Zwicky (Clusters) 1930s Rubin (Galaxies) 1970s ( M/L ~ R )

M ~ v2 R ~ R M/L ~ R [GMm/R2~mv2/R] Mass-to-Light Method Weigh cluster mass, Mclcl (R~1Mpc) M/L>>clcl = 300h mm = mm/critical critical

m m ~ 0.2 +-0.05 Weighing Clusters 3 Basic Methods Motion of galaxies [MRR ~ v22R] Temperature of hot gas [MRR~TR] Gravitational lensing [MRR]

Mass-to-Light Function (Bahcall, Lubin & Dorman 95; Bahcall and Fan 98) SDSS m=0.2 Theory vs. Observations (Bahcall, Yu, et al 01)

Cluster M/Li(R) Profile (SDSS, weak lensing 2x1044 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)

m= 0.2 +- .03 Flat M/L on large scales; SAME for ALL clusters! M/L Function: Conclusions M/L Function Flattens on Large Scales: Scales: M~L (on large scales)

reaching the end of Dark-Matter Total Mass-Density Mass-Density of Universe: m m = 0.2 +- 0.05 Baryons in Clusters [Stars and Gas]

bb/mm(cl) Mbb/Mtot tot(cl) = 0.13 (gas) + 0.03 (stars) = 0.16 (h= 0.7) (h=0.7) bb(BBN; CMB) = 0.042 (h=0.7) (h=0.7) m

m = b b/(b b/m m) = 0.26+-0.04 0.24 +- 0.04 corrected corrected for for gas gas outflow outflow Baryon Fraction vs. Scale ( 0.18)

(Bahcall (Bahcall & & Martin Martin 07) 07) m = 0.24 m from Baryon-Fraction bb/m m = 0.18 +- 0.02

h=0.7 (Clusters; (Clusters; CMB) CMB) bb = 0.042 +- 0.004 (BBN; (BBN; CMB) CMB)

m m = 0.24 +- 0.04 Weighing the Universe M/L> mm= M/L> Function Function = 0.2 0.2 ++- 0.05

0.05 Baryon 0.24 Baryon Fraction Fraction 0.24 ++- 0.04 0.04 Cluster 0.2 Cluster Abundance Abundance

0.2 ++- 0.05 0.05 and [[88 = and Evolution Evolution = 0.9 0.9 ++- 0.1] 0.1] Supernovae Supernovae Ia

Ia + + Flat Flat 0.25 0.25 ++- 0.05 0.05 CMB CMB + + L>SS L>SS + +h h+

+ Flat Flat 0.24 0.24 ++- 0.04 0.04 m m 0.23 +- 0.05 4% 4% Baryons Baryons + + ~20%

~20% Dark Dark Matter Matter Mass (R >~ >~ 1Mpc) 1Mpc) Mass ~ ~ Light Light (R

Cosmic Acceleration: Supernovae Cosmic Acceleraion: Supernovae (07) (07) m- ~ -0.5 Cosmic Microwave Background (WMAP) (WMAP)

CMB Spectrum Space Curvature The Cosmic Triangle m + + k = 1 (Friedmanns eq.) Mass Density: m m = 0.25

Dark Energy: = 0.75 Space Curvature: kk = 0 Mass-density, Curvature, Expansion H2(t) = 8G(m + )/3 - k/a2(t) k = 0 Flat geometry (no curvature) 1 Closed (positivly curved space) -1 Open (negatively curved space)

/H22 m m + + k k = 1 Friedmann Eq. m ~ a-3 ~ constant (IF

(IF Cosmological Cosmological Constant) Constant) Cosmic Triangle Mass Density of Universe: 25% Critical Universe will expand forever Dark Energy in Universe: 75% 75%

Universe expansion accelerates Universe Universe Space Curvature: 0 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 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 rep L>univ univ(L>oo/Vol) = m

m(Moo/Vol) Determine M, of clusters, SCs, LSS M/L>> rep rep [ 300h ] m m ~ 0.2 +-0.05

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

M/L M/L Function Function Flattens Flattens on on Large Large Scales Scales M M~ ~L

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/LBB is Anti-biased (M/LBB>mean) Asymptotic Cluster M/Lii(22Mpc) is same for ALL

Groups and Clusters, 362+-54h ! Mass-Density Mass-Density of of Univers: Univers: m 0.2 ++- 0.03 0.03 m = 0.2

III. Cluster Abundance and Evolution Powerful method to determine m and 88 m and 88 = Amplitude of mass fluctuations (initial seeds) 0.6 ncl 0.6 ~ 0.35 (z~0) 88 m 0.35

cl (z~0) m nclcl (hi (hi z) z) Breaks degeneracy degeneracy m and 88=0.9+-0.1 m=0.2+-0.05 and

88 (galaxies)(obs) (galaxies)(obs) ~ ~ 0.9 0.9 If (m)~ ~ 0.9 If Mass

Mass ~ ~ Light Light (on (on large large scale) scale) 88(m) 0.9 Cluster Mass-Function (SDSS)

(SDSS) (Bahcall, (Bahcall, Dong, Dong, et et al al 02) 02) Best-fit MF: mm=0.2 and and 88=0.9

Fit: m=0.2 8=0.9 mm - 88 constraints from MF: mm = 0.2 and and 88 = 0.9 m=0.2, 8=0.9 m - 8 constraints from

SDSS cluster MF [Bahcall etal 03 Rozo etal 09] m=0.2, 8=0.9 Cluster Abundance Evolution 88 (Bahcall (Bahcall &

& Bode) Bode) 8 Cosmological Constraints (Bahcall (Bahcall & & Bode) Bode) (from (from Low

Low and and Hi Hi redshift redshift cluster cluster abundance) abundance) Low z Hi z

Cosmic Acceleration: Supernovae (ESSENCE 08) Cosmological Constraints Supernovae, Supernovae, CMB, CMB, Clusters Clusters CMB Spectrum (Seivers etal 09)

SDSS Clusters (Rozo etal 09) Mass-to-Light Function (Bahcall, Lubin & Dorman 95; Bahcall and Fan 98) m = 1.0 m = 0.3 m=0.25

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)