WEIGHING THE UNIVERSE

1. WEIGHING THE UNIVERSE Neta A. Bahcall Princeton University

2. 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

3. 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)

4. Mass-Density (Units) • 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]

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

8. Mass-to-Light Method  <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

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

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

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

15. Cluster M/Li(R) Profile (SDSS, weak lensing2x104 clusters N= 3 to 220 (Sheldon etal 2008) Flat >~ 1Mpc M ~ L X=R(vir)

16. M/Li(r=22Mpc) vs. Mcl(SDSS; Sheldon etal ‘08) Ωm= 0.2 +- .03 Flat M/L on large scales; SAME for ALL clusters!

17. 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

18. 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 +- 0.04corrected forgas outflow

19. Baryon Fraction vs. Scale ( 0.18)(Bahcall & Martin ‘07)  m= 0.24

20. 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

21. 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)

22. Cosmic Acceleration: Supernovae

23. Cosmic Acceleraion: Supernovae (‘07)  Ωm- ΩΛ ~ -0.5

25. Cosmic MicrowaveBackground(WMAP)

26. CMB Spectrum

27. Space Curvature

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

29. 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 = 1Friedmann Eq.  m ~ a-3 • ~ constant (IF Cosmological Constant)

31. 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’

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

34. The Cosmic Triangle

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

37. 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)

38. Mass-to-Light FunctionM/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

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

40. 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

41. III. Cluster Abundance and Evolution  Powerful method to determine mand 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

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

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

44. m - 8 constraints from SDSS cluster MF[Bahcall etal ‘03 Rozo etal ’09] m=0.2, 8=0.9

45. Cluster Abundance Evolution  8(Bahcall & Bode) 8

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

47. Cosmic Acceleration: Supernovae (ESSENCE ‘08)

49. Cosmological ConstraintsSupernovae, CMB, Clusters

50. CMB Spectrum (Seivers etal ’09)