MASS-TO-LIGHT FUNCTION: from Galaxies to Superclusters MASS-TO-LIGHT FUNCTION: from Galaxies to Superclusters Celebrating Vera Rubin Neta A. Bahcall Princeton University Celebrating Vera Rubin Neta A. Bahcall Princeton University

“In a spiral galaxy, the ratio of dark-to-light matter is about a factor of ten. That's probably a good number for the ratio of our ignorance-to-knowledge. We're out of kindergarten, but only in about third grade.”

Vera’s Rotation Curves M/L Kaptyen (Local) 1920’s Zwicky (Clusters) 1930s Rubin (Galaxies) 1970s ( M/L ~ R )

Mass-to-Light Function M/L(R) 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?  rep L univ (L o /Vol) =  m (M o /Vol)  Determine M, of clusters, SCs, LSS  rep [≈ 300h  rep [≈ 300h ]    m ~  How does M/L depend on scale?  How and where is the mass distributed?  How use it to weigh Universe?  rep L univ (L o /Vol) =  m (M o /Vol)  Determine M, of clusters, SCs, LSS  rep [≈ 300h  rep [≈ 300h ]    m ~

Weighing Clusters 3 Basic Methods  Motion of galaxies[M R ~ v 2 R]  Motion of galaxies [M R ~ v 2 R] Temperature of hot gas[M R ~TR]  Temperature of hot gas [M R ~TR] Gravitational lensing[M R ]  Gravitational lensing [M R ] 3 Basic Methods  Motion of galaxies[M R ~ v 2 R]  Motion of galaxies [M R ~ v 2 R] Temperature of hot gas[M R ~TR]  Temperature of hot gas [M R ~TR] Gravitational lensing[M R ]  Gravitational lensing [M R ]

M/L(R) (Davis etal 1980) Galaxies Groups Clusters Ω m =1

Mass-to-Light Function 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: ~ no excess DM ! 3. Most of the DM is in huge halos around galaxies ( ~ Kpc) Ω m = 1.0 Ω m = 0.3 Ω m =0.25

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

M/L(R) Function: simulations (Bahcall, Yu, etal ’01) 1.Same shape as observed: FLAT on large-scales (M ~ L) 2.Cluster M/L increases with M cl. Explains M/L Groups to Clusters 3.Anti-Bias of Rich Clusters: their M/L B larger than average (L B low)

Cluster M/L versus T (or M) (Bahcall and Comerford ’02) M/L=( ) T kev Due to mergers (lowers L at a fixed Mass)? Increase in E-fraction; Older systems (L fades)? Data vs Sims

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

SDSS Cluster Mass Profile: Weak Lensing 2x10 4 SDSS clusters, N=3 to 220. (Sheldon et al 2008) X = R 200 NFW

Cluster M/L i (R) Profile (SDSS, weak lensing 2x10 4 clusters N= 3 to 220 (Sheldon etal 2008) X=R(vir) Flat >~ 1Mpc M ~ L

Cluster (M/L) 200 versus M 200 M/L ~ M

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

M/L Function: Conclusions M/L Function Flattens on Large Scales  M/L Function Flattens on Large Scales M ~ L  M ~ L (reaching end of Dark-Matter)  Dark Matter located mostly in large galactic halos ~300s Kpc) Group/Clusters: made up of Sp+E; no significant additional DM  Cluster M/L increases slightly with M (mergers?)  Rich clusters M/L B is ‘Anti-biased ’ ( M/L B >mean)  Asymptotic Cluster M/L i (22Mpc) is same for ALL Groups and Clusters, h !  Mass-Density of Univers:  m = M/L Function Flattens on Large Scales  M/L Function Flattens on Large Scales M ~ L  M ~ L (reaching end of Dark-Matter)  Dark Matter located mostly in large galactic halos ~300s Kpc) Group/Clusters: made up of Sp+E; no significant additional DM  Cluster M/L increases slightly with M (mergers?)  Rich clusters M/L B is ‘Anti-biased ’ ( M/L B >mean)  Asymptotic Cluster M/L i (22Mpc) is same for ALL Groups and Clusters, h !  Mass-Density of Univers:  m =

Improved Cluster Mass Tracer from SDSS (R. Reyes etal 2008)  Improved optical cluster mass tracer from SDSS, using weak-lensing calibration  Tested M 200 versus N 200 (richness), L 200, L BCG, and combinations (avail in many surveys)  Best tracer (least scatter, highest M cl ): Combination of Richness and L BCG : M ~ N 1.2 L BCG 0.7 M 200 = ( ) (N 200 /20) x [L BCG / (N 200 )]  L BCG important second parameter. Consistent with merger picture: At fixed M cl mergers produce Lower N and Brighter L BCG  Improved optical cluster mass tracer from SDSS, using weak-lensing calibration  Tested M 200 versus N 200 (richness), L 200, L BCG, and combinations (avail in many surveys)  Best tracer (least scatter, highest M cl ): Combination of Richness and L BCG : M ~ N 1.2 L BCG 0.7 M 200 = ( ) (N 200 /20) x [L BCG / (N 200 )]  L BCG important second parameter. Consistent with merger picture: At fixed M cl mergers produce Lower N and Brighter L BCG

M 200 vs. L BCG [at fixed N 200 ] (Reyes etal ‘08) M 200 = ( ) (N 200 /20) x [L BCG / (N 200 )]

Weighing the Universe  M/L Function  m =  Baryon Fraction  Cluster Abundance and Evolution [ 8 = ] and Evolution [ 8 = ]  Supernovae Ia + Flat  CMB + LSS + h + Flat   m ≈  4% Baryons + ~20% Dark Matter  Mass ~ Light  M/L Function  m =  Baryon Fraction  Cluster Abundance and Evolution [ 8 = ] and Evolution [ 8 = ]  Supernovae Ia + Flat  CMB + LSS + h + Flat   m ≈  4% Baryons + ~20% Dark Matter  Mass ~ Light

“ The joy and fun of understanding the universe is what we bequeath to our grandchildren and their grandchildren. With over 90% of the matter in the universe still to play with, even the sky will not be the limit.” Vera C. Rubin Vera C. Rubin “ The joy and fun of understanding the universe is what we bequeath to our grandchildren and their grandchildren. With over 90% of the matter in the universe still to play with, even the sky will not be the limit.” Vera C. Rubin Vera C. Rubin

Dedication to Women in Science Great Wall, China 1986 (Margaret, Anna, Vera, Neta)