Mass of the Coma ClusterSimon PorterApril 4, 2008Two Different Approaches•Hughes 1989:–Fit to X-ray data from Einstein, EXOSAT, and Tenma–Model based on star cluster with and without extra dark matter term•Kubo, Stebbins, Annis, Dell’Antonio, Lin, Khiabanian, and Frieman 2007–Fit to Sloan survey data–Fit to NFW galactic cluster modelHughes’s Approach•Assume the Coma cluster is spherical, with no subclumps–“I have chosen to ignore this complication”•Assume a virial mass in hydrostatic equilibrium•Find mass distribution•Find temperature distribution•Estimate massGas Mass Distribution•Assume isothermal, gas follows light•Find a best fit to Einstein Observatory datay = R/ Rcβ = 0.86Rc = 5.5’Hydrostatic Equilibrium•Uniform density gas in equilibrium:•Assume spherically symmetric and ideal gas:Gas PressureDark Matter/ Galactic GravityBinding Mass Distribution•Assume either King (1966) model (star cluster) or dark matter power law (n=3,4,5):•Which results in:t = T/T0h50 = hubble constant in 50 km s-1 Mpc-1Temperature DistributionKing Modeln=4 polynomialMass Follows (X-Ray) Lightβ=0.86,Rc=5.5’ β=0.76,Rc=9.8’ β=0.63 Rc=7.6’Mass Follows (X-Ray) LightNot much difference due to calibrationof Tenma space telescopeBinding Mass Distribution•Dashed line = 99% confidence•All intersect 1x10-25•Not much difference between King and n=3Mass Results•h50-1 = 2 h-1•Range: 0.6-1.5 x 1015 h-1Kubo et al.’s Approach•Select a set of galaxies from SDSS•Measure tangential shear across those galaxies•Convert tangential shear to a surface density•Fit that density to a Navarro, Frenk, and White (NFW) profile•Convert the density profile to a virial massObservations•Galactic data from the Sloan Digital Sky Survey Data Release 5 (SDSS DR5)•Used PHOTO pipeline to do object detection and shape measurement•200 deg2 region of the sky centered at NGC 4889 (13h02m0.2s, 27°41’26.6’’, J2000)Sample Selection•Only objects PHOTO identified as galaxies•Also cut ones with bad PSF•~270,000 galaxies totalTangential Shear•Break into radial bins from 0.05-10.5 h-1 Mpc•Use 1-D shear based on Castro et al. (2005):•γt = tangential shear for bin, et = tangential ellipticity of bin, N = number in binTangential Shear•Squares = γt with 1 σ error•Triangles = 45° shear•Total χ2 = 23.33Surface Density•Tangential shear relates to surface density:•Ds, Dl angular diameter distance to source or lens; Dls angular distance from lens to sourceNFW Profile•Fit to profile from Navarro, Frenk, and White:•The two parameters, rs and c can constrained by setting the virial radius r200 = c rs:Results!•Fitting the profile:•With χ2 = 3.87 for 4 degrees of freedom•For a mass of:Cross-Comparison1. Kubo et al. 20072. Geller et al. 19991. Hughes 19892. The & White