1ASU, 22 Feb. 2008Journal ClubSubstructure in theComa ClusterBy Carola Ellinger2ASU, 22 Feb. 2008Journal ClubOutline Fitchett & Webster 1987: “Quantify” substructure in position and velocity Dynamical model Colless & Dunn 1996: More detailed look at velocity substructure Another dynamical model Edwards et al. 2002: Substructure from giants and dwarfsI will talk about these three papers, in chronological orderThe first one, F&W, is the first one to quantify the significanceof the substructure that is seen in the positions of galaxies,and applies that also to the line-of-sight velocities. Theyidentify two subclumps in position, and possibly in velocity.They then proceed to making a dynamical model of how thecoma cluster may have evolved to this.The second paper, C&D, use a much larger sample than F&Wand analyze it (specifically the non-gaussian vel. Distribution)for subclumps in velocity space. After find evidence for twovelocity subclumps, they also make a dynamical model tofigure out what is going on.The third paper, Eea, looks at different galaxy types - giantsand dwarfs - to gain insight into the dynamical history. Theyalso find that Coma has not evolved to equil. Yet.The main focus is on the first paper, and I use the other twojust to supplement the conclusion of the first, so I will beskipping a lot of the last two papers, to stay in within theallotted time.3ASU, 22 Feb. 2008Journal ClubIntroduction The Coma Cluster is in equilibrium - or is it? X-ray distribution Velocity histogram (->Colless & Dunn) Two (c )D galaxies Radiogalaxies’ mean velocities timescaleThe coma cluster has always been assumed to be inequilibrium (because that is the easiest to do), but there aresome facts that shows that it might not be. F&W list severalarguments why the coma cluster cannot be in equilibrium:X-ray distribution doesn’t fit and equil. Distr. WellVelocity histogram is skew at 3% sign. Level -> not gaussian(if not gaussian, not equil)?D galaxies = massive giant elliptical galaxies thought to be atthe bottom of potential wells; since there are two, cannothave equil?D=dominant, cD= with halo, 10x more massivethan giantsMean vel. Of radio galaxies is higher than mean vel. Of cluster-> diff. components in cluster.Timescale arguments (from E. et al): dyn. Fric.~ 22Gyr fortypical galaxy (1e12Msol)4ASU, 22 Feb. 2008Journal ClubFitchett & Webster 1987:Spatial velocity substructure Maximum likelihood: “Lee”- function Statistical significance: calibrated usingMonte-Carlo simulations Case a: Case b:! "="0r! "="0r2+ rc2-to analyse the data, F&W use a ‘new’ statistical techniquebased on max likelihood to detect substructure: if you havee.g. 2-D positions (x,y) of the galaxies, plot them and thenproject the positions onto a line and then calculate the‘clumpiness’, L, of projected points. Repeat for differentorientation of the line -> get L(phi). First done by Lee(1979),therefore F&W call it Lee function. The advantages: works forelliptical cluster as well, assign statistical significance todetermined substructure, most sensitive to 2 clumps.-Since there is no expression for Lee-function, need tocalibrate its significance - use Monte-Carlo simulations forthat. This is done to determine if the clumping that is seen isreal, and not an effect of a certain galaxy distribution. It wastested for these two different profiles, where sigma denotessurface density. The core radius was taken as the radius of theanalyzed region, 9’.6.5ASU, 22 Feb. 2008Journal ClubFitchett & Webster 1987:Data sets All data for central region (within 19’.2 of NGC4874) DKG: from Kent & Gunn 1982. Complete to mV=15.7, 54 galaxies used Position, velocity DGP1: from Godwin and Peach 1977, selectedgalaxies in same range as DGK. 226 galaxies Position DGP2: subsample of DGP1 without backgroundcontamination. 75 galaxies. positionThey wanted to investigate the central region, which they takeas the region within 19’.2 of NGC4874DKG: they selected galaxies brighter than 15.7 mag in V, Theyclaim that all galaxies in this set belong to the cluster and thatit is complete to that magnitude.DGP1: covers 1.22 square degree field centered on comacluster. They picked out galaxies in the same spatial regionand magnitude as DGK.DGP2: subsample to DGP1. They select galaxies brighter thanV25=15.5 to remove some fo the background contaminationfrom this data set. The 25 refers to the isophote of the 25thmag.6ASU, 22 Feb. 2008Journal ClubFitchett & Webster 1987:DKG - dataTheir Fig. 1The left panel shows the positions on the plane of the sky ofthe first data set (DKG). Contours = density contours,triangles - actual galaxies. Substructure is obvious. The rightpanel shows the Lee function. <explain axes>7ASU, 22 Feb. 2008Journal ClubFitchett & Webster 1987:DGP1 - dataTheir Fig. 28ASU, 22 Feb. 2008Journal ClubFitchett & Webster 1987:DGP2 - dataTheir Fig. 39ASU, 22 Feb. 2008Journal ClubFitchett & Webster 1987:ResultsSignificanceCase bSignificanceCase aLrat0.48%0.12%2.34DGP227.6%11.9%1.35DGP112.5%6.5%2.03DKGThe measure of interest here is the ratio, Lrat, of the max andmin value of L.The significance levels are calibrated with the aforementionedMonte-Carlo simulations. Lower significance is better, itbasically tells us what the chance is that the clumps we see isdue to the distribution, and not real (?)Case b: expected to have lower significance since a constantdensity core can more readily lead to chance clumpingErgo: THERE IS SUBSTRUCTURE! (in positions)10ASU, 22 Feb. 2008Journal ClubFitchett & Webster 1987:DKG - velocity dataTheir Fig. 4There were velocities available for the DKG data set, so F&Wdid the Lee statistics in 3-D (x,y,v) on that, and just show theresults into the two most likely subclumps in space. Circles(red) are one subclump, triangles (blue) the other. So youactually not only have to spatial subclumps, but each also hasa distinct clumping in velocity. The double circle means highvelocity.Filled circle = 4874Filled triangle = 488911ASU, 22 Feb. 2008Journal ClubFitchett & Webster 1987:velocity histogramsallABAfter they established that there are subclumps, they take alook at the line-of-sight velocity histograms of the DKG dataset. Graphed are the histograms for all galaxies, andseparately for each clump. The x-axis on each is velocity inkm/s (?). Then they perform a bunch of statistical tests to seeto what degree these histograms are not