Dynamic modelling of luminous anddark matter in 17 Coma early-typegalaxiesPaper by: J. Thomas, R.P. Saglia, R. Bender, D. Thomas, K.Gebhardt, J. Magorrian, E.M Corsini, and G. WegnerPresentation by: William GrayJournal Club Spring 2008A Little Background• Elliptical Galaxies– Numerous among bright galaxies– Harbor significant fraction of stellar mass in theUniverse• Key Parameters for Elliptical GalaxyFormation– Central dark matter density– Scaling radius of dark matter– Stellar mass-to-light ratio– Distribution of stellar orbitsPurpose of Dynamic Modelling• Allows for reconstruction of mass structureand orbital state of galaxy– Requires high quality Line-of-Sight VelocityDistributions (LOSVDs) out to several Reff (1/2light radius)• What has been done:– Only large non-rotating Ellipticals have beenprobed with spherical models.– Authors will look at nonsymmetrical, rotating andnonrotating models.• Looking for evidence of dark matter• Goal: Analyze the luminous and dark matterdistributions and orbital structure of flattenedComa galaxiesObservations• Coma Sample: 17 early-type galaxies– 2 cD , 9 ordinary giant elliptical, and 6 lenticulargalaxies• -20.30 < Mb < -22.56• H0 = 69 km/(s*Mpc)• 3.3 < reff < 18.4 (arcsec)• Data obtained from HST (inner parts) andground based (outer parts)– Data obtained along 2 position angles• Apparent Major and Minor Axes.Deprojection and inclination• Surface photometry is deprojected toform 3D luminosity function (ν)• Inclinations– 3 different inclinations are used• I = 90º (edge on)• A minimum inclination that is found by requiringthe deprojection to be as flattened as an E7• Intermediate inclination for which thedeprojection looks like an E5– In many galaxies, inclination is poorlyconstrainedNGC 4624. E7 in Virgo NGC 4621. E5 in VirgoMass Model• Trial massdensity,combination ofstellar mass tolight ratio and darkmatter density.•Two different density functions are used to fit the kinematicdata. NFW distribution and a LOG distributionOrbital Superposition• S -> Boltzmann entropy• ƒ -> phase-space distribution function• Wi -> total amount of light on the orbit• Vi -> orbital phase-space volume• α -> regularization• χ2LOSVD -> deviations between data and mode• Betas -> AnisotrophyWhat is this α?• Controls the relative weight of data fitand entropy maximization.• The higher α the better the fit, butnoisier the DF becomes.• α = 0.02 for all modellingGoodness-of-fit• Best fit is determined by above eqn• Most fits are better than χ2min <0.1Model Inclinations• Most of the best fits are edge on– Does this mean there is a bias in model?• Possible biases– Using the same α for all galaxies– For face on galaxies, noise in kinematics– Non random inclinations– Bias due to extreme casesModel Inclinations 2• Top: Axial ratio from data (apparently)• Bottom: Axial ratio from models• If biased, we would see most galaxies at 1.Luminous and Dark Matter• Does mass follow light?– Best fitting models include a dark matterhalo.• All galaxies fall into 3 categories– Inconsistent with a constant mass to lightratio (8/17)– Models with and without dark matter differbut, evidence for DM is less than 2σ (5/17)– Evidence for DM is generally weak (4/17)Circular velocity curvesVelocity Anisotropy• Polar region– βυ= βϕ due to axial symmetry– Center is not constrained– Galaxies differ in amount of anisotropyVelocity Anisotropy• Equatorial Plane– Meridional• All have βν >0 over sampled range.• Average βν is related to flattening of galaxy• Poorly constrained– Azimuthal• Much more diverse than MeridionalPhase-Space DistributionFunction of the Stars• Stationary systems– DF is function of the isolating integrals– Constant along an orbit• Look at: Energy, Lz, 3rd integral, be positive– Since the Schwarzschild model exists, it ensures that the luminouscomponent of the model is stationary and physically meaningfulPhase Space DistributionFunction of Dark Matter• Without baryons, DF’s for halo profilesare known. But with baryons it is not so.• To find DM DF, solve:• But, with alpha = 0• Use dark matter profile as boundarycondition• Turns out that there does exist a DF forthe DM.LOG vs NFW• 13 of 17 best fit haloes are LOG• Significance of fit between profiles islow. No clear distinction can be made.• With kinematic data, one or the otherhalo type cannot be rules out.• Shape and structure of LOG halo DFsdo make them unlikely• Dark Matter phase space densitiesRegularization• α = 0.02 was chosen for all Coma Galaxies.α Influence on ModelKinematics• Minor Axis– Max entropy fits (α->0) yield isotropy– Lowering the weights (w) increases anisotropy• Major Axis– No trend as seen in minor axis– Variations in intrinsic velocity anisotropies withalpha are weaker than along minor axis• Bottom Line: No clear trend of velocityanisotropies with α is notableSummary I• 17 Coma Early-type galaxies surveyed– Axisymmetric Schwarzschild models usedto fit LOSVDs out to 1-4 Reff.– 2 Different profiles used– Models regularized towards maximumentropySummary II• Models with dark matter fit better than those without.• NFW haloes fit 4/17 best• LOG haloes fit 13/17 best• Central Dark matter densities are at least 1-2 ordersof magnitude lower than mass densities• Between 10-50 % of mass inside Reff is dark matter• Circular velocities is fairly constant over observedregion• All dark haloes are supported by al least 1 phasespace DFSummary III• Rotation comes from overpopulation ofprograde orbits and underpopulation ofretrograde orbits• Strong tangential anisotropy alongminor axis• α does not matter!Ok. Now I am done.• Questions? Comments? RudeRemarks?•