1The “Tuning Fork” Diagram“Early” “Late”Galaxy PropertiesFrom M. Longair “Galaxy Formation”2Trends in spiral galaxies(see CO Tables 25.1/25.2)• Mass/Light ratios•Sa Î Sc : M/LB= 6.2 Î2.6• Sc’s dominated by younger, hotter, more massive stars.•Colors•Sa Î Sc : B-V = 0.75 Î0.52• Bluer colors Î Sc’s dominated by younger, hotter stars.•Mgas/Mtotal•Sa Î Sd: Mgas/Mtotal= 0.04 Î 0.25• Molecular/atomic hydrogen•Sa Î Sd: MH2/MHI = 2.2 Î 0.3• Metallicity• Depends on absolute magnitude• No. of Globular Clusters/Total Luminosity dE{,∆ Ez S IrrE, dES, IrrCO Fig 25.12but Longair’s plot Î constantCO Fig 25.16Red BlueLow L High LH I Spectra of Spiral GalaxiesVsysVmax3Tully-Fisher Relation• Maximum rotation velocity-Luminosity relation [FIG 25.10]• Tully-Fisher relation •MB= -9.95 log10VMax+ 3.15 (Sa)•MB= -10.2 log10VMax+ 2.71 (Sb)•MB= -11.0 log10VMax+ 3.31 (Sc)Rotation CurvesSemi-derivation of Tully-Fisher Relation:• Mass interior to outermost R where rotation curve can be measured:•Assume • “Freeman Law” (observed fact ---maybe):• Convert to Absolute B-band magnitudes:GRVMass2max=4max2.4.../VconstLconstRLBrightSurfconstMassL×====πMB= -9.95 log10Vmax+ 3.15 (Sa)MB= -10.2 log10Vmax+ 2.71 (Sb)MB= -11.0 log10Vmax+ 3.31 (Sc).log10log5.2MMmax1010sunBconstVLLsun+−=−=Important as a DISTANCE calibrator!4EllipticalsHuge mass range:• Dwarf spheroidals: 107-108M• Blue compact dwarfs: ~109M• Dwarf ellipticals: 107-109M• Normal (giant) ellipticals: 108-1013M• cD galaxies in cluster centers: 1013-1014McD (NGC 3311)Giant E (NGC 1407)Dwarf spheroidal(Leo I)Dwarf ellipticals M32, NGC 205HST images• R1/4law usually fits radial surface brightness distribution• Also Hubble’s law• Modified Hubble’s law•+ others−−=133.34/110)(eRReIRI21)(+=ooRRIRI21)(+=ooRRIRI2/321)(+=ooRRIRIDiverges, but at least is projection of simple 3D distribution: GoodBetterBestcDr1/4Ellipticals5The Virial Theorem [CO 2.4]• For gravitationally bound systems in equilibrium• Total energy = ½ time-averaged potential energy.E = total energyU = potential energy.K = kinetic energy.E = K + U• Can show from Newton’s 3 laws + law of gravity:•½(d2I/dt2) -2K = U where I = Σmiri2= moment of inertia.• Time average < d2I/dt2> = 0, or at least ~ 0.• Virial theorem Î -2<K> = <U> <K> = - ½ <U><E> = <K> + <U> Î<E> = ½ <U>Mass determinations fromabsorption line widths• Virial Theorem 2K = -U<v2> = 3 <vr2>Î σ2r= GM/(5R)• See pp. 959-962, + Sect. 2.4• Applied to nuclei of spirals Îpresence of massive black holes• Also often applied to• E galaxies• Galaxy clustersRGMU253−=Nuclear bulge of M31Rot. VelocityVel. Disp6Mass determinations fromabsorption line widths• Virial Theorem •2K = -U• <v2> = 3 <vr2>• Î σ2r = GM/(5R)• See pp. 959-962, + Sect. 2.4• Applied to nuclei of spirals Îpresence of massive black holes• Also often applied to• E galaxies• Galaxy clustersRGMU253−=Fourier TransformsE galaxy = K star convolved with Gaussian velocity distribution of stars.K starStarGalaxyRatioGaussian fit: • Convolution turns into multiplication in F.T. space.• F.T. of a Gaussian is a Gaussian.Observed SpectrumFaber-Jackson relation: Le~ σ04(Absolute magnitude)7Homework Assignment 5Due Monday Oct. 1•CO 2ndedition problems 25.13, 25.14, 25.16• Same as 1stedition problems 23.11, 23.12, 23.14• There may be one addition derivation-type problem having to do with the stellar velocities found in E galaxies. It depends on whether I cover that in class with enough lead time.Do CO problem 25.20 ( = problem 23.18 in
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