Ellipticals. Ellipticals. Huge mass range:

Transcription

1 Ellipticals Huge mass range: Dwarf spheroidal (Leo I) Dwarf spheroidals: M Blue compact dwarfs: ~1 9 M Dwarf ellipticals: M Normal (giant) ellipticals: M cd galaxies in cluster centers: M Dwarf ellipticals M3, NGC 5 cd (NGC 3311) Giant E (NGC 17) Ellipticals cd r 1/ Hubble s law Io R 1 Ro HST images Modified Hubble s law devaucouleurs R 1/ law usually fits radial surface brightness distribution + others o o 3/ 1 R Ro I e I 1 1/ R 3.33 R e 1 Diverges, but at least is projection of simple 3D distribution: I r) 1 r Ro 1

2 True shapes requires statistical analysis Oblate = pancakes Prolate = footballs [CO figs 5., 5.3] True shapes requires statistical analysis Lower luminosity rotationally supported (V rot / ) ~ /(1- ) Higher L pressure supported (V rot / ) << 1 Ellipticity = 1 b/a CO pgs Curve expected for galaxies that are flattened by rotation (i.e. have isotropic random velocity dispersions) = low L ellipticals x = spiral bulges high L ellipticals Rotationally Supported Observed Spectrum K star (V/) * =.7 E galaxy = K star convolved with Gaussian velocity distribution of stars. From Binney & Tremaine, Galactic Dynamics

3 Statistics of = (1- b/a) Oblate, prolate spheroids can t fit the observed distribution. Summing over wide range of true values of would fill in the dip at obs =. Triaxial spheroids can fit. Nearly oblate triaxial spheroids seem best. Oblate, true =.7 Prolate, true =.5 observed 3 P ( obs ) Triaxial, Axis ratios 1:.8:.3 3 P ( obs ) 1 From Binney & Merrifield, Galactic Astronomy Other evidence for triaxial systems Isophotal twists Kinematics (star motions) From Binney & Merrifield, Galactic Astronomy 3

4 Orbits in E galaxies From Binney & Tremaine, Galactic Dynamics Some families of non-closed orbits in a mildly triaxial potential. E galaxies are transparent, but % still have some dust lanes Even if complete star formation at t=, stars must subsequently have lost gas. Detected by: X-rays (Brehmsstrahlung): M H I emission lines: M H II emission lines: M But gas can be lost by Supernova-driven winds Ram pressure stripping

5 The Virial Theorem [CO.] For gravitationally bound systems in equilibrium Time-averaged kinetic energy = - ½ time-averaged potential energy. E = total energy U = potential energy. K = kinetic energy. E = K + U Can show from Newton s 3 laws + law of gravity: ½ (d I/dt ) -K= U where I = m i r i = moment of inertia. Time average < d I/dt > =, or at least ~. Virial theorem -<K> = <U> <K> = - ½ <U> <E> = <K> + <U> <E> = ½ <U> Sorry I had left out the ½ when I showed this slide in class. Virial Theorem K = -U 3 GM U 5 R K = ½ M<v > = 3/ M < r > Mass determinations from absorption line widths [CO 5.1] M virial 5R r G See pp , + Sect.. Applied to nuclei of spirals presence of massive black holes Also often applied to E galaxies Galaxy clusters M3 5

6 Virial Theorem K = -U <v > = 3 <v r > K = ½ M<v > = 3/ M < r > 5R r M virial G See pp , + Sect.. Applied to nuclei of spirals presence of massive black holes Also often applied to E galaxies Galaxy clusters Mass determinations from absorption line widths 3 GM U 5 R Observed Spectrum Fourier Transforms K star E galaxy = K star convolved with Gaussian velocity distribution of stars. Star Galaxy Ratio Gaussian fit: Convolution turns into multiplication in F.T. space. F.T. of a Gaussian is a Gaussian. I e I e = surface brightness at R e L e = luminosity within R e 1/ 1 Faber-Jackson relation: L e ~ R R e (Absolute magnitude) 6

7 Mass-Luminosity relationships Faber-Jackson relation: L e ~ mag/arcsec D n - correlation. D n = diameter within which <I> =.75 B Fundamental plane in log R e, <I> e, log space R e = scale factor in R 1/ law <I> e = mean surface brightness within R e Different from I e! Intro. to Principle Component Analysis: astro-ph/99579 I e 1 1/ R 3.33 R e 1 CO give different coefficients??? r e 1. I -.8 e L.65 r.65 e From Binney & Merrifield, Galactic Astronomy Distribution of galaxy types Total number of galaxies Dense regions (cluster centers) predominantly ellipticals. Field galaxies predominantly spirals. On average, roughly even split between E and S. Fraction of population S S E Dressler 198 Log (Projected surface density of galaxies) 7

8 Schechter Luminosity Function (L)dL = L e -L/L* dl (M)dM = 1.(+1)M e 1.(M * -M) dm The Milky Way is an L * galaxy. [CO 5.36] Log (galaxies/mpc 3 ) [BM.1] more M luminous B more luminous Problem.15: Assuming that the highest velocity stars are near the escape speed, estimate the mass of the M.W. Correct: v esc = v circ + max v pec = + 65 ~ 3 km s -1. K.E. = Potential Energy mv esc GmM R Wrong: follow example.3.1 and calculate mass required to hold star in circular orbit with v = 3 km s -1 Rvesc M G Problem.36: Point mass M at center of MW + mass distributed with density (r) 1/r. (a) Show that M r = kr+m. Correct: r r C M r M ( r) dvol( r) M r dr M C r Black Hole Wrong: anything that does not show that you realized that you need to integrate over ( r) dvol( r) Rv M G esc r 8