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Lecture 6 Recap Lecture Introduction to Astronomy Galaxies Lecture 6 Recap Lecture Peder Norberg [email protected] Introduction to Astronomy PHYS1081 Lecture Summary 1. The Milky Way: mapping the Galaxy. 2. Galaxies - Morphology: the Hubble Sequence, Spiral and Elliptical galaxies 3. Galaxies - Distances: The Cosmic Distance Ladder 4. Clusters and superclusters. 5. Active galaxies, Quasars & Gamma-ray bursts Lecture 6 By the end of this lecture, we will have revisited: Our Galaxy: The Milky Way Galaxy Morphologies Galaxy Transformations Active Galaxies and Black Holes Redshifts and Distances Large Scale Structure: Groups, Clusters & Superclusters Masses of Clusters Gravity Galaxy Cluster Galaxy AGN Forces on a particle in 2 V GM (< R) 2 GM (< R) a = = V = a circular orbit: centripetal R R2 R Virial Theorem for 2 2 KE T = PE T σ R groups of stars / M E galaxies: 2 2 / G σ = (vi − v ) Kinetic and potential GM v2 2GM = R = energy of a particle: r 2 S c2 Our Galaxy: The Milky Way The Milky Way The structure of the Galaxy The Sun’s position within the Galaxy What lurks at the Galactic Centre? Galactic rotation, Dark halos and Dark Matter Future of our Galaxy… The Milky Way @ different wavelengths Optical Far-IR IR Structure of the Milky Way Our galaxy has been mapped using star counts and emission from HI gas: - The Disk is about 30 kpc across and only 0.6 kpc thick (contains Pop I+II stars) - The Bulge is about 2 kpc across (Pop II stars) - The Halo is a diffuse structure that 3 kpc reaches out to 100 kpc radius (Pop II) - There is a “thick” disk of Pop II stars (thickness ~2-3kpc) Several spiral arms (6) in disk: not a “fixed” pattern, but density waves. The Sun’s position within the Galaxy 6 Globular clusters (GC) are compact groups ~10 Mo pop II stars. Globular cluster distribution on the sky show Sun not centred in the galaxy. Use RR Lyrae stars to get distances to GCs. Sun is 8.0+/-0.6 kpc from Galactic Centre. The Galactic Centre ~0.5o ~75pc X-ray emission 10pc Stars orbiting the Galactic Centre Track positions of ~28 stars orbiting Sag A* over 20 years 6 Find mass: 4x10 M0 within a radius of 6.25 light hrs Venus Earth Radio inteferometry using global telescopes puts a limit on the size of Sagittarius A* of ~8 light minutes (< 1 milli-arcsec). So - is there a Black Hole at the centre of our galaxy? Schwarzschild Radius A Black Hole is a mass which is so compact that its escape velocity exceeds the speed of light. For a given mass, one can determine the Schwarzschild radius (“Event Horizon”): RS, the radius at which the vescape=c. If the mass is contained within a radius smaller than RS then the object is a Black Hole. To escape KE>PE: 2 2 GM v GM c 2GM = = RS = 2 r 2 RS 2 c 2GM 2 × 6.7 × 10−11 × 2 × 1030 For the Sun (1 M0): RS = 2 = 2 = 3km c (3 × 108 ) If the Sun’s mass was in a volume with r<3 km (& not ~7x105 km), then it would be a Black Hole => To be a BH, the Sun would need to be >1016 denser! Is there a BH at the Galactic Centre? Assuming Sag A* is a Black Hole, what is its radius? 6 Schwarzschild Radius for a mass of 3.6x10 M0: −11 6 30 2GM 2 × 6.67 × 10 × 3.6 × 10 × 1.99 × 10 7 RS = 2 = 2 ≈ 1× 10 km c (3 × 108 ) 10 8 −1 RS = 1× 10 m 3 × 10 ms = 35 lightseconds The radio interferometry size is ~8 light minutes, hence ~10x larger. Any mass this compact (e.g. dense star cluster) is unstable and would collapse to a black hole, so its very likely that Sag A* is a black hole. Dynamics of the Milky Way Solid Body orbits Solid body rotation 0 10 20 Keplerian rotation Distance from Galactic Centre (kpc) HI emission shows circular velocity of gas is constant from ~2-20kpc Hence mass in the galaxy is not uniformly distributed through-out (Solid body), nor is it concentrated at the centre (Keplerian) Galactic Rotation Curve For stars orbiting a galaxy at radius R with speed V on a circular orbit then centripetal acceleration balances acceleration from interior mass: V 2 GM (< R) GM (< R) a = = V = centripetal R R2 R (a) If all the mass in the galaxy GM V = ∝ R−1/2 was concentrated in the centre: Kepler R 4π R3ρ (b) If the mass is in a sphere M (< R) = 3 with constant density ( ): 3 2 ρ G 4π R ρ 4πGρR V = × = ∝ R Solid R 3 3 R R ρ0 2 (c) If the mass distribution M (< R) = 4πr dr = 4πρ0 dr = 4πρ0 R ∫ r2 ∫ follows an isothermal sphere, 0 0 -2 G whose density drops as R : V = × 4πρ R = 4πGρ ∝ Constant Isothermal R 0 0 Dark Halo Isothermal halo produces flat rotation curve, more extended than exponential light profile of the disk (and the stellar halo doesn’t contain a lot of stars) -1 Gravity of visible matter within solar orbit only (R~8 kpc) gives vc~150 km s So this massive halo has to be mostly dark 11 Within 20 kpc the total enclosed mass in MW is 2x10 Mo. 12 Total mass out to ~100 kpc is ~10 Mo (90% of mass of galaxy is dark). Dark Matter Dynamics of stars in galaxies (and galaxies within clusters) show that much of the mass is “dark” This Dark Matter could be either compact Baryonic objects (failed stars, planets or Black Holes, MACHOs) or elementary particles (Weakly Interacting Massive Particles, WIMPs) Microlensing searches for MACHOs in our galaxy have placed tight limits. Most of the Dark Matter must be WIMPs, still to be directly discovered! Galaxy Morphologies, Transformations and AGNs Hubble Tuning Fork Hubble’s classification scheme for galaxy morphologies: E0 E7 E=Elliptical S0=Lenticular S=Spiral SB=Barred spirals Im=Irregular Early-type Late-type Spiral Galaxies Main component of spiral galaxies is a rotationally-supported disk, with an exponential brightness profile: SB(R) exp [ R/R ] / − s Disks exhibit spiral arms. Other major component is the central bulge. Hubble classified spiral galaxies (Sa/Sb/ Sc/Sd) based on the visibility of the spiral arms, the tightness of their winding and the prominence of the central bulge. Sa Sb Sc Sd Elliptical Galaxies Elliptical galaxies have no spiral arms or no apparent disk. Hubble put ellipticals onto a sequence (E0, E1, E2, E3….E7) based on apparent ellipticity of the light (a − b) εapp = 10 distribution (major/minor axes of the ellipse: a,b): a E0 E7 oblate prolate The stars in elliptical galaxies have no axis of rotation, they follow complex/chaotic orbits. 90% of Ellipticals are prolate spheroids. The distribution of light is well-characterised by a decline of surface brightness with radius as R1/4: SB(R) exp (R/R )1/4 / − E h i Properties of Galaxy Populations Elliptical(+S0) Spiral(inc Barred) Irregular Proportion: 20% 75% 5% 5 11 8 10 7 9 Luminosities 10 to 2x10 Lo 10 to 5x10 Lo 10 to 10 Lo 5 13 9 12 8 10 Masses 10 to 10 Mo 10 to 2x10 Mo 10 to 3x10 Mo Sizes 1 to 100kpc 5 to 50kpc 1 to 10kpc Gas ~0% 4 to 25% >25% Colours Red (Pop II) Blue (Pop I+II) Blue (Pop I) Environments: High-density Low-density Low-density Clusters Groups+“Field” “Field” Note: Proportion should be understood as in the "local universe” above some “not too faint” brightness limit… Tully-Fisher/Faber-Jackson Relations Tully-Fisher: empirical relation between luminosity of spiral 4 galaxy and the circular velocity of the stars in its disk: L ∝ V c Faber-Jackson: empirical relation between luminosity of 4 elliptical galaxy and the velocity dispersion of its stars: L ∝ σ K M 2 2 Vc R 5σ RE M Spiral (< R) = M = G 2G Log Vc Use Vc or σ to get luminosity, compare to brightness -> distance. Rich Cluster: Coma Ellipticals & Mergers Ellipticals (and S0) galaxies are mostly found in clusters. Mergers can turn Spiral Galaxies into an Elliptical. Mergers likely to be common in dense regions (go onto become a cluster) at early times. Active Galaxies Seyfert galaxies: luminous point-like nuclei within galaxy and broad emission lines (~1000km/s) AGN Quasar (or QSO): AGN dominates galaxy (so appears point-like) and exhibits very broad emission lines (~10,000km/s) Radio galaxies: show relativistic jets of radio-emitting plasma Core Lobe Jet 1Mpc Unified Model Accretion Disks AGN powered by an accretion disk around a Supermassive 6 9 Black Hole. AGN are seen with Black Hole masses of 10 -10 M0 It is the mass accretion onto the accretion disk which creates the luminosity of the AGN (not necessarily the size of the BH). Accretion onto a SMBH Accretion onto a Black hole is a very efficient process for energy production: you get out ~25% of the rest mass of the material which falls in. Thus accreting Super-Massive Black Hole are believed to power some of the most luminous objects known: Active Galactic Nuclei (AGN) If we drop a mass m into a Black Hole, by the time it is orbiting at the Schwarzschild radius it will have lost potential energy equal to: 2 2 2GM GMm GMmc mc U = − = − = − RS = 2 c RS 2GM 2 A fraction of this energy (ε~0.5) goes into mc 2 E = ε heating the accretion disk.
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