Spiral Structure. m ( Ω Ω gp ) = n κ. Closed orbits in non-inertial frames can explain the spiral pattern

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1 Spiral Structure In the mid-1960s Lin and Shu proposed that the spiral structure is caused by long-lived quasistatic density waves The density would be higher by about 10% to 20% Stars, dust and gas clouds would move through the density waves during their orbits When viewing the galaxy in a non-inertial reference frame rotating with the global pattern speed Ω gp, the spiral pattern will appear stationary Individual stars will have larger and smaller speed, depending on their distance from the center

2 Spiral Structure At the corotation radius R C the stars and density waves will move with the same speed Massive O and B stars will die before leaving the density wave completely and will be found close to their birth place Less massive redder stars will live longer and will be distributed evenly throughout the galaxy

3 Spiral Structure Closed orbits in non-inertial frames can explain the spiral pattern m ( Ω Ω gp ) = n κ With Ω the unperturbed orbital speed and κ the epicycle frequency The example below is for (n = 1 and m = 2)

4 Elliptical Galaxies Initial classification scheme by Hubble based on apparent ellipticity not relevant for actual classification More important morphological features are size, absolute magnitude, surface brightness

5 Elliptical Galaxies cd galaxies are very large and bright galaxies up to 1 Mpc across E galaxies are normal and include compact ellipticals ce; they are kpc across de galaxies are dwarf elliptical galaxies 1 10 kpc across dsph galaxies are very low luminosity galaxies only detected close to the Milky Way; they are kpc across BCD galaxies are blue compact dwarf galaxies

6 Elliptical Galaxies Surface-brightness profiles for normal elliptical galaxies follow closely the r ¼ profile

7 Faber-Jackson Relation The central velocity dispersion in de s, dsph s E s and the bulges of spiral galaxies is related to M B Starting with the virial mass and making the assumptions for the derivation of the Tully-Fisher relation we obtain L σ 0 4 Here σ 0 is the central value of the radial velocity dispersion This relation is referred to as Faber- Jackson relation

8 Galaxies: Galactic Evolution

9 Interactions of Galaxies Nearly all galaxies are part of a larger ensemble of a galaxy cluster The density is relatively high, the spacing between galaxies is about 100 times larger than their size Hercules galaxy cluster Center populated more with elliptic galaxies than the outskirts

10 Interactions of Galaxies Mergers of galaxies will most likely trigger a burst of star formation due to the liberation of gas and supernovae, generating galactic superwinds Larger galaxies seem to be formed by merging from smaller ones Initial spiral structures seem to be often lost in collisions

11 Galaxy Collision Simulation Simulation of two colliding galaxies by Summers, Mihos, and Hernquist

12 Dynamical Friction Looking at a collision of two galaxies Stars are generally spread far apart in galaxies, which should make the collision of two stars very unlikely Interactions between stars will be mostly gravitational Imagining a small galaxy of mass M moving with speed v M through an infinite collection of stars, gas clouds and dark matter with a constant mass density ρ As the galaxy moves forward, other objects are pulled towards its path with the closest objects feeling the largest force This produces a region of enhanced density along the path The result is called dynamical friction C is a dimensionless numerical factor depending on how v M compares to the velocity dispersion of the surrounding matter f d = C G 2 M 2 ρ v M 2

13 Dynamical Friction To estimate the time scale associated with the action of dynamical friction acting on globular clusters of a galaxy From the flat rotation curves we can imply for the density of the dark matter halo ρ = v M 2 4 π G r 2 This yields for the dynamical friction force f d = C G 2 M 2 ρ v M 2 = C G M 2 4 π r 2 For a circular cluster orbit of radius r the angular momentum is given by L = M v M r

14 Dynamical Friction Dynamical friction acts tangentially to the orbit and opposes the cluster s motion, a torque is exerted on the cluster, reducing it s angular momentum τ = r f d = d L dt M v M d r dt = r C G M 2 4 π r 2 Integration leads to ri 0 t c r dr = C G M 4 π v M 0 dt

15 Dynamical Friction Solving for the lifetime of the cluster t c yields t c = 2 π v M r i 2 C G M This result can be inverted to find the most distant cluster that could have been captured within the estimated age of the galaxy r max = t max C G M 2 π v M ½

16 Dynamical Friction Example of a globular cluster orbiting the Andromeda galaxy M31 Assume cluster mass of M = M with a velocity v M = 250 km/s For globular clusters we can use C = 76 If the galaxy is 13 Gyr old we obtain r max = 3.7 kpc