7. Globular clusters 8. Galactic rotation 8.1 From halo stars

1. 7. Globular clusters 8. Galactic rotation 8.1 From halo stars 8.2 From disk stars – Oort’s constant, A 47 Tucanae ω Centaurii

2. Globular clusters • Large star clusters of roughly spherical shape • Each cluster contains 105 to 106 stars • Found in galactic halo and bulge (Popn II) • ~125 known but as many as 500 may exist • Centre of distribution defines galactic centre • (Shapley, 1918)

3. The two brightest globular clusters, 47 Tuc (left) and ω Cen (above)

4. The galactic distribution of globular clusters

5. Some well-known globular clusters name V distance (pc) diameter 47 Tuc 4.0 5100 10 ω Cen 3.6 5000 20 M3 6.4 13000 13 M5 5.9 8500 12 M13 5.9 7700 11 M22 5.1 3000 9

6. M5 colour-magnitude diagram

7. M3 colour-magnitude diagram

8. Colour-magnitude diagram for the globular cluster M13

9. HR diagrams of globulars • Red giant branch, nearly vertical, to MV = –3 • Horizontal branch, mainly A stars, MV = +0.6 • Subgiant branch, mainly F and G stars, covering • wide range in luminosity • Main sequence stars: cool red dwarfs (G, K, M) • Asymptotic giant branch: luminous cool red • giants, evolving off the horizontal branch, • with C or O cores and a He-burning shell

10. Distances to globular clusters Distances can best be obtained by fitting the horizontal branch stars to MV = +0.6. This absolute magnitude is known because globular HB contain a pulsating star called RR Lyrae stars. These are also found in the field near Sun, and their distances measured by a variety of methods.

11. Ages of globular clusters • Ages are derived from the theory of stellar • evolution, based on the predicted rate of • nuclear reactions in stellar cores. • In practice, shape of HR diagram, especially • location of the cluster turn-off point, is fitted • to theoretical isochrones. • Result: globular clusters are all 12 to 15 × 109 • years old

12. Conclusion • Globular clusters are among the first objects to • form in the Galaxy • They often have very low metal abundances, • with M/H in range 10-1 to 10-3 of the solar value • They formed at the time the Galaxy comprised • a large mass of H and He gas that was under- • going a rapid initial gravitational collapse

13. Galactic rotation • From halo stars: • Mean VR of 70 globular clusters is about • 200 km/s towards l = 270º • This is evidence that the Sun and other disk • stars are moving at about 200 km/s towards • l = 90º, as consequence of galactic disk • rotation

14. The so-called “asymmetric drift” showing the distribution of stellar radial velocities for stars in the solar neighbourhood. The Popn II stars have high velocities preferentially in the l = 270º direction, a result of galactic rotation

15. Galactic rotation parameters Circular velocity: Θo= 220 km/s Radius of solar orbit Ro = 8.5 kpc Angular velocity ωo = Θo / Ro = 26 km/s/kpc Orbital period Po = 2π/ωo = 240 × 106 yr Note that ω = ω(R) → differential rotation. ω = constant would imply solid-body rotation, but this is not observed.

16. The radial velocity, VR, relative to the Sun, of a disk star in a circular orbit about the galactic centre depends on its distance d from the Sun. For a given line of sight the radial velocity is a maximum when the angle α is zero, d = Rocosl.

17. From disk stars Radial velocity of star relative to Sun is Sine rule Now Hence

18. Approximations: Therefore

19. Define Oort’s constant for galactic rotation as: Hence A is a measure of the amount of differential rotation in the Galaxy. The best value for Oort’s constant A comes from distant B-type stars and Cepheids in galactic plane and is A = 15 km/s/kpc.

20. For stars in the disk of a given distance d, the radial velocities (measured by the Doppler effect in stellar spectra) show a double sign wave as a function of galactic longitude, l

21. Radial velocities of HII regions are plotted as a function of galactic longitude. The plot shows a double sine wave, like for disk stars, but with some deviations

22. End of lecture 4