1. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw 7. Globular clusters 8. Galactic rotation 8.1 From halo stars 8.2 From disk stars – Oort’s constant, A ω Centaurii 47 Tucanae

2. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw Globular clusters Large star clusters of roughly spherical shape Each cluster contains 10 5 to 10 6 stars Found in galactic halo and bulge (Pop n II) ~125 known but as many as 500 may exist Centre of distribution defines galactic centre (Shapley, 1918)

3. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw The two brightest globular clusters, 47 Tuc (left) and ω Cen (above)

4. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw The galactic distribution of globular clusters

5. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw Some well-known globular clusters nameVdistance (pc) diameter 47 Tuc4.0510010 ω Cen3.6500020 M36.4 13000 13 M55.98500 12 M135.9770011 M225.13000 9

6. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw M5 colour-magnitude diagram

7. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw M3 colour-magnitude diagram

8. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw Colour-magnitude diagram for the globular cluster M13

9. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw HR diagrams of globulars Red giant branch, nearly vertical, to M V = –3 Horizontal branch, mainly A stars, M V = +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. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw Distances to globular clusters Distances can best be obtained by fitting the horizontal branch stars to M V = +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. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw 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 × 10 9 years old

12. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw 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. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw Galactic rotation From halo stars: Mean V R 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. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw The so-called “asymmetric drift” showing the distribution of stellar radial velocities for stars in the solar neighbourhood. The Pop n II stars have high velocities preferentially in the l = 270º direction, a result of galactic rotation

15. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw Galactic rotation parameters Circular velocity: Θ o = 220 km/s Radius of solar orbit R o = 8.5 kpc Angular velocity ω o = Θ o / R o = 26 km/s/kpc Orbital period P o = 2π/ω o = 240 × 10 6 yr Note that ω = ω(R) → differential rotation. ω = constant would imply solid-body rotation, but this is not observed.

16. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw The radial velocity, V R, 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 = R o cosl.

17. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw From disk stars Radial velocity of star relative to Sun is Sine rule Now Hence

18. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw Approximations: Therefore

19. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw 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. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw 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. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw 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. ASTR112 The Galaxy Lecture 4 Prof. John Hearnshaw End of lecture 4