1. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw 8. Galactic rotation 8.3 Rotation from HI and CO clouds 8.4 Best rotation curve from combined data 9. Mass model of the Galaxy

2. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw Galactic rotation from HI and CO clouds For disk objects in a differentially rotating galaxy, The radial velocity, V R is a maximum at point P along a given line of sight, when α = 0 and R min = R 0 sinl.

3. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw At point P one obtains Procedure: For a number of longitudes l, find V R (max) for 21-cm radiation from HI clouds along that line of sight, and hence obtain Θ(R). This works for R<R 0 only.

4. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw HI cloud radial velocities along a given line of sight

5. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw HI radial velocities are a maximum in this direction for gas at position A, where the velocity is about 70 km/s. The cloud at A has a galactic orbital radius of R 0 sinl

6. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw For R>R 0 (directions 90º < l < 270º) there is no maximum in radial velocity. But for R>R 0 we can use CO in dense molecular clouds. These are often associated with star-forming regions, and there are ways to estimate distances to stars and hence to the CO Then obtain the outer parts of the galactic rotation curve from Note that when distance d to a cloud is known, then both angle α and orbital radius R are also known

7. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw Rotation curve for the Galaxy The best rotation curve Θ(R) for the Galaxy comes from combining radial velocity data for stars, HI clouds and CO in dense molecular clouds Result: Θ varies little with radius, though there are dips at around R = 3 kpc and 10 kpc Mean velocity of galactic orbits is Θ ~ 220 km/s This “flat” rotation curve is a major surprise Expected result, if galactic mass is from stars, is Θ ∝ R -½

8. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw Galactic rotation curve Θ(R) based mainly on CO. The “flat” (i.e. nearly constant) curve is evidence for extra mass in the form of dark matter in the Galaxy

9. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw Rotation curve for the Galaxy, based mainly on HI clouds

10. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw The galactic rotation curve R (kpc) Θ (km/s) P (10 6 yr) ω (rad/Myr) 1 220280.22 2 205600.10 3 195950.066 4 215 110 0.055 5 220 140 0.045 7 225 190 0.033 8.5 (R 0 ) 220 240 0.026 10 210 290 0.021 12 225 330 0.019 14 235 370 0.017 16 235 420 0.015

11. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw Mass model for the Galaxy (a) Models with essentially all the mass in the centre of the Galaxy. M mass of Galaxy P orbital period for stars at radius R; P = 2πR/Θ Θ(R) orbital velocity G gravitational constant

12. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw For central mass or point mass models Θ ∝ R -½ is not observed, showing that the Galaxy must move under the gravitational influence of a distributed mass.

13. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw (b) Models with a uniform star density everywhere This model predicts Θ ∝ R and ω=Θ/R= constant, (solid body rotation) which is also quite different from the observed rotation curve.

14. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw The discrepancy between the observed galactic rotation curve and those predicted by two very simple mass models of the Galaxy.

15. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw The real mass distribution The real mass distribution must be intermediate between a central mass concentration and a uniformly distributed mass. That is the mass is distributed throughout the Galaxy, but the density is decreasing outwards. The fundamental problem: The density from the masses of all the observed stars plus ISM also decreases outwards, but far more rapidly than can account for a flat rotation curve.

16. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw The rotation curve that would be produced by bulge and disk stars is not enough to produce the flat curve actually observed. A large dark matter halo must also be invoked.

17. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw Mass model of the Galaxy (M. Schmidt, 1965) Radius surface density mass inside cylinder R (kpc) σ (M ⊙ /pc 2 ) of radius R (10 9 M ⊙ ) 1. 1097 11 3. 64631 5. 42157 8.518198 10. 114 111 12. 66 123 14. 42 131 16. 28 138

18. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw Maarten Schmidt’s mass model of 1965 was a fairly early attempt. It had a total galactic mass inside a radius of 18 kpc of 1.43 × 10 11 M ⊙ More recent models give several times this mass, or about 3.4 × 10 11 M ⊙ Of this mass, dark matter in the halo may account for more than 2 × 10 11 M ⊙ while the remainder is observable mass in the form of stars or ISM.

19. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw The nature of dark matter? This is one of the big unsolved problems of astronomy. The dark matter in the Galaxy and other galaxies may be: lots of very low mass and low luminosity stars, such as red dwarfs, brown dwarfs or white dwarfs numerous black holes some form of matter, possibly as subatomic particles which are so far unknown to science

20. ASTR112 The Galaxy Lecture 5 Prof. John Hearnshaw End of lecture 5