7. globular clusters 8. galactic rotation 8.1 from halo stars

ASTR112 The GalaxyLecture 4

Pro

f. J

ohn

Hea

rnsh

aw

7. Globular clusters8. Galactic rotation 8.1 From halo stars 8.2 From disk stars – Oort’s constant, A

ω C

entaurii47 T

ucan

ae


Pro

f. J

ohn

Hea

rnsh

aw

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)


Pro

f. J

ohn

Hea

rnsh

awThe two brightest globularclusters, 47 Tuc (left) andω Cen (above)


Pro

f. J

ohn

Hea

rnsh

aw

The galactic distribution of globular clusters


Pro

f. J

ohn

Hea

rnsh

aw

Some well-known globular clusters

name V distance (pc) diameter47 Tuc 4.0 5100 10ω Cen 3.6 5000 20M3 6.4 13000 13M5 5.9 8500 12M13 5.9 7700 11M22 5.1 3000 9


Pro

f. J

ohn

Hea

rnsh

aw

M5 colour-magnitude diagram


Pro

f. J

ohn

Hea

rnsh

aw

M3 colour-magnitude diagram


Pro

f. J

ohn

Hea

rnsh

aw

Colour-magnitude diagram for the globular clusterM13


Pro

f. J

ohn

Hea

rnsh

aw

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


Pro

f. J

ohn

Hea

rnsh

aw

Distances to globular clusters

Distances can best be obtained by fittingthe horizontal branch stars to MV = +0.6.

This absolute magnitude is known becauseglobular HB contain a pulsating star calledRR Lyrae stars. These are also found in the field near Sun, and their distances measured by a variety of methods.


Pro

f. J

ohn

Hea

rnsh

aw

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


Pro

f. J

ohn

Hea

rnsh

aw

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


Pro

f. J

ohn

Hea

rnsh

aw

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


Pro

f. J

ohn

Hea

rnsh

aw

The so-called “asymmetricdrift” showing the distribution of stellar radial velocitiesfor stars in the solar neighbourhood. The Popn

II stars have high velocitiespreferentially in thel = 270º direction, a resultof galactic rotation


Pro

f. J

ohn

Hea

rnsh

aw

Galactic rotation parameters

Circular velocity: Θo = 220 km/s Radius of solar orbit Ro = 8.5 kpcAngular velocity ωo = Θo / Ro = 26 km/s/kpcOrbital 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.


Pro

f. J

ohn

Hea

rnsh

aw

The radial velocity, VR,relative to the Sun, of adisk star in a circularorbit about the galactic centre depends on itsdistance d from the Sun.For a given line of sightthe radial velocity is amaximum when the angleα is zero, d = Ro cosl.


Pro

f. J

ohn

Hea

rnsh

aw

From disk starsRadial velocity of star relative to Sun is

Sine rule

Now

Hence

lV sincosOR

OO

O cos)90sin(sinRRR

l

OOO/; / RR

lRlR

lRRVT

sinsin

sincos

OOO

OO


Pro

f. J

ohn

Hea

rnsh

aw

ldRR

RRdRd

cos)(

)(

O

O

O

O

ldRd

Rd

lRlddRd

lRRRdRd

V

2sin21

sin.cos

sin).(

O

O

O

OO

O

R

Approximations:

Therefore


Pro

f. J

ohn

Hea

rnsh

aw

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 galacticplane and is A = 15 km/s/kpc.

O

O21

dRd

RA

lAdVR

2sin


Pro

f. J

ohn

Hea

rnsh

aw

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 ofgalactic longitude, l


Pro

f. J

ohn

Hea

rnsh

aw

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


Pro

f. J

ohn

Hea

rnsh

aw

End of lecture 4End of lecture 4

7. globular clusters 8. galactic rotation 8.1 from halo stars

Documents