Main observations to explain

1. the rotation curve: speed vs distance from galactic centre
2. spiral structure
3. stellar populations: galactic halo, disk and centre

Note that only broad features of these observations are established with certainty. E.g. the galaxy has a spiral structure, but there isn't agreement on the structure of spiral arms.

GAIA - upcoming observations

• GAIA is a European Space Agency (ESA) mission.
• Launched 19 December 2013; orbits L2 point
• will map positions of 1 billion stars: position and motion
• covers about 1% of stars in the Milky Way

GAIA - diagram

Source: ESA Copyright: ESA

The Milky Way - rotation

Red - theory; Blue - observed; Yellow - the Sun

Source: Brews ohare CC-BY SA 3.0

Explaining the rotation curve

We need to explain the rotation curve, specifically these two features:

1. Higher than expected speeds near the galactic centre.
2. Flat curve beyond the Sun's orbit.

Keplerian orbits

Kepler's third law states that the cube of the radius r is proportional to the square of the period T and the mass M about which the body is orbitting:

r³ = constant × M T²

where M is the mass.

Note: we're considering a circular orbit for simplicity, but the argument holds for an elliptical orbit too.

Keplerian rotation curve

The circumference of a circle is 2π times r, so the speed in an orbit is given by dividing it by the period:

v= 2πr / T

Then, using Kepler's third law, we can substitute for T to give:

v² = constant × M / r

This tells us two important things:

1. The greater the mass M, the greater the speed.
2. The greater the radius r, the smaller the speed.

Mass distribution

• Kepler's laws were developed for the solar system: the mass is concentrated at the centre of the solar system in the Sun.
• So the fact that 2 is not observed tells us that this is not a good assumption for the Galaxy.
• The Milky Way must have a signficant mass that is located outside the galactic centre, in the disk.
• We cannot see this matter, hence the term "dark matter".
• This explains why the rotation curve is flat, rather than decreasing beyond the Sun's orbit.

Galactic centre

• The higher than expected speeds near the galactic centre indicate there is more mass concentrated there than we can see.
• The amount of mass within the volume is consistent with there being a supermassive black hole.
• The speeds suggest a value of M that is 4.1 to 4.5 billion solar masses.
• An intense radio emission source, called Sagittarius A, is further evidence of a compact object at the galactic centre.

Spiral arms - simplistic

• Imagine a galaxy exhibited straight arms or "spokes".
• Stars at different radii have different periods.
• Stars near the centre will complete one orbit in less time than stars further out.
• So it follows that the "spokes" could not last.
• The spokes would bend, leading to curved spiral arms.
• But this whole explanation is too simplistic - spiral arms are not a fixed structure. Consider waves...

Wave motion

• When a wave moves across water, the water is not moving horizontally, but up or down.
• When a sound wave travels through air, the molecules in the air are not travelling with the wave; they move back and forth as the wave passes.
• When you flick a light switch, the signal travels along the wire as an electromagnetic wave (at the speed of light), but the electrons in the wire drift along much more slowly.

Wave - animation

Source: Penn State University CC BY-NC 3.0

M51 - photograph

Source: NASA/ESA Public Domain

Spiral arms as density waves

• Spiral arms are thought to be the product of density waves moving around the galactic disk.
• The Sun is currently in a spiral arm, but this is just temporary.
• The spiral arm takes approx. 50 million years to "orbit" in the galaxy.
• The Sun takes 240 million years to orbit in the galaxy.

See animations here: en.wikipedia.org/wiki/Density_wave_theory

Spiral arms and star formation

• If the density wave theory is correct, spiral arms are over-dense regions of the galaxy.
• They should therefore have an enhanced rate of star formation.
• Observational evidence agrees: there are more high mass, luminous and therefore young stars in the spiral arms than between them; partly why spiral arms are brighter.

M81 - spiral galaxy

Source: NASA/ESA Public Domain

M81 - caption

M81 may be undergoing a surge of star formation along the spiral arms due to a close encounter it may have had with its nearby spiral galaxy NGC 3077 and a nearby starburst galaxy (M82) about 300 million years ago.

M81 is one of the brightest galaxies that can be seen from the Earth. It is high in the northern sky in the circumpolar constellation Ursa Major, the Great Bear. At an apparent magnitude of 6.8 it is just at the limit of naked-eye visibility. The galaxy's angular size is about the same as that of the Full Moon.

This image combines data from the Hubble Space Telescope, the Spitzer Space Telescope, and the Galaxy Evolution Explorer (GALEX) missions. The GALEX ultraviolet data were from the far-UV portion of the spectrum (135 to 175 nanometers). The Spitzer infrared data were taken with the IRAC 4 detector (8 microns). The Hubble data were taken at the blue portion of the spectrum.

(Edited from en.wikipedia.org/wiki/File:Sig07-009.jpg)

Populations I, II and III

Stars are placed into one of three possible populations:

• Population I stars:
  • have the highest metallicity
  • common in the galactic disk
  • formed more recently, e.g. the Sun
• Population II stars:
  • stars have low metallicity
  • common in globular clusters in the galactic halo
  • formed early in the Universe
• Population III stars:
  • have near zero metallicity
  • formed from pristine Big Bang material
  • hypothetical, only indirect observational evidence for them

Formation of the Milky Way

• The locations of the different populations give us clues to how the galaxy formed.
• The fact that the older population II stars are to be found in the galactic centre and halo tells us that these features formed first.
• The disk and the spiral arms are a more recent development.
• The spiral arms may be the result of collisions with other galaxies.
• There is also some evidence that there are two disks, an older thicker disk and thinner younger disk embedded within it.
• To understand galaxy formation better, we must look to a wider population of galaxies.