|Chapter 15. Galaxies and the Foundation of Modern Cosmology
A Universe of Galaxies
The Milky Way is an example of a disk, or spiral galaxy. As late as the 1920s, however, it was not proven that these "spiral nebulae", as they were known, were actually outside of our Galaxy.
In 1920 there was a famous public debate between Harlow Shapley and Herber Curtis about the nature of the spiral nebulae.
It was Shapley's contention that the spiral nebulae were within the Milky Way Galaxy and that the Milky Way Was the extent of the entire Universe.
Size of the Galaxy that he himself had calculated, some 32 kpc in diameter. Actually, he estimated the size to be almost twice too big because he did not take into account the dimming effects of dust in the Galaxy.
Spiral nebulae were directly observed to be spinning, i.e. proper motion was seen. If these spiral nebulae had measurable spins they must be nearby.
Spiral nebulae were not seen at all in the galactic plane on the sky. This is sometimes called the Zone of Avoidance. Shapley thought that the fact there seemed to be a connection between the plane of the galaxy and the distribution of observed spirals indicated that there is a direct physical connection between them, and that the spirals were therefore associated with the Milky Way (in the same sense that the globular clusters are).
Shapley was basically correct about the size of the Milky Way Galaxy, but the data of spinning was later shown to be in error. No proper motions are detectable.
Curtis argued that the spiral nebulae were actually star systems comparable to the Milky Way Galaxy and at great distances: Island Universes.
He believed the Galaxy to be much smaller than Shapley's measurements.
He noticed that the spiral nebulae had a 10 to 1 ratio in angular size on the sky. He reasoned that if they were all about the same size then the smallest ones on the sky must be 10 times farther than the closest ones, which was necessarily outside his small Galaxy.
Spectra of the spiral nebulae is consistent with a collection of stars rather than of a nebula.
Spirals could be much further if the zone of avoidance is just an obscuration effect from dust in the disk of the Milky Way Galaxy.
Curtis was right for some of the wrong reasons and Shapley was wrong for some of the the right reasons.
In order to settle the debate on the spiral nebulae direct determination of distances to them would be necessary.
The Distance Scale
There are a kind of Red Giant Star whose visible surfaces pulsate with a regular period. These stars can pulsate in radius while they are on the So-called instability strip in the H-R Diagram.
Low-Mass stars that pulsate while burning Helium in their cores are called RR Lyrae stars.
High Mass stars that pulsate while burning several elements in multiple shells surrounding their cores are called Cepheid Variable stars.
Pulstating stars change their Luminosity because their size is changing while the Temperature changes very little at the surface.
Bigger stars will have higher Luminosities and their period of pulsation is longer (they are bigger so it takes longer for their surfaces to rise and then fall back down).
This leads to a relationship between the average Luminosity of the star and it's period of pulsation.
The Period-Luminosity relationship.
If you observe the period of the star's variability then you can determine how Luminous the star is from this relationship. You measure the brightness of the star, and hence you can determine the distance.
In 1924 American Astronomer Edwin Hubble made careful observations of Cephied variables in the spiral nebulae. He found that the Great Nebula in Andromeda was some 600 kpc distant, much greater than the size of the Milky Way Galaxy.
It was then proved that the spiral nebulae were actually galaxies in their own right, and the Universe suddenly became a very, very big place. The Andromeda Galaxy is our nearest spiral galaxy and its light takes 2.5 million years to reach us (the current value for the distance is 770 kpc).
The Distance Ladder:
The Cepheid Period Luminosity Relationship must be calibrated with many Cepheids that are all at the same distance, and that distance must be known through independent means. The Large Magellanic Cloud, a dwarf galaxy orbiting the Milky Way (LMC) contains thousands of Cepheids and is used for this purpose. Distances to the LMC are determined a variety of ways and come up with a variety of answers. It is about 50 +/- 5 kpc distance. The uncertainty in the distance to the LMC propogates throughout the rest of the distance ladder.
One method that is used to determine the distance to the LMC uses the Luminosities of Main Sequence stars within clusters. If you compare the main sequence of a cluster that is farther away than another, then the closer one will appear to be brighter.
Example: The main sequence of the Pleiades Cluster is 7.5 times fainter than that of the Hyades cluster. Since we assume that the stars at the same points in the Main Sequences have the same luminosities this means that the Pleiades if farther away. The distance to the Hyades is known via Parallax to be 46.3 pc.
b = L/(4d2)
bHyades/bPleiades = 7.5 = d2Pleiades/d2Hyades
dPleiades = 126.8 pc
Distances to galaxies are difficult to determine once they are so far away that Cepheid variables or any individual stars cannot be resolved. There have been some relations empirically discovered between the velocities in a galaxy and its luminosity.
It is found that L v4 for galaxies, where v is a velocity measurement. This is called the Tully-Fisher Relationship. How v is measured differs for spiral and elliptical galaxies. So if the luminosity of an entire galaxy is inferred and a brighness measured, again we can find a distance.
There are indeed many other ways to determine distances, but most all use the idea of a "standard candle", i.e. something that you believe you know how how luminous it is and you can determine its distance by measuring its brightness. Examples: White Dwarf Supernovae, Planetary Nebulae and Globular Clusters distributions, The Tip of the Red Giant Branch, Surface Brightness Fluctuations.