29:50 Modern Astronomy
Fall 1999
Lecture 21 ...October 13, 1999
The Structure of the Milky Way Galaxy I

A week from today will be ``group activity''. Check Web Site for sample exam
Watch the skies! Watch the skies! Astronomy may have interfered with Seinfeld! Look at space weather today from SOHO Web page.

The Structure of the Milky Way galaxy

When you look out at the night sky, you see many stars. Clearly these stars are fundamental units in some larger system. What is the size and shape of this system? What processes govern its evolution? How old is it?

I will talk about these subjects today. If you are a person who needs instantaneous gratification and can't wait for the answer, you can look at the poster at the front of the room. Or you can look at the picture opposite the Acknowledgements near the beginning of your textbook.

It turns out we can learn an awful lot about the structure of the Milky Way from very simple observations. When you go out in a dark sky, you can see the Milky Way as a band of light across the sky.
Drawing on blackboard of simulacrum of Milky Way.
It is reasonable to conclude (correctly, it turns out) that this faint light is the aggregate light of many stars to faint to be individually made out.
The interpretation of this basic observation is simple. We are living in a disk-shaped system of stars. When we are looking in the plane of the Milky Way, we are looking into the plane of this disk. When we are looking far from the Milky Way, in the direction of the contellation Virgo for example, we are looking through the ``short side'' of the disk, and therefore don't see many stars.
Drawing on blackboard.

You can even do a little better than this with just naked eye observations without any numbers or mathematics. The Milky Way is not uniform in its brightness. It is much brighter in the direction of the constellation Sagittarius than it is towards Orion. The winter Milky Way is quite faint, while the summer Milky Way is much brighter.
Point to poster.

The interpretation of this is also simple; the center of the galaxy is in the direction of Sagittarius, and we are not near the center of things. An analogy would be looking at the lights at night in a great city. If you are out in the suburbs, you see a lot of light in the direction of downtown, and relatively faint light as you look out towards the countryside.

To progress further, we need to make some measurements and use some numbers. First, what is the thickness of this disk? You cannot define the thickness of the galactic disk in the same way that you would define the thickness of a book. Rather, you define it like you would the diameter of a forest. In the middle of the forest there is a high density of trees (large number of the number of trees per acre) . As you move out from the center of the forest the density of trees declines. When the density is zero, you say that you are completely out of the woods.

We can do something similar with stars. We have talked about how we can measure the distances to stars. We can look at their spectra, determine their spectral type and thus absolute magnitude, and then from measurement of their apparent magnitude determine their distance. We can then (at least in our minds) construct a 3D model of the stellar distribution, and see how the density of stars (# stars per cubic parsec) depends on height above or below the plane of this disk.
Drawing on blackboard of N(z) relation.

It is found that this thickness (technically referred to as the scale height of the stellar density) depends on the type of star. For stars like O stars, it is only about 50 parsecs. For stars like the Sun, the scale height is 350 parsecs. These numbers are extremely important right off the bat. When we look in the plane of the Milky Way, we can see objects at much greater distances.
Image of chi and h Persei, distance 2300 parsecs.
Image of Rosette Nebula, distance about 1200 parsecs.
This shows that the galactic disk is very narrow (thin) compared to its diameter, because we can see objects a couple of kiloparsecs away in the galactic plane, and we know there is more beyond.

Because of the presence of interstellar dust, we cannot see objects much more distant than a couple of kiloparsecs in the galactic plane. We certainly cannot see all the way to the galactic center in Sagittarius.

The final question has to do with the diameter of this disk. How far is it to the center, somewhere off in the direction of Sagittarius? The answer to this was a long time coming. The first value was obtained in the 1930's. I will describe the ``classic'' method of determining this distance. In the last decade, a number of entirely independent methods have developed which have refined this distance. I will talk about those too.

There are objects in the sky called globular clusters. I have talked about them some before. They are spectacular objects to see in small telescopes because they appear as big balls of stars.
Image of M13, other globulars.
This was known for a long time, but people didn't know how far away they are because in the 1920's people weren't sure what kind of stars they were looking at.

There is an interesting thing about globular clusters, which an amateur astronomer quickly comes to realize. They are great summertime objects. Almost all of them are in the early to mid evening sky in the summer when it is pleasant to be outdoors with your small telescope. There almost none to be seen in the winter night sky when you wish you had taken up model trains as a hobby.

The physical reason for this is that they are lying in the direction of the constellation of Sagittarius. This means most of them must be closer to the galactic center than we are.
Transparency showing globular cluster distribution, real sky and imaginary sky in which we are at the center of the galaxy.

It was then realized that if one could measure the centroid of the globular cluster distribution, you would presumably have the location of the Milky Way galaxy. The missing piece was a way of determining the distances to these globular clusters.

This ``missing link'' came about in the 1920's with the discovery of an important property of a kind of star called a Cepheid variable. These stars are named after the prototype of their class, the star Cephei. These stars change in brightness in a periodic fashion. They have a rhythm of their own. From fairly simple observations, in fact ones you could make visually through a telescope, one can determine the period of variability, which ranges from a couple of days on the short end, to perhaps one hundred days on the long end. One of the two brightest in the star Aquilae, which is on your SC1 chart. It has a period of about one week, and its magnitude range is from about 3.4 to 4.4. You can actually see the variations by observations with the naked eye.

Diagrams about Cepheids are given on pp445 and 446 of your textbook. This much was known for quite a while. The breakthrough came in the 1920's when two Harvard astronomers, Henrietta Leavitt and Harlow Shapley, found that there was a Period- Luminosity relation for Cepheids. In words, the Period-Luminosity relation says the longer the period of variations, the brighter is the star. This makes Cepheids ideal distance indicators. From measurements of the period of the variations, you can infer the absolute magnitude. If you know the absolute magnitude of a star, you know its distance.

With this knowledge, astronomers were able to measure the distances to globular star clusters. They are a long ways away. The brightest of the bunch in the northern hemisphere, M13 is 6400 parsecs away. The most prominent one in the whole sky is 4900 parsecs distant. The most distant ones known are about 15000 parsecs away.
Point to poster showing globulars.

with this information, astronomers were able to determine the centroid of the globular cluster distribution, and thus the center of the Milky Way galaxy. This distance is about 8500 parsecs. The present day uncertainy on this number, i.e. the extent to which the different methods disagree, is about 1000 parsecs.

This is a huge distance. To give an idea, let's go back to our scale model of the sky. Put the universe in a giant shrinking machine so 1 astronomical unit is 1cm. The nearest star is then 2.7 km away, or 1.6 miles. On this scale, the distance to the galactic center is 18500 km, or 3 Earth radii!

I want to talk about a more modern, and direct method of determining the distance to the galactic center. It also permits me to inject some new physics that we will use a lot in the rest of the course. The new physics is the Doppler Effect.

The Doppler Effect has to do with moving sources of radiation, and the wavelength that is measured by an observer. Let's let a source emit radiation (sound waves, electromagnetic waves, the works). The source emits radiation at a wavelength . If the source is in motion with respect to us (either by us being stationary and it moving, it stationary and us moving, or a combination of the two), we measure a wavelength which is different from . The formula relating , , v, and the speed of the wave c is

This equation is defined such that a positive velocity means motion away from us, and a negative velocity means motion towards us.

Illustrations of Doppler Effect.

Let's work out a couple of examples.
(1) The Earth moves around in its orbit at a speed of 30 km/sec = meters/sec. Let's say we observe a star (in the plane of the ecliptic) which has a spectral line ( ) of 650.000 nanometers. How much do we see it shift back and forth in wavelength?

When the Earth is moving towards the star, we see a ``blue shift'', or the wavelength is shorter than the rest wavelength. So . We have:

(2) Let's say we observe this same spectral line with a rest wavelength of 650.000 nm in another star. We observe it in a star at a wavelength nanometers. What is the motion of this star with respect to us?

First of all, the wavelength is longer than the rest wavelength so
Question for audience: is it moving towards us or away from us?
Let's grind out the numbers:

or 462 kilometers/sec.

Doppler Weather Radars use the Doppler Effect to measure the speed at which raindrops are falling.

What does this have to do with the distance to the center of the galaxy? With radio telescopes, we can see right down to the center of the galaxy. The reason for this is that the interstellar dust doesn't absorb radio waves like it does light waves. We see an interesting collection of objects close to the galactic center. A picture of them is given on p526 of your textbook.

What was observed about 15 years ago was an expanding shell of material in the galactic center.
Cartoon of expanding shell at galactic center.
This shell emitted radiation at a well-defined wavelength. We could see Doppler shifts of the spectral lines so we could measure the speed of expansion. It was also getting bigger in angular size. Let's simplify the problem and assume it started expanding from zero and some time t later had an angular size . This angle is given by:

So if we measure V from the Doppler Effect, the time t over which the expansion has occurred, and is the angle through which the source has expanded, we can solve for the distance to the galactic center.

When this measurement was carried out, it resulted in our value for the distance to the galactic center of 8.5 kiloparsecs.

Let's put all this information together in a ``front and side view'' of the Milky Way galaxy.
Transparency from Figure 22-28 of your textbook.
Here we see ourselves about 8.5 kiloparsecs, or 30,000 light years, from the center of the disk system. Viewed from side, we can see the disk to be about 100-200 parsecs thick. Viewed from the side we can also see the system of globular star clusters; as I mentioned before, there is also a ``population'' of stars which has a galactic distribution like the globular star clusters. In astronomical jargon these are referred to as the Population II stars, and they have ages of 10 - 15 billion years old. Fortuitously one of them, the bright Arcturus, is only about 11 parsecs away. Take your SC1 chart and find it!

Next, we'll start talking about how we can fill in the ``face-on'' picture of the Milky Way.

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