In this exercise we will make our own HR diagrams by "observing" various samples of nearby stars.

There are basically 2 ways that one could choose stars in the sky for measurement.

Selection by apparent brightness that is we only select the brightest appearing stars in their sky and measure their parallaxes and their colors.
Selection by position in the sky. choose a specific region of the sky and measure every star you can in that region.

In the simulation that you will be using, stars are represented by colored dots. The size of of the dot represents the apparent brightness of the sky (i.e. how much flux we receive on earth from that star). Remember, to get the intrinsic brightness (Luminosity) we must determine the distance - using stellar parallax measurements using F~L/d² or more precisely:

Luminosity = 4 d²f

Where f = the apparent brightness or flux of the star as measured on the earth and
d = the distance.

The color of the dot represents its color (or more properly, its B-V index).

Now remember, we already know what the "answer" looks like in terms of how the HR diagram should appear. That was presented in the previous lecture. Now we want to see if we can reproduce this "answer" by various sampling strategies.

We start up with by selecting a sample to measure on the basis of their apparent brightness. That is, we will make parallax measurements for the 30 brightest appearing stars in the sky.

Start the simulator (you can resize the simulation window)

Procedure:

Step 1:

Check the specify a catalog.
Select 30 bright stars as the catalog from the drop down list
Select a star for measurement by clicking on the star. The screen will re-center around that star annd the name of star will then appear on the screen and in the information panel.

Proceed to step 2:

(Scroll around the screen to select additional stars, or click on the specify a star check box and just select the stars sequentially through that list. (its probably easiest to do this). Note that you will need to keep track of what star you measured - however, if you measure the same star again (without knowing it) you will likely get slightly different results due to random measuring error!)

Now click on Step 2 to measure the parallax for the selected star.

You're now measuring the parallax of that star. Please do not adjust the error or the Plate parameter

Let a few orbits pass

When you think you have a well determined parallax, click on that value in the histogram you will see a point (its small) added to the HR Diagram preview window below the histogram.

Go back to Step 1 to select another star and randomly select about 20 of the 30 stars in this catalog for measurement. Hence your HR diagram should have 20 points on it.

Proceed to step 3:

After you have completed your measurement of 20 stars click on Step 3.

Compare your diagram to "the answer" shown below. What do you notice? Can you identify the main sequence in your data?

Now we repeat this exercise but this time select the catalog called 20 Nearby Stars. Compare the diagram for that sample to the one above - does it make more sense?

What we have now just learned is that the only representative sample that you can make in astronomy is a volume limited sample. That is, define a certain distance, and measure every object you mind within that radius.

As can be seen, for the 20 nearby stars they are either red lower main sequence stars, or white dwarfs. For the sample of 30 bright stars, these commons stars are mostly missing. Therefore, measuring a sample of only the brighest appearing stars is biased and misleading.

Discussion/Questions

How are these two catalogs of stars different on the HR diagram? Roughly, what is the most common type of star in terms of some combination of of dim, luminous, cool, hot?
Can you tell what spectral type these would be?
The figure to the right shows a volume limited sample that encompasses about 1000 stars. Which is the most common kind of star?
Be able to know how to read a Hertzsprung-Russell Diagram.
1. What do the vertical and horizontal axes represent? What is the direction of increasing quantities? What are the ranges in these scales (approximately)?
2. Where are the hot luminous (bright) stars?
3. Where are the hot dim stars?
4. Where are the cool dim stars?
5. Where are the cool bright stars?
6. What does a volume limited sample look like on the HR diagram?
7. Which stars are the most rare? Which are the most common?
8. What does a brightness-limited sample look like on the HR diagram?
Given that energy output increases as T⁴, it would seem logical that all stars with hot surface temperatures should be brighter than all cooler stars. But as the HR diagram shows (above), there are some stars with a hot surface temperature, but very dim. Moreover, there are a few red stars with large luminosities (really bright). So why is that? The relationship that energy output always increases with temperature⁴ is true for all objects with a temperature. Is something else going on?
You should know about the Hipparchos satellite mission (see end of 3C). Other than measuring the distances to several stars, why was it so important to stellar astronomy?