The above diagram is "the answer" in that this is the HR diagram for the parallax sample, when a representative sample of stars is chosen for measurement.

The data source is the Third Catalog of Nearby Stars.

Please notie the following characteristics of this solution.

• The yellow square represents where stars just like the Sun inhabit this diagram. Most of the main sequence stars in this sample are cooler and less luminous than the sun, in fact. most of the stars have luminosities less than 1% of the sun. All representative samples would show this population. If this population is not there, your sample is biased. (we will understand later today why these stars are the most numerous in the galaxy).

• There are extremely few Red Giants in this sample. These stars are Rare!

• There are not many stars on the main sequence that are hotter and more luminous than the Sun.

• Main sequence stars with luminosities greater than 10 times that of the sun are quite rare.

• There is another, less populated sequence of blue (hot stars) but with luminosities of 1/100 to 1/10,000 that of the sun. We will later see that these are very evolved stars and our Sun is destined to inhabit this part of the diagram when its nuclear fuel is exhausted.

Okay, so now let's choose sample and make our own HR diagrams and compare them to the answer above:

There are basically 3 ways that one could choose a parallax sample.

• Selection by apparent brightness
• Selection by apparent color
• Selection by position in the sky.

These features are part of the simulation as a) sky position is determined by scrolling around, b) the size of the dot on the screen is proportional to the apparent brightness of the star and c) the color of the dot represents its apparent color (from blue through red).

Selection by apparent brightness

Start the simulator

Procedure:
1. Check the specify a catalog button
2. Select 30 bright stars as the catalog.
3. Select a star for measurement by clicking on the star. The name of star will then appear. 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)
4. Now click on Step 2 Detector.
5. Your now measuring the parallax of that star. Please do not adjust the error or the Plate parameters.
6. When you think you have a well determined parallax, click on that value in the histogram you will see a point added to the HR Diagram preview window below the histogram.
7. Highlighting Step 3 will show the HR diagram which you can then compare to the solution at the top of this page.
8. Now go back to Step 1 and measure another star, etc, etc. Measure 15 of the available 30 stars in this manner. Just randomly select 15 stars from the drop down list.

9. After you have measured the stars, click the Create a Report button, which you find on Step 3. This should be done when you have finished making your HR diagram.

After doing all of this we are now in a position of comparing HR diagrams.

Now we repeat this exercise but this time select the catalog called 20 Nearby Stars.

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.

The Main Sequence

We have now established that, in the Hertzsprung Russel (HR) diagram, most of the stars populate this diagonal band called the Main Sequence.

Characteristics of the main sequence stars are the following:

Stellar Evolution is relatively simple to understand in basic terms. Here are the key concepts:

1. The evolutionary timescale is entirely driven by stellar mass. Massive stars evolve much more quickly than low mass stars.

2. The fusion rate in a star, which determines its total energy output is extremely sensitive to the core temperature. This is why massive stars burn up faster.

3. Stellar evolution is governed by a constant battle between Pressure (P) and Gravity (G). Keep in mind that a star is just a big ball of gas. Three things can happen:
   • P=G: the star is table; energy generation is occurring in its core This provides gas pressure which prevents the collapse of the star. Each mass has a unique value of P to stablize this which produces a unique core temperature. Thus the core temperature of a 2 solar mass star is larger than for a 1 solar mass star. Higher core temperature produces a much higher fusion rate this can be verified later in the In Class Exercise.

   • P > G: Pressure exceeds gravity and the star (ball of gas) expands.

   • G > P: Gravity exceeds pressure; The star (ball of gas) collapses.

   Note: Expanding bags of gas cool; collapsing bags of gas heat Ideal Gas Law.

4. When a star is generating energy in its core, it is stable (P=G).

5. If the star is not generating energy in its core, it is unstable and either must expand or collapse.

6. Low Mass (stars less than 4 Solar Masses) Evolution:
   1. A ball of hydrogen collapses until hydrogen fusion in the core stabilizes the star against further collapse. The star is now a main sequence star . All main sequence stars, regardless of their mass, fuse hydrogen in their cores. All main sequence stars are stable (P=G) and their core is at constant temperature.

   2. Fusion occurs via the proton-proton chain (see the ancient animations as hydrogen turns into helium in the core. This can be schematically shown as:
      

   3. When the core becomes pure helium, the temperature will be too low for helium fusion to occur. So, core energy generation stops and now G > P and the core begins to collapse and HEAT . This transition looks something like this:
      Animated view of Stellar Evolution in the HR Diagram Study this!