Investigating Stellar Classes

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In this section you will combined what you have learned about stellar distances, luminosity and mass to begin to understand why stars are arranged in different luminosity classes. In so doing you will gain insight into how stars evolve and how long stars "live".

The Main Sequence - and the Dominant Role of Mass

Figure 8.10 brings together two critical sets of ideas. The first is how to measure the distances to stars (parallax) and thereby determine the intrinsic brightness of stars (expressed as absolute magnitude). The second critical set of ideas came from spectroscopy which enable us to determine with great precision the surface temperatures of stars. When these ideas are applied to both the brightest stars in the sky as well as the ones nearest to us a very compelling graph (the H-R diagram) can be constructed. One of the most striking patterns in the H-R diagram is the diagonal scatter of stars stretching from upper left to lower right. This is the main sequence and it contains roughly 90% of the stars. If you position the mouse over the image you will see the major luminosity classes. The main sequence comprises the Dwarf or Class V stars.

Figure 8.13 Plot of absolute magnitude versus temperature for both the brightest visual stars (blue) and the nearest stars (green).

Since some of the main-sequence stars are binary systems astronomers can also plot mass as a function of luminosity. This is shown in Figure 8.11

The thin blue lines show how the mass of main sequence stars is related to their luminosity. For example, reading from Figure 8.11 you can conclude that a star 7.2 times as massive as the sun will burn a thousand times brighter than the sun! This can be expressed in a simple mathematical formula called the Mass-Luminosity Relation or: In this relation L represents the star's luminosity and M is the mass, both expressed in solar units. This relation is true only for main-sequence stars. You can use the applet MassLuminosity provided below to investigate this relationship further.

Figure 8.14 Thin blue lines show mass of main sequence stars is related to their luminosity.

Example 8.16 Altair has a luminosity of 10.7 times that of the sun. Estimate the mass of Altair.

Solution: You can re-arrange the Mass-Luminosity relation to be

Altair is approximately twice as massive as the sun.

Exploring the Other Luminosity Classes

Use the applet HR Diagram Explorer to investigate how the following properties of radius and luminosity vary as you change location on the H-R diagram. In particular we want to look at how the density of stars changes across the HR diagram - the result may surprise you!

Let's now consider the following worked example in which we can compare 3 stars from different luminosity classes

Example 8.17 Compare the average density of the Sun, Capella and Deneb. Use the following data to assist you:

Solution: Use the HR Diagram Explorer to determine the following:

Since density is defined as Mass/Volume we can calculate the average density for each star relative to the sun by setting up the following ratios (the Greek letter r "rho" is commonly used to denote density.)

If we use solar units then the ratios become:

So what does this mean? The sun is by far the most dense of the three stars! It is almost 250 times as dense as Capella and nearly 40 thousand times as dense as Deneb! BUT - before you conclude that the sun is "unusual" with respect to density you should investigate the regions below the main-sequence line. We will do that in a future chapter. There you will encounter objects millions of times denser yet than the sun!

Figure 8.15 summarizes what you have just learned about how the average density of stars varies across the HR diagram. As you will learn in a future section, the HR diagram tells us a great deal about how stars evolve and how their structure changes over time.

Figure 8.15 How density varies across the HR diagram

Star light, star bright - first star I see tonight

To conclude this section lets consider how the stars we see at night are related to our closest stellar neighbours. The answer to this may surprise you. Study Figure 8.16. As you move the mouse over the image it will toggle between the (apparently) brightest stars in the sky and the few dozen or so nearest stars. What do you notice?

Figure 8.16 Rollover image contrasting brightest stars with nearest stars.

Most of the stars that you see at night are in the upper half of the HR diagram. You see them because they are very bright and many can be seen at great distance. On the other hand, most of the nearby stars are in the lower half of the HR diagram and are too faint to be seen with the unaided eye. Tables 8.3 and 8.4 show the 25 brightest and 25 nearest stars respectively. While you are familiar with many of the stars in Table 8.3, you likely only know one or two of the stars listed in Table 8.4.

An important problem in astronomy is to try and determine the proportion of stars of various spectral classes. If you went only on the basis of the stars you can see with the unaided eye you would erroneously conclude that most are O - F class stars. This bias (due to the fact that very bright stars can be seen at great distance) is called a selection effect. When a more careful sample of stars is taken, based on distance from us, we get a much better idea of the true proportion of spectral types. By far, the majority of stars are less massive than our sun. This is shown in Figure 8.17.

Figure 8.17 Stellar Mass Distribution

Example - Looking in the Direction of Orion

To help illustrate the difference between what you see and what is "actually out there" look at the following roll-over image of the sky in the direction of Orion. As you roll-over the image you will see the nearest stars high lighted.

Figure 8.18 Rollover image showing nearby stars in the direction of Orion.

Most of the stars in the "nearby" image are too faint to be seen with the un-aided eye.

The followiing tables summarize the distinction between "brightest" and "nearest" stars.

Average distance of 25 brightest stars = 350 ly

Average distance of 25 nearest stars = 9.5 ly

Practice

1. A binary star is found to contain a Main Sequence star of mass 2.6 Mo and a White Dwarf of mass 0.85 Mo. Estimate the luminosity of the main sequence star. What spectral class is the main sequence star a member of?
2. Why can't you estimate the luminosity of a White Dwarf star by using the Mass-Luminosity relation?
3. Use stellarium to find any relevant information about the 7 brightest stars in Orion. Plot these stars on a copy of the HR diagram
4. Explain what the HR diagram is to a friend. How can you use the HR diaram to help determine the distance of a star?
5. In a random sample of 100 stars found within 1000 ps of earth - how many supergiant stars would you expect to find?
6. Inspect Figure 8.18 above. What do you notice about the colour of the nearby stars?

To understand the physical properties of stars in different luminosity classes

Chp 9.6

The Mass-Luminosity relation holds for main-sequence stars only and states that the luminosity of a main-sequence star is proportional to its mass raised to the 3.5 power.

mass is the most significant factor in determining the size, brightness and lifetime of a star.

Density is the ratio of Mass/Volume

Volume of a sphere is given by the expression:

Selection effect is a biasing of data created by the way it is sampled. Failure to account for selection effects leads to systematic errors.