READING: Chapter 10.5 - 10.7
Here is today's question.
You can make an argument that the HERTZSPRUNG–RUSSELL DIAGRAM or the H–R diagram is one of the most important tools of stellar astronomers. We are going to spend some time on interpreting these diagrams, which will lead us to answer many questions about stars themselves. Here are a few examples of HR diagrams to get us started:
The two quantities that get plotted in an HR diagram are LUMINOSITY (y-axis) and TEMPERATURE (x-axis). If you recall from last class, what we measure are the apparent brightness of a star (which depends on luminosity AND distance) and the color (which depends on temperature). Because we don't directly measure luminosity or temperature, most HR diagrams plot the observable quantities, which are MAGNITUDE (y-axis) and COLOR (x-axis). Because we plot color and magnitude, you often hear HR diagrams referred to as COLOR–MAGNITUDE DIAGRAMS. We are not going to spend much time on the magnitude system, but if you want to learn more you can go here (NASA/GSFC) or here (Cornell). What I will say about magnitudes is that they are a measurement of luminosity and the scale is backwards, the higher the luminosity of an object, the smaller its magnitude. The brightest objects have negative magnitudes. Another important note about the HR diagram is that the temperature scale on the x-axis is plotted BACKWARDS, that is, high temperatures are plotted on the left, cool temperatures on the right.
If you look at the two diagrams on the right, you will see that a lot of the region is empty space. Most of the stars are concentrated in a narrow band that snakes from the upper left to the lower right of the diagram. This band can be explained very simply if you remember the luminosity / temperature relationship for blackbodies:
The simplest version of this relationship (ignoring the radius), is that the hotter a star is, the brighter it will be, so the hottest stars are the brightest stars. The upper left corner of an HR diagram includes the hot, bright, blue stars. The coolest stars are much fainter than the hot stars, and they lie at the lower right. The band connecting the hot, bright stars at the upper left to the cool, faint stars at the lower right is called the MAIN SEQUENCE, and it includes stars from 3,000K up to 30,000K or so.
Astronomers developed a system of classifying stars based on how their spectra looked, and this system used to use the letters of the alphabet in order, A,B,C,D,E,F, etc. However, as our knowledge of stars improved, many of the classes were combined and all of the classes were reordered to go from highest temperature to lowest temperature. On the two diagrams on the left, above, you see that the order of stellar classes goes O, B, A, F, G, K, M from hottest to coolest. The hottest, brightest stars are O stars, while the coolest, faintest stars are M stars. Our Sun is a G star.
You should notice that there are many other stars in the HR diagrams above that are not on the Main Sequence. For example, in the diagram on the left, Sirius B is in the lower left of the diagram (blue color, faint luminosity), and Mira, Betelgeuse, and Arcturus are above and to the right of the main sequence (red colors, bright luminosities). If you consider the equation above that says that luminosity is proportional to both radius AND temperature, you should realize that a faint, blue star must be much smaller in radius than a bright, blue star. Also, a bright, red star must have a much larger radius than a faint, red star. For this reason, the lower left of the diagram is called the WHITE DWARF REGION, because this is where the small, blue-white stars are found. The upper right of the diagram is called the RED GIANT REGION, because this is where the large, red stars are found. White dwarfs have radii of about 0.01 times the Sun's radius (which is very similar to the Earth's radius), while red giants can have radii of several hundred times the Sun's radius (if a 300 solar radius red giant were located at the position of the Sun, it would enclose Mercury, Venus, and Earth and extend almost out to Mars).
In Monday's class we discussed how we measure distances to the nearest stars using the technique of PARALLAX. This allows us to measure the distance to stars that are within a few hundred parsecs of the Sun. As we will see as the semester progresses, the distance to astronomical objects is one of the most difficult measurements to make for astronomers. The more distant the object, the harder it is for us to measure its distance accurately. We are now going to talk about the method for measuring distances to stars that are too far away to have their parallax measured. Sometimes this technique is called SPECTROSCOPIC PARALLAX, but this is a confusing name because it doesn't involve the technique of parallax that we learned last time.
Here is how this technique works:
Here are a few things to keep in mind about using this technique:
The final property of stars that we will talk about in this section is their MASS. For single stars, there is no easy way to estimate their mass using the usual observations (apparent brightness, color, spectrum). Instead, we rely on BINARY STARS to make mass measurements of stars. Binary star systems are made up of two stars that are gravitationally bound to each other, so they orbit each other just like the Moon orbits the Earth. We can measure the masses of the stars in a binary system using Newton's version of Kepler's third law:
If you can measure the period of the binary star orbit, and the separation between the two stars, you can calculate the total mass of the system. Once you know the total mass of both stars, you can use some other physical relationships to measure the individual masses.
From binary star mass measurements, we know that: