# Chapter 16: Analyzing Starlight

How can we learn what other stars are like? We know a good deal about our Sun, but how can we learn about objects that are as distant as stars (we will discuss how the distances are measured in ch. 18)? Are other stars bigger or smaller than our Sun? Hotter or colder? Brighter or dimmer? In the next few chapters I will discuss how astronomers learn about stars and how to answer these questions.

Recall some points from last week's lecture on the blackbody spectrum and atomic spectra:

## 16.1 The Brightness of Stars

What is the difference between "apparent brightness" and "luminosity"? Demonstrate with a small light, at different distances from the class.

Luminosity, or actual brightness, is how much energy a star gives off each second, this only depends on the total energy output of a star. Apparent brightness is how much energy reaches our eyes, and it depends on the energy output of the star, and how far away the star is (also how much dust is between us and the star, but let's ignore that point for now). I will always use luminosity to refer to the total energy output of a star, and then brightness will always mean apparent brightness.

The brightness we see depends on both the luminosity of the star, and its distance from us. Are all stars the same distance from us? Do all stars have the same luminosity? The answer to both is no, so we cannot tell if a dim star is dim because it is far away, or because it doesn't produce much light. For now we will concentrate on measuring apparent brightness. In Ch. 18 I will discuss how to measure the distance to a star, and from these two measurements astronomers can determine the actual luminosity of a star.

### The Magnitude Scale

Because it will come up from time to time in the coming chapters, I will define the magnitude scale for stars. This is an overly complex system for brightness, so please just bear with me. The magnitude scale begins with Hipparchus, the ancient astronomer. He catalogued about 1000 stars, specifying their position and apparent brightness (to his eye). He used six categories, called magnitudes. The brightest stars he called first magnitude, and the faintest he called sixth magnitude.

Astronomers continued to use magnitudes, and in the 19th century they attempted to make the scale more precise. They decided that a magnitude 1 star is 100 times more bright than a magnitude 6 star. Then, each decrease of magnitude by 1 means that the brightness increases by a factor of 2.5.

The result is that today we have a scale that counts backward, the higher the magnitude, the fainter the object, and the brighter the object, the smaller (more negative) is the magnitude. The Sun is magnitude -26.2, Venus is -4.4 at its brightest, Sirius (the brightest star in the northern hemisphere) is -1.5. With the naked eye and a clear sky, we can see objects "down" to magnitude +6. Our most powerful telescopes can see objects "down" to magnitude 26 or so.

### Other Units of Brightness

#### Luminosity

Throughout this text, luminosity will be expressed in terms of the luminosity of the Sun, Lsun.

## 16.2 Colors of Stars

### Color Indices

A star's light follows a blackbody spectrum (ch. 4). The color of the star is determined by the peak in the spectrum which is determined by the temperature of the outer surface of the star. Astronomers have developed a technique of using a few color filters (3 or 4 or 5) to measure the brightness of the star in different color bands. This information is enough to determine the color and temperature of the star.

## 16.3 The Spectra of Stars

Most of what we know about stars comes from a detailed study of the spectra. To make a spectrum for a single star is quite a feat, requiring the light from just that star be collected from the telescope and taken to a spectrograph where it is spread out into its different frequency components and recorded on film or by an electronic detector.

While difficult to obtain, the spectrum contains a wealth of information about the temperature, composition, motion, and rotation of the star.

### Absorption Lines

The absorption lines seen in spectra vary among stars. While all stars are mostly hydrogen, not all have hydrogen absorption lines. If they don't have absorption lines for hydrogen, then they probably have of either neutral metal, or ionized metals. Which lines are present depends on the temperature of the star.

Around a very hot star, the hydrogen atoms (and most others as well) are ionized, meaning that the outermost electron is heated to the point that it breaks loose of the nucleus. When the electrons break loose, then we no longer see absorption lines due to that electron moving to different energy levels. Since hydrogen has only one electron, when it becomes ionized it can't absorb light at all.

Other atoms, like calcium, iron, and nickel, have many electrons, so if they are heated to the point where a few break free, there are still some that remain bound to the nucleus which can absorb light. Only now, they produce a set of absorption lines specific to the ionization state of the atoms. This seems to make life more complex (which it does), but it also allows astronomers to determine the temperature of the star, since the ionization state of an atom depends on its temperature.

### Classification of Stellar Spectra

Stellar spectra are classified by the types and strengths of spectral lines. An odd nomenclature is used that goes O (hottest), B, A, F, G, K, M, L, T (coldest). A discussion of the meaning of each type is given in Table 16.1. The types of spectral lines that are used to determine the spectral class are ionized helium, neutral helium, hydrogen, ionized metals, neutral metals, and molecules.

To see how this works, suppose we have a star where the hydrogen lines are half as strong as for an A class star. Then that star could be either B class or G class. If it also has helium lines then it's B class, and if it has lines of neutral and ionized metals it is G class. Notice that this system is unforgiving in that, a star with both strong helium lines and strong metal lines is not allowed!

Much of the early work of classifying stars was done by Annie Cannon of Harvard. She personally classified the spectra of 400,000 stars by hand! She also simplified a more complex scheme to the one given here that uses only 7 classes (the removed classes correspond to the missing letters, the order of the letters is due to our later understanding of the correspondence with temperature).

Notice the temperature ranges for the classifications: O stars are hotter than 28,000 K, while M stars are cooler than 3500 K. Then sun has a temperature of 5800 K and is class G (G2 to be precise). The more recently introduced classes L and T are for the red and brown dwarf stars seen with modern techniques.

### Effect of Size

Stellar spectra can tell us about the pressure of the gases in the photosphere of a star that produce the absorption lines. This information can tell us about the size of the star.

### Abundances of the Elements

The relative strength of the lines for a specific element can tell us about the abundance of that element in the star. While all stars are mostly hydrogen and helium, the amount of say iron in stars varies. The same is true for carbon, oxygen, neon, calcium, and so forth.

If a star is moving toward or away from us, then its absorption lines will be Doppler shifted. This again complicates the interpretation of stellar spectra, as now the lines of hydrogen are not at exactly the frequencies that we measure in the lab. But the shift is the same for all the absorption lines, so this effect can be sorted out, and it determines the speed of the star toward or away from us.

Note that this only lets us determine the component of a star's motion that is along our line of sight. The motion perpendicular to our line of sight is measured by carefully monitoring the star's position over a period of time. This determines the star's motion in arc seconds per year, which can be converted to velocity if we know the distance to the star (ch. 18).

### Rotation

The Doppler effect can also help to determine the rotation speed of a star. To understand how, look at Fig. 16.9. For convenience, let's think in terms of emission lines, though the same effect holds for absorption lines. If the star is not rotating, then all the emission lines will be at the same wavelength. If the star is rotating, then on the side of the star rotating towards us the emission lines are Doppler shifted to higher frequency (shorter wavelength). On the other side, the star is rotating away from us, and the emission lines from atoms over there are Doppler shifted to lower frequency (longer wavelength). As viewed from Earth, a star is just a point. We cannot resolve the different sides of the star. Therefore, all the emission lines from across the whole star are combined, and the result is a broadened emission line. The amount of broadening tells us how fast the star is rotating. Again, this makes the interpretation of the spectra more difficult, but all the lines (emission and absorption) are broadened by the same amount, and this helps to make the measurement.

### Summary

Stellar spectra are a rich source of information about stars. The existence of emission and absorption lines are crucial to extracting information from spectra. The lines tell us about the temperature of the photosphere, the abundances of heavy elements in the star, the size of the star, the radial motion of the star, and its rotation.