# Teacher’s Guide to Specific Sections

## Chapter 1

### Introduction: Color

Ask students what they see when they look at the stars. At least some of their answers should indicate that stars have different colors. Ask, “do you ever wonder *why* stars have different colors?” Tell them that in this project, they will learn why.

### Colors of Stars in the SDSS

The key to doing Explore 1 is using the Navigation Tool. Students should choose a random stripe and mosaic, then click randomly at different points on the mosaic to look at different zoom views. They should search freely through the stars in the Zoom window to find stars of different colors. Remind them to make sure they choose stars and not galaxies. The top of the browser window will show the object type and its magnitudes in the five wavelengths (u,g,r,i,z). Students should make a note of the star’s color on a sheet of paper, then click “Add to notes” to save the star in their notebook. A red check will appear next to “Add to notes” to show that the star’s information has been saved.

Sometimes, a bright star will be mis-classified as a galaxy. This misclassification happens because the software SDSS uses to classify objects classifies pointlike light sources as stars and extended light sources as galaxies. When the CCD sees a very bright star, some of the star’s light spills over into neighboring pixels, making the pointlike star look like an extended light source. You can recognize a bright star by diffraction spikes – bright crosses centered on the star – that occur as light bends inside the SDSS telescope.

In Explore 2, students should copy the information they saved in their online notebooks into a spreadsheet program. They should use their handwritten notes to enter each star’s color. They should then use the sort feature (under the Data menu in Excel) to look for patterns in the data. They should sort first by magnitudes (u,g,r,i,z), then by differences in magnitudes. When they see the colors begin to line up in some order (when stars of similar colors are in similar places on the list), they should make a note of how they sorted the data.

Ideally, they should find that the colors are sorted (blue stars on one end and red on the other) when the data are sorted by differences in magnitudes. Remind students that they shouldn’t expect every star to fit the pattern perfectly; they should expect to see only a general trend. If they are unable to see any trend at all, suggest that they return to the Navigation Tool and collect more data.

## Chapter 2

### The Definition of Color in Astronomy

This section builds on the work students did in the last section, offering a concise mathematical definition for color. Astronomers use this definition when they discuss color in their research.

Color is defined in terms of stellar magnitude. Students may be interested in learning the history of the magnitude system, which can seem arbitrary. The Did You Know? in the next section discusses the magnitude system’s history.

Remind students that magnitude decreases with increasing stellar brightness. So if a star emits more red-wavelength light than green-wavelength light, its red magnitude r will be less than its green magnitude g; therefore, g-r will be positive.

This section includes a “Try This” activity designed to give students intuition about magnitudes. Students shine two flashlights toward a specified point: one flashlight at 1 meter and the other at 1.58 meters. When they look at the two flashlights, the nearer one will appear about one magnitude brighter. The distances were calculated using the inverse-square law of light along with the definition of magnitude. The activity may work better with light bulbs, which are omnidirectional light sources. If you use light bulbs, make sure students are supervised so they do not burn themselves.

Use students’ intuitions about the word “filter” to express the concept of telescope filters. A filter is something that collects only what it is designed to collect. A telescope filter blocks all light except for light with the specific wavelength it was designed to see. Red telescope filters collect only red-wavelength light. Once astronomers have used a filter to collect light at a certain wavelength, they can calculate the star’s magnitude in that wavelength. If your school has a theater, you may borrow some colored gels from the theatrical lights to demonstrate what filters do.

If students are confused about why color should be defined by the difference in magnitudes, appeal to their intuitions. If a star looks red, it must emit more red light than green; therefore, the difference between its radiant fluxes in red light and green light should be positive. If they ask why color depends on the difference and not the ratio, tell them that this question will be answered in the next section.

### Color and Amounts of Light

This section relates a star’s color to a physical quantity: the amount of light it emits in different colors. If your students are not comfortable working with logarithms, you may skip this section.

This section introduces a mathematical definition of magnitude in terms of radiant flux, the amount of light that reaches a given area in a given time. Radiant flux is also known as “radiant power.” Radiant flux has units of power – Watts (Joules/second, or kg/m^{2}/s). Students do not need to know these units to complete the project.

The definition of magnitude required that each star’s magnitude be compared to a reference standard. The standard star is arbitrary. Vega, a bright blue star in the summer sky, was chosen because its magnitude would have been close to zero in Hipparchus’s ancient scale (see the Did You Know? section on the history of the magnitude scale for more information). Emphasize that even though Vega’s radiant flux is set to zero for all wavelengths, Vega is an ordinary star, with a color like any other.

Practice 1 requires only the definition of magnitude and algebra with logarithms. You may wish to pause here to give a quick review of the properties of logarithms. The Did You Know? section on the history of magnitude is an optional section for students who are curious about how the magnitude system came to be, and why the system is so confusing.

### What is Color?

Remind students that light is a wave, and that a wave can be described by the distance between successive peaks, or the *wavelength*. Have students play with the light wave animation, then study the visible light spectrum. Both give roughly accurate representations of the width of each color in the visible spectrum. Tell students that when light shines with a mix of different wavelengths, it appears white.

Next, have them study the diagram and table of the total electromagnetic spectrum. Show them that many of the phenomena they are familiar with, such as radio signals, microwaves, infrared waves (heat), and X-rays can be explained by the different wavelengths of the electromagnetic spectrum.

### SDSS Filters

This section explains the physical reason for SDSS’s five color filters: each filter lets in light at a specific wavelength.

Question 1 asks students to think about a graph of the amount of light given off by a star as a function of wavelength. Such a graph would be a simplistic spectrum, with only five points. Students are then asked to extend their picture by thinking of a graph with many more points.

This page includes an optional Did You Know? section about the SDSS’s five filters. The graph shows the sensitivity to light as a function of wavelength for each filter. Point out that the filters overlap slightly, allowing them to check one another. Also point out that the graph shows two sensitivities – a higher sensitivity in a vacuum and a lower sensitivity looking through air. Remind students that all of the SDSS’s observing will be done through air.

### Light From Stars

This section builds on Question 1 to give a simplistic explanation for the colors of stars: stars have different colors because they emit radiation with different peak wavelengths. Let students study the two curves to answer Question 2. If they have difficulty with Question 2, ask: “what color light are these stars emitting?” Question 3 should get students thinking critically about the explanation of peak wavelength. They key to Question 3 is to recognize that a star also emits light at other wavelengths around its peak wavelength. If students have trouble with Question 3, tell them to study the two curves above.

Explore 3 and Question 4 bring together what students have learned so far. These are difficult exercises designed to stretch students’ reasoning abilities. Stars that emit most of their light in the green wavelength are fairly rare in SDSS data; but, encourage students to look through the Navigation tool before clicking the Hint button. Encourage students to keep a record of the stars they look at, either on paper or with their online notebooks. The key to Question 4 is to recognize that the part of the spectrum corresponding to green is narrow, while the peak of the thermal radiation curve is broad. Even if the curve’s peak wavelength is in the green part of the visible spectrum, the star still emits enough blue light to appear white or blue.

The last section, “The Big Question,” is intended as a hook for Chapter 3, where students will learn why stars have different colors. If you intend to stop with Chapter 2, do not tell students to read this section. If they ask, encourage them to do the rest of the project on their own.

The Did You Know? section teaches students that SDSS’s images do not exactly represent what the eye would see looking at an object. This is an optional section; students do not need to know how SDSS images are constructed to finish the Color project.

## Chapter 3

### Color and Temperature

This section explains the observations students made in the last section. Stars have different colors because they have different temperatures.

Have students play the hot plate animation to get an intuitive feel for how the visual color of an object changes with temperature. When the fire symbol beneath the hot plate disappears, the plate is removed from the heat and begins to cool. The color sequence reverses. Emphasize that this color sequence depends only on temperature: it does not just apply to hot plates, and the sequence will be the same for any object studied. Question 4 acts as a quick review of the electromagnetic spectrum: students should realize that ultraviolet light has shorter wavelengths than violet light.

### Thermal Radiation Curves

Thermal radiation curves are often called *blackbody* curves. This term was chosen because the curve represents only the thermal radiation of “black bodies” – objects that do not reflect any light at any wavelength (remember that an object that does not reflect light will appear black). Stars are nearly perfect black bodies: their color comes almost completely from their own glow and not from other light that they reflect. The term “blackbody curve” is not used in this project because many students find the name confusing. “Thermal radiation curve” expresses the idea that any object that emits thermal radiation (that is, light emitted as a function of temperature) will show radiation whose intensity matches such a curve. The diagram shows thermal radiation curves for stars at three different temperatures.

Explore 4 lets students experiment with changing the temperature of an imaginary object and watching its thermal radiation curve change. Alternatively, they can drag the curve to change its peak wavelength, then see what temperature would be required to generate that curve. You should familiarize yourself with the Java applet before assigning this exercise to students. You may assign them to figure out the mathematical relationship between temperature and peak wavelength, or you may just have them develop an intuitive feel for how the curves change with temperature.

### Temperature and Peak Wavelength

The equation l_{peak}T = 2.897 x 10 ^{-3} m K can be used to predict the peak wavelength (in Angstroms) from the temperature (in Kelvin) of the thermal radiation curve, or vice versa. Practice 2 and 3 give students practice in using this equation, called “Wien’s Law” (pronounced *VEEN*) to solve problems.

If students ask, tell them that the Kelvin scale, named for British physicist Lord Kelvin, has the same degree size as the Celsius scale, which is larger than the Fahrenheit degree by a factor of 1.8. The Kelvin scale is set so that 0 K is equal to “absolute zero” – the temperature at which atoms stop moving. Kelvin temperatures are written without the degree symbol.

### Observed Spectra

This section introduces students to spectra – graphs of the intensity (amount) of light coming from a star as the function of the light’s wavelength. Be sure students understand what they are looking at. Actually, the thermal radiation curves in the last section are spectra of perfect thermal sources. However, on SkyServer, the term “spectrum” is reserved for an observation of a star. Point out to students how large the peaks and valleys of non-thermal radiation can be. Practice 4 and Explore 5 ask students to find stars’ peak wavelength from their spectra. To find the peak wavelengths, students may look at the blue curve superimposed on the spectra. However, tell students that this curve is not a thermal radiation curve, but only an approximated polynomial curve that matches with the broad trend of the observed spectrum.

Explore 5 asks students to use the Get Plates tool to look at observed SDSS spectra. Students calculate the temperatures of stars from their peak wavelengths, find an average temperature for SDSS stars, and compare this temperature to the Sun’s to see if the Sun is an average star. The Sun is about average for the stars in the SDSS database, but is hotter than average for the stars in our local part of the galaxy. The reason for this discrepancy is that a dim, distant star viewed from Earth will appear too faint to be detectable, even with the SDSS’s powerful telescope.

Emphasize the point made in “A Word of Warning”: the starlight that we see from Earth is all the light the star emits, from both thermal and non-thermal sources. Non-thermal sources are emission and absorption lines that arise from electrons changing energy levels in the star’s atoms. Students should have a sense for what electron energy levels are, but do not need to understand the process of energy level jumping.

Remind students that they can’t sort out the two effects, thermal and non-thermal, by looking at the star’s color alone. Tell them that the spectrum lets them sort out the two effects. Question 7 asks students whether the spectrum shown is a thermal source. Either yes or no is an acceptable answer, as long as students give reasonable justification for their response.

If you do not intend to have the class do the Color-Color diagram page, stop after Question 7. The last section of this page, “The Other 59,058,000 Stars” is a hook for the Color-Color diagrams section, asking what, if anything, astronomers can learn from looking at color alone.

## Chapter 4

### Color-Color Diagrams

This section teaches students how astronomers can learn the temperature of a star even if they do not have a spectrum for it.

Remind students what a telescope filter does, and remind them of the thinking they went through in Question 1. Have them study the diagram, and be sure they can explain how SDSS’s five filters give a snapshot of five points on the thermal radiation curve.

Remind students that the thermal radiation curve will describe any object in the universe as long as it’s a thermal source. Since the object doesn’t matter, every object in the universe with a single temperature, say 6000 K, will produce an identical thermal radiation curve.

### Making a Color-Color Diagram

This section teaches students how to make a color-color diagram. Color-color diagrams can be hard to explain in words, so students can click on the image to see what the axes on a color-color diagram are.

Have students study the diagram, and remind them that magnitudes decrease for brighter stars. Question 8 asks them to visualize what a u-g/g-r color-color diagram would look like for the thermal radiation curves shown. The key is to look at the u-g and g-r colors (represented by lines along the left and right axes) as x and y values, respectively, of the color-color diagram. The paragraph below Question 8 tells students how to extend the two points into a line, making a u-g/g-r for many stars. Question 8 asks what g-r/r-i and r-i/i-z diagrams would look like.

### A Color-Color Diagram for SDSS Stars

Explore 6, 7, and 8 let students make a color-color diagram for themselves, and then use them to learn which stars can best be thought of as thermal sources. To find the given stars, students should click the links, or use the “Find by ObjID” feature of the Object Explorer. A new window will open for the Object Explorer, and students should read the magnitudes u,g,r,i,z from the Object Explorer.

Explore 8 asks students to use a spreadsheet program to make a color-color diagram. The instructions tell how to use Microsoft Excel to make this diagram. If your students are more familiar with another graphing program, use that program instead. You may wish to pause here to give a quick tutorial of the graphing program. Question 10 asks students which end of the color-color diagram corresponds to hotter stars. If students get stuck, ask them to think about only one axis at a time.

In Explore 9, students make another color-color diagram, this time graphing u-g against g-r. Question 11 asks students to use this new diagram to find the limitations of using a color-color diagram to find stellar temperature. The trend in the u-g/g-r diagram turns quickly away from a straight line, meaning that only the very hottest stars can be thought of as thermal sources. Question 12 asks what might be responsible for the flat line at the top of the diagram. The answer is that these stars are red giants, which emit more red-wavelength light than other stars, no matter what their temperature. If your students have not learned about stellar evolution, you may skip this question.

## Chapter 5

### Colors of Other Objects

This section briefly introduces other astronomical objects – Population I stars, planets, interstellar dust, galaxies, quasars, and the universe – and describes their colors. If your students are interested in learning more about these objects, refer them to some of the other Projects on SkyServer. Links to these projects are given on this page.

### Colors in Astronomy Research

This section introduces the Research Challenge. The research challenge should not be done in the classroom. It is a completely open-ended exercise. Students think of an astronomical research question that can be answered using colors. They develop their question, choose objects from the SDSS database to examine, and perform all analyses needed to answer the question. Encourage students to complete this exercise on their own, for fun. You may wish to offer extra credit to students who do it. If they are interested in doing the exercise, you should discuss their research questions and approaches with them outside of class.

The question asked should be a fairly simple question that can be answered by examining 20-40 objects using a straightforward analysis. Most likely, students will either make color-color diagrams or analyze peak wavelengths of spectra to answer their question. Be sure that they use color somehow in finding their answer. The Research Challenge lists a few suggested questions that students can answer.

The research projects in the Research Challenge can easily be extended into Science Fair projects if students are interested. We encourage students to use SDSS data in Science Fair projects.