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 H-R Diagram Teacher's Guide - Goals - Background - Structure - Questions Specifics Correlations To Student Project

# The H-R Diagram

This project leads students through making an Hertzsprung-Russell (H-R) Diagram, one of the most basic tools of stellar astrophysicists.

The H-R diagram project is one of the most challenging projects on SkyServer. Several of the exercises involve analyzing large amounts of data; it would be useful if students knew how to enter data into a spreadsheet and have the spreadsheet do some of the calculations for them. Alternatively, a group of students could split up the data and do the calculations by hand, each student doing a certain number of stars. The last step involves using a simple search tool to collect data for hundreds of stars at a time. You will need a spreadsheet capable of importing a .csv file, such as Microsoft Excel.

There are many ways of making an H-R diagram, but the diagram always has some measure of luminosity on the y-axis and some measure of temperature on the x-axis. Luminosity can be measured in terms of absolute magnitude, or relative to the brightness of our Sun (in which case the Sun has a luminosity of 1). Temperature can be measured in terms of spectral type or in terms of color, given by a the traditional
b-v value or by the SDSS's g-r value.

For more information on how to make an H-R diagram, and on how astronomers use the diagrams, read the About Astronomy: Stars section of SkyServer, or look in an introductory astronomy textbook. Here are a few suggested references for further reading:

Stars, by James Kaler

Universe, 6th Edition, by Freedman and Kaufmann

# Project Goals

By the end of the project, students should be able to:

• Understand the definition of luminosity as the total energy output of a star
• Know that luminosity depends on the temperature and surface area of a star
• Understand the difference between apparent and absolute magnitude
• Know that the color of a star will tell you its temperature
• Explain how different filters can be used to determine the temperature of a star
• Make an H-R diagram using luminosity, absolute magnitude or visual magnitude on the y-axis, and temperatrue, spectral type, or color on the x-axis
• Explain how the closest stars to the Sun differ from the brightest stars in the night sky
• Calculate the distance to a star using parallax
• Calculate the absolute magnitude of a star using its apparent magnitude and the distance to the star
• Retrieve data from the Hipparcos mission using a web-based interface
• Recognize which stars belong to a star cluster
• Understand that all stars in a globular cluster are effectively the same distance away from the Earth
• Realize that sometimes large amounts of data are necessary to see a pattern develop
• Use the MAST search tool to retrieve information from the SDSS database
• Create an H-R diagram using data from the MAST search tool by importing it into a spreadsheet program

# Background Knowledge

The H-R diagram project is complex and involves many different skills. Students need to be well-prepared to tackle this project.

A lot of background on star colors and spectral types can be found in SkyServer's Color and Spectral Types projects. For the H-R diagram project, students need to know that spectral types tell you the temperatures of stars. Students will also need to know how stars' colors relate to their temperatures.

Graphing is a large part of this project. Students must know how to use a spreadsheet program, since the amount of data used in this lab makes graphing by hand tedious at best. The spreadsheet will also speed up the calculations of distances using parallax angles and absolute magnitudes from Hipparcos data. Exercise 7, the graph made from searching SkyServer's database, should not be attempted without a spreadsheet of some type.

The calculation of absolute magnitude in the Hipparcos section involves logarithms. Students should be comfortable with high school algebra to be able to do all the calculations necessary.

# Project Structure

The first two sections of the project give a basic introduction to H-R diagrams. They also illustrate the differences between the brightest stars we see in the night sky and the closest stars to our Sun. These two sections can be done on their own as a short lesson for a lower-level class, or if time does not permit a deeper exploration of the topic.

The next section gets into the difficulties of determining the distances to stars. It uses data from the Hipparcos satellite. Students learn how to calculate the distances to stars using parallax. They will use the distances to find absolute magnitudes and to create an H-R diagram for a star cluster.

There is an optional section on calculating the radius of a star. This problem involves a lot of math, but should be accessible to a strong Algebra II student. Not doing this section will not diminish the material on H-R diagrams, but some students may find it a rewarding challenge to find a fundamental property of other stars.

Globular clusters are very far away. You can assume that all the stars are at the same distance. Students will see the difficulty of creating an H-R diagram due to the large amount of data necessary. They will then use one of two simple tools to search the data and make and H-R diagram for a globular cluster using hundreds of data points.