HR diagram
Topic/Concept: HR Diagram
Type of Activity: small group + a little discussion at beginning and end
Prerequisite knowledge required:
-Parallax to measure distances to nearby stars.
-The Inverse Square Law of Light: a star’s flux decreases with the square of the distance.
-Being able to correctly apply the distance modulus = the apparent magnitude – absolute magnitude. This is equal to 5 Å~ log(distance in parsecs) – 5 (application).
Resources required: Blackboard and chalk. Some ‘simplified’ stellar spectra and some ‘real’ ones.
Learning Goals: In order to better understand how stars are constructed, astronomers look for correlations between stellar properties. The easiest way to do this is make a plot of one intrinsic property vs. another intrinsic property. An intrinsic property is one that does not depend on the distance the star is from the Earth (e.g., temperature, mass, diameter, composition, and luminosity). In 1912, two astronomers, Ejnar Hertzsprung (lived 1873—1967) and Henry Norris Russell (lived 1877—1957), independently found a surprising correlation between temperature (color) and luminosity (absolute magnitude) for 90% of the stars. These stars lie along a narrow diagonal band in the diagram called the main sequence . This plot of luminosity vs. temperature is called the Hertzsprung-Russell diagram or just H-R diagram for short. By the end of the class period, students should know how astronomers determine these intrinsic stellar properties and be able to construct their own HR diagrams for a sample of nearby stars.
Learning Objectives: – Students should be able to look at the spectra of two stars and know which one is the hotter of the two (hot stars are bluer than cooler stars). Not only will they know how to apply Wien’s law (T is proportional to 1/lamda_max), but they’ll have the more general understanding that subtracting the B filter magnitude from the V filter tells you the color and hence the hotness of a star. (Analysis).
– Students should be able to compute the luminosity of a star knowing its radius and surface temperature [L = (surface area of star) Å~ flux of energy through its surface = 4 x pi x r^2 x sigma x T^4]. Most importantly, they should know that luminosity depends on both the size of the star and its surface temperature. (knowledge).
o Students should be able to use the relationship between luminosity, surface area, and flux to determine the sizes of stars (analysis).
– Students should be able to make a graph of Luminosity vs Color (an HR diagram) for a sample of nearby stars (with the size of the dot on the graph scaled to the size of the star relative to the sun) (Synthesis).
– (This is a goal that will be accomplished to its fullest by the end of the next class period). Students should be able to recognize the usefulness of a tool like the HR diagram (i.e. the usefulness of classifying objects in order to more easily compare them to each other). Specifically, students should be able to look at a star’s position on the HR diagram and determine its evolutionary state, its mass, its radius (knowing its distance), ect.
Also, students should be able to determine a cluster’s age relative age (to other clusters) using their HR diagrams. (Evaluation).
Common misconceptions:
Opening activity:
The homework due at the start of this lesson had to do with finding distances to nearby stars using parallax. [The homework consisted of 2 images of a star, one taken half a year after the first. Students used the distance the star moved with respect to the background stars along with the earth-sun distance to determine the distance to the star.]
The lesson begins with 3 questions on the board as the students come into the classroom that opponents to the sun-centered Solar System used to deny the validity of the theory:
- If the Earth actually spun on an axis (as required in a heliocentric system to explain the diurnal motion of the sky), why didn’t objects fly off the spinning Earth?
- If the Earth was in motion around the sun, why didn’t it leave behind the birds flying in the air?
- If the Earth were actually on an orbit around the sun, why wasn’t a parallax effect observed? That is, as illustrated in the adjacent figure, stars should appear to change their position with the respect to the other background stars as the Earth moved about its orbit, because of viewing them from a different perspective (just as viewing an object first with one eye, and then the other, causes the apparent position of the object to change with respect to the background).
[diagram of parallax angle]
After a few minutes of time to think and look through their notes on using the parallax method to determine distances, have students discuss the third question in small groups.
Concept Activity:
In groups of 3, students classify a list of nearby stars with the eventual goal of placing them on a huge HR diagram on the board. All they are given to start with are spectra for the stars (from which they can get temperature and color), the parallax angle (from which to derive distance), and the star’s apparent brightness. Once they’ve worked out the star’s luminosity from knowing its distance and apparent brightness, they should be able to determine the star’s radius. Once they know the luminosity, color, and radius of each of their stars, they will then place them up on the “Class HR Diagram” on the front blackboard. Once all the points have been placed, we will then use the word HR diagram, talk about when and by whom it was first used, and how it can be manipulated to learn more about the stars.
Checking for understanding/Assessment
-After explaining how the color index works (and before explaining Wien’s law), put up two spectra (very simple curves with obvious maxima). Have the B wavelength and V wavelength clearly marked as well as their respective intensity values. Ask, which star is cooler than the other? Follow PI routine (moment to write, show of hands, peer instruction, 2nd show of hands).
-Another PI concept-test could be done for checking students understanding of how to determine the size of a star relative to our sun knowing its surface temperature and luminosity as compared to the sun.
-As the students place their stars on the board, the teacher will monitor and give help to groups who may not have understood.
The reading will be partly about absorption and emission lines, focusing in particular on the relation between the depths of hydrogen lines and the temperature of the star’s photosphere. This will be very useful for the homework. The students, in groups of 4, will be given spectra of a number of different types of stars (the spectra will be doctored a bit to make this work well and any redshifting of lines will have been taken out). Without having read about the OBAFGKM classification scheme, the students will classify their stars (hopefully along a temperature axis). At the start of the next period, they will join with another group of 4 and put their classifications schemes together. In class, they will read about spectral typing (and perhaps an aside on A.J. Cannon) and reclassify their stars accordingly. This is the next step in understanding the usefulness of the HR diagram.
Assessment: this is mostly done through interacting with the students as they work in groups.
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