Science

Objectives: Stars have a number of properties which, at first glance, may appear to be unrelated. But further analysis shows that they are related after all. Two astronomers, independently of each other, plotted the luminosities of a number of stars versus their temperatures to create what is now known as the “Hertzsprung-Russell”, or “H-R” diagram (named after the scientists who invented it), which allows us to study this relationship between properties.

In this lab, you will find that for the majority of stars there is a definite relationship between temperature and luminosity. You will also find out that other properties of stars are also related. In fact, the H-R diagram contains a surprisingly large amount of information in one simple graph.

I. Plotting and understanding the H-R diagram

In the two tables and graph that follow, Temperatures are in Kelvins (K), and Luminosities and Masses are given in units relative to the Sun; the units are called: “Solar Luminosities” and “Solar Masses” respectively, which are abbreviated as L☉ and M☉. Note that the values for the Sun in these units are 1.0 L☉ and 1.0 M☉ by definition. You may ignore the column “Spectral Type” in the tables.

 

First is a list of the 25 nearest stars in the sky, starting with the nearest:

Next is a list of the 25 visually brightest stars in the sky, starting with the brightest (this list shares a few entries in common with the previous list):

 

Finally, here is a graph showing each star’s Temperature versus Luminosity. Data for the nearest stars have been plotted using a box symbol, while data for the brightest stars have been plotted using an x. For the FIVE stars that appear on both lists, they are plotted on the graph using BOTH symbols — so you will see a box with an x inside, which looks rather like a filled-in box.

 

Print out or save a copy of this H-R Diagram (image opens in new browser window, or you can download a PDF of the graph here ) so you can draw and write on it in order to answer the following questions. You can either draw on a paper copy, or digitally annotate a copy of the file on your computer. Whether you choose the paper or computer drawing method, you will be handing in your drawing at the end, so be sure to follow all instructions that tell you to write or draw on it! Instructions to write or draw on the diagram will be indicated by an underline, like this.

1.

You should see a general trend among a majority of the stars. This trend is called the “Main Sequence”. Circle the main sequence on your diagram — that is, circle the stars which follow the trend that you observe; the stars are called “main sequence stars”, and the trend is the main sequence.

How many stars does it include?

Count the stars and type a whole number: stars.

2.

Describe this trend in one brief but complete sentence in your own words, making sure to include the properties of the stars that are represented (see the graph axes!) and HOW they are related to one another?

3.

Find and label by name the following seven stars on your paper graph: The Sun, Barnard’s Star, Sirius A, Sirius B, Regulus A, Deneb, and Betelgeuse.

Note that the tickmarks on the axes (shown on the top and sides) are not evenly spaced. Nonetheless, the small tick marks between each large tick mark represent equal sized numerical steps. E.g. on the vertical axis, between 1 and 10 are eight small tick marks, representing 2, 3, 4, 5, 6, 7, 8, and 9. And on the horizontal axis, between 3,000 and 10,000 there are six vertical dashed lines marking intervals of 1000, so representing 4000, 5000, 6000, 7000, 8000, and 9000. Moreover, between the dashed vertical lines for 3000 and 4000, there are nine small tick marks on the top axis (only) marking intervals of 100, so representing 3100, 3200, 3300… 3900.

Which of those stars are on the main sequence? Check all that apply.

A) The Sun

B) Barnard’s Star

C) Sirius A

D) Sirius B

E) Regulus A

F) Deneb

G) Betelgeuse

H) None of these are on the main sequence

4.

Which of those seven stars is closest to the top right corner of the graph? (Stars in this area are called Red Giants because their temperature is cool and thus their color is red, and they are swelled up to a huge “giant” size, making their luminosity very large.) Highlight correct answer below.

The Sun

Barnard’s Star

Sirius

ASirius

BRegulus

ADeneb

Betelgeuse

5.

Which of those seven stars is closest to the bottom left corner of the graph? (Stars in this area are called white dwarfs. They have high temperatures, glowing white or even blue, because they are the hot leftover core of a dead star. Their sizes are very small though, “dwarfs” in fact, because they are undergoing no nuclear fusion to keep them swelled up. Their small size gives them a small luminosity.) Highlight correct answer below.

The Sun

Barnard’s Star

Sirius

ASirius

BRegulus

ADeneb

Betelgeuse

6.

For the main sequence stars you have already labeled on your paper copy of the graph, write their Mass (given in the table) next to their label on the graph. Note: Barnard’s Star’s mass is 0.16 — this is missing from the table.

Now, label the location AND mass of the following additional four main sequence stars:

“L726-8A” (the eighth closest star),

“Ross 154” (the 12th closest),

“61 Cyg A” (16th closest), and

“Spica” (16th brightest; Mass = 10, which is missing from the table).

List the order that ALL of your labeled main sequence stars (these four plus those from the previous questions) appear on the main sequence, from highest to lowest luminosity.

7.

Look at the progression of masses that you just labeled along the main sequence. Do you notice a trend? (If not, you may wish to label the masses of a few additional main sequence stars until you do notice a trend.) Describe in a sentence or two the trend that you notice with mass, making sure to include the other two properties of the stars — as labeled on the graph axes — as well in your description.

II. Comparing Two Populations

Remember that the H-R diagram above has two different populations of stars shown on it: the 25 nearest stars, and the 25 visually brightest stars, or those that appear the brightest to us as viewed from Earth. Draw a legend on your graph labeling which symbol represents each population. (See the description preceding the graph above.)

8.

Look at how the two groups of stars are distributed on the H-R diagram. Carefully describe any differences you notice between these two groups. Aim for 1-2 complete sentences.

9.

Our galaxy is a collection of a couple hundred billion stars (and intervening material) all gravitationally bound to each other and orbiting their collective center of mass. If you could measure all of the stars in our galaxy and plot their properties on an H-R diagram, which set of stars on your paper (the nearest or the brightest) do you think would be a more representative sample of stars in the galaxy at large? Explain WHY.

Hint: As an example, use people as an analogy to stars. Think about last time you were in a big crowd of people, say at a large sporting event. Let’s say you made a list of the 25 fans sitting closest to your seat, and another list of the 25 fans that were the loudest you could hear. Which list of people — closest or loudest — would be more representative of most of the fans in the stadium?

Just to complete the analogy: stars=people, distance=distance, visual brightness=perceived loudness. Just for fun: maybe luminosity=obnoxiousness, temperature=propensity for cursing, and mass (the underlying property that determines the others)=alcohol consumption??

10.

If a star were measured to have a temperature of 3,500 K, predict, by examination of your H-R diagram, the luminosity which you think this star most likely has. In a couple of sentences, explain how you made your prediction, and any assumptions you made.

III. Star radius on the H-R diagram

There is another property of stars that is related to their temperature and luminosity: the star’s radius (or physical size). The most luminous stars have either a very large temperature (hot things glow brightly), or a very large radius (the more glowing surface area there is, the more the total luminosity given off), or both.

For the following exercise, you are going to consider six hypothetical stars in the table below:

Star name Temperature (in K) Luminosity (in L☉) Radius
Alpha 3,000 .00001 the same as star Beta
Beta 30,000 .1 the same as star Alpha
Gamma 3,000 .001 10x bigger than star Alpha
Delta 30,000 10 10x bigger than star Alpha
Epsilon 3,000 .1 100x bigger than star Alpha
Zeta 30,000 1000 100x bigger than star Alpha

A. Label the locations of these six stars on your H-R diagram.

B. Star Alpha and Star Beta have the same radius. Find these two points on your H-R diagram and draw a straight line connecting them. This line represents a line of constant radius on the diagram. All stars which fall on this line will have the same radius!

C. Stars Gamma and Delta also have the same radius as one another. Draw a straight line connecting these two stars.

D. Stars Epsilon and Zeta have equal radii. Draw a line connecting those two stars.

11.

The sun should fall almost exactly along one of the lines you drew. How does the Sun’s radius compare to Star Alpha? Highlight correct answer below.

The sun is 100 times smaller.

The sun is 10 times smaller.

The sun is the same size as star Alpha.

The sun is 10 times bigger.

The sun is 100 times bigger.

12.

You should now have three lines of constant radius on your H-R diagram. Each line you drew represents a radius that is ten times larger than the previous line you drew. Label the lines on your diagram accordingly, e.g. “Radius = 1xAlpha”, “Radius = 10xAlpha”, and “Radius = 100xAlpha”.

Given these, in which direction on the H-R diagram does the radii of stars increase? Your answer does NOT need to be a complete sentence; a few words is fine.

13.

Continue drawing several more lines of constant radius (or size) on your H-R diagram following the established pattern, where each line represents a change of radius by a factor of 10 as before, until you have encompassed all the labeled stars on your diagram. (You will have to draw lines representing both larger AND smaller radius than before.) Label each line with the corresponding radius as before: How many times bigger or smaller it is than Star Alpha?

Using these lines, estimate the size (i.e. radius) of the star Betelgeuse compared to the Sun’s size. You do not need an exact number; just estimate. Enter a decimal number only (e.g. 0.001, 1, 10000, etc. — or anything in between) in the box below:

Betelgeuse is about times ??? the size of the SUN. (Not hypothetical star Alpha!!! Now you’re comparing relative to the actual SUN.)

14.

Estimate the size of Sirius B, compared to the SUN’s size, as above. Enter a decimal number only (e.g. .001, or 1, or 10000, or anything in between) in the box at right. Sirius B is ???? times the size of the SUN. (Not hypothetical star Alpha!!! Now you’re comparing relative to the actual SUN.)

IV: Red Giants and White Dwarfs

In this section you will count stars in various categories and calculate the percentage of stars in each category. Do not include the hypothetical stars from the previous section. Only include the real stars that were originally plotted on your example H-R diagram — i.e. the stars from the tables at the beginning of the lab.

15.

Supergiant stars the very highest luminosity stars, with very high mass, and a wide range of temperatures, that are off the main sequence. Circle and label the group of supergiant stars on your diagram. How many supergiants on your diagram are in this area? Enter a number (only — no words) in the box: ???? supergiants.

16.

Red giant stars are relatively cool, but still quite luminous stars that are off the main sequence. (Our very own Sun will one day become a red giant star! But relax, this won’t happen for billions of years, after it “dies” — after its main sequence lifetime is over.) Circle and label the group of red giant stars on your diagram. How many red giants on your diagram are in this area? Enter a number (only — no words) in the box: ???? red giants.

17.

White dwarf stars are hot, low luminosity stars that are off the main sequence. (Our Sun will eventually end up as a white dwarf star after its red giant phase!) Circle and label the group of white dwarf stars on your diagram. How many white dwarfs on your diagram are in this area? Enter a number (only — no words) in the box: ???? white dwarfs.

18.

The purpose of this next question is to compare the number of main sequence stars to the number stars in the other three groups. Calculate the percentage of all stars on your example H-R diagram that are currently in EACH of these four groups. EXPLAIN exactly how you calculated each answer.

% of stars that are on the main sequence:

% of stars that are supergiants:

% of stars that are red giants:

% of stars that are white dwarfs:

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19.

Most Main Sequence stars go through a sequence of phases like our Sun will: Main Sequence, then Red Giant, then White Dwarf. Stars are being born and dying all the time in an ongoing cycle, like people. So at any given time, there are some stars in any of these stages. (As an analogy with people: there are always some newborn babies, some teenagers, some grown working adults, and some old retired people.) Your example H-R diagram shows a snapshot of what stage several dozen stars are in at one moment in time. Judging by what fraction of stars are in the Main Sequence, red giant, and white dwarf stages respectively, what can you conclude about the relative length of time a given star spends in each of those stages as it progresses through its life. Be specific, and explain carefully.

(Hint: it might be instructive to think more about the analogy with people. If you sampled 50 random people from the population, what fraction of them would you expect to be school children? Working adults? Senior citizens? How does this relate to the relative length of time a given person spends in each of those phases?)

V: Lifetimes of stars

Stars do not live forever. They are born and they die, sometimes passing through several different stages as they die, which causes their properties (namely Luminosity and Temperature) to change. If their properties change, their location on the H-R diagram changes. But their underlying property, Mass, does not appreciably change throughout their normal lifetime. The mass they are born with is the mass they have right up until they “die”. (Though their mass can change after they die, if they undergo some type of explosion or significant mass loss event, like a supernova or planetary nebula.)

The one underlying property that determines all other properties a star will have — and indeed dictates its whole life cycle — is mass. The mass a star is born with determines what Luminosity and Temperature it will have (and therefore its place on the H-R diagram), what radius it will have, and how long it will live on the main sequence (where it will spend the vast majority of its life). Below is a table showing the total lifetimes of different mass stars.

Star Mass (in solar masses) Main Sequence Lifetime
17.5 12 million years
7.6 34 million years
5.9 100 million
3.8 290 million
2.9 540 million
2.0 1.4 billion
1.6 7 billion
1.05 9 billion
0.92 18 billion
0.79 26 billion

20.

Using the table above, estimate the Sun’s Main Sequence lifetime. Enter a number in the first box, and type either “million” or “billion” in the second box: ???? (number only — no words) ???? (“million” or “billion”?) years

21.

Which of the following statements is true about the relationship between star mass and main sequence lifetime? Highlight correct answer below.

A) There is no relationship between a star’s mass and its main sequence lifetime.

B) The longest-lived stars are those with intermediate mass.

C) The highest-mass stars die the soonest.

D) The shortest-lived stars are those with intermediate mass.

22.

Looking at the mass labels you wrote onto your copy of the H-R diagram, and considering your answers in the previous section for how mass varies along the main sequence, in your own words: How does star lifetime vary along the main sequence? Be sure to refer to the other properties shown on the H-R diagram: Luminosity, Temperature, and Mass. Try to answer in about one full sentence.

23.

Stars often form in clusters, where a whole group of stars form at the same time. These stars form with a whole range of masses, spanning the whole main sequence. If you were to create an H-R diagram of all the stars in a brand new cluster, all age zero (“0 Myr” means 0 Million years), you should see the whole main sequence represented, as shown below. Keep in mind that a star’s properties are constant during its main sequence lifetime, so a star stays in the same location on the H-R Diagram during its whole main sequence lifetime, and only leaves the main sequence when it “dies”.

In a sentence or two, in your own words, describe how the Main Sequence of this H-R diagram would look if we could wait 5 billion years and measure the stars and make the H-R diagram again.

24.

And what if we could wait 25 billion years (longer than the current age of the Universe!) — how would the H-R diagram of this cluster look then?

Explain how we can take advantage of this phenomenon to estimate the age of a star cluster whose age is otherwise unknown. Explain carefully.

25.

Put the following three star clusters in order from oldest to youngest.

A,B, or C: very old

A,B, or C: moderately young

A,B, or C: extremely young

VI: Summary and Reflection

26.

Summarize the important concepts presented in this lab, as well as your main conclusions. Use full grammatical sentences, as always. Your summary should include, but not be limited to, a discussion regarding the properties of stars that can be represented on an H-R diagram, the trends in those properties across the graph, and the various groups of stars represented on an H-R diagram.

REQUIRED: Include your copy of the H-R diagram from the beginning of this lab, with all the many annotations you’ve been instructed to make on it throughout the lab, in your response. If you annotated your H-R diagram on paper, you will need to take a picture of your paper using a camera phone or other digital camera, or else scan it in. Follow the “instructions for uploading images” file found under the “Lessons” tab. Do not email your files to the instructor.

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