Lab_9__Stars_and_Selection_Effects_S24
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Date
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Lab 9: Stars and Selection Effects
Name:
Group Name:
Lab 9: Stars and Selection Effects
Open the NAAP Labs application, and then open
9. Hertzprung-Russell Diagram
.
PART A - BACKGROUND INFORMATION
Work through the background sections on Spectral Classification, Luminosity, and the
Hertzsprung-Russell Diagram. Then complete the following questions related to the
background information.
A1. The table below summarizes the relationship between spectral type, temperature,
and color for stars. Fill in the blanks, noting that the surface temperature of the stars in
the table increases as you move downward. (3 pts)
Star
Surface
Temperature
(K)
Spectral Type
Color
Betelguese
M2
Arcturus
4,300
Sun
G2
Yellow
Procyon A
F5
Yellow-White
Sirius A
A1
Rigel A
11,000
Delta Orionis
O9
1
Lab 9: Stars and Selection Effects
A2. Complete the following table related to stellar radius, surface temperature, and
luminosity (all in solar units) using the equation
.
Show your work in the
space below. See the next page for some math hints that may be useful. (4 pts)
Radius (R
⊙
)
Temperature
(T
⊙
)
Luminosity (L
⊙
)
1
1
1
1
2
1
9
1
1/2
2
64
2
Lab 9: Stars and Selection Effects
Math Hint:
If y
∝
x
4
, you can invert the proportionality to find that x
∝
y
1/4
.
Math Hint:
The “
∝
” sign means proportional to. Let’s take the example of y
∝
x
4
. This is
shorthand for ‘y scales with x
4
, and there is a constant of proportionality A such that y
= A x
4
, but we don’t need to worry about the value of A for our purposes today”. Let’s
say you know that x
1
= 2 and y
1
= 32. We also know that x
2
= 3, and we want to know
what y
2
is. You can set up the problem as:
By using ratios in this way, the constant of proportionality cancels out! Solve for y
2
and
then substitute in values for x
1
, x
2
, and y
1
:
A3. The mass luminosity relation
describes the mathematical relationship
between luminosity and mass for
main sequence
stars (that is—adult stars that are
fusing Hydrogen in their cores). The sun is a main-sequence star with 1 M
⊙
and 1 L
⊙
.
The mass-luminosity relation then implies that a main-sequence star with a mass of
2 M
⊙
would have a luminosity of (don’t forget your units! Show your work!; 1 pt):
3
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Lab 9: Stars and Selection Effects
A4.
Meanwhile a main-sequence star with luminosity of 3,160 L
⊙
would have an
approximate mass of: (1 pt)
PART B - HR Diagram Explorer
In the NAAP Labs application, open the
HR Diagram Explorer
. Begin by familiarizing
yourself with the capabilities of the Hertzsprung-Russell Diagram Explorer through
experimentation.
●
An actual
HR Diagram
is provided in the upper right panel with an active
location indicated by a red x.
This active location can be dragged around the
diagram.
The
options panel
allows you to control the variables plotted on the
x-axis and y-axis —we’ll leave these at defaults today.
One can also show the
main sequence, luminosity classes, isoradius lines, or the instability strip.
The
Plotted Stars
panel allows you to add various groups of stars to the diagram.
●
The
Cursor Properties
panel has sliders for the temperature and luminosity of
the active location on the HR Diagram.
These can control the values of the
active location or move in response to the active location being dragged. The
temperature and luminosity (in solar units) are used to solve for the radius of a
star at the active location.
●
The
Size Comparison
panel in the upper left illustrates the star corresponding
to the active location on the HR Diagram.
Note that the size of the Sun remains
constant.
4
Lab 9: Stars and Selection Effects
Exercises
●
Drag the active location around on the HR Diagram. Note the resulting changes
in the temperature and luminosity sliders.
Now manipulate the temperature and
luminosity sliders and note the corresponding change in the active location.
B1. In the table below, make a checkmark in the appropriate box corresponding to the
region of the HR diagram that fits each description. Make just one checkmark per row!
(1 pt)
Description
Top
Right
Bottom
Left
Hot stars are found at the:
Faint stars are found at the:
Luminous stars are found at the:
Cool stars are found at the:
●
Drag the active location around on the HR Diagram once again. This time focus
on the Size Comparison panel.
B2. In the table below, make a checkmark in the box corresponding to the appropriate
region of the HR diagram fitting each description. Only check one box in each row. (2
pts)
Description
Upper
Left
Upper
Right
Lower
Right
Lower
Left
Large Blue stars are found at the:
Small Red stars are found at the:
Small Blue stars would be found at the:
Really Large Red stars are found at the:
5
Lab 9: Stars and Selection Effects
●
Check
show
isoradius
lines
.
These are lines of constant radius, and are
labelled in units of R
⊙.
Use these isoradius lines to check your answers in the
table above.
B3. Recall from Question A2 that:
Use this proportionality to explain the results you found in the table of the previous
question. How does luminosity depend on the color and size of a star? (2 pts)
●
In addition to the isoradius lines, check
show luminosity classes
.
The green
region (“dwarfs V”) is known as the main sequence and contains all stars that
are fusing hydrogen into helium in their cores as their primary energy source.
Over 90% of all stars fall in this region on the HR diagram.
Move the active
cursor up and down the main sequence and explore the different values of
stellar radius.
●
The
background
pages
of
this
module
talked
about
the
mass-luminosity
relationship for stars on the main sequence:
6
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Lab 9: Stars and Selection Effects
B4. Describe the sizes (i.e., radii) and masses of stars along the main sequence. What
are stars like near the top of the main sequence, the middle, and the bottom? (2 pts)
B5. Use the results from the previous four questions to construct a “conceptual” HR
Diagram.
You simply want to draw arrows showing the direction in which variables are
increasing. (3 pts)
a)
Draw in an arrow on the y axis showing the direction of increasing “intrinsic
luminosity” of the stars. (This is completed for you, labelled with “L”.)
b)
Draw
in an arrow on the x-axis showing the direction of increasing surface
temperature of the stars. Label this arrow with “T”.
c)
Draw in an arrow showing the direction of increasing radius on the diagram.
(hint:
this must be perpendicular to the isoradius lines.) Label this arrow with “R”.
d)
Draw in an arrow showing the direction of increasing mass for main sequence stars
on the diagram.
(Note that his arrow only applies to main sequence stars, but that is
over 90% of stars.) Label this arrow with “M”.
7
Lab 9: Stars and Selection Effects
B6. Recall the mass-luminosity relation for main sequence stars: L
∝ M
3.5
. We can
approximate
that
the
main
sequence
lifetime
scales
as
𝛕 ∝
M/L, because M is
approximately the amount of fuel available for fusion, and L is proportional to how
rapidly the fuel is being used. We can then estimate how main-sequence lifetime
depends on stellar mass alone by substituting in for L:
𝛕 ∝
M/L
∝
M/M
3.5
∝
M
-2.5
The Sun’s main-sequence lifetime is roughly 10 billion years. Using the above scaling
relation to estimate how long will a star that is ten times the mass of our Sun will live.
How long will a star that is half the mass of our Sun live? How do these lifetimes
compare with the age of the Earth (4.5 billion years) and the time elapsed since the
Jurassic period when dinosaurs roamed the Earth (170 million years ago)? (4 pts)
8
Lab 9: Stars and Selection Effects
B7. In Lab 10, we’ll see that some galaxies have both blue and red stars, while other
galaxies mostly just have red stars. Based on what you’ve learned today, which stellar
population do you think includes more young stars—a population composed of red
and blue stars, or one with almost exclusively red stars? Explain your reasoning.
(2
pts)
Part C - Exploring Real-World Stars
Now let’s put some real stars on the H-R diagram!
●
Check the plotted stars option
the nearest stars
.
●
You may want to unselect
show luminosity classes
and
show isoradius lines
(but feel free to add these back in if they are helpful, later!)
C1. Describe the characteristics of the nearest stars.
Describe their luminosities and
temperatures. Are they mostly on the main sequence, or do they primarily belong to a
different luminosity class? (3 pts)
9
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Lab 9: Stars and Selection Effects
C2. Do you think these nearest stars are rare or very common among all of the stars of
our galaxy?
Explain your reasoning. Are any assumptions involved in your reasoning?
(2 pts)
●
Uncheck the plotted stars option
the nearest stars
and check
the brightest
stars
.
Why are these stars the brightest in the sky? Three students debate this issue:
Student A: “I think it’s because these stars must be very close to us. That would make
them appear brighter to us in the sky.”
Student B: “I think it’s because these stars are very luminous.
They are putting out a
tremendous amount of energy.”
Student C: “I think it’s because these stars are very close and very luminous.”
C3. Use the tools of the HR Diagram to support the views of one of the three students.
Why are the stars we perceive as bright in the night sky really bright?” (Hint: You may
find the options labeled
both the nearest and brightest stars
and
the overlap
useful.)
(3 pts)
10
Lab 9: Stars and Selection Effects
More space to answer question C3:
C4. Do you think that these bright stars are very common (make up a large percentage
of all stars in general)? Explain your reasoning. (3 pts)
11
Lab 9: Stars and Selection Effects
C5. Clearly, we find very different samples of stars if we select the brightest ones,
rather than the nearest ones. This is an example of a
selection effect
, which is to say
that what we observe in our sample is biased by how we select our sample. Give an
example of a selection effect in a context outside astronomy. You might think about
studies done in social science or health science, or political polling. Be specific about
how you think the selection process determines the sample or results of the study. (4
pts)
12
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