Stellar Magnitudes
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University of Missouri, Columbia *
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1010
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Astronomy
Date
Dec 6, 2023
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docx
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Stellar Magnitudes
I. Star Magnitudes & Distances
Millions of stars are scattered across the sky. Astronomers want to study these stars as carefully
as possible. This means measuring everything we can about them. All we have is the light that
reaches us from the stars and astronomers can really only
directly
measure three properties of
stars:
1) Position
2) Brightness
3) Spectrum (more on this in a future lab)
They then use these measurements to deduce many other properties of the stars. We have
already had practice measuring a star's position using the Altitude/Azimuth method. Now it is
time to look at the second stellar property:
brightness
.
Everyone agrees that stars come in different brightnesses – some are bright, and some are faint.
As discussed in the lecture slides, the
brightness
of a star as it appears in the sky is quantified as
a
magnitude
, where smaller numbers mean brighter stars. Magnitudes can even be negative for
very bright stars.
Now let us try to figure out what the brightness of a star can tell us. Remember, there are two
kinds of magnitudes –
Apparent Magnitude (m)
, which is how bright the star appears from
Earth, and
Absolute Magnitude (M)
, which is how bright the star would be if it were 10 parsecs
away.
Let us examine more closely
Luminosity
and
Distance
.
Luminosity
is a measure of how much
total light a star gives off every second. A star that looks dim to our eyes could be dim because it
has a low luminosity, or because it is far away. Which one is it? If we could measure the star's
distance, then we could answer that question.
II. Apparent and Absolute Magnitude
•
What TWO factors determine a star's apparent magnitude (how bright the star will appear to
be in our night sky)?
Luminosity and Distance
•
Which value, apparent or absolute magnitude:
a. Tells us how bright an object will appear from Earth? Apparent magnitude
b. Tells us which star is giving off more light? Absolute magnitude
•
You observe two stars: Canopus has an apparent magnitude of -0.65 and Bellatrix has an
apparent magnitude of +1.60.
•
Which star looks brighter? Canopus
•
You also observed a third, dimmer star. Make up a value for its apparent magnitude.
+1.83
•
The star Deneb has an apparent magnitude of +1.25 and is located 433 parsecs away. Which
of the following values is likely the absolute magnitude for Deneb? (No calculation needed)
•
-6.93
•
1.25
•
7.31
Explain your reasoning: 433 parsecs is a huge distance and as the distance increases, the
absolute magnitude decreases.
Refer to the following table for questions 5-7:
Apparent Magnitude
Absolute Magnitude
Star A
1
1
Star B
1
2
Star C
5
4
Star D
4
4
•
Which object appears brighter from Earth? Star C or D? Explain reasoning.
Star D because its’ apparent magnitude is less than Star C’s apparent magnitude and that is what
is used to determine how bright they are.
•
Which object is more luminous: Star A or Star D? Explain reasoning. Star A is more luminous
than Star D because Star A has a lower absolute magnitude.
•
For each star (A-D), state whether the star is closer than, farther than, or exactly 10pc away
from Earth. Explain reasoning.
Star A: The star is exactly 10 pc away from Earth since the apparent magnitude and absolute
magnitude are equal.
Star B: The star is closer than 10pc away from Earth. The absolute magnitude is greater than the
apparent magnitude.
Star C: The star is greater than 10 pc away from Earth. The apparent magnitude is greater than
the absolute magnitude.
Star D: The star is exactly 10 pc away from Earth since the absolute magnitude and apparent
magnitude are equal.
•
In general, which will be a larger number in the following situations:
(Apparent Magnitude, Absolute Magnitude, Neither)
a.
If a star is
further than 10pc
away:
apparent magnitude
b. If a star is
closer than 10pc
away:
absolute magnitude
c. If a star is
exactly 10pc
away:
neither
•
Would the apparent magnitude number of Star A increase, decrease or star the same if it
were located at a distance of 40pc?
increase
What about the absolute magnitude number? Stays the same
Explain your reasoning.
As the star gets further away, the apparent magnitude increases, but
the absolute magnitude
stays the same.
III. Orion
Start
Stellarium
. Turn off the
Atmosphere (A)
and
Ground (G)
. Click on a few stars randomly. For
each selected star, its information will appear, as usual, in the upper left-hand corner of the
screen. The star's
magnitude
will be listed in the 2
nd
line of information below the star's name.
This is the star's
Apparent Magnitude
.
Let's use the constellation Orion as our subject of study. Using
Stellarium
, determine the
properties of the 7 brightest stars in Orion and fill out their corresponding data tables on the
next page.
You can use the
Search window (F3)
to type in the name of the star. The distances
must be in parsecs (not light years)!
See Appendix A to determine how to calculate the distance
from parallax (p). Since this version of Stellarium gives these star distances in “mas” or “milli-arc-
seconds” you will take 1000 divided by the parallax to get the distance (instead of 1/parallax
when it is given in arcseconds).
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m: apparent magnitude – from 2
nd
line
M: absolute magnitude – from 3
rd
line
p: parallax – near the bottom of the info pane. Record only the number before the +/- sign.
d: distance –
need to calculate
by taking 1000/parallax. Distance will be in parsecs.
Do not
copy
distance from the info pane; it will be in light years and will not work in our equations!
(If doing this in Word, you may need to delete excess rows to see this diagram display correctly)
•
Which star in Orion is the brightest?
Rigel
•
Which of these 7 stars is the most luminous?
Alnilam
•
Betelgeuse is a red supergiant star near the end of its life. Any time in the next 1000 years,
Betelgeuse will go supernova and its luminosity will increase by a factor of 10
5
for a few
weeks. At its peak, the absolute magnitude will reach M = -18.3. What will its
apparent
magnitude
be? Use the distance modulus equation from Appendix B.
•
Imagine that 1 billion years from now, Saiph is now twice as far away from us than it is today.
Besides its distance, assume (unrealistically) that the star, Saiph did not change in any way.
•
By what fraction does the brightness change? (no calculation needed):
It would appear ¼
of the distance away
•
Will its absolute magnitude change?
No it will not since the distance doesn’t affect the
absolute magnitude.
•
Calculate its new
apparent magnitude
:
0.5125
•
The Sun's absolute magnitude is +4.74. How does its luminosity compare to these 7 stars?
(no calculation needed, just describe it)
They are no where even close to the Sun’s absolute
magnitude. The highest absolute magnitude among the 7 stars is -2.84.
•
a. What is the closest star in Orion?
Bellatrix
•
What would the Sun's
apparent magnitude
be if it were at this distance? The Sun’s
apparent magnitude would be significantly smaller if the Sun were to be at this distance.
•
Would we be able to see it naked eye?
•
The naked eye limit is m = 6 magnitudes. Determine how close a star like the sun has to be in
order to be visible with the naked eye. Use the equation for distance from Appendix B.
•
The star distances on the previous page were calculated from parallax. Choose two stars and
calculate their
distance
from the rearranged distance modulus equation (Appendix B).
Compare this distance to the distance you get from parallax. Give the values. Are they the
same?
Yeah, they are the same. They might not be the EXACT answer, but they give a close
answer.