AST 114 – Spring 2002
Magnitudes and Stellar Brightness
MAGNITUDES AND STELLAR BRIGHTNESS
What will you learn in this Lab?
For the first time we’ll be looking at the stars tonight as something more than just pretty
points of light. We’re going to take special note of their location, their relative
brightnesses, and even their colors. These types of observations were the fundamental
work of both ancient and modern amateur astronomers alike – giving us a unique record
of the brightnesses of stars through the course of history.
What do I need to bring to the Class with me to do this Lab?
For this lab you will need:

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




A copy of this lab script
A pencil
A scientific calculator
Your flashlight
Your field guide
Your star charts
Your star wheel
© 2002 Arizona State University
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AST 114 – Spring 2002
Magnitudes and Stellar Brightness
Introduction:
This exercise is designed to help the student become familiar with the magnitudes (i.e.,
apparent brightnesses) and colors of stars. While completing tonight's work, you should
learn the naming convention used to identify stars.
Magnitudes: To describe how bright individual stars are and to express differences in
brightness, astronomers assign each star a magnitude according to its brightness. The
magnitude system was first used by the Greek astronomer Hipparchus, who divided the
stars into six categories. He called the brightest stars in the sky `first magnitude' and the
faintest `sixth magnitude'. Stars of intermediate brightness were assigned a number
between 1 and 6. We still use a modified version of this system, with extensions to
encompass a larger range of brightnesses by using numbers smaller than 1 and larger
than 6.
The first thing you should notice about this system is that its ordering is backward: a small
number (like 1, or even a negative number) denotes a brighter star than a large number
(like 8 or 9). The brightest star in the night sky, Sirius, has a magnitude of -1.5 while the
faintest star that can be seen with the unaided eye is about magnitude 6. For comparison,
the magnitude of the Sun is -26.5. An easy way to remember that the magnitude system
runs backward is to think of magnitudes in terms of rank. A `first-rank' star is brighter than
a `second-rank' star, which in turn is brighter than a `third-rank' star, etc.
Another important feature of the magnitude system is that it is a logarithmic scale. When
the system was first setup, it was thought that 1st magnitude stars were about twice as
bright as 2nd magnitude stars, which were twice as bright as the 3rd magnitude stars, etc.
Following this pattern, one would expect a 1st magnitude star to be about 32 (= 2 x 2 x 2 x
2 x 2) times brighter than a 6th magnitude star, but careful measurements have shown
that this is not correct. Instead, the jump from 1st magnitude to 6th magnitude actually
represents a change of 100 times in brightness. Each increase of one magnitude
corresponds to a decrease by a factor of about 2.512 (  5 100 ) in brightness. For
example, how does the brightness of a star with magnitude 1 compare to that of a star
with magnitude 4? It is 3 magnitudes brighter, which means that is 15.85 (=2.512 x 2.512
x 2.512) times as bright.
Finally, the basic magnitude system used here is one based on the apparent brightnesses
of stars. That is, how they appear in the sky. Hence, we call these apparent magnitudes.
Without knowing the distance to an individual star, we cannot say anything about its
intrinsic brightness. A truly bright star that is very far away can appear to be fainter than
an intrinsically dim star that is very close by.
Colors: Astute observers will note that the brighter stars have discernable colors.
While most stars look whitish to the eye, some have a distinctive blue, yellow, or reddish
appearance. The perceived color depends primarily on the energy distribution of the star's
emitted light, which is a function of the star's surface temperature. For blackbodies (and
stars approximate blackbodies!), Wien's Law specifies the wavelength at which the peak
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Magnitudes and Stellar Brightness
intensity occurs. For high temperature stars this peak is at short wavelengths, while for
cool stars the peak shifts to long wavelengths.
Another factor that influences the perceived color is the spectral response of the human
eye, which is most sensitive to light in the green/yellow portion of the spectrum,
diminishing at both blue and red wavelengths. Hence, hot stars will appear bluish to the
eye, and cool stars will look reddish, provided they are sufficiently bright. Dim stars simply
do not register enough light to trigger a color response from the eye, so the faint stars all
appear white. Interested students should investigate the nature of rods and cones in the
human retina.
Names of Stars: The brightest stars in the sky were given names in antiquity. Many of
these, some from Arabic and Greek, are still used today (e.g., Sirius -- the brightest star in
the sky). Fainter stars are sometimes named for the person who first noticed them (e.g.,
Barnard's star was found because of its very high proper motion across the sky). The
majority of stars are simply designated by a catalogue number (e.g., BD +59º1915A is in
the +59º declination zone of the Bonner Durchmusterung Catalogue).
The entire sky is divided into 88 constellations, so that every star is located in a
constellation. Most of the brighter stars can be designated by a lower-case Greek letter
and the (often abbreviated) constellation name (e.g.,  Cas and  Ori). Usually the stars
are named in order of brightness, with  being the brightest,  the next brightest, etc.
Thus, the brightest star in Taurus (Aldebaran) is also called  Tau. Because this Greek
letter/constellation name syntax is so common, you should become familiar with the lowercase Greek alphabet.
The Lower-case Greek Alphabet








alpha
beta
gamma
delta
epsilon
zeta
eta
theta








iota
kappa
lambda
mu
nu
xi
omicron
pi








rho
sigma
tau
upsilon
phi
chi
psi
omega
Inverse Square Law: this grand sounding title is given to the common sense
phenomenon that the farther away you hold a light the fainter it appears to be. Since the
light emitted from any light, including a star, spreads out in all directions, its intensity can
be related to the surface area of a sphere. If you like, the light is being spread over the
surface of a sphere: the further you get from the star, the larger the sphere must be, and
so the greater the spreading, or fading, of the light intensity. This predicts that the further
away you are from a star the fainter that star will appear. Now the equation for the surface
2
area of a sphere is 4 R , where R is the radius of the sphere. So if you move double the
© 2002 Arizona State University
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Magnitudes and Stellar Brightness
distance away from a star, the surface area of the corresponding sphere quadruples.
Similarly if you move three times farther away, the sphere’s surface area goes up nine
times. But since the same amount of light is being spread over the surface of this sphere,
the light intensity falls by proportion. This is why the relationship is called the inverse
square law.
Stellar Distance and Magnitude: It stands to reason that if you know how bright a star
appears to be and how bright the star really is, then you can figure out how far off that star
should be. This raises the issue of the two main types of magnitudes that you will see
referred to in Astronomy textbooks: Apparent and Absolute Magnitudes. The former of
these is the regular observed magnitude we’ve been talking about already. The latter of
these is something new. If you’re going to classify stars and describe them by how bright
they are intrinsically, then you need a system by which to measure that intrinsic
brightness. But how do you do that when the brightness of star depends on your distance
from it? The way this is done is to define a standard distance from which to measure or
define the standard brightness of star. This distance is 10 parsecs. The magnitude of a
star measured at a distance of 10 parsecs is called the Absolute Magnitude and is the
meter rule by which we classify stars of different types.
An equation relates the apparent and absolute magnitudes of a star (m and M
respectively) to the distance to the star from the observer (d, measured in parsecs):
m  M  5log 10 d  5
so if you know both m and M you can figure out the distance to the star.
© 2002 Arizona State University
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Magnitudes and Stellar Brightness
Procedure
This exercise will give you the opportunity to attempt to replicate how stellar photometry
(literally: the measurement of light) was done by civilizations such as the Ancient Chinese
and Arabs. These peoples did their measurements totally by eye, and to this day this
approach is still practiced by many amateur observers to keep track of variable stars as
they change their apparent brightness in our night sky.
Choose a constellation, or two adjacent constellations, located high above the horizon,
consisting of at least eight or more stars visible to your eye. Carefully draw this
constellation, indicating the brightnesses of the stars in the same manner as they do on
the star charts: with different sized dots, using larger dots for brighter stars and smaller
ones for the fainter stars. Use your star charts to identify the stars you’ve drawn. In a
table rank the stars in order of decreasing brightness, as they appear to you. (The
brightest star should be first, the next brightest second, etc.). Record the star’s name and
the constellation in which it resides. For each star make an estimate of its magnitude
using your charts and/or the field guide. Use the legends on the charts to aid in your
estimates. Also make an estimate of the star’s color.
Colors of stars indicate their surface temperatures. The hottest stars (T = 10000 to 25000
K) appear quite blue, while the coolest stars (T = 3000 to 5000 K) look reddish. Using
these facts estimate which of the stars you’ve recorded is the hottest and which the
coolest.
Now, return to looking at the sky and pick an area in the constellation you studied to
examine more carefully. Pick your location well – it should have a good selection of bright
and faint stars. Use a 40 mm eyepiece you have a nice wide angle view, and center the
telescope on what you choose to be the best place. First, look through the finderscope,
once the telescope is locked and driving, and make a quick finderchart to indicate where
in the constellation you’re looking and label the main stars in the region, so you have a
road map to your location. Make a detailed and proportional drawing of your field, as seen
through the main telescope. Make sure your field has 2-3 stars of known brightness in it.
Your TA will have AAVSO star charts for the region. These charts indicate stellar
brightness in magnitudes for many stars. The table at the end of this lab script also lists
the brightness for many of the main stars in the sky tonight.
Once you have a working diagram, start to estimate the brightnesses of the other stars in
the field. There are a variety of ways to do this, but the one recommended here is to use
the known stars to estimate how far between, or beyond, the brightness of the known
stars your unknown star lies. Use the example on the next page as a guide to how you
should proceed.
© 2002 Arizona State University
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Magnitudes and Stellar Brightness
In this set of stars we have some brighter labeled stars, together with some unknown
intermediate and faint stars. For this example let’s look at the star immediately between
,  and . If we know that  has a magnitude of 2.3,  is 3.8 and  is 4.5, then we can
make some estimate of how bright the unknown star is. This star is very close in
brightness to , but is slightly fainter. From looking at how much fainter than  looks, and
knowing that that corresponds to a magnitude drop of 0.7 magnitudes, we can estimate
how much fainter the star in question is than . I would estimate it to be about 0.1
magnitudes fainter, at most, giving it a magnitude of 4.6.
Again, let’s assume that we don’t know the brightness of  – but it appears to be
somewhere between  and  in brightness. What estimate of its brightness can you make
given the known values for  and ? This is how the process works, and how thousands of
amateur astronomers around the world monitor the brightness of known variable stars to
make their contribution to the world of astronomical research.
Use this technique to estimate the brightness of all the stars in your telescopic field. Also
make some estimate of their color. Once you’ve done that, assume that all of the stars in
your field have an absolute magnitude of +1.0. Calculate the corresponding distance to
each star in parsecs based on your visual estimates of their apparent magnitudes.
Questions
Your lab report should address the following questions:
1. From analysis of your tables of stellar brightness data, is it always true that the star
labeled  is always the brightest, and  the second brightest, etc.? If not, why do you
think that this might be so?
2. How accurate do you think the measuring technique you used tonight really is? Why
do you think this approach is better than just making a solitary measurement without
comparing it to two or three stars at once? How reliable would you say amateur
observations of variable stars are after having walked in their shoes?
© 2002 Arizona State University
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Magnitudes and Stellar Brightness
3. The magnitude system may seem an archaic one, but now you have seen how it was
originally formulated and applied to stars in the sky. Given that the system is
essentially logarithmic, how many times brighter in appearance is the brightest star we
know of in the sky (Sirius with an apparent magnitude of 0.0) compared to a star down
at the limit of our naked eye vision (at a magnitude of 6.0)? It is an astounding number
and gives testament to how broad a range of light conditions our eyes can handle.
4. In the instructions, you were asked to pick an area of sky to do your observations that
was well above the horizon. Why was this?
Indoor Alternative
In the event of bad weather, when the roof cannot be used to view stars in the sky, follow
these instructions.
Using your star charts, pick a constellation and transcribe what you see drawn for the area
of sky in question. Pay particular attention to naming the stars and getting their relative
positions right. Do not just trace the positions, we’ll be able to tell! If any of the stars you
draw are listed in the table at the end of this script then mark their numerical magnitude
next to the star’s position and name. Extend your drawing to include the fainter stars that
are unlabeled – assign some names to these stars (or numbers) so you can identify them.
Using the technique discussed at the top of page 5, make estimates of the magnitudes of
all the stars in your drawing.
As in the fair weather exercise, assume that each star has an absolute magnitude of +1.0,
and use this fact to calculate the distance to each of your stars in parsecs.
Write up a report on what you did/learned and don’t forget to address the issues raised by
the questions above. Your report should also demonstrate your understanding of the
material in the lab script when you discuss your results. How did you arrive at your final
answers? Why does knowledge of both the apparent and absolute magnitudes of a star
allow you to calculate the distance? Explain what you’re doing as well as just doing it.
The correct form of the equation for distance is actually:
m  M  5log 10 d  5  A
what do you think the constant A is? Note that for a given absolute magnitude M, it
increases, ie. makes fainter, the apparent magnitude m. Ask your TA to explain what
Olber’s paradox is. Why do you think the night sky is not, therefore, as bright as the Sun?
© 2002 Arizona State University
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Magnitudes and Stellar Brightness
Appendix: Magnitudes of Brightest Stars in Some Spring Constellations
Auriga










0.09
1.90
1.65
3.72
2.99
3.75 var
3.17
2.69
2.62
3.97
Cassiopeia








2.24
2.27
2.47
2.68
3.38
3.66
3.45
4.15
Gemini
















1.99,2.85
1.15
1.93
3.52
2.98
3.79 var
3.20 var
3.59
3.80
3.57
3.58
2.88
4.15
3.37
4.16
4.07
Leo













1.36
2.14
2.61,3.80
2.55
2.96
3.43
3.52
3.34
3.93
4.31
3.88
3.52
3.85
Orion














0.50 var
0.08
1.64
2.23,6.85
1.70 var
1.77,4.21
3.35
2.77
2.04
3.39
4.12
3.19,4.36,
3.69,3.72,
4.47
3.81
3.60
© 2002 Arizona State University
Canis Major








-1.47
1.98
4.10
1.84
1.50
3.02
2.40
3.04,3.78
Perseus


















1.79
2.12 var
2.93
2.99
2.88
2.83
3.76
4.05
3.80
4.29
4.13
3.77
4.03
3.83
3.39 var
3.95
3.56
4.06
Taurus












0.86
1.65
3.63
3.76
3.54
2.99
2.86
3.41,3.85
3.47
3.91
3.74
3.60
Ursa Major

















1.79
2.36
2.44
3.31
1.76
2.05,3.96
1.86
3.18
3.14
3.66
3.45
3.04
3.48
3.36
3.77
3.69
3.01
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