Download Color and Temperature of Stars

Thomas Durkin
Engaging in Science: Astronomy for Teachers
Barbra Shaw Ph. D.
Portland State University
March 19, 2010
Laboratory: Stellar Color Analyzer
I.
Introduction: This computer laboratory activity is an extension of an astronomy
unit. This unit includes a power point presentation that is based on the resource
Astronomy Picture of the Day (APOD). Using APOD, students determine the color
spectrum of their chosen star, providing data and charts of the color. Students use
easily available tools to measure colors and record their results.
II.
Concepts Addressed: Stellar color spectrums can be used to determine the surface
temperature of a star. From this temperature, the elements present in the star can be
inferred.
III.
Lab Goals: Students will determine the average color of various stars and correlate
these colors to star temperatures
IV.
Benchmarks Addressed:
A.
Science Grade 7
7.3 Scientific Inquiry: Scientific inquiry is the investigation of the natural world
based on observation and science principles that includes proposing questions or
hypotheses, designing procedures for questioning, collecting, analyzing, and
interpreting multiple forms of accurate and relevant data to produce justifiable
evidence-based explanations.
7.3S.1 Based on observations and science principles propose questions or
hypotheses that can be examined through scientific investigation. Design and
conduct a scientific investigation that uses appropriate tools and techniques to
collect relevant data.
7.3S.2 Organize, display, and analyze relevant data, construct an evidence-based
explanation of the results of an investigation, and communicate the conclusions
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including possible sources of error.
7.3S.3 Evaluate the validity of scientific explanations and conclusions based on
the amount and quality of the evidence cited.
B.
Science Grade 6
6.1E.2
Describe the properties of objects in the solar system. Describe
and compare the position of the sun within the solar system, galaxy, and
universe.
C.
Science Grade 8
Interaction and Change: Systems interact with other systems.
8.2E.1
Explain how gravity is the force that keeps objects in the solar system in
regular and predictable motion and describe the resulting phenomena. Explain
the interactions that result in Earth’s seasons.
D.
Mathematics Grade 7
7.2 Number and Operations, Algebra and Geometry: Develop an understanding
of and apply proportionality, including similarity.
7.2.1 Represent proportional relationships with coordinate graphs and tables,
and identify unit rate as the slope of the related line.
7.2.3 Use coordinate graphs, tables, and equations to distinguish proportional
relationships from other relationships, including inverse proportionality.
V.
NASA Big Questions: Astrophysics Questions
A.
When and how did the elements of life in the Universe arise?
http://nasascience.nasa.gov/big-questions/when-and-how-did-the-elements-oflife-in-the-universe-arise
1.
Following the Big Bang and the gradual cooling of the Universe, the
primary constituents of the cosmos were the elements hydrogen and helium.
Even today, these two elements make up 98% of the visible matter in the
Universe. Nevertheless, our world and everything it contains—even life
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itself—is possible only because of the existence of heavier elements such as
carbon, nitrogen, oxygen, silicon, iron, and many, many others. How long
did it take the first generations of stars to seed our Universe with the heavy
elements we see on Earth today? When in the history of the Universe was
there a sufficient supply of heavy elements to allow the formation of
prebiotic molecules and terrestrial-like planets upon which those molecules
might combine to form life?
All elements heavier than hydrogen and helium are manufactured
inside stars, or produced when a star’s life ends as a supernova.
NASA seeks to study the way stars evolve over time, and how
they end their lives in order to learn about how the Universe has
transformed itself from a place of only two simple elements to
one with a molecular complexity sufficient to support life.
Understanding how stars form, how they evolve over their lives, and how
they die, is key to understanding the history of heavy elements in the
Universe. By studying stellar nurseries in which stars are born as well as
the supernovae, debris shells, white dwarves, and neutron stars left behind
when they die will reveal how the Universe has created and disseminated
complex elements throughout its history. This will permit us to predict when
there was a sufficient quantity of these elements such that life creation
would have been possible. Knowing when the Universe was capable of
supporting life will help us evaluate the likelihood that other life exists in
the cosmos.
VI.
Sources
A.
http://en.wikipedia.org/wiki/Color_temperature
B.
http://www.webexhibits.org/causesofcolor/18B.html
C.
http://www.nasa.gov/worldbook/star_worldbook.html
D.
http://sunearthday.gsfc.nasa.gov/2009/TTT/65_surfacetemp.php
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E.
VII.
http://en.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram
Introduction
Color and temperature
A.
Color temperature is a characteristic of visible light that has important
applications in lighting, photography, videography, publishing, manufacturing,
astrophysics, and other fields. The color temperature of a light source is the
temperature of an ideal black-body radiator that radiates light of comparable hue
to that light source. The temperature is conventionally stated in units of absolute
temperature, Kelvin (K). Color temperature is related to Planck's law and to
Wien's displacement law. Higher color temperatures (5,000 K or more) are cool
(blueish white) colors; lower color temperatures (2,700–3,000 K) are warm
(yellowish white through red) colors.
B.
Stars great and small, and their life cycles
A star’s color is critical in identifying the star, because it tells us the star’s
surface temperature in the black body radiation scale. The sun has a surface
temperature of 5,500 K, typical for a yellow star. Red stars are cooler than the
sun, with surface temperatures of 3,500 K for a bright red star and 2,500 K for a
dark red star. The hottest stars are blue, with their surface temperatures falling
anywhere between 10,000 K and 50,000 K.
Stars are fuelled by the nuclear fusion reactions at their core. There is a dynamic
equilibrium maintained throughout the star’s life between the expanding heat of
the reactive core and gravitational forces holding the star together. Fusion
produces extremely high energy. Fusion releases some of the energy that binds
the particles of the nucleus together, unleashing remarkable power.
Stars begin as a mass of dust and gas dense enough to start collapsing inwards
under the pressure of its own gravity. If this protostar is massive enough, it will
eventually initiate a nuclear reaction in its hot, dense core. This initiates the
main sequence of a star’s life cycle, when hydrogen forms helium at the star’s
core through the process of nuclear fusion. Heat from the star’s core radiates
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outwards through the layers of the star to the photosphere, the visible surface,
which emits electromagnetic energy and charged particles as a solar wind.
A star does not stay the same color throughout its lifecycle, since the surface
temperature alters depending on the type of fusion reaction fuelling the star at
the time. Depending on the initial mass of the star, it will evolve along the lines
of one of three main star types: low-mass stars, intermediate-mass stars (like our
sun) and high-mass stars.
C.
If you look carefully at the stars, even without binoculars or a telescope, you
will see a range of color from reddish to yellowish to bluish. For example,
Betelgeuse looks reddish, Pollux -- like the sun -- is yellowish, and Rigel looks
bluish.
A star's color depends on its surface temperature. Astronomers measure star
temperatures in a metric unit known as the Kelvin. One Kelvin equals exactly 1
Celsius degree (1.8 Fahrenheit degree), but the Kelvin and Celsius scales start at
different points. The Kelvin scale starts at -273.15 degrees C. Therefore, a
temperature of 0 K equals -273.15 degrees C, or -459.67 degrees F. A
temperature of 0 degrees C (32 degrees F) equals 273.15 K.
Dark red stars have surface temperatures of about 2500 K. The surface
temperature of a bright red star is approximately 3500 K; that of the sun and
other yellow stars, roughly 5500 K. Blue stars range from about 10,000 to
50,000 K in surface temperature.
Although a star appears to the unaided eye to have a single color, it actually
emits a broad spectrum (band) of colors. You can see that starlight consists of
many colors by using a prism to separate and spread the colors of the light of the
sun, a yellow star. The visible spectrum includes all the colors of the rainbow.
These colors range from red, produced by the photons (particles of light) with
the least energy; to violet, produced by the most energetic photons.
Visible light is one of six bands of electromagnetic radiation. Ranging from the
least energetic to the most energetic, they are: radio waves, infrared rays, visible
light, ultraviolet rays, X rays, and gamma rays. All six bands are emitted by
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stars, but most individual stars do not emit all of them. The combined range of
all six bands is known as the electromagnetic spectrum.
Astronomers study a star's spectrum by separating it, spreading it out, and
displaying it. The display itself is also known as a spectrum. The scientists study
thin gaps in the spectrum. When the spectrum is spread out from left to right, the
gaps appear as vertical lines. The spectra of stars have dark absorption lines
where radiation of specific energies is weak. In a few special cases in the visible
spectrum, stars have bright emission lines where radiation of specific energies is
especially strong.
An absorption line appears when a chemical element or compound absorbs
radiation that has the amount of energy corresponding to the line. For example,
the spectrum of the visible light coming from the sun has a group of absorption
lines in the green part of the spectrum. Calcium in an outer layer of the sun
absorbs light rays that would have produced the corresponding green colors.
Although all stars have absorption lines in the visible band of the
electromagnetic spectrum, emission lines are more common in other parts of the
spectrum. For instance, nitrogen in the sun's atmosphere emits powerful
radiation that produces emission lines in the ultraviolet part of the spectrum.
There is a precise relationship between the temperature of a body and its color,
which comes from the fact that a heated surface does not emit the same amount
of energy at all possible electromagnetic wavelengths. In fact, the light follows a
unique curve deduced by physicist Maxwell Planck. We call it the 'Planck
Blackbody Curve' because all bodies, from iron bars, to the distant stars, follow
this same curve as the emit light at a specific temperature. Figure 2 shows a few
of these curves for different temperatures. Notice that the wavelength of the
peak of the curve where most of the light is emitted, shifts from short
wavelengths (bluish color) near 500 nm to longer (reddish color) wavelengths
near 800 nm as the temperature decreases. This is why a cooling iron bar first
appears 'white hot' then changes to yellow to orange to red as it cools.
D.
By measuring the exact amount of light produced by a star at specific
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wavelengths from the ultraviolet to the infrared, astronomers can 'fit' a unique
Planck Curve to this data and deduce the star's surface temperature - one of the
most fundamental things you can ever hope to learn about a star without actually
visiting it!
Another thing that goes along with the temperature of a gas is the pattern of
‘fingerprint’ lines its constituent atoms produce. As atoms collide, their
electrons make jumps from one energy to another in specific steps. Each step
downwards in energy causes a photon of light to be emitted. The particular
pattern of lines for an element is unique to that element, so astronomers can tell
which elements are present in a star’s atmosphere by carefully studying these
‘spectral lines’. A cool star has elements that produce many of these lines, while
a hot star can be so hot that electrons are stripped out of the atoms, thereby
reducing the number of lines that can be produced in the atoms (or ions!)
fingerprint. By carefully studying the spectra from stars, astronomers can order
them from hottest to coolest.
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E.
The Hertzsprung–Russell diagram is a scatter graph of stars showing the
relationship between the stars' absolute magnitudes or luminosity versus
their spectral types or classifications and effective temperatures.
Hertzsprung-Russell diagrams are not pictures or maps of the locations of
the stars. Rather, they plot each star on a graph measuring the star's
absolute magnitude or brightness against its temperature and color.
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The lab is divided into two parts, the Excel session and the GIMP sessions.
1. Students will create the Excel spreadsheet, Color_Analyzer, during the first computer lab
session. Look at the screen shots of Excel for more detailed instructions. I found this
preparation to be extremely helpful during the GIMP Color Picker sessions.
2. Students analyze saved photograph files of two stars using GIMP Color Picker functions.
The instructions for this are detailed in step 3.
VIII. Procedure:
1: Create the Excel document Color_Analyzer. See example below.
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2: Download four pictures:
APOD Image
Saved as:
January 8, 2010: The Mystery of the Fading Star
EpsilonAurigae_wong900
January 6, 2010: The Spotty Surface of Betelgeuse
Betel_haubois800
December 21, 2009: Star Cluster R136 Bursts Out
30dor_hst
August 5, 2009: Betelgeuse Resolved
Betelgeuze_eso
3: Open Gimp.
● File menu: “Open” the December 21st picture Star Cluster R136 Bursts Out saved as
30dor_hst, and abbreviated as “Hot” in these directions. I selected this to set my “hot
star” point in my data.
● Find the brightest area. Using the rectangle select tool, highlight a large portion of that
area.
● View menu: under “Zoom” enlarge to 800%.
● Again find the brightest area. Using the rectangle select tool, highlight a large portion of
that area.
● View menu: under “Zoom” enlarge to 1600%
● Because you selected the area for the “brightest”, use the rectangle upper left corner as
the fixed spot.
● Select the rectangle tool again, and re-adjust the size of your rectangle to 5 pixels across
and 5 pixels down, with the upper left corner as your starting point. This will give us a
25 point sample of the brightest area.
Rectangle Select Tool
Selected area anchor point
Area adjusted to 5 across and 5 down
1600% magnification
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4: Open Excel and record the location of your 5x5 grid (on the picture below, I used the
following abbreviations:
o U = upper
o L = lower
o L = left
o R = right
o H = horizontal
o V = vertical
● On Column A, record the grid location on your picture as Grid 1.1 for row 1 column 1,
1.2 for row 1, column 2, etc.
● Back on the Gimp menu, select the “Color Picker” tool.
● Using that tool, point on the pixel 1.1 and click on that color.
● The color will appear in this box (foreground color) in your Gimp menu.
o If that color appears in the lower box, you need to switch to foreground. Click
this button.
● Click on that box, and this menu (Change Foreground Color) will appear.
● Note the numbers on the right side? They are values for:
o H = hue
o S = saturation
o V = value
o R = red
o G = green
o B = blue
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● Use those titles for columns B-G in Excel.
● Record each value in the appropriate column for Grid 1.1.
● Point the “Color Picker” on the next
pixel, row 1, column 2 (Grid 1.2) and
click.
● Move your “Color Picker” tool to the
box in the Gimp menu and click.
● That will give you the values for this
next color in the Change Foreground
Color menu.
● Record those values for Grid 1.2.
● Be sure that you always use the
foreground color, rather than trying to
swap between foreground and
background colors. Simplifies the data
collection procedures.
● Using the “Color Picker” tool, point to
pixel Grid 1.3 (1st row, 3rd column) and
click.
● Move the “Color Picker” tool to the
foreground color box on the Gimp
menu and click.
● Record those data from the Change Foreground Color menu.
● Repeat for each pixel in your 5x5 square. You should end up with 25 rows of data, 6
columns deep.
● Find the average of each column, H, S, V, R, G, and B. You now have the average color
for the hot stars.
● Betelgeuse is a cool star, and we use that to set the cool end of stars. Repeat all these
steps using the August 5, 2009: Betelgeuse Resolved picture.
● Students create a line chart using these two sets of data. They compare and contrast the
data
● Do not use the Spotty Surface of Betelgeuse. Students might ask questions about Spotty
color and the Resolved pictures. A line of inquiry might be: Does their data support the
average temperature for Betelgeuse in both pictures? Does that support the Spotty
Surface data?
5: Students will need to spend some time researching temperatures and stars, and once they
get them set with a few known stars, they can analyze their colors, and then see if color is a
good predictor of temperature.
IX.
Materials and Costs:
A.
Materials
1.
B.
Access to the internet, specifically APOD site
List the equipment and non-consumable material and estimated cost of each
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Item: Computer(s) with software installed:
Web Browser, Microsoft Word, Microsoft Excel, GIMP2 (GNU Image
Manipulation Program), or other paint program,
Internet access (preferably DSL or High Speed)
Estimated total, one-time, start-up cost:
1.
C.
$0.00
http://www.gimp.org/
List the consumable supplies and estimated cost for presenting to a class of 30
students
Estimated total, one-time, start-up cost:
D.
$0.00
Time:
Preparation time:
1 hr. - Lab to set up the student Excel Color Analyzer
spread sheet
Instruction time:
1 hr - Lab to run Color Picker and complete Color
Analyzer spreadsheet
1 hr - Lab to run Color Analyzer spreadsheet and graphing
Clean-up time:
X.
none
Assessment (include all assessment materials):
Students will be assessed through observation of their efforts in the lab, and their
finished products, Color Analyzer spreadsheet and chart
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