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NOVA scienceNOW: Dark Matter

Viewing Ideas

Before Watching

1. Demonstrate a way to prove invisible matter has mass. Matter is anything that occupies space and has mass. Dark matter is matter that does not emit or reflect light, but whose existence is inferred from gravitational effects on visible matter. To help students get comfortable with the idea that dark matter is invisible, but contributes a significant amount of mass to the universe, start by asking them the following questions:

   • Do you know of any substances that are invisible, but have mass (the amount of matter in something)? Air and other gases.
   • If you can't see something, how do you know it has mass? One can weigh it or see the effect it has on other things. For example, you can feel the molecules in the air when you sit on front of a fan and on your face when you ride a bike.

   Challenge students to prove that air has mass given the following materials:

   • two identical balloons
   • one wooden dowel approximately 2 feet long
   • three pieces of string of equal length, approximately 1 foot long
   • straight pin
   • air pump

   Suggested solution: Make a simple balance scale using air-filled balloons as the weights.

   1. Mark the midpoint of the dowel and tie one of the pieces of string around the dowel at that mark.

   2. Inflate both balloons to the exact same size. Using a pump will avoid introducing unequal amounts of saliva or water vapor.

   3. Tie one balloon near each end of the dowel using the other two pieces of string. Make sure that both balloons hang at the same height.

   4. If necessary, slide the strings along the dowel so that the "scale" is perfectly balanced when held by the center string.

   5. Keeping the "scale" level, insert the pin into a thick part of one of the balloons. The goal is to let the air escape slowly so the balloon stays intact. The balloon that is full of air now has more mass than the popped balloon. The scale is now unbalanced, with the dowel tilted toward the side with the inflated balloon. Since the balloons are identical, the mass difference must be due to the air in the inflated balloon. To prove this, pop the second balloon to rebalance the scale.

2. Discuss the art of detection. If, as scientists suspect, most of the mass in the universe is dark matter, there should be dark matter particles all around us here on Earth. In fact, there could be millions of dark matter particles streaming through our bodies every second. But, if we can't see or feel these particles, how can we possibly grab a hold of one? The video introduces one detector located deep underground and cooled to just a fraction of a degree above absolute zero. Scientists think it might be capable of directly detecting these elusive dark matter particles. Go through the following steps to help students understand why scientists have such an approach in trying to capture dark matter.
   
   First, have students brainstorm to create a list of objects that detect things they can't see. Some examples: ears (sound), nose (smells), skin/nerve endings (heat, UV rays), cell phone (radio waves), x-ray machine film (x-rays), and metal detector (hidden metal). Next, lead a discussion about how the location of a detector might affect signal quality and what types of things might interfere with the detection of a desired signal. Signals can be blocked (e.g., cell phones don't work in tunnels or your skin doesn't tan when you wear a long-sleeve t-shirt), or signals may be masked or confused by "noise" or other stronger signals (e.g., you can't hear your mother calling you to dinner because your stereo is too loud).
   
   Explain that scientists suspect that dark matter may be made of particles that interact weakly with normal matter, meaning they collide very rarely and are extremely difficult to detect. The ability to detect these particles is further complicated by the fact that we are constantly bombarded by high-energy subatomic particles from space known as cosmic rays. Cosmic rays—typically protons, electrons, or atomic nuclei—cause "background noise" on dark matter particle detectors. Cosmic rays are constantly streaming through us here on the surface of the Earth. If you were to hold out your hand, an average of one cosmic ray per second will pass through it. Have students hypothesize where dark matter detectors might be placed in order to minimize the influx of cosmic ray particles.

   Use medical x-rays as a way to get students to think about shielding and the possibility of putting the detector deep underground. High-energy x-rays easily pass through soft tissue, but not as easily through bone and denser tissue. Similarly, cosmic rays are impeded by Earth's rock and soil. For instance, at the Soudan underground lab highlighted in the video, the detector is located far underground. The result is that the cosmic ray flux is decreased by a factor of 100,000 from that at the surface. Instead of one cosmic ray per second striking the detector, they may have to wait a whole day or longer for just one to strike.

   The dark matter detectors shown in the video are cooled to near absolute zero temperatures. To demonstrate why, remind students that molecular motion depends on temperature (the higher the temperature, the faster the particles vibrate). If you are trying to detect a very weak interaction, your detector has to be very still so as to be able to pick up even the faintest signal. Use a hole-puncher to create a handful of paper confetti. These paper dots will represent dark matter particles. Ask two students to volunteer to be ‘detectors.' Have them stand at the front of the classroom on either side of you, with their hands out in front of them, palms up, and with their eyes closed. One student will be a detector at room temperature—he or she should shake their hands quickly back and forth parallel to the ground. The other student will be a detector cooled to near absolute zero and should hold their hands still. Every few seconds, for a time period of 20-30 seconds, drop individual paper dots simultaneously onto the two detectors. At the end of the time interval, compare how many dark matter particles each detector felt hit his/her hands.

   The student whose hands were kept still should have detected more "cosmic rays" due to a higher level of sensitivity in his/her detector. This is a good analogy for dark matter detectors. Because dark matter particles are believed to interact weakly with ordinary matter, their arrival at the detector will be difficult to detect—perhaps impossible if there are high levels of thermal vibrations in the detector.

3. Demonstrate how a star's orbital speed depends on the mass of the galaxy in which it orbits. Dark matter was first suggested in the 1930s by astronomer Fritz Zwicky, but it wasn't until the late 1960s when Vera Rubin observed stars in the outer portion of the Andromeda spiral galaxy orbiting much faster than expected, that dark matter entered mainstream physics. Because the inner region of a spiral galaxy has the highest concentration of visible stars, it was long assumed that most of the mass (and therefore gravity) of a galaxy would also be concentrated toward its center. If this were true, stars farther from the galactic center should have slower orbital speeds than stars closer to the center, just like the outer planets in the solar system travel much more slowly around the Sun than do the inner planets. The fast orbital speeds of stars in the outer portion of the Andromeda galaxy meant that there must be a significant amount of unseen matter exerting strong gravitational forces all the way out to the edges of the galaxy. Rubin's calculations led her to conclude that galaxies must contain approximately ten times more dark mass than luminous mass (that which can be accounted for by stars). She had discovered compelling evidence for the dark matter proposed by Zwicky 30 years earlier.
   
   To demonstrate what Vera Rubin observed, first construct a simple device to demonstrate uniform circular motion. You will need a long piece of string, a small two-holed rubber stopper, a paper clip, a plastic tube (a ball point pen tube will work), a handful of metal washers, and some black tape. Tie one end of the string securely onto the rubber stopper. Thread the string through the tube and tie a couple of washers to the free end of the string. The rubber stopper represents a star in the outer region of a galaxy and the washers represent the mass of the inner stars in the galaxy. Place the paper clip on the string just below the tube to fix the orbital radius of the star.
   
   Swing the stopper around over your head at a constant speed in a horizontal circle parallel to the floor. Have students take note of how fast the "star" is orbiting. Have them count how many times the star orbits in ten seconds. Ask students to predict what they think will happen to the orbital speed of the star if the galaxy had more mass (if there was dark matter)—will it orbit slower, faster, or at the same speed? Have them explain their reasoning. Then, tape several more washers together with black tape to represent dark matter in the galaxy. Attach them to the washers already on the string to increase the overall mass of the galaxy. Keeping the same orbital radius as before, repeat the demonstration. The stopper will orbit noticeably faster than it did before the dark matter was added (the orbital velocity of the stopper/star is proportional to the square root of the mass of the washers/galaxy). Explain to students that what they have just observed with this simple demonstration is a very similar to the observations that led to some of the most compelling evidence for dark matter.

After Watching

1. Defend the existence of dark matter. Have students write a one or two paragraph summary describing the evidence for dark matter and defending the position that something does not have to be visible in order to be understood or explained by science. They should provide at least one example from everyday life of something that exists but is not visible, and what proof they have for the existence of that invisible entity. It may be useful to ask students to do some research either before or after viewing so they are familiar with dark matter before they attempt to defend a position.

2. Make a quantitative comparison of luminous and dark matter to estimate how much mass is missing. Before scientists knew about dark matter, they estimated the mass of galaxies based on the mass of luminous matter (stars) in the galaxy. They would use observations of the galaxy's overall brightness along with knowledge of the galaxy's distance to determine the absolute brightness or luminosity of the galaxy. Finally, they would estimate a total mass based on knowledge of the mass of stars and the relative abundances of different types of stars in a typical galaxy. Using this brightness method, the mass of the Triangulum galaxy, a spiral galaxy about 3 million light years from our home Milky Way galaxy, was estimated to be about 7 x 10⁹ (7 billion) times the mass of the sun (within a radius of 4.0 x 10²⁰ m of the galactic center). Have students use Newton's Second Law, the Law of Universal Gravitation and the properties of uniform circular motion to calculate the mass of the Triangulum galaxy based on the observed orbital speed of stars 4.0 x 10²⁰ m from the center of the Triangulum galaxy (123 km/s). How does this mass compare to the mass estimated by the brightness method? What percentage of mass in the Triangulum galaxy is dark matter?

   Useful Equations and constants
   Newton's Second Law: F = ma
   Law of Universal Gravitation: F_g = GMm/r²
   acceleration during uniform circular motion: a = v²/r
   G = 6.67 x 10^-11 Nm²/kg²
   M_sun = 2.0 x 10³⁰ kg
   

   Solution

   1. Apply Newton's 2^nd Law.
      The acceleration of a star in uniform circular motion in a galaxy is caused by the pull of gravity of all of the mass interior to that star, so the centripetal force on the star is equal to the gravitational force between the star and the rest of the galaxy (F_c = F_g):

      mv²/r = GMm/r²

      (m is the mass of the star, v is the star's orbital velocity, r is the star's orbital radius, G is the gravitational constant, and M is the mass of the galaxy.)

   2. Rearrange the equation to solve for M.
      M = v²r/G

   3. Substitute in known values for v, r, and G and calculate M in kg.
      M = (123 x 10³ m/s)² x (4.0 x 10²⁰ m)/(6.67 x 10^-11 Nm/kg²) = 9.07 x 10⁴⁰ kg

   4. Convert the mass to units of M_sun.
      9.07 x 10⁴⁰ kg x (M_sun/2.0 x 10³⁰ kg) = 45 billion M_sun

   5. Calculate the mass of dark matter in the galaxy.
      M_{dark matter} = M (orbital method) – M (brightness method)
      M_{dark matter} = 45 billion M_sun – 7 billion M_sun = 38 billion M_sun

   6. Calculate the percentage of dark matter in the Triangulum galaxy.
      % dark matter = M_{dark matter}/M_galaxy x 100 = (38 billion M_sun/45 M_sun) x 100 = 84%

3. Make a model of a gravitational lens using the base of a wine glass. Although no one yet knows exactly what dark matter is made of, we do know that dark matter shares one very important property with normal (atomic) matter—mass, the amount of matter in an object. According to Einstein's general theory of relativity, mass warps or curves space-time, and can deflect the path of light rays. Gravitational lensing occurs when the gravity of a massive foreground object, such as a galaxy, a black hole, or dark matter, bends the light coming from a far more distant galaxy directly behind it. Gravity focuses the light from a distant object, producing multiple or distorted images of the background object as seen by the observer. These images can look like rings, arcs, crosses, or copies of the original galaxy, depending on the distribution of the mass and the relative positions of the observer, lens, and source. Since both normal matter and dark matter produce lensing effects, gravitational lensing provides great insight into how dark matter is distributed throughout the universe.
   
   Below are two different ways to create a simple model of a gravitational lens with the base of a wine glass. Both methods require that you break off the stem of the wine glass just above (approx. 1 cm) the base. Follow proper safety precautions and file down sharp edges.

   Method 1
   Draw a small dot representing a distant galaxy on an overhead transparency. Prop the base of the wine glass up around the outer rim with small risers so that the lens is raised approximately one half to one inch above the dot (with the flat side down). With the lens centered over the dot, have students observe how the image is spread into a circular ring in a mimic of the gravitational effect of mass positioned between Earth and a distant galaxy. If you move the lens slightly off axis, you will see two arcs instead of a full ring.

   Method 2:
   From a distance, shine a bright LED (representing a distant galaxy) through the wine glass base. Have a volunteer carefully hold the lens or use an optical bench with a lens holder or a stand with a clamp to keep the lens in place. To project the image onto a TV screen, use a video camera as the "observer" and connect the camera to the TV set. Have students observe the effect created by the gravitational lens. Adjust the distance and alignment of the LED to vary the lensing effect.

   Have students compare their observations to images in the Hubble gallery of gravitational lensing

   • www.hubblesite.org/newscenter/
     archive/releases/1999/18/image/a/format/web_print

Web Sites

NOVA scienceNow multimedia dispatch—The Dark Matter Mystery www.pbs.org/wgbh/nova/sciencenow/dispatches/080111.html
Discusses how a galaxy collision provides evidence for the existence of dark matter.

NOVA scienceNow multimedia dispatch—A Cosmic Enigma www.pbs.org/wgbh/nova/sciencenow/dispatches/070822.html
Offers a podcast conversation with MIT physicist Max Tegmark about the nature of dark matter and why it remains so mysterious.

Scientific American Frontiers—The Dark Side of the Universe
www.pbs.org/saf/1405/index.html
Discusses evidence for the existence of dark matter and showcases different methods and experiments designed to directly detect dark matter.

Stephen Hawking's Universe—On the Dark Side
www.pbs.org/wnet/hawking/strange/html/dark.html
Discusses evidence for dark matter, dark matter candidates, and what impact dark matter may have on the fate of the universe.

WMAP's Universe
map.gsfc.nasa.gov/universe/uni_matter.html
Discusses what the universe is made of, WMAP and other dark matter probes, and dark matter candidates.

Soudan Underground Laboratory Homepage
www.soudan.umn.edu/index.html
Introduces the Soudan Underground Laboratory experiments and facilities and offers educational posters about the search for dark matter.

The Large Hadron Collider at CERN
public.web.cern.ch/public/en/LHC/LHC-en.html
Discusses the LHC particle accelerator that scientists hope will be able to create dark matter particles.

Books

In Search of Dark Matter
by Ken Freeman and Geoff McNamara. Springer Praxis Books, 2006.
Describes the dark matter problem from its initial 'discovery' to current theories and explanations for the nature of dark matter and its role in the origin and evolution of the Universe.

Dark Matter: In Search of Our Universe's Missing Mass and Energy
by Dan Hooper. Collins, 2006.
Takes readers on a quest to discover what makes up dark matter and dark energy.

Dark Side of the Universe: Dark Matter, Dark Energy, and the Fate of the Cosmos
by Iain Nicolson. The Johns Hopkins University, 2007.
Discusses key discoveries, underlying concepts, and current ideas about dark matter and dark energy, and how our understanding of the nature and content of the universe have developed over time.

Activity Author

Erin Bardar is a curriculum developer in Cambridge, MA. She has a bachelor's degree in Physics from Brown University and a doctorate in Astronomy from Boston University. In addition to writing physics, astronomy, and Earth science curriculum for a number of projects, Erin also created the Light and Spectroscopy Concept Inventory for evaluating college astronomy students' understanding of light and spectroscopy, and has a U.S. patent for a binocular spectrometer.