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Dark MatterDark Matter

Join me on the Dark Side

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Mass and Gravity

• All mass has gravity.• Gravity attracts all things with mass.• Kepler’s Third Law tells us how mass

moves due to gravity.• Use Kepler’s Third Law to find out how

much mass is where.

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Mass and Luminosity

• Most mass gives off light.• Amount of light tells how much mass is

present.• Where there’s more light, there is more

mass.– More light from galaxy centers vs. edges.– Conclude more mass in center vs. edges.

Copyright – Kelly & Henden

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Dark Matter

• Look at:– Our galaxy.– Other galaxies.– Pairs of galaxies.– Clusters of galaxies.

• Mass due to gravity.• Mass indicated by luminosity.• Same?• No! Dark Matter.

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Galaxy Rotation

• Objects in the disk, orbit in the disk.

• Kepler’s Third Law gives the total mass in orbits.

Mass Total

)(Separation)(Period

32 AU

yrs

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Distributed Mass• In Kepler’s Law, the total mass is the

mass “inside” the orbit.

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What should we expect?

• Solar System:

Planet Separation (AU)

Velocity (km/s)

Mercury

0.5 48

Earth 1 30

Saturn 10 10

Pluto 40 5

+

V

D

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What do we see?• From variable stars we know distances.• From Doppler shift we know rotation

velocity.

• Edges of Milky Way go too fast.• Must be extra mass near edges of galaxy.

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+

V

D

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Concept Test• Which rotation curve would you get

from a typical amusement park Merry-Go-Round?

None of theabove.

a.

V

D

e.

D

b.

V

c. d.

D D

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Other Galaxies

• Observe HI in other galaxies.

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Rotation Curves

• If HI gas is rotating or moving, the 21cm radiation will be Doppler Shifted.

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Dark Matter

• Look at the stars and gas giving off light at the very edge of the galaxy.

• Still going just as fast as inner part of galaxy.

• Must mean there is still more mass affecting the edges of galaxies.

• How much?– Mass/Luminosity = 90!– Conclude 90% of matter is “dark.”

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More Galaxy Masses

• Apply Kepler’s Laws to galaxy pairs.• Get mass due to gravity.• Look at total light from both galaxies.• Estimate mass from luminous objects.

1818M/L ~ 20 – 130!

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Even More Galaxy Masses

• Look for gravitational lenses near galaxy clusters.

• More lensing means more mass.

• Compare mass from lensing to luminosity.

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Gravitational Lensing

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What is it?

• Dark Matter: Ordinary or Extraordinary?

• What kind of ordinary matter is dark?– Black holes– Black dwarfs (cool white dwarfs)– Brown Dwarfs (failed stars)– Planets– Bowling Balls

1818Brown dwarfs and planets, Copyright – G. Schneider et al. (U of A)

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More Gravity Lensing

• MACHO project.

• Look for lensed stars in our galaxy.

• Not enough MACHOs to account for all Dark Matter.

• WIMPS?

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Conclusions

• We see the effects of gravity.• More gravity than the luminosity would

suggest.• See this on all scales:

– Individual galaxies.– Pairs of galaxies.– Groups of galaxies.– Clusters of galaxies.

• Maybe 90% mass of Universe is “dark.”

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Concept Test

• Which of the following measurements can NOT be used to measure the amount of dark matter in galaxies?a. The speeds of galaxies orbiting a cluster center.b. The speed of material orbiting a galaxy’s center.c. The deflection of light rays from a background

object passing by the outskirts of a galaxy cluster.

d. The properties of x-rays emitted by gas that has been heated by falling into the cluster.

e. None of the above.

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Homework #17Homework #17

• For 3/22 Read: Bennett Ch 20.4, 22.5 – 22.6

• Do Ch 20:– Problem 14

• Do Ch 22:– Problems: 15