dark matter friday, october 17. the sun goes around the center of the milky way galaxy on a nearly...
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Dark MatterDark Matter
Friday, October 17
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The Sun goes around the center of the Milky Way Galaxy on a nearly circular orbit.
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Orbital radius = 8000 parsecs = 26,000 light-years Orbital speed = 220 km/second = 490,000 miles/hour
Orbital period = 200 million years
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Sun moves on a (nearly) circular orbit rather than a straight line because of the
mass within its orbit.
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A satellite will have a circular orbit if its initial speed = circular speedcircular speed ( vcirc )
r
GMvcirc
r = radius of circular orbit M = mass of object being orbited
Flashback:
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Question of the day: What is MM, the mass required to keep the Sun on its
orbit around the Galactic center?
This requires a little math.
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r
GMvcirc
r
GMv2
circ
square each side:
rearrange:
G
r v M
2circ
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G
r v M
2circ
vcirc = 220 km/sec = 2.2 × 105 meters/sec
r = 8000 parsecs = 2.5 × 1020 meters
G = 6.7 × 10-11 Newton meter2 / kg2
M = 2 × 1041 kg = 9.5 × 1010 solar masses
(Mass of stuff = 95 billion times the mass of the Sun.)
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The Sun is “anchored” to the Milky Way Galaxy by a mass
equal to 95 billion Suns.
1st hypothesis: Inside the Sun’s orbit, there are 95 billion stars, each equal in
mass & luminosity (wattage) to the Sun.
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2nd hypothesis: Inside the Sun’s orbit, most mass is provided by “dim bulb”
stars like Proxima Centauri.
Observation: inside the Sun’s orbit, the wattage is 17 billion (notnot 95 billion)
times the Sun’s luminosity.
95/17 = 6.3 Solar Masses per Solar Luminosity.
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Observation: In the Milky Way Galaxy, vcirc of stars is nearly constant with
distance from the Galactic Center.
vcirc
(km/sec)
r (light-years)
vcirc nearly constant
with distance.
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This is very differentvery different from the behavior of planets in the Solar System.
vcirc
(km/sec)
r (A.U.)
vcirc drops steeply
with distance.
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Milky Way Galaxy
Solar System
Why the difference? Let’s ask Newton.
r
GMvcirc
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r
GMvcirc
In the Solar System, 99.8% of the mass is in the Sun.
As r increases, M is nearly constant: vcirc decreasesdecreases with distance from Sun.
r
1GMvcirc
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r
GMvcirc
In the Milky Way Galaxy, vcirc is
observed to be nearly constant.
As r increases, vcirc is constant:
M must increase linearly with r.
r = 16,000 pc → M = 190 billion solar masses
r = 8000 parsecs → M = 95 billion solar masses
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Out to the edge of its visible disk, the Milky Way Galaxy contains:
200 billion solar masses, but only
20 billion solar luminosities.
Conclusion:Conclusion: There must be dark matterdark matter in the outer regions of the Galaxy.
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Dark matterDark matter = stuff that doesn’t emit, absorb, or otherwise
interact with photons.
Other galaxies are found to have dark matterdark matter, too.
Andromeda Galaxy
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bright stars
dark “halo”: nearly spherical distribution
of dark matter
The new view of galaxies:
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Dark matter could also be called “invisible matter”.
The properties of invisible objects are rather difficult
to determine.
We know dark matter exists because of its gravitational pull on luminous matter;
otherwise, information is lacking.
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Some of the dark matter in galaxy “halos” consists of Massive Compact Halo Objects
(MACHOs, for short).
MACHOs can be “failed stars”; balls of gas smaller than a star
but bigger than Jupiter.
MACHOs can be “ex-stars”; burnt-out, collapsed stellar remnants
(white dwarfs, neutron stars).
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Only 20% of the dark matter is MACHOs: Some of the dark matter in galaxy “halos”
consists of exotic matter.
Suppose there existed a type of massive elementary particle that didn’t
absorb, emit, or scatter photons.
We’d detect such a particle only by its gravitational pull on luminous matter.
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Particle Physics
Electron: low mass, negative charge
Proton: higher mass, positive charge
Neutron: ≈ proton mass, no charge
Neutrino: VERY low mass, no charge
↑ ordinary ↓ exotic
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Neutrinos, they are very small. They have no charge and have no mass And do not interact at all. The earth is just a silly ball To them,
through which they simply pass, Like dustmaids down a drafty hall Or
photons through a pane of glass.
Cosmic Gall (John Updike)
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What’s the exotic dark matter made of?What’s the exotic dark matter made of?
NeutrinosNeutrinos make up part of the
exotic dark matter.
Although detecting neutrinos is difficult, it
has been done!
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electron
Although we don’t know the mass of neutrinos exactly, we know it’s tiny…
Neutrinos provide < 10% of the dark matter.
neutrinos
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Most of the dark matter must be particles other thanother than neutrinos.
One candidate for the office of “dark matter”:
the WIMPWIMP.
WIMPWIMP = WWeakly IInteracting MMassive PParticle
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According to particle physics theory, WIMPs should be much like neutrinos
only more massive.
Neutrinos have already been detected: particle physicists are
still trying to detect WIMPs.
I predict a Nobel Prize for the 1st to
succeed!
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Clusters of galaxies contain Clusters of galaxies contain lots of dark matter.lots of dark matter.
How do we know? Galaxies in clusters move very rapidly: if there weren’t dark matter to anchor
them, they’d fly away.
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Monday’s Lecture:
Reading:
Chapter 5
Why is it dark at night?