PLATO: Cosmology 1
PLATO: Cosmology
Dark Matter• About 90% of the mass in the universe is dark matter
• Initial proposals:
★ MACHOs: “massive compact halo objects”
✦ Things like small black holes, planets, other “big” objects
✦ They must be dark (so we cannot see them)
★ WIMPs: “weakly interacting massive particles”
✦ These are particles that do not interact with light - like neutrinos, but heavier
✦ That means: they cannot be the stuff that atoms are made of
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PLATO: Cosmology
MACHOs• These have been ruled out
★ If there were lots of “MACHOS” around...
★ ...we would expect “Gravitational Microlensing”
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PLATO: Cosmology
MACHOs• These have been ruled out
★ If there were lots of “MACHOS” around...
★ ...we would expect “Gravitational Microlensing”
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✘NOT O
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PLATO: Cosmology
WIMPs• When WIMPs collide:
★ they create other particles
★ we can see that process through radiation
★ but it is rare (“weakly interacting” means rarely interacting)
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PLATO: Cosmology
Is there More?• Let’s go back to Hubble’s diagram
★ In matter only universe...
★ ...Hubble constant always drops with time
★ ...Universe slows down
• Is this, in fact, what we observe?
★ hint: it’s not...
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PLATO: Cosmology
Luminosity Distances• Standard candles:
★ Suppose you know how much light is emitted by an object
★ Measure how much light is received
★ Compare received light to emitted light and calculate the distance!
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PLATO: Cosmology
Luminosity Distances• All standard candles are relative measures:
★ Compare two objects and determine their relative distance
• Examples of standard candles:
★ Variable stars
★ Supernovae
★ Ordinary stars
★ Galaxies
★ Burning neutron star surfaces
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PLATO: Cosmology
Supernovae• Why are supernovae good standard candles?
★ They are bright!
★ We kind of understand them!
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PLATO: Cosmology
grav
ity
• With this much mass, the Sun has enormous gravity
★ (30 times higher than Earth at surface)
• What keeps the Sun from collapsing?
★ Hydrostatic equilibrium!
★ The Sun is hot and dense at its center
⇒ It has larger pressure
★ Pressure decreases towards surface
⇒ Net outward force
The Sun’s Structure
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PLATO: Cosmology
• With this much mass, the Sun has enormous gravity
★ (30 times higher than Earth at surface)
• What keeps the Sun from collapsing?
★ Hydrostatic equilibrium!
★ The Sun is hot and dense at its center
⇒ It has larger pressure
★ Pressure decreases towards surface
⇒ Net outward force
★ This force balances Gravity
The Sun’s Structure
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PLATO: Cosmology
Solar Power• Things that radiate cool down
⇒ Sun constantly loses energy
★ If Sun cools, pressure decreases
★ If pressure decreases, Sun must shrink
⇒ With just gravity, Sun would slowly shrink
★ But: The Sun’s size is constant
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grav
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pre
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PLATO: Cosmology
• Einstein: E=mc2 ➛ mass is a form of energy!
• Let’s add up the mass on the left and right side of the reaction:
• 0.7% of the mass released as energy!
+
Thermo-Nuclear Fusion
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+ +++
+
0.7% differencebefore
after
PLATO: Cosmology
Thermo-Nuclear Fusion• So, is this easy? No!
★ Protons are positive charges
⇒ Protons repel each other
★ The closer they get, the more they repel each other (until the strong force takes over)
★ Slow protons never get close enough
⇒ You have to slam them into each other to stick
⇒ Need hot gas - thus the “thermo-nuclear”
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PLATO: Cosmology
The Sun in Balance• The sun is in a state of equilibrium:
★ It stays at constant temperature and size
• This requires two things: The sun must...
★ ...generate just as much energy in its core as it radiates away at its surface
★ ...be hydrostatic
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PLATO: Cosmology
• Equilibrium can be
★ stable...
★ ...or unstable
Stable or Unstable?
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PLATO: Cosmology
• Equilibrium can be
★ stable...
★ ...or unstable
Stable or Unstable?
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PLATO: Cosmology
Solar Equilibrium• Suppose the Sun were somehow to increase in size...
★ Larger radius = weaker gravity = weaker pressure
✦ Lower pressure and temperature = less power generation
★ Larger radius = bigger surface area
✦ Radiation lost into space would increase
★ The Sun would radiate more energy and generate less
✦ It would cool
✦ It would shrink back to its equilibrium size
• Solar equilibrium is stable (phew...)
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PLATO: Cosmology
Solar Equilibrium• Suppose the Sun were somehow to increase in size...
★ Larger radius = weaker gravity = weaker pressure
✦ Lower pressure and temperature = less power generation
★ Larger radius = bigger surface area
✦ Radiation lost into space would increase
★ The Sun would radiate more energy and generate less
✦ It would cool
✦ It would shrink back to its equilibrium size
• Solar equilibrium is stable (phew...)
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PLATO: Cosmology
Main sequence stars
• Most stars we see are burning hydrogen
• This makes them all similar:
Stellar structure mostly determined by stellar mass
Mass determines temperature and luminosity
“Main sequence”
They evolve slowly ! ! ! (not along the main sequence)
The stellar “main sequence”:Determined by mass
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low mass
high mass
PLATO: Cosmology
Main sequence stars
• Most stars we see are burning hydrogen
• This makes them all similar:
Stellar structure mostly determined by stellar mass
Mass determines temperature and luminosity
“Main sequence”
They evolve slowly ! ! ! (not along the main sequence)
The stellar “main sequence”:Determined by mass
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low mass
high mass
PLATO: Cosmology
Main sequence stars
• What happens when fuel runs out?
For sun: tfuel ~ 10 billion years
More massive stars burn more quickly
Once hydrogen is gone, collapse?
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PLATO: Cosmology
• We could burn 3 x Helium ➛ 1 x Carbon...
• We could burn 1 x Carbon + 1 x Helium ➛ 1 x Oxygen...
• Can we go on like this forever?
Main sequence stars
net
ener
gy lo
ss
net
ener
gy g
ain
It becomes harder to fuse (requires more pressure)
Gain energy until we hit iron
Above iron: it takes net energy to fuse
Iron is the end of the line!
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PLATO: Cosmology
• We could burn 3 x Helium ➛ 1 x Carbon...
• We could burn 1 x Carbon + 1 x Helium ➛ 1 x Oxygen...
• Can we go on like this forever?
Main sequence stars
It becomes harder to fuse (requires more pressure)
Gain energy until we hit iron
Above iron: it takes net energy to fuse
Iron is the end of the line!
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PLATO: Cosmology 19
PLATO: Cosmology 20
PLATO: Cosmology
White Dwarf Stars• After Helium burning:
★ Sun will shrink quickly (25 million years)
• But something magical happens:
★ Quantum mechanics!
★ Electrons are anti-social
★ They don’t like to be close to each other
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PLATO: Cosmology
• After sufficient compression:
★ Electrons become “degenerate”, (too close together)
★ Resist further compression
✦ No more contraction✦ No more burning (stops
at carbon or oxygen)✦ Just cooling
★ New equilibrium where gravity is! ! ! ! ! ! balanced by degeneracy pressure a white dwarf
Normal gas(50 km thick)
Degenerate matter (helium, carbon, oxygen)
5000 km
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White Dwarf Stars
PLATO: Cosmology
White Dwarf Stars
• Electron “degeneracy”:
★ Pressure independent of temperature
★ White dwarfs cool, but don’t shrink
• Stable equilibrium:
★ if star is compressed, its pressure goes up more quickly than gravity
• White dwarf stars are ~ Earth sized
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PLATO: Cosmology
White Dwarf Stars
• Electron “degeneracy”:
★ Pressure independent of temperature
★ White dwarfs cool, but don’t shrink
• Stable equilibrium:
★ if star is compressed, its pressure goes up more quickly than gravity
• White dwarf stars are ~ Earth sized
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PLATO: Cosmology
White Dwarf Stars
• Electron “degeneracy”:
★ Pressure independent of temperature
★ White dwarfs cool, but don’t shrink
• Stable equilibrium:
★ if star is compressed, its pressure goes up more quickly than gravity
• White dwarf stars are ~ Earth sized
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Size comparison with regular stars
PLATO: Cosmology
• Degeneracy resists compression
★ Center never gets hot and dense enough for
O + He ➛ Ne
burning
★ No more burning...
★ No more heating...
★ ...No more shining
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White Dwarf Stars
PLATO: Cosmology
White Dwarf Stars
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• A “fun fact” about white dwarf stars:
★ The more mass they have, the smaller they are!
★ The smaller they are, the faster the electrons move
• Above 1.38 solar masses:
★ Electrons move close to the speed of light
★ This changes the “equation of state” (pressure vs. energy)
PLATO: Cosmology
White Dwarf Stars
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• Such a star is unstable:
★ When compressed, gravity rises faster than pressure
★ This is the famous “Chandrasekhar limit”
★ 1938 Nobel Prize
• Stars with core masses above 1.38 solar masses...
★ ...cannot become white dwarfs!
PLATO: Cosmology
• But stars under 1.38 M⊙ remain stable...
★ ...unless we add some some
• Once mass reaches 1.38 M⊙...
★ ...collapse!
★ ...density increases
★ ...fusion reactions restart
Supernovae
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PLATO: Cosmology
• But stars under 1.38 M⊙ remain stable...
★ ...unless we add some some
• Once mass reaches 1.38 M⊙...
★ ...collapse!
★ ...density increases
★ ...fusion reactions restart
★ ...BOOM!
Supernovae
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PLATO: Cosmology
Supernovae• Recipe for a supernova:
★ Take one 1.38 M⊙ white dwarf
★ Add mass
★ Take cover!
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PLATO: Cosmology
Supernovae• How to add mass to a star...
★ Most stars are in binaries
★ Suppose our white dwarf has a companion
• Nothing will happen...
★ ...until star #2 runs out of fuel
• Then...
★ ...it will swell up
★ ...to become a red giant
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PLATO: Cosmology
Supernovae
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White Dwarf
Red Giant Companion Star
PLATO: Cosmology
Supernovae• How does this make them good
standard candles?
• 1.38 solar masses of thermonuclear fuel
★ Produces a well defined amount of Nickel
★ Luminosity: Radioactive decay from Nickel
★ ...Bingo!
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PLATO: Cosmology 32
Tycho Supernova Remnant