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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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!

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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

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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