Astro 130 PSU Exam 1

Penn State

What is a black hole?

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* A black hole is an object whose gravity is so strong that nothing can escape it, not even light moving at the fastest possible speed in the universe.
* Massive small dot

Black Hole Sizes

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* The size (ie radius of the event horizon) of a black hole depends only its mass
* Theoretically anything can become a black hole if compressed enough as long as  Vesc (escape velocity)=speed of light

What would happen to Earth’s orbit if the sun suddenly became a black hole?

Earth’s orbit would not change

Force of Gravity Equation

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* F(Force of gravity)g = G M(ass of one object)1 x M(ass of 2 object)2 / d(istance squared)^2

How far is the closest SMBH

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* The nearest known black hole, A0620-00, is about 3000 ly away (light years)

Gravity

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* Any object that has a mass pulls on all other objects in the universe that have a mass
* Attractive force

Newtons law of gravity

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* Force of Gravity = (Gm1)(M2) / d^2
* F = gravitational force
* M1= mass 1 (kg)
* M= mass 2 (kg)
* d= distance between masses (m)
* G- gravitational constant

Why is gravity the dominant force in nature?

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* Because it dominates on a large scale. It only depends on the mass of an object.
* The electromagnetic force depends on a charge which can be positive or negative so that the charges can cancel each other out

Gravity is pretty weak

Unimportant on the atomic scale

Galileo found that objects of different masses

feel same acceleration from earth

Newtons second law

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* F=ma (force = mass x acceleration)

reason different masses feel same acceleration

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* F=ma (force = mass x acceleration)
* f= GmM/r^2
* GmM/r^2 = m a
* two forces are equal, but accelerations are different

Objects in any orbit are in…

constant freefall

Satellites

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* It takes 2πr/v to complete one orbit (period)

Gravity Assist

Gravitational Slingshot

What is a black hole?

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* an object with gravity so strong that even light can’t escape it
* An object whose escape velocity exceeds the speed of light

Escape Velocity

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* Velocity required to leave the gravitational field of an object
* The escape velocity from any object depends on it’s mass, and on the starting distance
* The escape velocity is larger for larger mass and smaller distance

Escape Velocity Equation

*vesc* = √2*GM* / *r*

How big is a black hole?

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* “Singularity” (much small than an atom) (center; size of 0)
* “Event horizon” or Scartzchild radius (outsides)  (boundary where escape velocity starts to exceed speed of light)

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* The event horizon is the point of no return and it has a radius called schwarzschild radius 
* Schwarzschild Equation

Rg = 2GM/c2

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* How would the radius of the event horizon change if a black hole gained mass?

Increase

The surface of a black hole is the radius at which…

the escape velocity equals the speed of light

“Dark Star” of John Mitchell (18th Century)

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* For a star with solar density, but 500 times bigger
* Radius= 500 x solar radius
* Mass = 500^3 x solar mass
* Escape velocity=  500 x escape velocity of the sun
* This is the speed of light!
* (IMPORTANT: It doesn’t make sense)

if escape velocity is larger than the speed of light…

we cannot see that star; hence the name “dark star”

What is the difference between Dark Star’s and Black holes?

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* Dark star: Produces light. Emitted light is always recaptured (curves back)
* A nearby observer would see light
* Black Hole: No light can get out at all
* A nearby observer would see nothing

How do black holes form?

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* Black holes form from dying massive stars that blow up in supernova explosions

3 ways for a star to die

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* White dwarf- the size of earth
* Neutron star- the size of a city
* Black hole- no size

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* What makes some stars end up as white dwarfs, neutron stars, or black holes?

The star’s mass

Why does the mass of a star determine its lifetime?

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* A star with a higher mass has a core with:
* Higher gravity
* Higher pressure
* Higher temperature
* Consumes hydrogen faster in fusion
* Higher mass = shorter life
* Lifetimes range from millions to trillions of years depending on their mass

How does the sun produce its energy?

Fission

Fusion

Fission

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* Big nucleus splits into smaller pieces 
* (Example: Nuclear power plants, atom bombs)
* If the atom bigger than iron, this releases energy

Fusion

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* Small nuclei stick together to make a bigger one
* (Example: the Sun, hydrogen bombs, fusion reactors)
* If the atom is smaller than iron, this releases energy

Law of conservation of mass and energy

• sum of mass and energy converted to correct units must always remain constant in any physical process

Why does fusion produce energy?

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* The net result of the proton-proton chain (4H-> He) is to turn 4 hydrogen atoms into 1 helium atom
* But there is a mass defect- the 4 hydrogen atoms have 0.7% more mass than the helium atom
* Where did the missing mass go?
* E=mc^2 Energy!

All stars have masses between…

0\.08 Msun and 150 Msun

Brighter stars on the main sequence have…

Higher masses

All white dwarfs have masses…

There is no pattern to the masses of…

red giants

Main sequence stars are fusing ------ into ------- in their ------- like the sun

1) Hydrogen

2) Helium

3) Cores

Mass is the main determinant of how long the star….

will live and how the star will die

More massive stars go through their lives much ----- than low mass stars

Faster

Evolution of stars

The lifecycle of stars

How does the sun produce its energy?

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* In order to keep up the gas pressure (and prevent collapse), the center of the sun must continually replenish the energy that it lost. This is done by nuclear fusion (of hydrogen). The energy produced maintains hydrostatic equilibrium

Nuclear fusion

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* combining of light nuclei into heavier ones produces a great amount of energy
* Nucleus 1 + nucleus 2= Nucleus 3 + energy
* Mass of nucleus < (nucleus 1+nucleus 2)

Even while on the main sequence…

the composition of a star’s core is changing

Stages of a star leaving the main sequence

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* 1) Normal main sequence star fusing hydrogen into helium
* 2) Once all hydrogen has been exhausted from the core, the core contracts
* 3) As the core shrinks, it heats up to the point where hydrogen begins to fuse outside the core. We call this shell burning.
* 4) The increase in temperature and energy generate from shell fusion push out the outer layers and the star expands
* 5) The star becomes a red giant

1-2 = Subgiant phase

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* Core: no fusion in core
* Shell: H -> He in the shell which causes the outer layers of star to expand

2-3 = Red giant

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* Core: no fusion in core
* Shell: H -> He; gravity shrinks the core further and heats it up
* As the core onctinues to shrink, the outer layers of the star expand and cool
* Star is not a red giant, extebnding out as far as the orbit of mercury

@ 3 = Helium Flash

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* Thermal pressure in the core is too small to counteract gravity, so the core keeps on shrinking until it becomes supported by electron degeneracy pressure (electrons are packed so close together that they provide a pressure of their own)
* Core heats up without expanding, and eventually the increase in temperature causes He fusion to happen rapidly ending in helium flash
* Core: Sudden start of the He -> C fusion
* Shell: H -> He

4 = Helium fusion

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* Once the core temperature has risen to 100,000,000 K, the helium in the core starts to fuse
* Remember that T=10^7K is needed for H to fuse into He, because only at this temperature do H nuclei have enough speed to overwhelm their mutual electromagnetic repulsion. Because He nuclei have a greater positive charge (2 nuclei) their electromagnetic repulsion is greater so higher temperatures are needed for them to fuse.

4 = Horizontal Branch

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* Core: He -> C (and O)
* Shell: H -> He
* Decrease in luminosity, increase in temperature
* Stars with masses of more than about 3 solar masses do not experience a helium flash- helium burning starts gradually.

2 = Subgiant (before He fusion)

The core shrinks before He fusion starts and the outer layers expand

4 = Horizontal branch

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* The core expands when He fusion begins, and the outer layers shrink
* T around expanding core drops so the H-shell burning fusion reduces its energy output and the star’s overall energy output decreases. This allows the star’s outer layers to contract and heat up

5 = Asymptotic Giant Branch (AGB) (Red Giant again)

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* Core: Inert C (and O) fusion in core ends
* The core shrinks, heats up the layers next to it and forms another burning shell
* Shell 1: He -> C (and O) (around core)
* Shell 2: H -> He (around the lower shell)

11 = AGB

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* The star’s outer layers expand
* The carbon core shrinks but never starts fusing again. The core becomes supported by the degenerate pressure of electrons

Sun-like stars never become hot enough for fusion past ---- to take place

Carbon

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* There is no more outward fusion pressure being generated in the core, which continues to contract

6 = Planetary nebula

The outer layers of the star expand to form a planetary nebula

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* Core is made out of carbon and supported by electron degeneracy pressure
* The outer layers of the star drift away from the star propelled by thermal pulses

12:

Planetary Nebulae

The star now has two parts

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* A small, extremely dense carbon core supported by electron degeneracy pressure
* An envelope about the size of our solar system
* The envelope is called a planetary nebula, even though it has nothing to do with planets- early astronomer viewing the fuzzy envelope thought it resembled a planetary system

7: White Dwarf

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* Once the nebula has gone, the remaining core is extremely dense (degenerate) and extremely hot, but quite small. It is luminous only due to its high temperature
* Only core: made of carbon and oxygen and supported by electron degeneracy pressure

Pauli Exclusion principle

No two fermions can share the same quantum state (position, spin, momentum)

Degeneracy pressure

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* If we squeeze matter 10,000 times the density of a rock, the electron cloud around each nucleus gets squashed 10,000-fold
* With so little space available, electrons shake uncontrollably 
* Electrons bang around and kick against adjacent electrons. In this state, electrons are degenerate
* The more you squash the matter, the more degeneracy pressure you get

Electron degeneracy pressure

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* Quantum mechanics tells us that you can only squash a certain number of electrons into a small space- they can only get so close together
* This means that at very high densities and pressure, the electrons will resist being shoved closer together
* This is called “electron degeneracy pressure”
* This is what keeps white dwarfs from collapsing even though fusion isn’t happening in their cores
* If there’s too much mass piling up, however, gravity can overcome the electron degeneracy pressure

White Dwarfs

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* A star that is highly squeezed and is supported by electron degeneracy pressure (balances against gravity)
* White dwarfs emit thermal radiation (because they are hot) and they cool off, but they don’t shrink b/c they are supported by degenerate pressure
* Example: Sirius B (the nearest white dwarf) radius = 4,900 km, mass = 1.05 M density = 2.1 ton/cm^3

Size of White Dwarfs

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* White dwarfs with the same mass as sun are about same size as earth
* Higher-mass white dwarfs are smaller! (Because of degeneracy pressure)
* Maximum mass for white dewars: 1.4Msun (Chandrasekhar limit) **(MEMORIZE THIS NUMBER)**

Why is there an upper limit to the mass of a white dwarf?

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* The more massive the white dwarf, the greater the degeneracy pressure, and the faster the speeds of its electrons. Near 1.4 Solar Masses, the speeds of the electrons approach the speed of light, so more mass cannot be added without breaking the degeneracy pressure.

Evolution and Death of High-Mass Stars

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* Mass determines all the rest of a star’s major properties and irs evolutionary path
* (0.08 Msun = Brown Dwarfs, planets, etc
* Mass too low for H fusion
* 0.08-8 Msun= “Low mass stars”
* Become white dwarfs
* 8-150 Msun = High mass stars
* Explode as supernova and then become neutron stars, or if M> 30Msun black holes)

Demographics of stellar masses

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* Observations of star clusters show that star formation makes many more low-mass stars than high-mass stars

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* Evolution and Death of Massive Stars

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* High-mass stars produce heavy elements in their cores before violently blowing apart in supernova explosions
* Core-collapse supernovae can leave behind remnants: neutron stars or black holes
* Most elements with an atomic number higher than Fe are formed during a supernova explosion

Evolution of Massive Stars

• High-mass stars are hotter

• Different fusion processes

  • High-mass main-sequence stars fuse H to He at a higher rate using carbon, nitrogen, and oxygen as catalyst

• Different internal structure

• High stellar winds!

Why can nothing (including light) escape a black hole?

  

Because the required escape velocity exceeds the speed of light

 

Which one of these object has the LARGEST escape velocity?

  

Earth

 

  

Moon

 

  

Sun

 

  

White Dwarf star

 

White Dwarf Star

How far away is the closest known black hole to us? 

 

3000 ly away

How many black holes do we estimate to be in our Milky Way Galaxy alone? 

10^8

What does a shape of an orbit depend on?

Initial velocity

Compared to the escape velocity from a black hole, the escape velocity from Earth is smaller by approximately:

27,000

Let’s say that you wanted to make a cannonball (example from lecture) orbit around the Earth in a circle.  Assume that there are no mountains on Earth, approximate Earth as a plain sphere, and that the cannonball will be in orbit just above the surface. Calculate the orbital circular velocity the cannonball would need to orbit around Earth. 

Assume the mass of Earth is 6\*10^24 kg, radius of Earth = 6371 km, G=6.67\*10^(-11) m^3/(kg\*s)

The units should be in km/s.

7\.9 km/s

How many black holes are in the universe?

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* There are roughly 10^11 galaxies in the universe
* Black Holes in (Observable) Universe: 10^11 x 10^8 = 10^19 BHs

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What is the difference between John Mitchell’s Dark Star and a Black Hole?

 

Pick ***all*** that apply to the dark star:

  

Produces light.

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No light can get out at all.

 

  

Emitted light is always re-captured (curves back).

 

  

A nearby observer would see nothing.

 

  

A nearby observer would see light.

 

Produces light.

Emitted light is always re-captured (curves back).

A nearby observer would see light.

Explain why massive stars go through their life faster than low-mass stars?

(Why does the mass of a star determine its lifetime?)

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High-mass stars undergo nuclear fusion at a much faster/higher rate than low-mass stars due to the increase in elements produced in their core. This means that they burn up those elements much faster than low-mass stars.

Explain the steps that the Sun goes through after the Sun runs out of Hydrogen in its core up to the point where it is fusing He into C in the core.  Make sure to include terms such as: temperature, the fusion reactions occurring at each step, electron degeneracy pressure.  Feel free to use diagrams. 

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Evolution of Massive Stars

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* High-mass stars, like all stars’ leave the main sequence when there is no more H fuel in their cores
* Similar phases- hydrogen shell, then a core fusing He -> C and H -> He fusing shell
* H, He, C, O, Ne, Mg, Si, Fe
* The energy released from simultaneous shells fusing is so powerful that the star’s outer layers expand tremendously resulting in a supergiant star

End of a massive star

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* Each stage in the fusion process is shorter than the previous one. For example a 25Msun star fuses:
* H in 7 million years
* He in 800,000 years
* C in 500 years
* O in ½ a year
* Si in 1 day
* Core collapses in ¼ a second
* When a star has burnt all the Si in its core, it will collapse since Fe cannot be fused into higher elements (not enough energy)

Supernove Explosion Summary

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* Core electron degeneracy pressure goes away because electrons combine with protons, making neutrons and neutrinos
* E- + p+ -> n0 + neutrino
* Neutrons collapse to the center
* The collapse pauses because neutrons have a degeneracy pressure of their own, neutron degeneracy pressure
* What remains after a supernova is either a neutron star or a black hole

What determines if a core-collapse supernova will form a neutron star or a black hole?

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* If the mass of the remaining core >3 Msun, which is massive enough to overcome the neutron degeneracy pressure, then the star will collapse further to a size of almost nothing with infinite density, i.e. a black hole!

Binding Energy of Atomic Nuclei

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* Binging energy is the energy required to break the nucleus into its constituent parts

Increasing Binding Energy

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* A nuclear reaction releases energy if it increases the binding energy in a nucleus
* Moving from H to He or He to C,increases the binding energy, so fusing H or He releases energy.

Decreasing Binding Energy

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* However, fusing Fe to make heavier elements decreases the binding energy. To fuse Fe into the next element requires energy!
* Iron is a dead end for fusion because nuclear reactions involving iron do not release energy. These reactions absorb energy!
* Because this process absorbs energy from the core of the star, it lowers the temperature and pressure. Therefore Fe fusion cannot sustain itself

Why is each consecutive Nuclear Fusion Reaction Faster in the Core of the Star?

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* He fusion produces only ¼ of the energy compared to H fusion
* So when the star is fusing H e-> C the pressure inside the star is lower than when it is fusing H-> He. The core must contract
* This compression of the material leads to an increase in the reaction rate, so helium is used up more quickly
* Maintaining the star stable is like trying to keep a leaky balloon inflated
* The energy is carried from the core to the rest of the star via convection and radiation
* Once C -> O fusion begins, energy starts being carried away by neutrinos -neutrino cooling
* As thermal energy pours out of the core through neutrinos, the outer layers of the star shrink to support the star. This increases the star’s density and temperature, driving the increase of the rate of nuclear reactions
* Neutrino cooling is what makes the star evolve much more rapidly

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Why is each consecutive nuclear fusion reaction faster in the core of the sun: Summary

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* He -> C doesn’t release as much energy per reaction as H->He fusion. Hence, the star must compress to increase the fusion rate.
* Once C-> O fusion starts, energy from the core is carried away by neutrino cooling, rather than convection and radiation

Supernova Explosion: Summary

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* Core electron degeneracy pressure goes away because electrons combine with protons, making neutrons and neutrinos
* Neutrons collapse to the center
* The collapse pauses because neutrons have a degeneracy pressure of their own, neutron degeneracy pressure
* What remains after a supernova is either a neutron star or a black hole

The Collapse of the Core

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* Once Si- Fe fusions is complete, the Fe core of the star is no longer supported by nuclear fusion reactions and the massive star begins to collapse
* Similar to low-mass stars, as the core collapses, density and temperature skyrocket. The core becomes electron-degenerate.
* Core T is about 10^10 K (Kelvin) (10 billion kelvins!)
* Density > 10^10 kg/m^3 - 10 times the density of an electron-degenerate white dwarf
* The mass of the star is large enough to compress the core and overcome electron degeneracy 
* At such extreme T and density, the core is filled with Gamma-ray radiation
* Gamma-rays are so energetic that they can break up the Fe nuclei apart into He nuclei - photodisintegration
* Photodisintegration absorbs thermal energy and reverses the results of nuclear fusion
* The pressure in the core is now so great that e- are forced into atomic nuclei
* They combine with protons and produce n^0 and neutrinos
* This process is called charge destruction
* Both photodisintegration (Fe breaking up into He) and charge destruction (e- + p+ -> n^0 +neutrino) absorb a lot of energy
* Neutrinos carry away a great deal of energy as they leave the star and te collapse accelerates
* The collapse of the core happens at the speed of 25% of the speed of light (roughly 70,000 km/s) and it only takes less than a second!

The Core Bounce and Supernova

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* The material in the collapsing core exceeds the density of an atomic nucleus. This makes the strong force repulsive
* About ½ the core suddenly slows its inward fall. The remaining half slams into the innermost part of the core at a significant fraction of the speed of light and bounces. Sending a shock wave outwards into the outer layers of the star
* The massive star explodes as a Supernova! It becomes a billion times more luminous than the sun!
* The core bounce is amplified by a neutrino shock wave
* About ⅕ of the mass of the core is converted to neutrinos that immediately leave the star
* A smaller fraction of neutrinos get trapped by the dense material in the core. Their energy drives pressure and temperature up and inflates a bubble of hot gas and radiation
* The pressure of the bubble adds to the strength of the shock wave moving throughout the star
* The massive star explodes as a supernova! It becomes a billion times more luminous than the sun

Supernova

incredibly luminous

a one-time event - once it happens, there is little or nothing left of the progenitor star

2 kinds, both equally common: Type 2 and type 1a

Type 2

Death of a high-mass star

Type 1a

White dwarf/carbon-detonation supernova

Supernova 1987A

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* Located in the large magellanic cloud
* Kamiokande 2 detected about two dozen neutrinos out of 10 billions- conformation of the theoretical models for core collapse SN

What remains after supernova explosions?

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* Neutron star (can be a pulsar) if the mass of the stellar core is