Stellar Death

Question 1

What is the size of a 1 MSun white dwarf?

Answer 1

About the same size as Earth

Question 2

What happens to the size of a white dwarf as it increases in mass?

Answer 2

It gets smaller.

Question 3

What is the Chandrasekhar limit?

Answer 3

Quantum mechanics says that electrons must move
faster as they are squeezed into a very small space
• As a white dwarf’s mass approaches 1.4MSun, its
electrons must move at nearly the speed of light
• Because nothing can move faster than light, a white
dwarf cannot be more massive than 1.4MSun, the
white dwarf limit (or Chandrasekhar limit)

Question 4

What can happen to a white dwarf

in a close binary system?

Answer 4

Mass falling toward a white dwarf from its

close binary companion has some angular momentum. The matter therefore orbits the white dwarf in an accretion disk.

Question 5

What is a nova?

Answer 5

Friction between orbiting rings of
matter in the disk transfers angular
momentum outward and causes the disk to heat up and glow. The temperature of accreted matter eventually becomes hot enough for hydrogen fusion. Fusion begins suddenly and explosively, causing a nova

Question 6

What is a Type I supernova? How is it useful for knowing the age of the universe?

Answer 6

White dwarf supernova: Carbon fusion suddenly begins as white dwarf in close binary system reaches
white dwarf limit (1.4 MSun), causing total explosion. If we know the mass and luminosity, we can measure the distance. It is consistent because we know the limit.

Question 7

What is a Type II supernova?

Answer 7

Massive star supernova: Iron core of massive star reaches white dwarf limit and collapses into a
neutron star, causing explosion

Question 8

How can you tell the difference between a Type I and II supernova?

Answer 8

One way to tell supernova types apart is with a light
curve showing how luminosity changes with time. Type I will have consistent slope downwards. But better way to tell is that white dwarf will not see any absorption lines of hydrogen because it has cast off atmosphere. Massive supernova will have absorption lines because outer atmosphere being cast off.

Question 9

How can you tell the difference between a nova and supernova?

Answer 9

Supernovae are MUCH MUCH more luminous!!!
(about 10 million times)
• Nova: H to He fusion of a layer of accreted
matter, white dwarf left intact
• Supernova: complete explosion of white dwarf,
nothing left behind

Question 10

What is a neutron star? And how is it supported?

Answer 10

A neutron star is the ball of neutrons left behind by a massive-star supernova. Degeneracy pressure of neutrons supports a neutron star against gravity

Question 11

How long does it take for free neutrons to decay? What had to have happened in the beginning of the universe for us to be here?

Answer 11

Free neutrons days in 10.3 minutes back into electron and proton. But it won’t decay if it’s wrapped in atoms because of the strong nuclear force.

Question 12

What is the size of a neutron star?

Answer 12

Same size as small city.

Question 13

How were neutron stars first discovered? And by who?

Answer 13

Using a radio telescope in 1967, Jocelyn Bell
noticed very regular pulses of radio emission
coming from a single part of the sky
• The pulses were coming from a spinning
neutron star—a pulsar

Question 14

What is a pulsar? Give an example.

Answer 14

A pulsar is a neutron star that beams radiation along a magnetic axis that is not aligned with the rotation axis. Pulsar at center of Crab Nebula pulses 30 times per second. The radiation beams sweep through space like
lighthouse beams as the neutron star rotates

Question 15

Why must pulsars be neutron stars?

Answer 15

The spin rate of pulsars are about 1000 cycles per second and going 60,000km/s or about 20% speed of light. Anything else would be ripped to shreds.

Question 16

What is an x-ray burst?

Answer 16

Matter accreting onto a neutron star can eventually become hot enough for helium fusion. The sudden onset of fusion produces a burst of X-rays. Similar to nova created by friction of accretion disk in white dwarf.

Question 17

What is a black hole?

Answer 17

A black hole is an object whose gravity is so

powerful that not even light can escape it.

Question 18

What happens to the escape velocity from an

object if you shrink it? Why?

Answer 18

It increases. Using Newton’s Universal law of Gravitation: (escape velocity)^2 / 2 = G * mass / radius. As you decrease radius, the escape velocity increases.

Question 19

How small would the Earth have to be so that light would not be able to escape it?

Answer 19

< 1 cm

Question 20

What is the event horizon?

Answer 20

The “surface” of a black hole is the radius at which

the escape velocity equals the speed of light. This spherical surface is known as the event horizon.

Question 21

What is the Schwarzschild radius?

Answer 21

The radius of the event horizon is known as the

Schwarzschild radius = 2GM/c2

Question 22

How large is a 3MSun black hole?

Answer 22

The event horizon of a 3 MSun black hole is also about as big as a small city

Question 23

What is special relativity?

Answer 23

“inertial” - i.e. non-accelerating – frames of reference:

Question 24

What is general relativity?

Answer 24

accelerating frames of reference

Question 25

What are Lorentz transformations?

Answer 25

Lorentz transformations: as v increases, mass, length and time will change according to the factor. (1-v^2/c^2)^1/2

Question 26

What mass would something have if it were moving at the speed of light?

Answer 26

As v approaches c, mass becomes so large that it would take more and more force to accelerate the mass; at v = c, mass is infinite, so an infinite force would be required to accelerate the object any further.
Therefore we can say that c is the speed limit for anything having mass in the universe. We can also say that anything moving at the speed of light must have zero mass.

Question 27

How does general relativity affect space-time around the event horizon?

Answer 27

Near large gravitational fields, space-time becomes “curved”, and objects in motion are accelerated; general relativistic effects must be taken into account. Time passes more slowly.

Question 28

What are some experimental proofs of general relativity?

Answer 28

precession of perihelion of Mercury’s orbit

deflection of starlight passing close to Sun – eclipse of 1919

gravitational redshift – photons lose energy as they climb up out of a gravity well

gravity waves – binary neutron stars – they radiate gravity waves, therefore lose energy, therefore their orbit gets smaller (and faster – Kepler’s 3rd Law).

Question 29

What occurs in a black hole?

Answer 29

Nothing can escape from within the event
horizon because nothing can go faster than light.
• No escape means there is no more contact with
something that falls in. It increases the hole
mass, changes the spin or charge, but otherwise
loses its identity.

Question 30

What is a singularity?

Answer 30

Matter must be crushed to an infinite density, i.e. a point – zero volume - a singularity. Beyond the neutron star limit, no known force can resist the crush of gravity.
• As far as we know, gravity crushes all the matter
into a single point known as a singularity.

Question 31

What is the no-hair theorem?

Answer 31

mass: defines Schwartzschild Radius
e-m charge – small, because most e-m energy is radiated away in
gravity waves or e-m radiation as BH is being formed
angular momentum i.e. spin.

a rotating Black hole will have a ring-shaped singularity, and a spheroidal (not perfectly spherical) region – the Ergo-region – around the event horizon. Space-time will be distorted within the ergo-region.

No other properties - no hair theorem.

Question 32

What is the neutron star limit?

Answer 32

Quantum mechanics says that neutrons in
the same place cannot be in the same state
• Neutron degeneracy pressure can no longer
support a neutron star against gravity if its
mass exceeds about 3 Msun

Question 33

How do we know black holes exist?

Answer 33

Need to measure mass
— Use orbital properties of companion
— Measure velocity and distance of orbiting gas
• It’s a black hole if it’s not a star and its mass
exceeds the neutron star limit (~3 MSun)

Question 34

What is an example of a black hole?

Answer 34

Some X-ray binaries contain compact objects of mass
exceeding 3 MSun which are likely to be black holes. 1971 - Cygnus X-1; X-rays which vary over time scales of a few milliseconds; i.e. physical size of emitter can’t exceed a few thousand km;

Question 35

How are black holes formed?

Answer 35

Type II supernova, with core > 3 Ms
White Dwarf or Neutron star in binary, accreting mass > 3 Ms
Two Neutron stars colliding, with total mass > 3 Ms.

Question 36

What are supermassive black holes?

Answer 36

At centers of galaxies - M87 – a giant elliptical galaxy; there is a small, bright source at its center,
moving at hundreds of km/s; Kepler’s 3rd Law interior mass must be ~ 3 x 10^9, in an area smaller than the Solar System!

Question 37

What is Hawking radiation?

Answer 37

Quantum uncertainty allows for virtual pairs (electron, positron) to be momentarily created “out of nothing”, but they instantly annihilate each other. But if this pair production occurs near the event horizon, one particle
may disappear into the BH, leaving the other particle intact (and flying off). The mass must come from the BH, so it is “evaporating”.

Question 38

What is the “temperature” of a black hole?

Answer 38

So, we can say that a BH has another property, i.e. “temperature”, a measure of the rate at which it is evaporating. The temperature varies inversely as the mass; a 5 Ms black hole acts like a blackbody with a temperature of only 1 x 10 –7 K. A small black hole (1015 kg) has a temperature of 109 K!

Question 39

What are gamma-ray bursts? When were they first detected?

Answer 39

They must be among the most powerful explosions in the universe—could be the formation of a black hole Brief bursts of gamma-rays coming from space were
first detected in the 1960s

Question 40

What causes gamma-ray bursts?

Answer 40

Observations show that at least some gamma-ray
bursts are produced by supernova explosions
• Some others may come from collisions between
neutron stars