Lecture 10 - Stellar Remnants

Announcements

Midterm #2 is next Tuesday, May 13, covering chapters 6, 14.1-14.2, 15.1-15.2, 16.1, 17.1-17.3, 18.1-18.3, and 19.
The midterm focuses on material since Midterm #1 but builds on chapters 1-5.
Friday's discussion section will be a midterm review.

Stellar Evolution: Low-Mass vs. High-Mass Stars

Low-Mass Stars ( < 2 M_{sun} ):
- Follow a specific life cycle.
High-Mass Stars ( > 8 M_{sun} ):
- Have a different, more dramatic life cycle.
Intermediate-Mass Stars (2-8 M_{sun}):
- Similar to high-mass stars but end as white dwarfs.

Life Cycle of Low-Mass Stars

Fusion occurs in the core during stages 2 (Main Sequence) and stages 3, 4, 5.
White dwarfs do not have fusion; they are supported by degeneracy pressure.
As white dwarfs age, they get smaller, fainter, and cooler, eventually disappearing from view as they become too cool to emit any more visible light.

Life Cycle of High-Mass Stars

In high-mass stars, various fusion reactions occur as the star evolves.
Like low-mass stars, high-mass stars go through stages with and without core fusion.
Advanced nuclear fusion requires extremely high temperatures, attainable only in high-mass star cores.
The star ends up with numerous fusing shells in the core.

Death of High-Mass Stars

The core is left with degenerate iron (Fe).
The iron core cannot support itself under the star's crushing weight.
Electrons and protons combine to form neutrons and neutrinos.
The core collapses to form a degenerate neutron core.
The star explodes in a supernova, leaving behind a neutron star.

Supernovae and Element Creation

Supernovae release huge amounts of energy, creating elements heavier than iron.
The explosion sends these heavy elements into space, where they collapse into new clouds and form new stars and planets.
We are "star stuff!!"

Supernova Trigger

Iron cannot undergo fusion, so it can’t release energy into the star.
Without outward pressure, the core collapses.

Stellar Remnants

Stars leave behind remnants such as:
- White dwarfs
- Neutron stars
- Black holes

Object Support Against Gravity

The Sun: gas pressure (thermal energy)
White Dwarfs: electron degeneracy pressure
Neutron Stars: neutron degeneracy pressure
Black Holes: NOTHING

White Dwarfs

Exposed carbon core of a dead low-mass star.
Radius similar to Earth's.
Mass comparable to the Sun, making them extremely dense.
A sugar cube of white dwarf material would weigh more than a ton on Earth.

Degeneracy Pressure

Particles (electrons, neutrons) can’t be in the same place and have the same speed (Pauli Exclusion Principle).
Does NOT depend on temperature, just density.
Electrons can’t occupy the same space simultaneously, halting contraction.

Bizarre Properties of White Dwarfs

More massive white dwarfs have smaller radii.
This contrasts with the main sequence behavior.
Maximum mass of 1.4 M_{sun} (Chandrasekhar Limit): gravity overcomes electron degeneracy pressure, and electrons move close to the speed of light.
No white dwarf more massive than 1.4 M_{sun} has been found.

Chandrasekhar Limit

Subrahmanyan Chandrasekhar (1910-1995) studied compact objects.
Awarded the Nobel Prize in Physics in 1983.
Predicted the upper mass limit for white dwarfs at 1.4 M_{sun}.

White Dwarf Mass and Radius

A 1.2 M{sun} white dwarf has a smaller radius than a 1.0 M{sun} white dwarf.

White Dwarf Crystallization

Once cooled, white dwarfs can crystallize into diamond-like carbon.
These are the largest diamonds in the Universe!

White Dwarf Mass Gain and Supernovae

Half of all stars are in binary systems.
A bloated red giant can transfer mass to its white dwarf companion.
If a white dwarf exceeds 1.4 M_{sun}, gravity overcomes degeneracy pressure.
The core collapses, the temperature rises, and carbon fusion occurs, triggering a carbon 'flash'.
The carbon fusion destroys the star, resulting in a white dwarf supernova with consistent properties.
Useful for distance measurements.

Neutron Stars

Low-mass star death: planetary nebula leaves behind a white dwarf.
High-mass star death: supernova leaves behind a neutron star (or a black hole).
A neutron star is a ball of neutrons from the collapsed iron core of a supernova.
Neutron degeneracy pressure supports a neutron star against gravity.

Neutron Star Properties

Neutron stars are denser than white dwarfs, with a radius of only 10 km.
A teaspoon of neutron star material would weigh more than Mt. Everest!

Neutron Star Discovery

Jocelyn Bell (graduate student) discovered regular radio pulses from a specific sky position in 1967.
The period was 1.337301 seconds.
Pulsars are neutron stars emitting regular pulses.

Crab Nebula Pulsar

Some pulsars are located in the middle of supernova remnants.
The Crab Nebula Pulsar pulses thirty times a second.
Crab Nebula is the remnant of a supernova from 1054 AD.

Pulsar Size and Rotation

Rotation speed indicates small size.
Speed = distance / time \frac{2 \pi R}{ \frac{1}{30} \text{ sec}}
Speed must be less than c (speed of light), so R < 1600 km for this specific pulsar.

Pulsars

Pulsars are spinning neutron stars.
The strong magnetic field creates a radiation beam that sweeps by us.
Fast repeating light pulses are observed, similar to a lighthouse beam.

Neutron Star Mass Limit

Neutron degeneracy pressure cannot support a neutron star if its mass exceeds about 3 M_{sun}.
Cores of some massive stars are so large that neutron degeneracy pressure cannot support them during a supernova.
The core forms a black hole when contraction is unstoppable.

Black Holes

An object with gravity so strong that not even light can escape.
The escape velocity exceeds the speed of light.

Escape Velocity

For a black hole, v_{escape} > c (speed of light).

Black Hole Characteristics

Black holes are defined by the amount of mass within a given radius.
In theory, black holes can have any mass if small enough.
Squashing the Sun into a 3 km radius or Earth into a ~1 cm radius would create a black hole.

Black Hole Definitions

Event Horizon: The radius where escape velocity equals the speed of light.
Schwarzschild Radius: The radius of the event horizon.

Black Holes and Space-Time

General Relativity (Einstein, 1915) describes gravity as curvature in space-time caused by mass.
Black Hole: An object with high density warping space-time so severely that a "bottomless pit" forms, preventing light from escaping.

Schwarzschild Radius

R{Schwarzschild} = 3 \times M{sun} \text{ km}
The event horizon of a 3 M_{sun} black hole is about the size of a small city.

Event Horizon

Nothing can escape from within the event horizon because nothing can travel faster than the speed of light.
Material falling in increases the black hole’s mass, electrical charge, or angular momentum but loses its identity.

Black Hole Effects

If the Sun were replaced by a black hole of the same mass, Earth's orbit would remain unchanged.
Black holes are not cosmic vacuum cleaners.

Detecting Black Holes

Detected by their gravitational influence and accretion disks.
Measure mass using orbital properties of orbiting stars or gas.
If an unseen object has mass > 3 M_{sun} or enough mass in a small radius, it is likely a black hole.

Cygnus X-1

The earliest object thought to be a black hole is Cygnus X-1.
It consists of a luminous star with a mass of 19 M{sun} and an unseen companion with a mass of ~15 M{sun}.

X-ray Binaries

Cygnus X-1 emits X-rays from an accretion disk of hot material falling toward the black hole.
X-ray binaries indicate an object with a strong gravitational pull.
Mass determination can confirm whether the object is a white dwarf, neutron star, or black hole.

First Black Hole Image

The Event Horizon Telescope released the first "picture" of a black hole in April 2019.

Black Hole Effects on Space and Time

Near a black hole, both space and time are distorted.
General relativity: time passes more slowly near the event horizon.
At the event horizon, time appears “frozen” to an outside observer.

Gravitational Redshift

Photons lose energy escaping the gravity near a black hole and become gravitationally redshifted.
Observed in white dwarfs: spectral lines are redshifted compared to main sequence stars.
Different from the Doppler effect caused by motion.

Time Dilation

Time slows down in a gravitational potential well.
GPS relies on general relativity to account for time dilation; without it, GPS would fail within hours.