Neutron Stars and Black Holes
Chapter 14
When stars like the sun die, they leave behind white dwarfs, but more massive stars leave behind the strangest beasts in the cosmic zoo. Now you are ready to meet neutron stars and black holes, and your exploration will answer five essential questions:
• How did scientists predict the existence of neutron stars?
• What is the evidence that neutron stars really exist?
• How did scientists predict the existence of black holes?
• What is the evidence that black holes really exist?
• What happens when matter falls into a neutron star or black hole?
Guidepost
Answering these questions has challenged scientists to create new theories and to test them critically. That raises an important question about science:
• What checks are there against fraud in science?
This chapter ends the story of individual stars, but it does not end the story of stars. In the next chapter, you will begin exploring the giant communities in which stars live – the galaxies.
Guidepost
I. Neutron StarsA. Theoretical Prediction of Neutron StarsB. The Discovery of PulsarsC. A Model PulsarD. Recognizing Neutron StarsE. Binary PulsarsF. The Fastest PulsarsG. Pulsar Planets
II. Black HolesA. Escape VelocityB. Schwarzschild Black HolesC. Black Holes Have No HairD. A Leap into a Black HoleE. The Search for Black Holes
Outline
III. Compact Objects with Disks and JetsA. X-Ray BurstersB. Accretion Disk ObservationsC. Jets of Energy from Compact ObjectsD. Gamma-Ray Bursts
Outline (continued)
Formation of Neutron Stars
Compact objects more massive than the
Chandrasekhar Limit (1.4 Msun) collapse
beyond the formation of a white dwarf.
Pressure becomes so high that electrons and protons
combine to form stable neutrons throughout the object:
p + e- n + e
Neutron Star
A supernova explosion of a M > 8 Msun star blows away its outer layers.
The central core will collapse into a compact object of
~ a few Msun.
Formation of Neutron Stars (2)
Properties of Neutron Stars
Typical size: R ~ 10 km
Mass: M ~ 1.4 – 3 Msun
Density: ~ 1014 g/cm3
a piece of neutron star matter of the size of a
sugar cube has a mass of ~ 100 million tons!!!
A neutron star (more than the
mass of the sun) would
comfortably fit within the
Capital Beltway!
Discovery of Pulsars
=> Collapsing stellar core spins up to periods of ~ a few
milliseconds.
Angular momentum conservation
=> Rapidly pulsed (optical and radio) emission from some objects interpreted as spin period of neutron stars
Magnetic fields are amplified up to B ~ 109 – 1015 G.
(up to 1012 times the average magnetic field of the sun)
Pulsars / Neutron Stars
Wien’s displacement law,
max = 3,000,000 nm / T[K]
gives a maximum wavelength of max = 3 nm, which corresponds to X-rays.
Cas A in X-rays
Neutron star surface has a temperature of~ 1 million K.
Pulsar Periods
Over time, pulsars lose energy and
angular momentum.
=> Pulsar rotation is gradually
slowing down.
Pulsar Winds
These winds carry away about 99.9 % of the energy released from the slowing-down of the
pulsar’s rotation.
Pulsars are emitting winds and jets of highly energetic particles.
Lighthouse Model of Pulsars
A Pulsar’s magnetic field has a dipole structure, just like Earth.
Radiation is emitted
mostly along the magnetic
poles.
Images of Pulsars and Other Neutron Stars
The Vela Pulsar moving through interstellar space
The Crab nebula and
pulsar
The Crab Pulsar
Remnant of a supernova observed in A.D. 1054
Pulsar wind + jets
The Crab Pulsar (2)
Visual image
X-ray image
Light Curves of the Crab Pulsar
Proper Motion of Neutron Stars
Some neutron stars are moving rapidly through
interstellar space.
This might be a result of anisotropies during the supernova explosion,
forming the neutron star.
MagnetarsSome neutron stars have magnetic fields ~ 1000 times stronger even than normal neutron stars.
These care called Magnetars.
Earthquake-like ruptures in the surface crust of Magnetars cause bursts of soft gamma-rays.
Binary PulsarsSome pulsars form binaries with other neutron stars (or black
holes).
Radial velocities resulting from the orbital motion lengthen the pulsar period when the pulsar is moving away from Earth...
…and shorten the pulsar period when it is approaching
Earth.
Neutron Stars in Binary Systems: X-ray Binaries
Example: Her X-1
2 Msun (F-type) star
Neutron star
Accretion disk material heats to several million K => X-ray emission
Star eclipses neutron star and accretion disk periodically
Orbital period = 1.7 days
Pulsar PlanetsSome pulsars have planets orbiting around them.
Just like in binary pulsars, this can be discovered through variations of the pulsar period.
As the planets orbit around the pulsar, they cause it to wobble around, resulting in slight changes of the observed pulsar period.
Black Holes
Just like white dwarfs (Chandrasekhar limit: 1.4 Msun), there is a mass limit for neutron stars:
Neutron stars can not exist with masses > 3 Msun
We know of no mechanism to halt the collapse of a compact object with > 3 Msun.
It will collapse into a single point – a singularity:
=> A Black Hole!
Escape VelocityVelocity needed
to escape Earth’s gravity from the surface: vesc ≈
11.6 km/s.
vesc
Now, gravitational force decreases with distance (~ 1/d2) => Starting
out high above the surface => lower escape velocity.
vesc
vesc
If you could compress Earth to a smaller radius => higher escape velocity from the surface
The Schwarzschild Radius
=> There is a limiting radius where the escape velocity
reaches the speed of light, c:
Vesc = cRs = 2GM ____ c2
Rs is called the Schwarzschild Radius.
G = Universal const. of gravity
M = Mass
Schwarzschild Radius and Event Horizon
No object can travel faster than the speed of light
• We have no way of finding out what’s
happening inside the Schwarzschild
radius.
=> nothing (not even light) can
escape from inside the Schwarzschild
radius
“Event horizon”
Black Holes in Supernova Remnants
Some supernova
remnants with no pulsar /
neutron star in the center may contain black
holes.
Schwarzschild Radii
“Black Holes Have No Hair”
Matter forming a black hole is losing almost all of its properties.
Black Holes are completely determined by 3 quantities:
Mass
Angular Momentum
(Electric Charge)
General Relativity Effects Near Black Holes (1)
At a distance, the gravitational fields of a black hole and a star of the same mass are virtually identical.
At small distances, the much deeper gravitational potential
will become noticeable.
General Relativity Effects Near Black Holes (2)
An astronaut descending down towards the event horizon of the BH will be stretched vertically (tidal effects) and squeezed
laterally.
This effect is called “spaghettification.”
General Relativity Effects Near Black Holes (3)
Time dilation
Event Horizon
Clocks starting at 12:00 at each point.
After 3 hours (for an observer far away
from the BH):Clocks closer to the BH run more slowly.
Time dilation becomes infinite at the event horizon.
General Relativity Effects Near Black Holes (4)
Gravitational Red Shift
Event Horizon
All wavelengths of emissions from near the event horizon are stretched (red shifted).
Frequencies are lowered
Observing Black HolesNo light can escape a black hole
=> Black holes can not be observed directly.
If an invisible compact object is part of a binary, we can estimate its mass from the orbital period and
radial velocity.
Mass > 3 Msun
=> Black hole!
Candidates for Black Hole
Compact object with > 3 Msun must be a
black hole!
Compact Objects with Disks and Jets
Black holes and neutron stars can be part of a binary system.
=> Strong X-ray source!
Matter gets pulled off from the companion star, forming an accretion
disk.
Heats up to a few million K
X-Ray Bursters
Several bursting X-ray sources have been
observed:
Repeated outbursts: The longer the interval before the burst, the
stronger the burst.
Rapid outburst followed by
gradual decay
The X-Ray Burster 4U 1820-30
In the cluster NGC 6624
Optical Ultraviolet
Black-Hole vs. Neutron-Star Binaries
Black Holes: Accreted matter disappears beyond the event
horizon without a trace.
Neutron Stars: Accreted matter produces an X-ray flash as it impacts on the neutron star surface.
Black Hole X-Ray Binaries
Strong X-ray sources
Rapidly, erratically variable (with flickering on time scales of less than a second)
Sometimes: Quasi-periodic oscillations (QPOs)
Sometimes: Radio-emitting jets
Accretion disks around black holes
Gamma-Ray Bursts (GRBs)
Short (~ a few s), bright bursts of gamma-rays
Later discovered with X-ray and optical afterglows lasting several
hours – a few days
GRB a few hours after the GRB
Same field,
13 years earlier
Many have now been associated with host galaxies at large (cosmological) distances.
A model for Gamma-Ray Bursts
At least some GRBs are probably related to the deaths of very massive (> 25 Msun) stars.
In a supernova-like explosion of stars this massive, the core
might collapse not to a neutron star, but directly to a black hole.
Such stellar explosions are termed
“hypernovae”