Neutron Stars and Black HolesChapter 14
The preceding chapters have traced the story of stars from their birth as clouds of gas in the interstellar medium to their final collapse. This chapter finishes the story by discussing the kinds of objects that remain after a massive star dies.
How strange and wonderful that we humans can talk about places in the universe where gravity is so strong it bends space, slows time, and curves light back on itself! To carry on these discussions, astronomers have learned to use the language of relativity. Throughout this chapter, remember that our generalized discussions are made possible by astronomers studying general relativity in all its mathematical sophistication. That is, our understanding rests on a rich foundation of theory.
This chapter ends the story of individual stars. The next three chapters, however, extend that story to include 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. The Evolution of PulsarsE. 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)
Neutron Stars
The central core will collapse into a compact object of ~ a few Msun.
A supernova explosion of a M > 8 Msun star blows away its outer layers.
Formation of Neutron StarsCompact objects more massive than the
Chandrasekhar Limit (1.4 Msun) collapse further.
Pressure becomes so high that electrons and protons combine to form stable neutrons throughout the object:
p + e- n + ne
Neutron Star
Properties of Neutron Stars
Typical size: R ~ 10 km
Mass: M ~ 1.4 – 3 Msun
Density: r ~ 1014 g/cm3
Piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons!!!
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,
lmax = 3,000,000 nm / T[K]
gives a maximum wavelength of lmax = 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.
Lighthouse Model of Pulsars
A Pulsar’s magnetic field has a dipole structure, just like Earth.
Radiation is emitted
mostly along the magnetic
poles.
Neutron Star
(SLIDESHOW MODE ONLY)
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
Binary Pulsars
Some 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 gravityM = Mass
Schwarzschild Radius and Event Horizon
No object can travel faster than the speed of light
Þ 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
Þ “Event horizon”
Schwarzschild Radius of Black Hole
(SLIDESHOW MODE ONLY)
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
An astronaut descending down towards the event horizon of the BH will be stretched vertically (tidal effects) and squeezed
laterally.
General Relativity Effects Near Black Holes (2)
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 (3)
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!
End States of Stars
(SLIDESHOW MODE ONLY)
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 BurstersSeveral bursting X-ray sources have been observed:
Rapid outburst followed by gradual decay
Repeated outbursts: The longer the interval, the stronger the burst
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
Radio Jet Signatures
The radio jets of the Galactic black-hole candidate GRS 1915+105
Model of the X-Ray Binary SS 433
Optical spectrum shows spectral lines from material
in the jet.
Two sets of lines: one blue-shifted, one red-shifted
Line systems shift back and forth across each other due to jet
precession
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 of May 10, 1999: 1 day after the GRB 2 days after the GRB
Many have now been associated with host galaxies at large (cosmological) distances.
Probably related to the deaths of very massive (> 25 Msun) stars.
neutron starpulsarlighthouse modelpulsar windglitchmagnetargravitational radiationmillisecond pulsarsingularityblack holeevent horizonSchwarzschild radius (RS)
Kerr black holeergospheretime dilationgravitational red shiftX-ray burster
quasi-periodic oscillations (QPOs)
gamma-ray burstersoft gamma-ray repeater (SGR)
hypernovacollapsar
New Terms