Neutron Stars and Black Holes

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 + e

Neutron Star

Properties of Neutron Stars

Typical size: R ~ 10 km

Mass: M ~ 1.4 – 3 Msun

Density: ~ 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,

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.

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

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 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”

Schwarzschild Radius of Black Hole

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 Bursters

Several 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

Quiz Questions

1. What is the lower limit for the mass of neutron stars?

a. About 0.08 solar masses.b. About 0.4 solar massesc. Exactly 1 solar mass.d. About 1.4 solar masses.e. Between 2 and 3 solar masses.

Quiz Questions

2. White dwarfs and neutron stars are both end products of stellar evolution. White dwarfs are composed of mostly carbon, oxygen, and electrons, whereas neutron stars are composed of mostly neutrons. What happens to the protons in the atomic nuclei and the degenerate electrons that were inside the star that creates a neutron star?

a. The protons and electrons, being charged particles, are all ejected during the supernova event by the strong magnetic field.b. The electrons and protons combine to form neutrons and neutrinos.c. Protons decay into neutrons and positrons and neutrinos. The positrons combine with the electrons and form pairs of gamma rays.d. The protons remain in the neutron star and the electrons are ejected by the magnetic field.e. Our understanding of atomic nuclei is not yet good enough to determine what happens to them.

Quiz Questions

3. Why don't we use visible-wavelength telescopes to locate neutron stars?

a. Neutron stars have wavelengths of maximum intensity in the X-ray band of the electromagnetic spectrum.b. Neutron stars are too cold to emit visible light.c. Neutron stars have strong magnetic fields.d. Neutron stars pulse too rapidly.e. Neutron stars are very small.

Quiz Questions

4. What prevents neutron stars from contracting to a smaller size?

a. Gas pressure fueled by hydrogen fusion.b. Gas pressure fueled by helium fusion.c. Gas pressure fueled by carbon fusion.d. Degenerate neutrons.e. Degenerate electrons.

Quiz Questions

5. Why do we expect that neutron stars spin rapidly?

a. The law of conservation of energy.b. The law of conservation of angular momentum.c. Equatorial jets spin them up.d. Both a and b above.e. All of the above.

Quiz Questions

6. Why are pulsars so hot?

a. Helium flash.b. The CNO cycle proceeds rapidly.c. Active fusion of elements heavier than carbon.d. Gravitational energy was converted into thermal energy during formation.e. Active fusion of elements heavier than iron produces vast amounts of energy.

Quiz Questions

7. Why does the short length of pulsar pulses eliminate normal stars as possible pulsars?

a. Normal stars are unchanging and eternal. b. Normal stars are too cool to emit radio pulses.c. Normal stars do not have strong enough magnetic fields.d. The small size of normal stars prohibits the emission of pulses this short.e. An object cannot emit pulses that are shorter than the time it takes light to cross its diameter.

Quiz Questions

8. How can a neutron star not be a pulsar?

a. Its magnetic field may be too weak to generate beams of radiation.b. A pulsar may be too old and rotate too slowly to pulse.c. A pulsar's magnetic field may not sweep past Earth.d. Both a and b above.e. All of the above.

Quiz Questions

9. What type of pulsars have been observed to emit visible pulses?

a. Young pulsars.b. Slow pulsars.c. Old pulsars.d. Nearby pulsars.e. Both b and c above.

Quiz Questions

10. Why are all pulsars not located in supernova remnants?

a. Pulsars persist longer than supernova remnants.b. Some pulsars given high velocities upon formation can flee the scene of destruction.c. Some pulsars are the result of mergers rather than supernova events.d. Both a and b above.e. All of the above.

Quiz Questions

11. Why do the millisecond pulsars spin so fast?

a. They have all been formed recently.b. The impact of a large planet has spun them up.c. Accretion of matter from a nearby binary companion spins them up.d. Their strong magnetic field couples with the interstellar magnetic field.e. They really spin at half their pulse rate, as both magnetic poles sweep past Earth.

Quiz Questions

12. Which of the following is an accurate description of the Schwarzschild radius?

a. It is the radius of a black hole singularity.b. It is the radius to which an object must shrink to become a black hole.c. It is the radius of the event horizon surrounding a black hole singularity.d. Both a and b above.e. Both b and c above.

Quiz Questions

13. What is the difference between a Schwarzschild black hole and a Kerr black hole?

a. Mass.b. Electric charge.c. Angular momentum.d. Both b and c above.e. All of the above.

Quiz Questions

14. What changes would occur if the Sun were replaced with a one-solar-mass black hole?

a. Earth's orbit would not change.b. Earth would be sucked into the Sun.c. The planets would disappear from view.d. Extreme tidal forces would severely fracture Earth's lithosphere.e. Both a and c above.

Quiz Questions

15. What property does matter inside the event horizon of a black hole retain?

a. Mass.b. Mass and angular momentum.c. Mass, angular momentum, and electric charge.d. Mass, angular momentum, electric charge, and temperature.e. Mass, angular momentum, electric charge, temperature, and luminosity.

Quiz Questions

16. Which of the following describes the gravitational red shift?

a. The reddening of starlight by interstellar dust grains.b. A reduction in the energy of photons as they move away from objects.c. The angular change in a star's position when observed during a solar eclipse.d. The alternating Doppler effect due to two bodies whose orbital plane contains our line of sight.e. We are unable to tell whether an object is moving away from us or we are moving away from the object.

Quiz Questions

17. What observational evidence do we have that stellar death black holes really exist?

a. Hollowed-out green spheres are sucking up matter in star forming regions and emitting gamma rays.b. Some X-ray binaries have an unseen object with masses greater than 3 solar masses.c. Some X-ray binaries emit pulses of radiation at radio wavelengths.d. We see areas that block the light from more distant objects.e. The observed glitches in the periods of pulsars.

Quiz Questions

18. What is the source of the continuous X-rays emitted by a close binary system that contains a compact object?

a. The system’s magnetic field accelerates ionized matter, emitting synchrotron radiation.b. An accretion disk around the compact object is heated by friction.c. Matter impacting the surface of the compact object. d. The companion star is superheated by tidal forces.e. The hot surface of the compact object.

Quiz Questions

19. Some X-ray novae emit bursts of energy and others do not. In addition, those with energy bursts are about 100 times as luminous as those without bursts. What type of compact objects are responsible for these two types of X-ray novae?

a. Those with bursts contain black holes and those without bursts contain neutron stars.b. Those with bursts contain neutron stars and those without bursts contain black holes.c. Those with bursts contain white dwarfs and those without bursts contain neutron stars.d. Those with bursts contain neutron stars and those without bursts contain white dwarfs.e. Those with bursts contain black holes and those without bursts contain white dwarfs.

Quiz Questions

20. What may be responsible for the observed gamma ray bursters?

a. Neutron star merger.b. Hypernovae.c. Magnetars.d. Both a and b above.e. All of the above.

Answers

1. d2. b3. e4. d5. b6. d7. e8. e9. a10. d

11. c12. e13. c14. e15. c16. b17. b18. b19. b20. d