neutron stars and black holes
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Neutron Stars and Black Holes
Chapter 20
Mass Loss From StarsStars like our sun are constantly losing mass in a
stellar wind ( solar wind).
The more massive the star, the stronger its stellar wind.
Far-infrared
WR 124
The End of a Star’s LifeWhen all the nuclear fuel in a star is used up,
gravity will win over pressure and the star will die.
High-mass stars will die first, in a gigantic explosion, called a supernova.
Less massive stars will die
in a less dramatic
event, called a nova
The Final Breaths of Sun-Like Stars: Planetary Nebulae
The Helix Nebula
Remnants of stars with ~ 1 – a few Msun
Radii: R ~ 0.2 - 3 light years
Expanding at ~10 – 20 km/s ( Doppler shifts)
Less than 10,000 years old
Have nothing to do with planets!
The Formation of Planetary Nebulae
The Ring Nebula in Lyra
Two-stage process:
Slow wind from a red giant blows away cool, outer layers of the star
Fast wind from hot, inner layers of the star overtakes the slow wind and excites it
=> Planetary Nebula
The Dumbbell Nebula in Hydrogen and Oxygen Line Emission
Planetary NebulaeOften asymmetric, possibly due to
• Stellar rotation
• Magnetic fields
• Dust disks around the stars
The Butterfly Nebula
The Remnants of Sun-Like Stars: White Dwarfs
Sunlike stars build up a Carbon-
Oxygen (C,O) core, which does not
ignite Carbon fusion.
He-burning shell keeps dumping C
and O onto the core. C,O core collapses
and the matter becomes
degenerate.
Formation of a
White Dwarf
White DwarfsDegenerate stellar remnant (C,O core)
Extremely dense:1 teaspoon of WD material: mass ≈ 16 tons!!!
White Dwarfs:
Mass ~ Msun
Temp. ~ 25,000 K
Luminosity ~ 0.01 Lsun
Chunk of WD material the size of a beach ball would outweigh an ocean liner!
White Dwarfs (2)
Low luminosity; high temperature => White dwarfs are found in the lower left corner of the
Hertzsprung-Russell diagram.
The Chandrasekhar LimitThe more massive a white dwarf, the smaller it is.
Pressure becomes larger, until electron degeneracy pressure can no longer hold up against gravity.
WDs with more than ~ 1.4 solar masses can not exist!
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.
• only 5 supernovas have been observed in the past century.
Supernovae• Explosion that
produces high luminosity – sometimes more than 10 billion times that of our sun
• Makes observation easy….sometimes.
• Type I– No visible H lines
• Type II– Visible H lines in
spectrum– Produced by collapse
of core in massive stars (8-25 solar masses)
– Occurs when Silicon has finished fusing to Iron – a white dwarf with the outer layers of a red giant.
Types of Supernovae
• Electrons react with protons in Iron atoms; give off neutrinos
• Object 0.6-0.8 SM contracts to 5 km radius (in just a few seconds)
• Density gets so high that it stops collapsing – this is a neutron star
• The star pushes outward and creates a shockwave of stellar materials that the neutrinos speed along– Supernova remnant
Type II Supernovas
• The light we see is 1% of the total energy released
• Brightness increases first but then drops off; remains luminous for years
• Example: Supernova 1987A– In Large Magellanic
Cloud– First SN to provide
time of explosion and source star
– Neutrinos were detected before the visible light.
Type II Supernovas
• Most violent occurrence in the universe
• Gamma rays, light and radio waves all emitted– Gammas in narrow
beams– Many invisible –
estimated 1500 per day
• Energy equal to 10s to 1000s of supernovae
• Occur when the core of a massive star collapses
• Accompany supernovae
Gamma Ray Bursts
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.
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”
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!
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
1. Has the existence of neutron stars been sufficiently tested to be called a theory, or should it be called a hypothesis? What about the existence of black holes?
2. Why would you expect an accretion disk around a star the size of the sun to be cooler than an accretion disk around a compact object?
3. In this chapter, we imagined what would happen if we jumped into a Schwarzschild black hole. From what you have read, what do you think would happen to you if you jumped into a Kerr black hole?
Discussion Questions
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
Red Dwarfs
Stars with less than ~ 0.4
solar masses are completely
convective.
Hydrogen and helium remain well mixed throughout the entire star.
No phase of shell “burning” with expansion to giant.
Star not hot enough to ignite He burning.
Mass
Sunlike Stars
Sunlike stars (~ 0.4 – 4 solar masses) develop a helium core.
Expansion to red giant during H burning shell phase
Ignition of He burning in the He core
Formation of a degenerate C,O core
Mass
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