Download Neutron Stars and Black Holes

Neutron Stars and Black Holes
Outline
I. Neutron Stars
A. Theoretical Prediction of Neutron Stars
B. The Discovery of Pulsars
C. A Model Pulsar
D. The Evolution of Pulsars
E. Binary Pulsars
F. The Fastest Pulsars
G. Pulsar Planets
II. Black Holes
A. Escape Velocity
B. Schwarzschild Black Holes
C. Black Holes Have No Hair
D. A Leap into a Black Hole
E. The Search for Black Holes
Outline (continued)
III. Compact Objects with Disks and Jets
A. X-Ray Bursters
B. Accretion Disk Observations
C. Jets of Energy from Compact Objects
D. Gamma-Ray Bursts
Neutron Stars
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
Compact 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
Angular momentum conservation
=> Collapsing stellar core spins
up to periods of ~ a few
milliseconds.
Magnetic fields are amplified up to
B ~ 109 – 1015 G.
(up to 1012 times the average
magnetic field of the sun)
=> Rapidly pulsed (optical and radio) emission from
some objects interpreted as spin period of neutron stars
Pulsars / Neutron Stars
Neutron star surface has a temperature of
~ 1 million K.
Cas A in X-rays
Wien’s displacement law,
lmax = 3,000,000 nm / T[K]
gives a maximum wavelength of lmax = 3 nm,
which corresponds to X-rays.
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
Pulsar wind + jets
Remnant of a supernova observed in A.D. 1054
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
Orbital period =
1.7 days
Accretion disk material heats to
several million K => X-ray emission
Star eclipses neutron
star and accretion
disk periodically
Pulsar Planets
Some 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 Velocity
Velocity needed to
escape Earth’s
gravity from the
surface: vesc ≈ 11.6
km/s.
Now, gravitational
force decreases
with distance (~
1/d2) => Starting out
high above the
surface => lower
escape velocity.
vesc
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:
2GM
Rs = ____
c2
G = Universal const. of gravity
M = Mass
Rs is called the
Schwarzschild Radius.
Vesc = c
Schwarzschild Radius and Event Horizon
No object can travel
faster than the
speed of light
=> nothing (not
even light) can
escape from inside
the Schwarzschild
radius
 We have no way
of finding out what’s
happening 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
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.
Event Horizon
General Relativity Effects Near Black
Holes (3)
Gravitational Red Shift
All wavelengths of emissions
from near the event horizon
are stretched (red shifted).
 Frequencies are lowered.
Event Horizon
Observing Black Holes
No 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.
Matter gets
pulled off from
the companion
star, forming
an accretion
disk.
=> Strong X-ray source!
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
Accretion disks around black holes
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
Radio Jet Signatures
The radio jets of
the Galactic blackhole 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
GRB of May 10, 1999:
1 day after the GRB
2 days after the GRB
Later discovered with X-ray and optical
afterglows lasting several hours – a few days
Many have now been associated with host
galaxies at large (cosmological) distances.
Probably related to the deaths of very
massive (> 25 Msun) stars.
New Terms
neutron star
pulsar
lighthouse model
pulsar wind
glitch
magnetar
gravitational radiation
millisecond pulsar
singularity
black hole
event horizon
Schwarzschild radius
(RS)
Kerr black hole
ergosphere
time dilation
gravitational red shift
X-ray burster
quasi-periodic oscillations
(QPOs)
gamma-ray burster
soft gamma-ray repeater
(SGR)
hypernova
collapsar
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 masses
c. 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.
2.
3.
4.
5.
6.
7.
8.
9.
10.
d
b
e
d
b
d
e
e
a
d
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
c
e
c
e
c
b
b
b
b
d