Transcript Neutron Stars and Pulsars

Endpoints of Stellar Evolution
White Dwarfs, Neutron Stars, and
Black Holes
Stellar Evolution Summary
• Low mass star (0.08 M⊙ <M < 0.4M⊙)→helium
white dwarf.
• Medium mass star (0.4 M⊙ < M < 8 M⊙) →red
giant→carbon white dwarf + planetary nebula
• High mass star (8 M⊙ < M < 20 M⊙) →red
supergiant→massive star supernova + neutron star
• Very high mass star (M > 20 M⊙) →red
supergiant→massive star supernova + black hole
Accretion Disks, Novae, and
White Dwarf Supernovae
Summary of Neutron Star Properties
• Radius ~ 10 km (about 600 times smaller than Earth).
• Mass ~1.4 to 3 times the mass of the Sun.
• Density ~ 1017 kg per cubic meter. A ½ inch cube of this
material with would weigh more than 100 million tons.
• Neutron degeneracy prevents it from collapsing further
• Spins very rapidly.
• Has a powerful magnetic field.
• Spin rate and magnetic field strength normally decrease
with time.
Rotation Rate and Magnetic Field
Assuming no mass loss from the collapsing core, the law of conservation of angular
momentum requires that its rotation rate increase; i.e., that its rotation period decrease.
2
R 
P2   2  P1
 R1 
How fast would the Sun rotate if it collapse to R = 10 km?
P1  25 days  25  86400s  2.16 106 s
R1  7  105 km
R 2  10km
2
 10km 
7
P2  
  2.16  10 s 
5
 7  10 km 
 4  10 3 s
As the star collapses, its magnetic field is concentrated in a smaller area, becoming as
much as a trillion times as strong as that of the Sun.
The stellar core was already hot, but the collapse raises the temperature further.
Pulsar Properties
• Periods from a few milliseconds to several seconds.
• Pulses last for as little as 1 millisecond.
• Pulses occur with great regularity. For the first pulsar discovered, P =
1.33730119 s.
• Period decreases at the rate of a few billionths of a second per day.
• Glitches (sudden drops in pulsar period) occur.
Name
Period (sec)
Rate of Change
of Period
(sec/sec)
1937 + 21
0.001557
1.07×10-19
1855 + 09
0.005362
4.64×10-11
0531 + 21
0.033326
4.21×10-13
0833 - 45
0.089234
1.24×10-13
What is a Pulsar?
• Pulsating main sequence star or white
dwarf? No - pulsations too fast.
• Rotating main sequence star or white dwarf
with a hot spot? No - Either of these would
disintegrate if it rotated this fast.
• Pulsating neutron star? No - these would
pulsate too fast.
• Rotating neutron star. Yes, the pulsar
periods are consistent with this.
The Lighthouse Model
Neutron stars can rotate rapidly without
disintegrating.
They initially have strong, polar magnetic
fields.
Strong, accelerated magnetic field lines create
a powerful electric field.
Strong electric field creates and accelerates
charged particles.
Electrons are trapped by the magnetic field
and forced to travel along magnetic field lines
away from the magnetic poles at speeds near
the speed of light.
Accelerated electrons emit “synchrotron”
radiation, resulting in twin beams of
electromagnetic radiation from the north and
south magnetic poles of the neutron star.
A pulsar “pulse” arrives at Earth
whenever a beam sweeps across Earth.
Rotational energy is converted into
synchrotron radiation, so the neutron star
slows down, with periodic “glitches” (sudden
increases of the rotation speed).
Are glitches due to “starquakes”? Some
probably are, but these are not frequent
enough to account for all glitches.
Most are probably due to “vortex events”,
triggered by slowing of rotation. Angular
momentum of a large number of vortices
is transferred to the crust.
Pulsar in the Crab Nebula Supports the Lighthouse Model
Black Holes
Escape Velocity and Black Holes
No physical object can travel faster than light. The speed of light, according to special
relativity, is an absolute upper limit.
What is the radius of an object of given mass that has an escape velocity equal to the speed
of light?
2GM
ve 
R
2GM
c
Rs
2GM
c 
Rs
2
2GM
Rs  2
c
 2GM  M
Rs  
M
2
 c

2  6.67  1011 1.99  1030 kg 
2GM
3


3.0

10
m  3.0km
2
2
8
c
 2.998  10 m / s 
R s   3.0km  M
M in solar masses and Rs in km
2GM M
Rs  2
cM
The Event Horizon of a Non-rotating
(Schwartzschild)Black Hole
If the core of a dead star has a mass greater than about 3M , nothing
can stop it from collapsing to zero volume; it becomes a "singularity".
According to general
relativity, the singularity is
enclosed by a spherical
surface called the event
horizon. The radius of the
event horizon, Rs, is called the
Schwartzschild radius.
Nothing can cross the event
horizon in the outward
direction. Since this includes
light, we can’t observe
anything inside the event
horizon.
RS
Summary of Schwartzschild
Black Hole Properties
• Nothing that enters the event horizon can escape from the
black hole.
• No force can stop collapse to zero volume.
• Time slows down and light is red-shifted as the event
horizon is approached.
• Tidal forces squeeze, stretch, tear apart, and ionize material
before it reaches the event horizon.
Kerr (Rotating) Black Holes
• A black hole can have only three properties: mass, angular
momentum, and charge.
• Stellar black holes are electrically neutral.
• A neutral rotating black hole is called a Kerr black hole.
• Outside its event horizon, a Kerr black hole has a region,
called the ergosphere, in which spacetime is dragged along
with the rotating black hole. In principle, energy can be
extracted from the ergosphere.
• An object dropped into the ergosphere can break into two
parts. One of them drops through the event horizon. The
other leaves the ergosphere with more energy than the
original object had, and the mass of the black hole
decreases.
Searching for Black Holes
• Isolated black holes are impossible for us to see from Earth, because
they’re small and emit no light.
• A black hole is more likely to be recognized if it has a visible
companion that isn’t a black hole.
• A black hole with a visible companion will be a strong source of xrays. The x-ray emission intensity should exhibit rapid fluctuations
because of the chaotic nature of the processes that cause the x-ray
emission.
• So, we search for binary systems in which (a) one of the objects is
visible, (b) the other is invisible and (c) there are x-ray sources that
have short time scale fluctuations
• We deduce the mass of the visible companion from its spectrum.
• Having the mass of the visible companion and some information about
the orbit, we can find a lower limit to the mass of the invisible
companion. If it’s greater than about 3 times the mass of the Sun, it’s
probably a black hole. Otherwise, it’s likely to be a neutron star.
Behavior of a Blob of Matter Falling Toward a Black Hole
Event Horizon or Onto a Neutron Star
Neutron star – Blob of matter
spirals inward, hits the hard
surface, and explodes,
producing a powerful burst
of high energy radiation.
Black hole – Blob of matter
spirals inward, reddens, and
gradually disappears. Very
little radiation escapes from
the blob.
http://science.nasa.gov/headlines/y2001/ast12jan_1.htm
 3.8M
Some Black Hole Candidates
Object
Location
Companion
Star
Orbital
Period
Mass of
Compact
Object
LMC X-3
Dorado
B3 V
1.7 days
~ 10
A0620-00
Monoceros
KV
7.75 hours
10 ± 5
V404 Cygni
Cygnus
KV
6.47 days
12 ± 2
X-Ray Bursters, Gamma Ray
Bursters, QPO’s, and SS433
X-Ray Bursters
• Powerful bursts of energy at irregular intervals.
• The longer the period between bursts, the stronger the
burst.
• Explanation: Neutron star with a normal star companion.
• Close enough for normal star material to pass through the
inner Lagrangian point, form a disk around the neutron
star, and accrete onto it.
• As the mixture of hydrogen and helium accumulates on the
surface of the neutron star, the hydrogen fuses steadily and
a layer of helium builds up.
• When the layer of helium becames dense enough and hot
enough, it fuses to form carbon and emits a burst of x-rays.
The burst lasts just a few seconds, but emits ~1037 Joules
of energy.
• The helium layer can then build up until another burst
occurs.
Quasi-periodic
Oscillations
•
•
Observation: X-ray pulses from
accretion disks around neutron stars
and black holes. Pulses have very short
periods – as short as 0.00075 s. Pulse
periods decrease rapidly before the
pulse vanishes completely. Because of
the changing pulse period, these are
called QPO’s (quasi-periodic
oscillations).
Explanation: Blobs of material near
the surface of a neutron star or black
hole emit x-rays while orbiting in the
accretion disk. The period decreases
because the blob moves faster as it
spirals into the compact object.
http://science.nasa.gov/headlines/images/blackhole/cygxr1w.jpg
Calculate the orbital period for a blob of material 20 km from the center of a neutron star
of mass 2.0 times the mass of the Sun.
d  vt
d
t
v
v  vc 
GM
r
 d   2   2  104 m   1.26  105 m
 6.67  10  4  10 
11
v
2  10
d  2r
M  2M  2   2  1030 kg   4  1030 kg
30
4
r  20km  20  103 m  2  10 4 m
 1.15  10 m / s
8
1.26  105 m
t
1.15  108 m / s
 0.0011s
SS433
•
•
•
•
•
One set of spectral lines is blue-shifted and another is red-shifted.
Model: neutron star or black hole with a normal star companion.
Accretion disk and bipolar jets.
Disk and jet precess with a 164-day period.
Jet velocity ~ ¼ the speed of light.
Gamma Ray Bursters
•
•
•
•
•
•
Short (seconds or minutes)
bursts of high energy gamma
rays.
Seen in all directions →
originate outside our galaxy.
Measured red shifts indicate that
they are billions of light years
away.
What are they?
Binary neutron star systems?
They emit energy in the form of
gravitational waves and
eventually merge. This results in
a black hole + a short burst of
high energy gamma rays.
Hypernovae (collapsars)? High
mass star collapses, but
supernova is suppressed by
infalling mass from the star’s
envelope.→ Star collapses to
form a black hole. → Bursts of
high energy gamma rays along
the polar axes.
Afterglow of a gamma burst coincides with
A supernova in a galaxy billions of light
years away.
06/05/2002
http://antwrp.gsfc.nasa.gov/apod/ap020405.html