1

Neutron Stars and Pulsars

Formation of a Neutron Star

Stars with masses less than 8M will end up as white dwarfs with a mass less than 1.4M .

Stars with masses between 8M and 20M will die in a supernova explosion and theircores will become neutron stars.

In the collapsing core, gamma rays break up the atomic nuclei into their constituent protons andIn the collapsing core, gamma rays break up the atomic nuclei into their constituent protons andneutrons.

-eThe density of the core is so great that the reaction p+ e n occurs, converting most

of the protons into neutrons.→ +ν

The mass of this dead star is between 1.4M and 3M .

Neutrons like electrons are fermions (particles with a spin of 1/2) so they obey the PauliNeutrons, like electrons, are fermions (particles with a spin of 1/2) so they obey the Pauliexclusion principle. Under the conditions of the dead high mass star, the neutrons are as tightly packed as possible. Just as white dwarfs are supported by electron degeneracy pressure, these dead stars are supported by neutron degeneracy pressure.

2

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• 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.

Properties of Neutron Stars - Density and Size

27 15n nMass and "radius" of a neutron are approximately m 1.67 10 kg and r 1 10 m.− −= × = ×

4 ( )34

How dense is a neutron star?

3n

4V r3

= π ( )3154V 1 10 m3

−= π × 45 3V 4 10 m−= ×

n

n

mdensityV

=27

45 3

1.67 10 kg4 10 m

−

−

×=

×17 34 10 kg / m= × 14 34 10 g / cm= ×

How big is a 2M neutron star?

MdensityV

= density V M× =MV

density= ( )30

17 3

2 2 10 kg

4 10 kg / m

× ×=

×13 310 m=

34V R3

= π 33V 4 R= π 33V R4

=π

1/ 33VR4

⎛ ⎞= ⎜ ⎟π⎝ ⎠

1/ 3133 104

⎛ ⎞×= ⎜ ⎟π⎝ ⎠

41 10 m= ×

R 10km=

3

Rotation Rate and Magnetic FieldAssuming no mass loss from the collapsing core, the law of conservation of angularmomentum requires that its rotation rate increase; i.e., that its rotation period decrease.

2

22 1

1

RP PR

⎛ ⎞= ⎜ ⎟⎝ ⎠

How fast would the Sun rotate if it collapse to R = 10 km?1R⎝ ⎠

61P 25 days 25 86400s 2.16 10 s≈ = × = × 5

1R 7 10 km= × 2R 10km=

( )2

72 5

10kmP 2.16 10 s7 10 km

⎛ ⎞= ×⎜ ⎟×⎝ ⎠34 10 s−= ×

A th t ll it ti fi ld i t t d i ll b iAs 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.

Internal Structure of a Neutron Star

4

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 (s) Rate of Change of Period (s/s)

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 the source of the pulsar phenomena?

• 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• Pulsating neutron star? No - these would pulsate too fast.• Rotating neutron star. Yes, the pulsar periods are consistent with this.

5

Lighthouse Model

• Neutron star can rotate rapidly without disintegration.• Has a bipolar magnetic field.• Strong, moving 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 lightfield 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 magnet poles of the neutron star.

• A pulsar “pulse” is detected at Earthwhenever a beam sweeps across Earth.

• Rotational energy is converted intosynchrotron radiation, so the neutron starslows down.

• Are glitches due to “starquakes”? Some probably are,Rotation

Axis

MagneticAxis

g q p y ,but these are not frequent enough to accountfor all glitches.

• Most are probably due to “vortex” events,triggered by slowing of rotation. Angularmomentum of a large number of vortexesis transferred to the crust.

s

Pulsar in the Crab Nebula Supports the Lighthouse Model

6

X-Ray Image of the Vela Pulsar

Additional Pulsar-Related Discoveries

• Millisecond pulsars• Millisecond pulsars• Binary pulsars• Pulsar planets• Magnetars

H l X 1• Hercules X-1

7

Hercules X-1

Black Holes

8

Escape Velocity and Black HolesNo physical object can travel faster than light. The speed of light, according to special relativity, is an absolute upper limit.

e2GMv

R=

s

2GMcR

= 2

s

2GMcR

=s 2

2GMRc

= s 2

2GM MR

c M=

2GM MR ⎛ ⎞

What is the radius of an object of given mass that has an escape velocity equal to the speed of light?

s 2Rc M

⎛ ⎞= ⎜ ⎟⎝ ⎠

( )( )( )

11 303

22 8

2 6.67 10 1.99 10 kg2GM3.0 10 m 3.0km

c 2.998 10 m / s

−× ×= = × =

×

( )sR 3.0km M= M in solar masses and Rs in km

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.

RS

Nothing can cross the eventhorizon in the outward direction. Since this includes light, we can’t observe anything inside the event horizon.

9

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.• The radius of the event horizon is called the

“Schwartzschild radius”.• Time slows down and light is red-shifted as the event

horizon is approached.Tid l f t t h t t d i i t i l• 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.

10

Searching for Black Holes• Isolated black holes are virtually 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 visibleA 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 source of x-rays. 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.i h f h i ibl i d i f i b• 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,

d i f l bproducing 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

11

Some Black Hole Candidates

Object Location Companion Star

OrbitalP i d

Mass ofC t

3.8M>

Star Period Compact Object

LMC X-3 Dorado B3 V 1.7 days ~ 10

A0620-00 Monoceros K V 7.75 hours 10 ± 5

V404 Cygni Cygnus K V 6.47 days 12 ± 2

X-Ray Bursters, Gamma Ray Bursters, QPO’s, and SS433

12

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• 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.

How long would it take the Sun to produce the amount of energy in a typical x-ray burst?

26 26L 4 10 W 4 10 J / s≈ × = × 37burstE 10 J≈

burstamount rate time E L t= × → =

37burst

26

E 10 JtL 4 10 J / s

→ = ≈×

102.5 10 s= ×10

7

2.5 10 s3.2 10 s / yr

×=

×1000 years≈

Quasi-periodic Oscillations

• Observation: X-ray pulses from accretion disks around neutron stars

d bl k h l P l h h tand 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 blackthe 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

13

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.

cGMv v

r= =d vt= dt

v→ = d 2 r= π 3 4r 20km 20 10 m 2 10 m= = × = ×

rv

( )( )4 5d 2 2 10 m 1.26 10 m⇒ = π × = × ( )30 30M 2M 2 2 10 kg 4 10 kg= = × × = ×

( )( )11 30

4

6.67 10 4 10v

2 10

−× ×=

×81.15 10 m /s= ×

5

8

1.26 10 mt1.15 10 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.

14

Gamma Ray Bursters• Short (seconds or minutes)

bursts of high energy gamma rays.

• Seen in all directions → originate outside our galaxy.

Afterglow of a gamma burst coincides withA supernova in a galaxy billions of light years away.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 rayshigh 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.

http://antwrp.gsfc.nasa.gov/apod/ap020405.html06/05/2002