Neutron Stars and Black Holes

Question 1

Neutron Stars or Pulsars

Answer 1

• One possible product of the SN explosion we discussed in the last lecture is a Neutron Star.
• This extremely dense object can be left over containing the residual 10% of the star’s mass (the rest of the mass is in the Super Nova Remnant - SNR).
• Mass ~2 M₀ and radius ~ 10km

Question 2

Pulsars

Answer 2

• Pulsars were discovered in 1967 by Jocelyn Bell – a British PhD student doing radio studies of the sky for her thesis.
• Pulsars have extremely intense magnetic fields - of the order 1012 Gauss (c.f. our Sun which has a field strength of 1 Gauss = 10-4 Tesla).
• The intense magnetic field produces pairs of charged particles which spiral along the magnetic field lines producing beams of electromagnetic radiation.

Question 3

Pulsar - Continued

Answer 3

• Detailed X-ray image from the Chandra Observatory. It clearly shows material being ejected from the pulsar into the surrounding nebula. Some of this ejected material travels at 0.5c
• The general trend is for the pulsar to gradually slow down as it loses energy. But sometimes “glitches” occur …. These events are attributed to a sudden change in the NS structure.

Question 4

Neutron Star composition

Answer 4

The main ingredient of a neutron star is degenerate neutrons in a superfluid state. But in addition, other states of matter exist and the crust made be primarily made of iron.

Glitches occur when the tensions inside this rapidly spinning object build up to breaking point and then briefly restructure part of the NS. This may be caused by the fluid rotating faster than the crust.

Question 5

Millisecond Pulsars

Answer 5

• In 1982 a pulsar (PSR1937+21) was discovered with a spin period of 1.5ms (= 642 rev/s!)
• Since then more than 80 other pulsars have been discovered with periods between 1-10ms.
• The majority are in close binary systems with orbital periods of 10-100d.
• It is probable that the binarity of these systems has played a major role in producing such rapid spin periods.

Question 6

Recipe for a millisecond Binary pulsar

Answer 6

• Start off with a high mass star and a low mass star
• The high mass star evolves most rapidly and eventually goes SN producing the pulsar.
• This newborn pulsar has a spin period of a few times a second (like the Crab pulsar).
• After a few billion years the low mass star reaches the red giant phase and expands, filling its Roche lobe, and transferring material on to the NS.
• This transferred material carries with it angular momentum which spins up the pulsar to periods of a few ms.

Question 7

Neutron Star - Material to temperature

Answer 7

The transfer of material on to the NS increases its luminosity at high energies (eg X-rays). As the material falls into the deep gravitational well of the NS it gets extremely hot producing large amounts of hard radiation.

Question 8

Novae & Bursters

Answer 8

The infalling material onto a compact object (white dwarf or NS) may sometimes lead to a brief flash of thermonuclear burning on the surface of the object.

If the material is falling on to a WD it is called a Nova, or on to a NS it is called a Burster.

These effects occur when the pressure of the infalling material is sufficient to increase the surface temperature to the needed thermonuclear temperatures (107K).

Question 9

Black Holes and the Equivalence Principle

Answer 9

One of the first major things to come out of GR was the Equivalence Principle.

This states that you cannot distinguish between the effects of gravity and the effects of acceleration.

Question 10

Curved Space

Answer 10

To explain the Equivalence Principle Einstein stated that gravity is caused by space being curved around any mass.

Far from the effects of mass, spacetime is flat and clocks tick at their normal rate. Close to any mass, spacetime is curved and clocks run at a different, slower speed.

Question 11

Curved Space proof

Answer 11

Experimental Test 1 : observing a star during a total eclipse in 1919

Experimental Test 2 : Precession of Mercury’s orbit by 43 arcsec/100yrs

Experimental Test 3: Clocks run slower and photons are red-shifted in a gravitational field (or if spacetime is warped).

Question 12

Gravitational Redshift vs Doppler Redshift

Answer 12

Do not confuse gravitational redshift with Doppler redshift.

• In the Doppler redshift (measured as part of the expansion of the universe) the change in photon wavelength is due entirely to motion.
• In the case of gravitational redshift no motion is involved, just the warping of spacetime due to the presence of mass.

Question 13

Gravitational Waves

Answer 13

• So far unproven is the prediction that moving masses should produce gravitational waves.
• These would travel at the speed of light but only very weakly interact with matter (i.e. they are very hard to detect!).
• New gravitational telescopes are being built on the earth and in space to try and test this part of the theory.

Question 14

Black Holes

Answer 14

• Perhaps one of the most astounding predictions is what will happen if large amounts of mass are concentrated in very small volumes.
• GR predicts that if the matter is sufficiently dense, then the curvature of spacetime will be so great that there is no path out of the object for matter or light – a Black Hole.

Question 15

2D representation of Space-time

Answer 15

Again, a 2-d representation of curved spacetime, but now the central well is infinitely deep.

Question 16

First Blackhole discovered

Answer 16

• The first Black Hole discovered was in a binary system.
• This is known as Cygnus X-1 and it is thought to be a 30M₀ BH in partnership with a B0 supergiant star.
• One characteristic often found associated with Black Holes is the presence of jets of particles.
• These jets often have velocities of up to 0.25c.
• It is thought that the jets are formed by very strong electric and magnetic fields in the material around a rotating BH.

Question 17

Supermassive Black Holes

Answer 17

• It is believed that most (or all) galaxies host a supermassive black hole at their centre.
• Such galaxies may have a mass of 10¹¹M₀ • The BH can have a mass of anything from 10⁶M₀ to 10⁹M₀.
• It is probable that these BHs occur naturally in the formation of galaxies.

Question 18

Event Horizon

Answer 18

Non-Rotating Black Holes.

R_Sch is the Schwarzchild radius – effectively the size of the BH.

This also called the Event Horizon

This is the radius at which the Escape velocity = speed of light.

Balancing forces at this radius for an orbiting test particle:

Kinetic energy = gravitational energy

^{1 ⁄}₂mv² = GMm/r

where M = mass BH, m= test particle mass, v= velocity of test particle, G=constant

But in this case v = c and r= R_Sch so this gives us for the Schwarzschild radius:

R_Sch = 2GM/c²

A cube dropped into a BH distorts into a long thin object as it approaches the event horizon.

A safe distant observer would also see the probe change colour due to an increasing gravitational redshift.

The same observer will see the effects of time dilation and the probe will take an infinite amount of time to reach the event horizon.

Question 19

Hawking Radiation and Wormholes

Answer 19

Do BHs exist forever? Not if Hawking radiation exists