• Summary
• Reading List
• Problem Set
• Answers

Week 2 - Rotation-Powered Neutron Stars [1] [3]

Summary

The first neutron stars to be positively identified are the rotation-powered neutron stars, specifically the radio pulsars. The most famous of the radio pulsars is the source at the center of the Crab supernova remnant, the Crab pulsar. The emission from these neutron stars is powered by the rotation of the neutron star coupled to electromagnetic radiation through the magnetic dipole moment of the star.

• Monday 11 January,
  Thursday 14 January: Rotation-Powered Neutron Stars

Check out this Java Applet that simulates the electric field from a moving charge.

ATNF Pulsar Catalog and the sounds of pulsars at Princeton Pulsar Group.

Reading List

• ``Rotating Neutron Stars as the Origin of the Pulsating Radio Sources''
  [ PDF ]
  REF: Gold, T. 1968, Nature, 218, 731 .

• ``Rotating Neutron Stars, Pulsars and Supernova Remnants''
  [ PDF ]
  REF: Pacini, F. 1968, Nature, 219, 145 .

• ``Pulsar Electrodynamics''
  [ ADS, PDF ]
  REF: Goldreich, P., Julian, W. 1969, Astrophys. J., 157, 869
  Read Sections I, II, III(a) and IV only.

Problem Set

Problem 1 - Spinning Neutron Stars

We will estimate how quickly we would expect neutron stars to spin, how much energy is stored in their spin and other interesting facts about spinning neutron stars.

1. The sun rotates every 24-30 days depending on latitude. How quickly would it rotate if it were compressed to 10km in radius while conserving its angular momentum? Its current radius is 7 x 10¹⁰ cm.
2. How fast could a neutron star rotate without breaking up? Consider the neutron star to be 1.4 and have a radius of 10 km and compare the centripetal acceleration of a bit of material on the surface to the gravitational acceleration.
3. How much angular momentum and rotational energy does a neutron star have? Use

   I ≈ 0.21

   M R2 1-2 G M R c2

and a spin period of break-up, 1.6 ms, 33 ms and 6 s.

Problem 2 - Original Spin

If you know the age of a neutron star, its current period and its period derivative, you can estimate its original spin.

1. Using the results from the lectures, derive a formula for P₀ in terms of the age, current period and period derivative of a pulsar.
2. The table below lists pulsars that are associated with historical supernovae. Complete the table by calculating the original spin of these neutron stars.

   Name	Age [yr]	Period [s]	P-dot [10-15 s s-1]	P0 [s]
   B0531-21	949	0.0331	422.69
   B0540-69	1000	0.050	480
   B1951+32	64000	0.0395	5.8
   J0205+6449	822	0.06568	193

3. Why do we know the age of the first and last pulsars so accurately?