• Summary
• Reading List
• Problem Set
• Answers

Week 1 - The Discovery of Neutron Stars [2]

Summary

The first evidence for neutron stars was uncovered during the sixties. The stability and frequency of radio pulsars alone was sufficient to make a convincing argument that they were neutron stars.

• Tuesday 5 January, Thursday 7 January: LMXBs, HMXBs, GRBs, QSOs, PSRs

I encourage you to follow check out this interesting take on the discovery of pulsars: A Science Odyssey: On The Edge: Little Green Men. Also see how the birth of x-ray astronomy has affected our everyday life at AS&E.

Reading List

• ``Evidence for X Rays from Sources outside the Solar System''
  [ ADS, APS, PDF ]
  REF: Giacconi, R., Gursky, H., Paolini, F., Rossi, B. 1962, Physical Review Letters, 9, 439 .

• ``Observations of a Rapidly Pulsating Radio Source''
  [ PDF ]
  REF: Hewish, A., Bell, S. J., Pilkington, J., Scott, P. F., Collins, R. A. 1968, Nature, 217, 709 .

Problem Set

Problem 1 - The Eddington Luminosity

There is a natural limit to the luminosity a gravitationally bound object can emit. At this limit the inward gravitational force on a piece of material is balanced by the outgoing radiation pressure. Although this limiting luminosity, the Eddington luminosity, can be evaded in various ways, it can provide a useful (if not truly firm) estimate of the minimum mass of a particular source of radiation.

1. Consider ionized hydrogen gas. Each electron-proton pair has a mass more or less equal to the mass of the proton (m_p) and a cross section to radiation equal to the Thompson cross-section (σ_T).
2. The radiation pressure is given by outgoing radiation flux over the speed of light.
3. Equate the outgoing force due to radiation on the pair with the inward force of gravity on the pair.
4. Solve for the luminosity as a function of mass.

Problem 2 - Minimum Masses

The observations of Sco X-1 can give a lower limit on the mass of the sources if they are gravitationally bound.

The source discovered by Giacconi et al. is now known as Sco X-1.

1. What is the most likely distance to Sco X-1 given its location on the sky?
2. At this distance given the flux estimate in the Giacconi et al., what is the luminosity of Sco X-1?
3. What is the minimum mass of Sco X-1?