1. Black holes, neutron stars and binary star systems

2. Black holes
A region of space where the gravitational field is so strong nothing can escape from it – not even light. Black holes are usually detected by their interactions with nearby matter. e.g. Stars orbiting around a black hole.

3. A black hole warps space itself

4. History
The idea of a black hole was first put forward in the late 1700s. In 1915, Einstein proved that gravity could warp space itself meaning light could be affected even though it has zero mass. A few months later Karl Schwarzschild calculated the radius.

5. The Schwarzschild radius
This is the radius of the event horizon of a black hole. The event horizon is the boundary beyond which light cannot reach an observer i.e. Escape from the black hole’s massive g-field.

7. Karl Schwarzschild
What a legend!

8. Derivation – non relativistic
The gravitational potential energy is equal to the ‘kinetic’ energy of the photon. ½ mc2 = GMm/r ½ c2 = GM/r r= 2GM/c2

9. Example
Calculate the Schwarzschild radius for a black hole of mass 100 solar masses.
r= 2GM/c2
r= 2 x 6.67 x x100 x 1.99 x 1030/(3x108)2
r= 295 km
An object or photon this close to the black hole or less cannot escape its pull.

10. Supermassive black holes
Supermassive black holes of up to 150 million solar masses have been observed. What is the Schwarzschild radius for such a black hole? Convert this to AU. Answer: 4.42 x 1011m or 2.94 AU

11. What is the Schwarzschild radius of the Earth?
Answer: about 9.5 mm. That is, if the Earth’s mass was placed into a sphere of radius 9.5 mm, it would collapse into a singularity.

12. Example
A star of mass 3 x 1030 kg is in orbit around a black hole of mass solar masses at a distance of 35 million km. Calculate the speed of orbit and the time period of one revolution.

13. Hawking Radiation
In 1974 Stephen Hawking predicted that black holes would emit thermal radiation following a black body spectrum. If a black body is emitting energy then its mass must decrease according to Einstein’s E=mc2. A black hole emitting at a faster rate than it is accreting is said to be evaporating.

14. Stephen Hawking 1942-
What a legend!

15. Evaporating black holes
The CERN collider is allegedly looking to create micro black holes to investigate this phenomena.

16. Neutron Stars
The remnant of a supernova, they typically have masses from solar masses. The radius is typically of the order 12km. Calculate ‘g’ at the surface of a neutron star with mass 1.5 solar masses and radius 12km.

17. Cross section. Densities given in terms of density to make neutrons physically touch

18. Neutron stars spin extremely rapidly
As the core collapses, angular momentum is conserved. This causes a speed increase as the radius decreases. Like an ice skater spinning on the spot and moving the arms in.

19. Pulsars Highly magnetised, rapidly rotating neutron stars.
Emit electromagnetic radiation periodically.
Been likened to an interstellar lighthouse because of the radiation.

20. A pulsar

21. The first pulsar was observed in 1963 by Anthony Hewish and Jocelyn Bell – Hewish received the Nobel Prize

22. Example
The pulsar discovered by Hewish and Bell has a time period of 1.33s. Assuming a radius of 12 km, calculate the linear speed of rotation and the angular velocity. State the maximum linear speed of rotation according to Einstein’s theory of relativity.

23. Answer v= 2πrf v= 2π x 12 000 x 0.75 v = 5.65 x 104 ms-1 ω = 2πf
ω = 4.72 rad.s-1
The linear speed cannot exceed c, the speed of light.

24. Binary Star Systems
The majority of stars seem to be part of a binary or multiple star system. Detected by either: the wobble of their orbits as by Newton 3, every action has an equal & opposite reaction. the change in light intensity as one star eclipses another.

25. Some nice animations

26. Barycentre
The centre of mass where two astronomical bodies orbit each other.

27. A multiple star system will give extreme seasons for any moon or planets

28. A binary sunset

29. Binary star time periods
Calculations involving binary stars are more demanding than those for planets.
For an Earth-Sun system, we can consider the barycentre to be at the centre of the Sun.
Clearly, this doesn’t hold for stars.

30. Binary sunset as seen in Tunisia