1. Unit 12: Stellar Remnants: White Dwarfs, Neutron Stars, and Black Holes Mr. Ross Brown Brooklyn School for Law and Technology

2. In this unit we will learn about: The types of objects left behind by stars after their nuclear fuel has been consumed The characteristics of white dwarfs and why there is an upper limit to their mass The characteristics of neutron stars Why pulsars rotate so rapidly How gravity can prevent an object from emitting any light, creating a “black hole” The nature of the curvature at the edge of a black hole The differences in types of supernova that result in black holes instead of neutron stars The methods of detecting black holes

3. What are the general properties of White Dwarfs? White Dwarfs: – Hot, compact stars. Mass of about our Sun but radius of our Earth (about 1% of the Sun) – Little surface area means they are dim, even though hot – Light not from burning fuel, as none is left – Light from residual heat as they cool – Temps range from 25,000K-4,000K

4. Homework #19 5 April 2016 What is a neutron star?

5. What are the general properties of White Dwarfs? 6 April 2016 Do now: How can we measure the mass of a white dwarf? – Think about this, based on all you know at this point in the year. Would you use luminosity, color, temperature, etc? Really impress me with this one.

6. What are the general properties of White Dwarfs? After ejection of planetary nebula shell, the core is what’s left. That’s our white dwarf Mainly C and O 2, trace H and He on crust Cools rapidly (by universal standards) Eventually dies out, like an ember in a fire Becomes so dark referred to as a black dwarf

7. What are the general properties of White Dwarfs?

8. Gravity – Very compact, no fuel – Still hydrostatic equilibrium, but not from fusion – Limit to amount of electrons occupying a given space – If we increase mass, a white dwarf would shrink!

9. What are the general properties of White Dwarfs? Degeneracy Pressure – There’s a limit on number of electrons that can occupy a given space – Remember Ideal Gas Law: P = ρ * R * * T – In a white dwarf, as we add more mass, the gas heats up but it DOES NOT raise pressure – Thus, more mass would make it shrink due to GRAVITY

10. What are the general properties of White Dwarfs? Chandrasekar Limit – 1931, Indian astrophysicist Subrahmanyan Chandrasekhar (who was only age 21!) – He later won the Nobel Prize – The limit to how large a white dwarf can be before it collapses is about 1.4 M ☉

11. What are the general properties of White Dwarfs? 7 April 2016 Do now: How can you tell whether something is moving toward or away from you by using your eyes alone? Ears alone? Sense of touch alone?

12. What are the general properties of White Dwarfs?

13. Gravitational Redshift – For light to escape a star, it must fight gravity – Sort of like a ball rolling up a hill loses energy, the light loses some energy (while still traveling at the speed of light, which is a constant) – Longer, stretched wavelengths correspond to red

14. What are the general properties of White Dwarfs? In much the way we use luminosity and temperature to measure a white dwarf’s radius, we can use wavelength to measure it’s mass.

15. Homework #19, part 2 7 April 2016 Review your notes from the Fall semester. Explain the concept of escape velocity (you needn’t use math.)

16. What are the general properties of Neutron Stars? 8 April 2016 Do now: How do the different elements of an atom (proton, neutron, electron) interact with each other? Think in terms of their various charges.

17. What are the general properties of Neutron Stars? 1932, the neutron is discovered Astronomers surmised there must be Neutron Stars produced by a massive star collapses Like the Chandrasekar Limit in white dwarfs, there’s a limit to how large an iron core can be

18. What are the general properties of Neutron Stars?

19. But there was no evidence of neutron stars, so it remained just a theory for 30 years. 1967, astronomers noticed odd radio signals, pulsing at a precise rate – They call it “LGM-1” – Ultimately, called these Pulsars

20. What are the general properties of Neutron Stars? Period-density relation: the pulse rate depends on the inverse of the square root of the pulsar’s density – The higher the density, the shorter the period (so it’s faster)

21. What are the general properties of Neutron Stars? The pulsation of a neutron star is caused by its spin.

22. What are the general properties of Neutron Stars? Conservation of Angular Momentum – Affects objects spinning around an axis, like a top or a figure skater – L=mvr (mass, velocity, radius)