Explorations: An Introduction to Astronomy (Arny), 7th Edition

Chapter 15: Stellar Remnants: White Dwarfs, Neutron Stars, and Black Holes

Problems

Your Results:

1			Calculate the density of a white dwarf star of 1 solar mass that has a radius of 104 kilometers.
2			Calculate the escape velocity from a white dwarf and a neutron star. Assume that each is 1 solar mass. Let the white dwarf 's radius be 104 kilometers and the neutron star's radius be 10 kilometers.
3			A neutron star has a radius of about 10 km. What is the circumference of the equator of a neutron star? If you could stand on it, it would be a very visibly curved surface. Imagine walking along the neutron star's equator. How many kilometers along the circumference would correspond to moving 7° around the star? How far is 7° along the surface of the Earth (radius of 6400 km)? Seven degrees was the difference in angle Eratosthenes measured when he determined the circumference of the Earth in ancient times, a task that would be a little faster to do on a neutron star (if you could survive the high temperature and gravity!).
4			The mass of a neutron is about 1.7 × 10-27 kg. Suppose the mass of a neutron star is about 3.4 × 1030 kg. How many neutrons does such a star contain?
5			The volume of a neutron is about 10-45 cubic meters. Suppose you packed the number of neutrons you found for problem 4 (above) into a cube so that the neutrons touched edge to edge. How big would the volume of the cube be? How big across would the cube be? Hint: The volume of a cube with sides of length X is X3. How does the cube's size compare to the size of a neutron star? What can you conclude about the spacing of neutrons in a neutron star?
6			Very approximately, the core of a high-mass star about to collapse to form a neutron star in a type II supernova might be as large as 104 km and have a rotational period of around a half a day. If the core collapsed to a radius of 10 km, what would be the period of the resulting neutron star? (Use the answer to Thought Question 4). How does this compare to the periods of the pulsars discussed in the chapter?
7			Calculate the Schwarzschild radius of the Sun.
8			Calculate your Schwarzschild radius. How does that compare to the size of an atom? How does it compare to the size of a proton?
9			Use Wien's law to determine the wavelength of light generated by 10 million K gas in an accretion disk. What type of photons have this wavelength?
10			You observe a main sequence K0-type star that moves as if it is in a binary system, but no companion is visible. If the period of the system is 34 days and the semimajor axis is 0.5 AU, what is the mass of the system (remember to convert 34 days to years to use Kepler's law as discussed in section 13.4)? What is the mass of the companion (you can look up the mass of a K0 star in the appendix, table 9)? What kind of compact star do you think the companion is? What other observational evidence would you look for to confirm this hypothesis?
11			You observe a main sequence B5-type star that moves as if it is in a binary system, but no companion is visible. If the period of the system is 8.4 years and the semimajor axis is 8 AU, what is the mass of the system? What is the mass of the companion (you can look up the mass of a B5 star in the appendix, table 10)? What kind of compact star do you think the companion is? What other observational evidence could you look for to confirm this hypothesis?
12			You observe a main-sequence A0-type star that moves as if it is in a binary system, but no companion is visible. If the period of the system is 4 years and the semimajor axis is 4 AU, what is the mass of the system? What is the mass of the companion (you can look up the mass of an A0 star in the appendix, table 10)? What kind of compact star do you think the companion is? What other observational evidence could you look for to confirm this hypothesis?

E-mail Your Results Date: My name: E-mail these results to: E-mail address: Format: Me: HTML Text My Teacher: HTML Text Other: HTML Text