1	Homework #9 Q 1 We see the Crab Nebula is about 1.35 parsecs in radius and is expanding at a rate of 1400 km/s. Estimate when would the supernova have exploded? d. 920 years ago. Time = distance/rate = 1400 km/s x 1.35 pc. Must convert parsecs to km using 1 pc = 3.1 x 10¹⁶ m = 3.1 x10¹³ km, so we get 4x10¹³ km, which we can now divide by 1400 to get the answer in seconds: 2.9x10¹⁰ s, which must be converted to years (3.1x10⁷ seconds per year), which gives us 920 years.
2	Homework #9 Q 2 If the stars turning off the main sequence in the H-R diagram of a star cluster have masses of about 15 times solar, how old is the cluster? a.About 1 million years. b.About 11 million years. c.About 90 million years. d.About 500 million years. e.About 3 billion years. We need the main sequence lifetime, which is the mass of the star raised to the -2.5 power (giving us an answer in solar lifetimes, where the solar lifetime is 10 billion years). 15^-2.5 = 0.0011, which when multiplied by 10 billion years gives us 11 million years.
3	Homework #9 Q 3 White dwarfs supported by degenerate electron pressure do not shrink with time because a.degenerate electron pressure does not depend upon temperature. b.denenerate neutron pressure does not depend upon temperature. c.fusion keeps their temperature constant. d.no light can escape from them so they cannot cool with time. e.Newtonian laws of gravity do not work for these small objects. This one is covered in the text/slides, and is a general property of degenerate matter.
4	Homework #9 Q 4 If a type G star like the sun expands to become a giant star with a radius 20 times larger, by what factor will its average density decrease? a.20 times b.40 times c.80 times d.400 times e.8000 times Density is mass divided by volume. Volume depends on the radius cubed. 20 cubed is 8000.
5	Homework #9 Q 5 Formation of the elements heavier than Fe occured primarily a.during the big bang. b.by energy generating fusion processes in solar mass stars. c.by the r and s process of neutron capture. d.by the r and s process of proton capture. This occurs in supernova explosions, not during any stellar fusion process while the stars are burning. This is not really covered in the textbook and something I usually add, but didn’t this semester due to the travel. Sorry. This question will count as extra credit.
6	Homework #9 Q 6 As a star runs out of hydrogen in its core, as seen from the OUTSIDE the star a.becomes hotter and more luminous. b.becomes cooler and more luminous. c.becomes hotter and less luminous. d.becomes cooler and less luminous.e.becomes larger in radius and hotter. Yes, this is the star turning into a RED GIANT!
7	Homework #9 Q 7 The Ring Nebula is a photogenic planetary nebula in the constellation Lyrae. The Ring has an angular diameter of 72 arcseconds, and we estimate it is 5000 light years away. What is its linear diameter? (Hint: you will need to dig up the good old small angle formula from chapter 3.) a.0.17 light years b.0.34 light years c.1.7 light years d.3.4 light years e.17 light years Angular diameter /206265 arcsec = linear diameter/distance Straightforward without unit conversions needs. Linear diameter = (72/206265)x 5000 light years = 1.7 light years.
8	Homework #9 Q 8 The catastrophic explosion of a star which occurs when its degenerate core grows larger than 1.4 solar masses is called a a.nova b.supernova c.solar flare d.helium flash Yes, breaking Chandrasekhar’s limit.
9	Homework #9 Q 9 If we discover a type 1a supernova in a distant galaxy that at its brightest has an apparent magnitude of 17, how far away is the galaxy? (Assume the supernova has an absolute magnitude of -19.) a.1.6 Mpc. b.16 Mpc c.160 Mpc d.1600 Mpc e.16000 Mpc Using the distance modulus formula, d(pc) = 10^(m-M+5)/5 we can do this. m=17, M=-19, so d(pc) = 10^8.2 = 1.6x10⁸ pc, which is 160 Mpc.