SCCC 116 Homework 3 - Due 9 February 2006
Review and Discussion: 20-5, 21-3, 21-12
Problem: 21-6, 21-7
Prof. Christina Lacey

R&D 20-5

What makes an ordinary star a become a red giant?

When a star runs out of hydrogen in its core, the core collapses. As a result, the core's temperature increases and additional energy is radiated away. With a higher temperature, the fusion in the hydrogen shell around the core becomes more efficient. So the core puts out even more energy than it did as a main sequence star. The increased gas pressure pushes on the outer part of the star, expanding it into a red giant.

R&D 21-3

What is a light curve? How can it be used to identify a nova or supernova?

A light curve is a diagram that plots the changes in the brightness of an object such as a star, as a function of time. Time is plotted on the horizontal axis; brightness on the vertical axis. The light curves of novae and supernovae appear rather different. In particular, if the amount of brightening were observed, supernovae are known to brighten about one million times more than novae. How the light dims after the explosion is noticeably different for novae and supernovae.

R&D 21-12

How can astronomers estimate the age of an isolated star?

The youngest stars have the highest abundances of the heavier elements. Spectroscopic analysis of an isolated star, along with knowledge of stellar evolution, allows astronomers to determine an approximate age.

P 21-6

A supernova at a distance of 150 pc has an absolute magnitude, M=-20. Compare its apparent magnitude with that of (a) the full Moon and (b) Venus at its brightness. would you expect a supernova to occur this close to enough.

$m-M=5\log{\frac{D}{10~pc}}$

Apparent magnitude of the supernova:
$m=M+5\log{\frac{D}{10~pc}}=-20+5\log{\frac{150~pc}{10~pc}}$
$m=-20+5\log{(15)}=-20+5(1.2)=-20+5.9=-14$

(a) Apparent magnitude of Moon: m=-12.5; so the supernova appears 1.5 magnitudes brighter or a factor of $2.512^{1.5}$=4 times brighter than the Moon.

(b) Apparent magnitude of Venus at its brightest: m=-4.4; so the supernova appears 9.6 magnitudes brighter or a factor of $2.512^{9.6}$=6900 times brighter than Venus.

P 21-7

What is the total energy output of the Sun assuming it maintains its current energy output? Compare to the energy released in a supernova.

$L_\odot=4\times 10^{26} W$ and 1 W=1 J/s

The total energy output over its entire lifetime (10 billion yrs= $1\times 10^{10}$ yrs) is:

Total Energy= $4\times 10^{26} \frac{J}{s} (1\times 10^{10} yrs) (3 \times 10^7 \frac{s}{yr})=1\times 10^{44}$ J

A supernova emits about $10^{43}$ J in visible light and $10^{45}$ J in the form of neutrinos. The total energy released by the Sun in its lifetime is only an order of magnitude more than than the visible light energy released by a supernova.