Physics 441/541
Spring 2012
Solutions for Problem Set 1
1. [Phillips 1.1] Hydrostatic Equilibrium:
This problem works out the gravitational potential energy, EGR , average pressure required
for virial equilibrium, P , and the dependence of pressure on rad
Ph 441/541
Problem Set 5
Due: Friday, March 2, 2012
1. Saha Equation:
The text explored the Saha equation using pure hydrogen gas as an example. Now consider the
more complicated 4 He atom with its two electrons and work out the coupled pair of equations
Ph 441/541
Problem Set 4
Due: Friday, February 24, 2012
1. Electron and Radiation Equations of State:
a. Consider a classical electron gas with number density ne = 1030 m3 in equilibrium with
radiation at temperature T . Find the value of the temperature,
Ph 441/541
Problem Set 1
Due: Friday, February 3, 2012
1. Hydrostatic Equilibrium: Consider a sphere of mass M and radius R. Calculate the gravitational potential energy of the sphere assuming (a) a density which is independent of the distance from the ce
Ph 441/541
Problem Set 2
Due: Friday, February 10, 2012
1. Stars near the Sun: In this problem you will use the on-line services of the Centre de Donnes Astronomiques de e Strassbourg (CDS; Astronomical Data Center in English) to identify stars near the S
Ph 441/541
Problem Set 3
Due: Friday, February 17, 2012
1. Understanding the Main Sequence:
Simple physical arguments can yield an approximate understanding of the relations between
mass (M), radius (R), luminosity (L), and eective temperature (Tef f ) of
Ph 441/541
Problem Set 6
Due: Friday, March 30, 2012
1. Convection:
a. In the mixing-length theory of convection, the mixing length, , is usually taken to be a
constant of order one times the pressure scale height:
1
h
P
dP
dr
1
.
Use hydrostatic equilibr
Ph 441/541
Problem Set 7
Due: Friday, April 6, 2012
1. Solar Neutrinos:
The ux of energetic neutrinos from 8 B decays in branch III of the proton-proton chain is very
dependent on the central temperature of the Sun. Conrm this by showing that the rate of
Ph 441/541
Problem Set 8
Due: Friday, April 13, 2012
1. Clayton model:
Consider a star of mass M and radius R in which the pressure gradient is given by
4
dP
= G2 r exp(r2 /a2 ),
c
dr
3
where a is a length parameter and c is the central density; see Phill
Ph 441/541
Problem Set 9
Due: Friday, April 27, 2012
In this homework set you will examine the results of some real stellar evolution calculations. These results were generated by the EZ code accessed through the EZ-Web interface
(http:/www.astro.wisc.edu
Stars and Star Formation Physics 441/541 Lecture 1
January 17, 2012 Introduction to course. Introduction to structure in the universe and the properties of stars.
Ph 441/541 Stars and Star Formation
Joint undergraduate/graduate course
Separately graded;
Lecture 2
January 20, 2012 Introduction to structure in the universe and the properties of stars.
News
Undergraduate talks by astro faculty candidates
Noon 1 PM (free pizza and soda); Serin 401 Undergraduates can earn extra credit by handing in a 1-2 pa
Lecture 5
January 31, 2012 Introduction to Stellar Structure and Evolution Properties of Stars
News
Hand in reviews of faculty candidate talks by
today. First homework due Friday, February 3rd
Available on class website Can discuss the homework with cla
Lecture 6
February 3, 2012 Properties of Stars
News
Undergraduate-level talks by astronomy faculty
organized by Rutgers Astronomical Society
Thursday nights, ~8:00 PM 9:15 PM Next talk: Professor Chuck Keeton, "Black Holes and the Fifth Dimension"
Seco
Lecture 7
February 7, 2012
Properties of Stars
News
Undergraduate-level talks by astronomy faculty
organized by Rutgers Astronomical Society
Thursday nights, ~8:00 PM 9:15 PM
Next talk: Professor Chuck Keeton, Black Holes
and the Fifth Dimension
Secon
Lecture 8
February 10, 2012
Properties of Stars
News
Second homework due today.
Answers will be posted on the website later today.
Third homework due Friday, February 17
Will be available on class website by sometime on
Saturday at the latest.
Spectra
Physics 441/541
Spring 2012
Solutions for Problem Set 3
1. Understanding the Main Sequence:
This problem had you work out some simple scaling relations between the mass of main
sequence stars and their luminosity or radius.
4
a) Combining the denition of
Physics 441/541
Spring 2012
Solutions for Problem Set 4
1. Electron and Radiation Equations of State:
a) [Phillips 2.8] A classical electron gas has the pressure Pe = ne kT (Phillips Eq. 2.19).
Radiation at temperature T has the pressure Prad = aT 4 /3 (P
Physics 441/541
Spring 2012
Solutions for Problem Set 5
1. Saha Equation:
This problem considers the ionization of pure helium gas. In a real star both hydrogen
and helium are usually present and the ionization stages of the two elements are coupled
throu