Exam # 1 Solutions
Lots of partial credit given, so give at least a qualitative answer to each item. Some
useful constants are given at the end of the exam.
1. Extensive spectral observations often show two peaks in high excitation emission molecular line

Solutions for Homework # 7
1. In 1959, Kopal determined that the Roche lobe radius RR with
nearly the same volume as the Roche lobe surrounding the star
m which is orbiting the star M is
RR = 0.46D
1/3
m
.
M+m
D is the distance between the stars and they

Homework # 8, due 26 Apr
1. Show that a simple closed-box model with instantaneous recycling
results in the gas-phase metallicity increasing linearly with time.
If this is true, what cosmic time does [Fe/H]=-3 correspond to?
Also show in this model that t

Homework # 8 Solutions
1. Show that a simple closed-box model with instantaneous recycling results in
the gas-phase metallicity increasing linearly with time. If this is true, what
cosmic time does [Fe/H]=-3 correspond to?
From the notes, we see that Z =

Homework # 9, due 3 May
1. Do problem 5.8 in the text.
2. Do problem 5.13 in the text. Determine the ratio of the two areas
of the zones in the disk where 2 and 4 armed spirals are stable.
Does this depend on the value of p ?
3. Do problem 5.15 in the tex

Homework # 9 Solutions
1. Do problem 5.8 in the text.
Using V 2 = GM(< r )/r , and using (r ) = (3a2 M/4 )(a2 + r 2 )5/2 we
nd
3/2
M (< r ) = Mr 3 a2 + r 2
and
V (r ) =
GMr a2 + r 2
3/4
.
The maximum occurs when 3r 2 /2 = r 2 + a2 or r = 2a.
The spider di

Homework # 10, due 9 May (no penalty up to 17 May)
1. Compute the deection angle of a star whose light just grazes the
limb of the Sun. Also compute the deection angle of a star whose
light just grazes the limb of a 1.4M neutron star, if the neutron
star

Homework # 10 Solutions
1. Compute the deection angle of a star whose light just grazes the limb of the
Sun. Also compute the deection angle of a star whose light just grazes the
limb of a 1.4M neutron star, if the neutron star was at the same distance
fr

Major Topics
1. Introduction
Stars, the Milky Way, Other Galaxies, Cosmology
2. The Galaxy and its Components
Luminosity/Mass Functions, Distances, Clusters, Rotation
3. The Interstellar Medium
Gas, Dust, Emission and Absorption
4. Galactic Dynamics
Gravi

The Local Milky Way Color-Magnitude Diagram
15,630 stars
d < 100 pc
M0
age dierences
Half of stars with
MV > 10 are not
detected.
metallicity dierences
white dwarfs
J.M. Lattimer
AST 346, Galaxies, Part 2
red giants
F0 G0 K0
red clump
Distances from Hipp

Importance of the Interstellar Medium
Gas has important diagnostic
properties
Role in the star/gas cycle
facilitates ongoing star
formation
repository for element buildup;
integral for chemical evolution
Gas can cool, so its collapse is
dissipational
Hot

Stellar Dynamics
Stellar systems vs. gases
Gravitational potential
Spherical and disk potentials
Orbits in the stellar neighborhood
Orbits of single stars
Orbits of stars in clusters
The virial theorem
Measuring masses from motions
Eective potentials and

Homework # 7, due 7 Apr
1. In 1959, Kopal determined that the Roche lobe radius RR with
nearly the same volume as the Roche lobe surrounding the star
m which is orbiting the star M is
RR = 0.46D
1/3
m
.
M+m
D is the distance between the stars and they are

Homework # 6 Solutions
1. Demonstrate that the temperature applicable to a stellar system is
T=
m < v 2 (x) >
3k
where it is assumed that the stars have equal mass m, v (x) is the velocity of a
star relative to the center-of-mass, and <> represents an ave

Homework # 6, due 22 Mar
1. Demonstrate that the temperature applicable to a stellar system
is
m < v 2 (x) >
T=
3k
where it is assumed that the stars have equal mass m, v (x) is the
velocity of a star relative to the center-of-mass, and <> represents
an a

Exam # 2, 10 May
Lots of partial credit given, so give at least a qualitative answer to each
item. Some useful constants are given at the end of the exam.
1. In this problem, you will explore a closed box model for galactic
chemical evolution in the disk.

Homework # 1, due 10 Feb
1. Show that an extinction of A = 1 magnitude leads to
a ux F decrease to 40% of its original value.
2. Assuming dust grains are 0.1 m in radius, that the
gas density in the ISM is nH = 1 cm3, and the number density of dust grains

Homework # 1 Solutions
1. Show that an extinction of A = 1 magnitude leads to a ux F decrease to
40% of its original value.
1 magnitude is equivalent to a reduction of intensity of 102/5 = 0.398.
2. Assuming dust grains are 0.1 m in radius, that the gas d

Homework # 2, due 17 Feb
1. Suppose the initial mass function is the Salpeter mass function with a lowmass cuto of 0.1 M and a high-mass cuto of 100M . Determine the
normalization from the local disk column mass density (i.e., the number density
integrate

Homework # 2 Solutions
1. Suppose the initial mass function is the Salpeter mass function with a lowmass cuto of 0.1 M and a high-mass cuto of 100M. Determine the
normalization from the local disk column mass density (i.e., the number density
integrated v

Homework # 3, due 24 Feb
1. Calculate the size of a Stromgren sphere in a gas of density 103 cm3 surrounding an O3 star. This is the volume of gas nearly completely ionized by
the star. Assume the recombination rate of protons and electrons to form
neutra

Homework # 3 Solutions
1. Calculate the size of a Stromgren sphere in a gas of density 103 cm3 surrounding an O3 star. This is the volume of gas nearly completely ionized by
the star. Assume the recombination rate of protons and electrons to form
neutral

Homework # 4, due 3 Mar
1. In this problem, you are asked to calculate the expected extinction
from a cool cloud. Assume it is spherical and located at a distance
of 100 pc from the Earth. Assume the cloud is isothermal with
a temperature of 10 K. Assume

Homework # 4 Solutions
1. In this problem, you are asked to calculate the expected extinction from a cool
cloud. Assume it is spherical and located at a distance of 100 pc from the
Earth. Assume the cloud is isothermal with a temperature of 10 K. Assume i

Homework # 5, due 10 Mar
1. In example given in the notes describing the observations of collapsing clouds, it is indicated in some cases that there is a locus
of points for which vr is constant. vr is the radial velocity seen by
an observer in the z dire

Homework # 5 Solutions
1. In example given in the notes describing the observations of collapsing clouds, it is indicated in some cases that there is a locus
of points for which vr is constant. vr is the radial velocity seen by
an observer in the z direct

The Local Group and Galactic Evolution
The Local Group
Satellite Galaxies
Cepheid Variables
Tides and the Roche Limit
Local Spirals
Chemical Evolution
Dwarf Galaxies
Future of the Local Group
J.M. Lattimer
AST 346, Galaxies, Part 5
The Local Group
J.M. La