ASTR 222 - Homework #3

1. Population Synthesis

(You can code this one up in Python, or alternatively an Excel-type spreadsheet would work great for this problem, as well...)

We are going to make galaxies by mixing stars. Here are the four types of stars we are going to use. For each type of star, describe in words what kind of star it is: what evolutionary stage it is in, what kind of lifetime it has, what limits (if any) you can place on its age. Then calculate its stellar mass-to-light ratio (M/L)*.
(Remember that mass-to-light units are solar units, so the Sun has a mass-to-light ratio of (M/L)* = 1 Msun/Lsun. And also remember that the Sun has an absolute magnitude of Mv=4.82 and a B-V color of 0.65.)



Star 1
Star 2
Star 3
Star 4
Spectral Type
A2V
G2V
K5V
K2III
Mv
1.3
4.82
7.35
0.5
B-V
0.05
0.65
1.15
1.16
Mass (Msun)
2
1
0.67
1.1
(M/L)* (fill this in!)





Now let's build some galaxies. The galaxies should each have a total V luminosity of Lv=1010 Lsun. The fraction of V light each star contributes to each galaxy is given in the table below. Calculate the total (aka "integrated") B-V color and stellar V-band (M/L)* ratio,  as well as the fraction of each star by number for each model galaxy. Show your work, by walking through one example by hand in exquisite detail.


Fraction of V-band light from each star

Star 1
Star 2
Star 3
Star 4
Galaxy 1
15%
40%
25%
20%
Galaxy 2
30%
0%
0%
70%
Galaxy 3
45%
25%
20%
10%
Galaxy 4
0%
30%
70%
0%
Galaxy 5
0%
30%
50%
20%

Now, a "typical" color for a spiral galaxy like the Milky Way is B-V=0.7, an elliptical might have a color of B-V=1.0, and a starburst galaxy might have B-V=0.4. Which of these galaxies is a good match for an elliptical, which for a spiral, and which for a starburst? Which two galaxies don't make sense? Argue your answer both from integrated colors and from the mix of stellar types.


To give you a push in the right direction, here is what my spreadsheet looks like if I put in a mix of 25% of each type of star. So use this as a test case, if you can get these numbers for that kind of mix, you've got it right:


(In this spreadsheet, masses are given in solar masses (Msun), and luminosities are in solar luminosities in the V filter  (Lsun,V)


2. Disk Galaxies: Surface Brightness and Luminosity

Problem 2 is no longer part of HW3. It will be restructured and included as part of HW4.


3. The Tully-Fisher Relationship