Orion Nebula

ASTR 221 — Stars & Planets

Homework Set 1

Ryden & Peterson Problems:

1.2, 1.6, 1.9, 3.1, 3.2, 3.5, 3.6, 3.8

Non-book Problems:

1. On a clear night, go outside and look at the night sky. Sketch what you see, being sure to include the Moon, planets, and bright stars. Be sure to make a note of the date, time, and your location. What constellations are visible? What other sky objects are you able to identify?

Homework Set 2

Ryden & Peterson Problems:

5.5, 5.7, 5.8, 6.1, 6.2, 6.4, 6.6

Non-book Problems:

A person has a surface area of 1.6 m2 at a skin temperature of roughly 306 K (92°F). Consider this person to be an ideal radiator standing in a room at a temperature of 293 K (68°F).

  1. Calculate the energy per second radiated by the person in the form of blackbody radiation. Express your answer in watts.
  2. Determine the peak wavelength λmax of the blackbody radiation emitted by the person. In what region of the electromagnetic spectrum is this wavelength found?
  3. A blackbody also absorbs energy from its environment, in this case from the 293 K room. The equation describing the absorption is the same as the equation describing the emission of blackbody radiation, L = AσT4 Calculate the energy per second absorbed by the person, expressed in watts.
  4. Calculate the net energy per second lost by the person via blackbody radiation.

Homework Set 3

Ryden & Peterson Problems:

13.2, 13.3, 13.4, 13.5, 13.6, 13.8

Non-book Problems:

The file yaletrigplx.txt is a catalog of real stellar data; we are going to make some Hertzprung-Russell Diagrams out of it. The dataset is the Yale Trigonometric Parallax Dataset, and the data is as follows:

  1. Use python, numpy, matplotlib, and other related libraries to make an H-R diagram using the entire dataset. That is, make a plot with B-V color on the x-axis, and absolute magnitude on the y-axis.
  2. Now, on your HR diagram, label the various types of stars (main sequence stars, red giants, white dwarfs, etc) and also indicate where the Sun would appear. (hint: matplotlib.pyplot.text() lets you specify arbitrary text at a given location)
  3. And then make 3 more H-R diagrams:
    1.  One using stars with parallax uncertainties smaller than 100 millarcsecs
    2.  One using stars with parallax uncertainties smaller than 50 millarcsecs
    3.  One using stars with parallax uncertainties greater than 100 milliarcsecs
  4. Explain why the different parallax error limits lead to the differences you see in the four H-R diagrams you've made.  Make sure to pay attention to the kinds of stars that show up, the numbers of stars that show up in different regions (i.e., how many red giants vs how many red dwarfs, for example), and the properties of the main sequence. (HINT: think about possible observational biases!)

Tips — Label your axes! Don't use really big point sizes! You are going to plot over 6000 stars on this plot, so use small dots or it'll all run together. H-R diagrams should have bright stars AT THE TOP and blue stars TO THE LEFT. Try manually setting axis limits to integers near the max/mins of the data.

Homework Set 4

Ryden & Peterson Problems:

15.1, 15.2, 15.3, 15.4, 15.5, 17.4, 18.1, 18.4, 18.5

Homework Set 5

The Beehive Cluster.* 

In this assignment, you'll be studying the Milky Way open cluster M44, also known as the "Beehive" for its swarm-like appearance. It is one of only a few Galactic open clusters that is visible to the naked eye -- a faint, fuzzy patch of light in the constellation Cancer. The file beehive.txt contains data for 2880 stars in the region of M44 from the Gaia parallax satellite. The columns in the file are: 
0: an ID number
1: right ascension "RA" ("longitude"; in degrees)
2: declination "Dec" ("latitude"; in degrees)
3: parallax angle (in milliarcseconds "mas")
4: parallax error (in mas)
5: proper motion in RA (apparent motion on the sky; in mas/year)
6: proper motion in Dec (in mas/year)
7: apparent magnitude in Gaia's G filter (in magnitudes)
8: color index in Gaia's Bp and Rp filters (Bp - Rp; in magnitudes)
-- Note: the data have been selected so that only stars in the approximate distance range of M44 are included, between 150 and 240 parsecs.

a. Make a "map" of the stars in the dataset. Use RA on the x axis, and Dec on the y axis. Note that the convention of many astronomical images is that North (increasing Dec) is up and East (increasing RA) is on the left, so you want to flip the limits of the x axis so that numbers increase from right to left. Your final plot should look like a circle of scattered points, with increased density in the center: this is the cluster!

b. Using the parallax angle, calculate the distance (in parsecs) to each star in the dataset.

c. *show your code for this step!* The central RA and Dec of M44 is (130.1, 19.67). Calculate the distance (in degrees) of each star in the dataset from the center of the cluster. (TIP: remember that longitude lines converge at the poles, so you need to multiply RA by cos(Dec) to get the correct linear distance.) Divide the data into three separate categories: stars less than 1 degree from the center, stars between 1 and 3 degrees from the center, and stars more than 3 degrees from the center. Use the stars that are less than 1 degree from the center to determine the median distance (in pc) to the center of the cluster.

d. Using the median distance you just calculated and the distance in degrees from the center of the cluster, determine the projected distance (in pc) of each star from the center of the cluster.

e. Make a histogram (bar chart; see matplotlib.pyplot.hist for an example of how) of the distance from part b (in pc) for each of the three categories from part c. You want to see the distribution of stars in the cluster, so use a reasonably large number of bins; 100 is probably a safe bet. From these histograms and the median distance, determine how wide you think the cluster is in distance space. Calculate the distance of each star along the line of sight from the median distance.

f. Combine the distances of each star from parts d and e to get a 3D distance from the cluster center.

g. Because cluster stars all form from the same cloud of gas, and are gravitationally bound to each other, ON AVERAGE, all the stars will be moving the same direction in the sky. Use the proper motion data to determine which stars in the dataset are actually members of the cluster. Plot the Dec proper motion vs. the RA proper motion, and determine a set of limits you can use to select cluster member stars.

h. Select the stars that you think belong to the cluster by combining the limits on proper motion you determined in part g with the 3D distance from the cluster center from part f, and assuming the cluster is a sphere, the size of the cluster you determined in part e. 

i. Make a duplicate of the plot from part a, but now, highlight the stars you've selected to be part of the cluster in a different color. Does the distribution of stars that belong to the cluster seem reasonable to you?

j. Make a color-magnitude diagram (CMD) of the just the stars that belong to the cluster by plotting apparent magnitude (column 7) vs. color index (column 8). What kinds of stars are found on this CMD? Think about evolutionary states.

k. Determine the distance to M44 using the main-sequence fitting technique. Read the isochrone.txt file to get the evolutionary track for stars in this cluster (you only need columns 8, 9, 10: these are the absolute magnitudes in G, Bp, and Rp, respectively). Plot the isochrone on top of the stars in the CMD, and use the distance modulus to adjust the apparent magnitude of the isochrone. Use your eye to find the "best fit" distance. Does this best fit distance agree with the distance you determined with parallax in part c? Why or why not? (Time to speculate again!!)

l. The isochrone provided has a metallicity equal to that of the Sun and an age of 1 billion years. Based on what you know about stellar evolution and the locations of stars in the HR diagram, do you think the cluster is older or younger than 1 billion years? Justify your answer.

* This assignment is based loosely on a data analysis activity designed by Blaise Whitesell, class of 2019, as part of an astronomy capstone project. 

Homework Set 6

Ryden & Peterson Problems:

8.2, 8.4, 9.4, 9.9, 9.10, 10.5, 10.6, 10.9, 12.1, 12.6

Non-book Problems:

TBD python problem about exoplanets!