Project 1 - Star Clusters Color-magnitude plot
We learned from the Stefan-Boltzmann and Wien laws that temperature is equivalent to color and vice versa. It is faster to measure a star's color than its spectrum because, to obtain a spectrum, you must disperse the light (recall the diffraction gratings we used). Dispersing the light means the intensity at any given point on your eye or on a detector is lower; lower intensity then requires a longer time to measure it to high precision. Measuring a color does not require as much time (no dispersion of the light) but the accuracy of the inferred temperature is lower. This can be fine: lower accuracy is compensated by measuring more stars. It's a trade-off: better accuracy, longer exposure time, and fewer objects versus lower accuracy, shorter exposures, and many objects.
Astronomers improve the accuracy of the color measure by using precisely-calibrated filters through which they measure the star's color. This then provides an improved measure of temperature T (but without any information on absorption lines). Well-calibrated and oft-used filters are the B = Blue and V = "Visual" = yellow filters. The temperature measure of the star comes from calculating B - V.
We also know that an object's brightness may be expressed using any consistent quantity. Up to this point in the class, we have only used luminosity (in units of the Sun's luminosity). We could just as easily use a quantity known as a 'magnitude.'
There are two types of magnitude: apparent magnitude (mv), based on the measured apparent brightness of an object, and absolute magnitude (MV) which is the apparent magnitude corrected for distance. 'Magnitude', then, is a number representing a brightness, either apparent or absolute, as appropriate.
For this exercise, answer the questions below.
1. Figure 1 plots the magnitudes and colors from Table 1. The data were obtained by observing the open cluster known as the Hyades. This plot is called a 'color-magnitude' diagram (obvious, right?) -- what is an alternative name? Interpret the nature of the approximately diagonal line of data points. For reference, the values for the Sun are MV = +4.85, B - V = +0.63.
2. Theoretical Stellar Models and Evolutionary Tracks
The theoretical 'Zero-Age Main Sequence' (=ZAMS) is defined as the set of computer models representing stars that have just started converting H to He in their cores via thermonuclear fusion.
a. Plot the 4 ZAMS data points for each mass from Table 3. Then connect those points using dashed-line segments. The 4 ZAMS points are those points with age = zero.
b. A set of evolution models for a specific mass is defined as an 'evolutionary track' as it shows how a star evolves in time as its temperature and luminosity change. An evolutionary track starts at age = zero. Connect the points of a specific track with straight-line segments. Clearly label each track with its correct stellar mass.
3. For the Hyades, interpret the nature of the stars near (1.0, 1.0) -- what type of star are they?
4. Predict approximately the value of stellar mass you would assign to the stars at (1.0, 1.0). Is there any danger in predicting these masses?
5. Describe what is occurring near (B --V) = 0.1-0.2, absolute magnitude = 1.0-2.0?
6. Comparison of cluster M45 to the Hyades: plot the points from Table 2. What does it show? Contrast and distinguish the M45 plot from the Hyades plot.
7. The main sequence is the only stable location in (T, L) or equivalently, (B - V, MV) for any ball of gas converting H to He in its core. Note the difference between points at (0.6, 10) and (0.6, 5) in Figure 1. Calculate how much you must slide the points of M45 vertically to match the Hyades.
8. Summarize what you did in question 7 from the point of view of astrophysics (Think! Think hard about the y-axis of the plot.). Describe or express the importance of the 'vertical sliding' in a brief description of its value to astrophysics.
9. Compare Figure 2 with your plot of the Hyades and M45 (= Figure 1). What is different about this plot? Distinguish it from Figure 1 and describe what is occurring. How distant is the cluster? Why are there so few stars at magnitudes fainter than 16 and B - V > 1.0?
Note - All tables and figures are in attached file.
Project 2 - Cosmology Inquiry: Hubble Deep Field
The Hubble Deep Field is a long exposure (~1 week), using the Hubble Telescope, of a small portion of the sky to investigate the galaxy evolution and the large-scale structure of the universe. (How small? With a pen, put a dot on your thumbnail. Now hold it at arm's length.)
You will need at least one computer per group to access the HDF image. The exercise comes in two parts: A will be done today; B will be presented in a few weeks.
A: 0. Predict what you will see in comparing a galaxy's shape to its color based on your understanding of stellar evolution.
A: 1. Access the online HDF. The green circle in the upper left corner of the page is a magnifying glass that you may drag around the image. The HDF image is about 8 circles wide and about 10 circles tall.
Most of the objects in the image are galaxies. Several are stars.
a) By what characteristic can you identify the stars?
b) How many stars can you find? (Hint: more than 1, less than 10)
A: 2. How many galaxies are in this image? The answer is not 10,000 as stated. To answer the question, there are two paths: the 'smart' path and the 'not-so-smart' path.
a) Define the procedure for each path (be specific).
b) State any assumption(s) you have made for the 'smart' road.
A: 3. Some of the galaxies in the image are orange-red, some are white, and some are blue.
a) Tabulate galaxies by color. What is the most common color?
b) Describe the procedure by which you determined your answer.
A: 4. If we assume that all of the galaxies in this image have the same diameter, then closer galaxies appear larger and more distant galaxies are smaller.
a) Compare the galaxies in the image -- are most relatively near or relatively far?
b) Summarize the evidence that supports your answer.
c) Critique the fundamental assumption that all galaxies have the same diameter. List evidence in the image that supports or refutes the assumption.
A: 5. Construct rough sketches of the 5 closest galaxies you find in the image.
a) Compare your sketches and predict the most common type of nearby galaxy? Describe your reasoning and provide specific evidence. Investigate the accuracy of your prediction by examining the next 5 nearest galaxies.
b) Interpret the data in the following table. What conclusions or generalizations may you draw? Summarize your reasoning and provide specific evidence (eg, by drawing a graph).
|
Circle Sample Number
|
No. of Red-orange Galaxies
|
No. of blue-white galaxies
|
|
1
|
7
|
27
|
|
2
|
10
|
16
|
|
3
|
15
|
19
|
|
4
|
10
|
29
|
|
5
|
12
|
27
|
A: 6. For submission: You've been asked to write a news brief based on the results you've studied in this exercise so far. Report your conclusions and describe the evidence to support your statements. The summary should be a sensible length, but not less than ~100 words.
B: For this question, your task is the design of a question that (i) interests you and your group; and (ii) can be answered by the HDF data. That means that data not present in the image may not be used. Your 'report' will be presented to the class as a poster ("adult science fair"). A summary will be submitted for a grade (instructions will be posted). Your report will consist of the following sections, all of it fitting onto a single, large sheet of paper.
a) Formulate a specific research question (do not ask 'silly' questions: eg, how many galaxies are in the HDF? what color are most galaxies in the image? Why 'silly'? Both have been addressed in part A of this exercise.)
b) Develop a step-by-step procedure to collect the evidence.
c) Display your data in a table or graph. Interpret the data and synthesize one or more conclusions.
d) Argue for your evidence-based conclusion(s). Predict, if possible, additional insights to be gained from more data. Critique your assumptions.
In addition, for the submitted summary, briefly summarize your results and what you have learned about science through this exercise. Write the summary as if you were describing it to someone unfamiliar with the HDF. Instructions will be provided regarding submission.
Attachment:- Assignment Files.rar