Astronomy 122 First Homework Assignment: Measuring stellar brightnesses and stellar colors.

Submit your measurements using this worksheet

Be sure to keep saving your work by clicking "Submit your work". It will store it for you. Therefore you don't need to do the whole assignment at once. When you have completed it, there is a cell at the very bottom that says "Is this your final submission?". Answer yes so we know when to grade the assignment. Unanswered questions will be graded, regardless after the due day. After each submission, a dialogue box will ask for your name. Note that you can type in the worksheet as the worksheet cell will expand vertically to encompass your text.

Part I:

Below you will use the CCD simulator to make the relevant measurements and you should following example in Lecture D of Module 1.

Procedure:

Make all measurements in a box of dimension 10x10 pixels.

For this assignment you will be making measurements via a simulation that has 4 different kinds of observing conditions (the conditions are unknown to you). These observing conditions have a big effect the kinds of stars that can be detected. In some cases, you will be unable to detect all of the stars.

For each of the four cases referenced below (and in your worksheet):

1. Determine the minimum exposure time required to believe that you can even "see" the star, using just your eye, with your virtual detector.

2. Determine the minimum exposure time so that the difference between the numbers in the green box labelled mean and red box labelled mean is approximately 100. Remember, the star is centered in the green box while the detector background (e.g. the brightness of the virtual night sky in each case of the simulation) is registered in the red box.

Case 1

Case 2

Case 3

Case 4

From this exercise it should be apparent to you that for any given exposure of the sky with any given telescope plus detector there will be many stars that are simply too faint to register on the detector and different detectors will require different amounts of exposure time to produce similar quality data (i.e. in this case 100 net counts as the detection).

Part II

Download the blackbody simulator for this part

This simulator will reproduce the blackbody spectrum as a function of temperature. The X-axis is wavelength increasing to the right (decreasing energy per photon). The Y-axis is the amount of energy emitted at that wavelength. Clicking anywhere on the graph will indicate the wavelength (value of the X-axis) at location of the cursor. This is useful when you need to identify the wavelength of the peak emission. A background corresponding to the optical spectrum is superposed on the blackbody curve to ease in identification of color. Light with wavelength shorter than about 3200 angstroms does not penetratre our atmosphere. This is where the ultraviolet region of the electromagnetic spectrum begins.

As you change the temperature (T) you will see the curve changing but you will also see the numercial values in the B-V V-R U-B and T fields changing. For this exercise we will only care about the values in the T and B-V fields.

Answer the following questions in the worksheet for this assignment.

1. Set the temperature to approximately 8000 by using the slider bar (note the arrow keys on your keyboard can be used for fine temperature adjustment. What is the wavelength of the peak emission?

2. Now set the temperature to approximately 4000. What is the wavelength of the peak emission?

3. What is the ratio of the two wavelengths? (a ratio is two numbers divided by each other). Is this ratio what you expect?

4. What color would a star appear to be which has a temperature of 8000?

5. What color would a star appear to be which has a temperature of 4000?

6. If the temperature of the star was 6000 what would you predict its color to be and why? (be honest and answer this before you actually set the temperature to 6000).

   Now click on the box that says "Draw Limits of Integration" -the white lines that appear there represent filter band passes of standard astronomical filters. To measure stellar temperatures, astronomers put filters in front of their digital cameras and measure the flux ratio between the two filters. For B (blue) and V (visual or green) this ratio is encoded as the index value B-V. The lower that number, the hotter the star (more flux is emitted in the B filter than the V filter. A value of B-V = 0.5 means that approximately the same amount of energy is emitted in the blue filter as the green filter.

7. What temperature produces a B-V value of 0.5?

8. Suppose that I can measure B-V to an accuracy of 1% (.01 in B-V). For the case of B-V = 0.5, what change in temperature produces this 1% change in B-V? (i.e. B-V moves to 0.51 or 0.49 when you change the temperature)

9. What change in temperature would produce a 10% change in B-V (e.g. 0.1 change in B-V)

   As you can see, the B-v index is a sensitive indicator of stellar surface temperature for stars with temperatures of around 6000 (like our Sun). However, for very hot stars B-V starts to loose its sensitivity to temperature simply because the B and V wavelength regions contain very little of the total energy flux of the star. We can verify this by doing the last situations and compare that to what was just done.

10. Set T to 15000. At this temperature, what temperature change is required to change B-V by +/- 0.1?

11. What kind of observations would you need to do to be able to accurately measure the temperatures of very hot stars?