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

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This assignment consists of two parts that each make use of a simulator.

Tutorial on how to use the Detector Simulation for Part I below: READ IT.

The Assignment:

Part I:

Launch the detector.

Increase the exposure time to 40 seconds and measure the net counts (using the procedure shown in the tutorial) for Star 1 and Star 3. Report those values on the template worksheet.

Set the exposure to 1 second. Report the counts in the background at 1 second. Then measure the background counts at 10 seconds and 100 seconds and report all those values on the tempalte worksheet.

Explain what you notice in the background counts as a function of exposure time.

Does it make a difference where you place the aperture on the image for the backgound counts? If not, what does this tell you?

Now set the exposure back to 1 second and measure and report the net counts for Star 4.

Explain why you can barely detect Star 4 at an exposure time of 1 second.

Launch Simulation A Make the exposure time 25 seconds and report the net count value.

Launch simulation B Again make the expoure time of 25 seconds and report the net count value.

The star is the same between simulation A and B. Suggest what might be different about the observing conditions for these two cases and why this star is harder to detect in one of these cases.

Launch simulation C Make the expoure time of 100 seconds and report the net count value.

Suggest in this case why this same star is almost impossible to detect under the observation conditions associated with simulation C.

Launch simulation D Make the expoure time of 100 seconds.

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 in terms of net counts of signal.

Part II
Open the blackbody simulator for this part (right click to open in a new window)
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. The total area under the curve is equal to the total energy emittted by the blackbody at a fixed size (radius of the object).

In the middle of the X-axis is a small color bar that shows the the wavelength limits of human vision. At the long wavelength end, our vision dies out around 8000 angstroms (800 nanometers) as our eyes, compared to nocturnal predators, are not sensitive to infrared radiation.

Light with wavelength shorter than about 3200 angstroms (320 nm) does not penetrate our our atmosphere. This is where the ultraviolet region of the electromagnetic spectrum begins.
As you change the temperature (T) with the temperature slider you will see the curve shift and change. Note that clicking in the temperature slider area will changed the temperature by 10K, for fine adjustments needed below.
Answer the following questions in the worksheet for this assignment.

What is the temperature that corresponds to a peak wavelength of 725 nm? Make sure to click the indicate peak wavelength box. What color would the star appear?

What blackbody temperature would produce most of the energy in the blue part of the spectrum (refer to the small color bar on the wavelength scale).

Set the temperature to approximately 8000 by using the slider bar . What is the wavelength of the peak emission?

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

What is the ratio of the two wavelengths? (a ratio is two numbers divided by each other). Is this ratio what you expect? Explain why or why not.

Now set the Temperature to 10,000 K and click on the filters tab; beneath the blackbody curve you will now see 4 filter shapes (called bandpasses) - these filters are UBVR (Ultraviolet, Blue, Visual (or green), and Red). In the color index box make the first filter B and the second filter V. The value of B-V = -0.02 should appear for T = 10000.

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.

What temperature produces a B-V value of 0.5?

Suppose that I can measure B-V to an accuracy of 10% ( +/- 0.1 in B-V). For the case of B-V = 0.5, how many degrees does the temperature have to change to move B-V from 0.5 to 0.6

Set T to 20000. At this temperature, B-V = -0.34. How many degrees does the temperature have to change to reach B-V = -0.24?

Explain now why the B-V index loses temperature sensitivity for these hot stars.

What kind of observations would you need to do perform in order to accurately measure the temperatures of very hot stars?

Go back to the curves tab and compare two temperature curves, one of 6000K and one of 4000K. This means the hotter star is 1.5 times hotter than the cooler star and both of these stars have the same radius. Adjust the scale with the slider to the right most reading is 2 microns. By visually insepcting the areas under the two curves, approximately determine the ratio of the area under the hot star to the area under the cool star.

The total area under the curve is equal to the energy output of the star. You should notice/determine that although the hotter star is 1.5 times hotter than the cooler star, the area under the hot star curve (i.e. the energy emitted by the hot star) is a lot greater than 1.5 times the area under the cool star. What does this tell you about the relationship the temperature of a star and the total amount of energy emitted?