Brightness and Surface Brightness https://dept.astro.lsa.umich.edu/ugactivities/Labs/brightness/brightness.html

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Brightness and Surface Brightness

This document is adopted from Michigan Astronomy and edited to make it applicable for Tarleton State University, Stephenville TX, Astronomy course under Creative Common License (https://dept.astro.lsa.umich.edu/ugactivities/Labs/copyright.php)

Worksheet

Part 1: Surface Brightness

Your instructor will set up the planetarium with Orion up and the lighting set to about the same level as the light pollution at the Tarleton Observaotry.

1. When the planetarium is ready, compare what you see in the planetarium to the magnitude charts to determine which chart matches best with what you see. Record the chart number in Table 2. 2. Your GSI will adjust the sky brightness to simulate the other locations in Table 2. For dark sites, it is helpful to pay attention to the area around Orion's belt. Your GSI will bring up the lights so you can pick which magnitude chart best matches on a good night. 3. Your GSI will point out the Orion Nebula, which is a glowing cloud of gas with new-born stars. Label it on one of your sky charts. 4. Use the sky charts and Table 1 in the Introduction to determine the sky surface brightness in mag/arcsec2 for these observations, and enter the values in Table 2.

Table 2 Orion Chart Sky Surface Brightness Limiting Magnitude Setting Nebula Number/N (mag/arcsec2) (mag) visible? ELM

Tarleton Observatory

Downtown Dallas

Stephenville

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Brightness and Surface Brightness https://dept.astro.lsa.umich.edu/ugactivities/Labs/brightness/brightness.html Part 2: Limiting Magnitude

5. Your GSI will point out a star and tell you its name. Compare it to the stars in Orion and determine its magnitude from the sky charts. The number of the sky chart shows the magnitude of the faintest stars shown. Record the star's name and magnitude here:

6. Use your sky chart to determine the limiting magnitude above which stars are invisible for the observations in Table 2, and enter the values in the Table.

Concluding Questions:

1. Estimate the surface brightness of the Orion nebula. Explain how you obtained it.

2. Most of the Andromeda galaxy has a surface brightness of 22.3 mag/arcsec2. Could you see this from Tarleton Observatory? From Dallas? Explain your answers.

3. Explain why the surface brightness of the Milky Way is roughly the same as the surface brightness of the Andromeda galaxy (22.3 mag/arcsec2), even though the latter is 1000 times farther away than most of the Milky Way.

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Brightness and Surface Brightness https://dept.astro.lsa.umich.edu/ugactivities/Labs/brightness/brightness.html 4. A laser emits light only in a concentrated beam in a single direction. Explain why the observed brightness of a laser does not follow the inverse square law for light. This is why a laser should never be pointed at your eye, no matter how far away it is.

5. The star Betelgeuse is magnitude 0.2. How much more light do we receive from it than from the star whose magnitude you estimated in Question 5 part 2? Show your work.

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Brightness and Surface Brightness https://dept.astro.lsa.umich.edu/ugactivities/Labs/brightness/index.html

Table 1 gives the approximate surface brightness of the sky for several values of the Naked Eye Table 1 Limiting Magnitude (NELM). To estimate the NELM, we will use charts designed by the GLOBE at SB NELM Night program. With these charts, match the visible stars in the constellation Orion to one of the (mag/arcsec 2) pictures. The picture number corresponds roughly to the NELM. You can practice doing this at the website: http://www.globeatnight.org/observe_practice.html. 0 13 1 15 An extended object must have a brighter surface brightness than the sky for it to be visible to the 2 16 naked eye. A sky of 18 mag/arcsec 2 will completely wash out a galaxy whose surface brightness is 20 mag/arcsec 2. However, this is partly dependent on the color. Looking at Orion in a dark sky, most 3 17 observers can see that Betelgeuse is a red star and Rigel is a blue star, and that they are similar in 4 18 brightness. In a city where streets are lit with yellow sodium vapor lights, the sky tends to have an 5 19 orange color. In that case, Betelgeuse shows less contrast with the orange sky than Rigel, so Rigel 6 21 will appear brighter. Similarly, a reddish nebula with a surface brightness of 18 mag/arcsec 2 may be completely invisible in a 20 mag/arcsec 2 sky because its 7 23

Figure 2: The field of view covers an area on the object that is 9 times larger when the same object is at a

Whereas the brightness of an object depends on its distance, the surface brightness is independent of distance. At a greater distance from the observer, the same field of view will include a larger area on that object, as shown in Figure 2. However, recall that the brightness of the light received from that object decreases with the square of the distance, as discussed above. Therefore, although light from a larger area on the object is received in the same field of view, the brightness of that light is reduced by the same factor, so that the surface brightness stays the same. For example, Figure 2 shows that if the same object is three times farther, the same field of view includes 9 times as much area on the object, but the brightness of the object is 9 times less. Thus, the surface brightness, which is the brightness per area, of the object remains the same, regardless of its distance.

Additional Resources

GLOBE at Night program. The Conversion Calculator used to generate the data in Table 1 is at http://www.unihedron.com/projects/darksky /NELM2BCalc.html. The references at the bottom of the page have links to the papers with the full details on how to determine sky brightness. Note: MPSAS is the magnitude per square arcsecond. Astrophotography for the Amateur by Michael A. Covington (1998, 2d). See esp. Appendix A, pp. 259-261 for an explanation of Surface Brightness Visual Astronomy of the Deep Sky by Roger N. Clark gives the Surface Brightness and magnitudes of many deep sky and solar system objects. See esp. Appendix E. Learn more about light pollution and its effects beyond making the sky orange at the international Dark Sky Association website, http://www.darksky.org

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