magnitudes lab (Complete)

THIS LAB EXERCISE IS WORTH 2.5 POINTS In astronomy, it’s vitally important to be able to measure the amount of light we see from a star. Without knowing how bright a star really is, we can’t accurately determine many of its other properties. Unfortunately, eyeballing a star in the sky is no better than walking into a darkened room with an unknown light source and trying to figure out how it compares to another light source. The ancient astronomers knew how bright stars APPEARED, and so they created a system of magnitudes to keep track of this appearance. Later, when we understood more about the actual amount of light coming from the stars, we adjusted the magnitude system to reflect this information. Stars now have two major magnitude designations – absolute and apparent . Which quantity – absolute or apparent – do you think tells you something about the actual amount of light from a star? Explain: Absolute tells you about the actual amount of light coming from a star. If you were to look at two light bulbs and gauge their brightness from your location in your house, are you gauging the absolute or apparent magnitudes of the bulbs? Explain: I think you would be gauging the apparent magnitudes of the bulb, not the actual absolute magnitude. Page 1 LAB ACTIVITY 8 MAGNITUDES SUCK

The magnitude system in astronomy is the cause of many headaches because the scale seems to go in the wrong direction. Large absolute magnitudes represent objects that have low luminosities. Small (and negative) absolute magnitudes represent objects with high luminosities. One way to think about this peculiar system is to compare it to a golf scoreboard, where the number relative to shooting ‘par’ is often displayed. A golfer who completes a round with fewer strokes than another is a better (brighter) golfer. Consider the following scoreboard: Which golfer(s) had the WORST round? I.Poulter, who has +2. Which golfer(s) had the BEST round? P.Mickelson and J.Kelly who both have -5. Does a positive number correspond to a better or worse golfer? A positive number corresponds to a worse golfer. The more negative a number is, the better. Now consider the following list of APPARENT magnitudes: Star A +1 Star B 0 Star C -3 Page 2 LAB ACTIVITY 8 MAGNITUDES SUCK

THE MAGNITUDE SCALE The stellar magnitude scale is such that FIVE steps in magnitude represent a factor of 100 in intensity. A single step in magnitude represents a factor of 2.512 in intensity. Thus if Star A has an apparent magnitude of 1, we receive 2.512 times as much light from it as we do from Star B, which has an apparent magnitude of 2. In addition, a star with an absolute magnitude of 1 has a luminosity that is 2.512 times greater than a star with an absolute magnitude of 2. The apparent magnitude of the Sun as seen from 10 parsecs away is 4.74. This is also the value of its absolute magnitude because 10 parsecs is the standard reference distance. The absolute magnitude of the star Sirius is -1.44 (it’s a negative quantity). Which of the following is true? a. the Sun is about 6 times as luminous as Sirius b. Sirius is about 6 times as luminous as the Sun c. the Sun is over 100 times as luminous as Sirius d. Sirius is over 100 times as luminous as the Sun e. there is no way to compare the luminosities of these objects without more information Fully justify your answer: Since the apparent magnitude of the Sun can be seen from 10 parsecs away, with the information provided the magnitude of Star A would have to be at least 100 (due to the 5 steps). We can assume that it’s over 100, due to the fact that its luminosity is 2.512. Return now to the Excel table you created in the lab activity on parallax in Unit 1. Within Excel, select the entire data set and sort by vmag (apparent magnitude) from smallest to largest. The star at the top of the list is (select all correct answers): a. the one that appears dimmest b. the one with the smallest luminosity Page 4 LAB ACTIVITY 8 MAGNITUDES SUCK

c. the one that appears brightest d. the one with the greatest luminosity Explain your choice(s): Write the name, vmag, class, and distance for your FIRST FOUR STARS and LAST FOUR STARS below. name vmag class distance First star: ___ HIP 5496 ____ ____ 9.80 ____ _____ STAR K0 _____ ____ 7.474959 ____ Second star: _ HIP 51317 ______ ____ 9.65 _____ ____ STAR M2 _____ ___ 7.474959 ___ Third star: _ HIP 88574 ____ ____ 9.37 ______ _____ STAR M2V _____ ___ 7.474959 ___ Fourth star: _ HIP 49986 ___ ____ 9.26 _____ ______ STAR M3 ____ ___ 7.474959 ____ 4 th to last: _ HIP 10625 ___ _____ 11.96 ______ ____ STAR M4e _____ ___ 7.474959 ___ 3 rd to last: _ HIP 76901 ___ _____ 11.83 _______ ____ STAR M5 _____ ___ 7.474959 ___ 2 nd to last: _ HIP 93449 ___ _____ 11.57 ________ ____ STAR A5II ______ __ 7.474959 ____ Last Star: _ HIP 33499__ __ _____ 10.81 _____ ____ STAR M4 _____ ___ 7.81311 ____ Which star is APPARENTLY the brightest of the 8 stars? The one with the smallest vmag on the list is the 4th star (HIP 49986), whose vmag is 9.26. Does this star also have the largest luminosity? ___ no ______ Explain: When taking a look at the classes for the stars, HIP 49986 is listed as a M3 star, meaning that it’s actually one of the weakest stars. HIP 93449’s listed as a A5II star, which means that it could be listed higher. Which star is APPARENTLY the dimmest of the 8 stars? Star HIP 33499, who’s vmag is 10.81. Does this star also have the smallest luminosity? ___ no _____ Explain: Despite the fact that this star’s class is a M4, it’s actually not the one with the smallest luminosity. Rather, that would go to HIP 76901, which is classified as Star M5. Page 5 LAB ACTIVITY 8 MAGNITUDES SUCK

Limit Results To: rows Output Format: Show All Parameters: Select to display all catalog parameters instead of only defaults Change “Output Format” to “excel compatible.” Now select a vmag range. You are welcome to choose any magnitude range, as long as the resulting list has at least 20 stars. The lowest magnitude you can choose is -1.44 (this corresponds to the star Sirius, the brightest star in the night sky) and the greatest is 14.08. At first try ranges of 1 magnitude, but this might have to be adjusted depending on your starting magnitude. Delete any stars for which the Class is “UNIDENTIFIED.” If your resulting list has more than 20 stars, delete the rows after the 20 th star. Now sort the list according to vmag from smallest to largest. The star at the top of the list is (select all correct answers): a. the one that appears dimmest b. the one with the smallest luminosity c. the one that appears brightest d. the one with the greatest luminosity Explain your choice(s): I chose B for this because with the larger positive numbers, this means that the luminosity is actually very dim; the list represents the stars as it gets brighter. Assuming that the magnitude is the absolute value, the stars located at the bottom are actually the brightest, not the top. Compare this list to the one you generated when you selected stars by their parallax. Can you see any obvious differences between the lists? Be sure to look at all the various values you’ve tabulated, even though you have not yet been introduced to all of them. An easy way to do this is to “sort” by those values in each list and look at any trends. Describe any differences between the lists in detail. Yes, the list is much more filled in comparison to the first list. When looking, I noticed that the set of particular stars were much closer and similar to each other, than the previous one. There’s no sharp jumps in the rankings, so I can assume that the stars MIGHT be closer to each other than the ones from the first set would be. Which list (if either) do you think is most representative of the stars in the universe: The parallax-selected list or the magnitude-selected list? I think the magnitude-selected list is more representative of the stars in the universe. Explain your choice: Page 7 LAB ACTIVITY 8 MAGNITUDES SUCK

I chose this choice because the data for the table seems more completed than the one for the parallax. As we know, the closer the object is, the dimmer the light is. However, while apparent magnitude is similar (to a degree), it can be backed up by the absolute magnitude, thus giving us an actual answer for the luminosity. We will return to these data in later activities. The exact relationship between apparent magnitude, absolute magnitude, and distance is: Mv = Vmag – 5logd +5 Where Vmag is the apparent VISUAL magnitude, Mv is the absolute magnitude, and d is the distance to the star in parsecs. We are now in a position to find the absolute magnitudes of the stars in the table from the Parallax Activity. To do this, you will need to open that table, click f(x) and choose SUM. Then enter in the various boxes to be summed. They are: 5 (the cell number for vmag) -5*LOG10(cell number for distance) Cut out your resulting data table and paste it here: Page 8 LAB ACTIVITY 8 MAGNITUDES SUCK

After examining the chart, I can say that the stars in my chart would have to be stars that are lesser than G2. All of the magnitudes listed are greater than 4.74, which means they are less luminous than the Sun. ONCE YOU HAVE ANSWERED THE QUESTIONS AND CREATED YOUR DATA TABLES, TURN THIS LAB ACTIVITY IN VIA BLACKBOARD. Be sure to meet the specific lab deadline. Page 10 LAB ACTIVITY 8 MAGNITUDES SUCK