Name Homework number 6: Due October Astronomy 70B Profs. Rieke Helping Henrietta Leavitt Measure Cepheid Variables Ms. Henrietta Leavitt has invited you to join her at Harvard College Observatory to look for Cepheid variable stars in the Magellanic Clouds (nearby galaxies in the southern sky)..) Ms. Leavitt has been shipped a series of photographic plates taken of the Magellanic Clouds from the Harvard College Observatory Boyden Station, Arequipa, Peru,(picture below) and she is now preparing a machine called a blink comparator to allow her to compare the plates and find any variable stars. She has selected three of plates where the telescope was pointed to about the same place. Before comparing the star brightnesses on these plates, she has to align them so the star images coincide exactly. Help her do this! Go to http://astro.unl.edu/naap/vsp/animations/registrationsimulator.html When you enter the web page, it just has field (photographic plate ) in the box. Ms. Leavitt wants you to place field (plate ) in the blink comparator and adjust its position (using precise screw adjusters) so the images of both plates coincide. To do this, click on the box for starfield, and also on the box "make top field transparent" in general, the plates would be somewhat transparent, so this is realistic. Use your computer cursor (hold down the left mouse clicker) to move plate so the star images coincide with those on plate. Record the x and y offsets when field is registered on field. x offset = y offset = Go through the same steps for starfield (plate ) and record the offsets for it. x offset = y offset = The two of you spend the rest of the morning lining up all the other plates and recording the offsets so you can put them into the machine again and look for variable stars..) You have taken a break for lunch, but now it is time to look for variables. Go to http://astro.unl.edu/naap/vsp/animations/blinkcomparatorsimulator.html The "epoch" column identifies the photographic plates by the time when they were taken. The numbers are days and fractions of days. Therefore, the first number,.7, means the first day of the
observation series, plus 0.7 times hours past when the day was defined to start, or just over 7 hours, 0 minutes. Ms. Leavitt will show you how to load combinations of pictures into the blink comparator (it is easiest to start with only two). She tells you to click on the epoch, and then on the add button. To see all of the epochs, use the slider to the right of the list. Once you have two plates loaded, click on the blink button, and then click on "show crosshairs" and identify the variable stars you can find. Enter their positions into the table below, when you center the crosshairs on them with the cursor of your computer. Because the variable stars change brightness at different rates, you need to compare plates at a number of epochs to find them all; you may also find it useful to load or plates to be sure. See how many you can find (there should be ). Variable # x position y position 0 Now find three reasonably bright stars that do not vary and enter them in the table below. x position 97 y position Ms. Leavitt and you will use measurements of these stars as a reference in case one of the nights had thin clouds or something else that made all of the stars appear a little fainter than usual. However, this has taken all afternoon, so it is time to go home.. ) Ms. Leavitt got in early this morning and has set up a photographic plate for you to practice measuring star brightnesses on (a process astronomers call "photometry"). To find it, go to http://astro.unl.edu/naap/vsp/animations/photometrysimulator.html There are two double apertures you can move around to center on stars or put on blank regions. Use them to measure the stars at the positions in the table below. To make a measurement, center the apertures on the star (locating the star in the field to the left and then centering using the windows to the right, arrow keys will move the star). Then record the average counts for the inner disc, and the average counts for the outer ring. The outer ring gives a measure of the signal from blank sky, so the difference of averages for inner disc and outer ring gives the signal from the star minus the contribution from the sky. That number is the measurement of the brightness of the star
Star X position Y position Average inner Average outer Difference disc ring example 87.6 0.7.88 86 70 79 6 9 0 9 7 How accurate are these numbers? We can use the dual apertures to find out by putting them on areas with no stars, measuring the inner disc and outer ring averages, taking their differences, and seeing how much signal we get. Do this for five positions and enter the results in the table below: Position # X position Y position Average inner disc Average outer ring Difference From all these measurements, are there any pairs of stars among the five you measured that could be the same brightness? Yes or No If so, which ones?.) Well, that took all morning. After lunch, Ms. Leavitt had to go to a meeting with Director Pickering and left you to look for variable stars on the plates you started with. Go to http://astro.unl.edu/naap/vsp/animations/variablestarphotometryanalyzer.html First, compare your three non varying stars in pairs, to see if they are really constant in comparison with each other. To do so, move the cursor to center on one of the variable stars and left click, then move the cursor to another of the stars and left click. The "observations plot" to the upper right shows the differences in the brightnesses of those two stars for ALL of the epochs when plates were taken. Compare the three stars in pairs to be sure they are all non variable, and if one of them is variable keep comparing pairs to identify which one and reject it as a reference for brightness.
Good news!!! Ms. Leavitt has compared the reference stars for all the epochs and says that the nights were good, except for night 6 when it rained. Oh yes, on night the observer was sick, so no plates were taken on that night either. But for all the other nights, so long as we measure relative to one of our non varying stars we should have full data. You can now compare selected variable stars with one of the non varying ones. The specific stars can be identified by coordinates again, using the cursor/crosshairs. You will see the differences in brightness of your stars over the days of the measurements in the upper right. Use the upper right graph to identify possible Cepheids you will need to consult the class notes to see what the variations by a true Cepheid should be like: http://ircamera.as.arizona.edu/natsci0/natsci0/lectures/galaxies.htm They should vary in brightness smoothly, with periods between about. and 00 days. For each of the variable stars you found in Section, decide if it looks like a possible Cepheid variable and if it is estimate the period of its variations. To the lower right, there is a graph that lets you zero in on the best determined period. There are days along the lower axis, and a graph that should show a dip at the correct number of days for a periodic star. Slide the triangle until the line below it goes right through the bottom of the deepest dip. See what is happening to the vertical lines in the upper right graph also; they mark the periods. To determine accurate periods and get the pattern more exactly, zoom the bottom plot, and locate a broad low point on the curve which indicates a periodicity. Move the arrow at the top to put the vertical line right at the low point and read off the period. If you also click on the "phase" option at the bottom of the "observations plot" and it will fold all the measurements on top of each other. When you have the arrow at the right place, the observations plot will show all the data in the variation pattern which can be compared to the pattern in the lecture notes. Enter all this in the table below: Variable # x position y position Cepheid? Yes or No Period Days Remember that the fainter the star, the greater the uncertainty will be in its measurement the "observations plot" for faint stars will scatter up and down more than for bright ones, even if they are not varying. From the period luminosity relation in the class notes, http://ircamera.as.arizona.edu/natsci0/natsci0/lectures/milkyway.htm
what is the rough luminosity of the Cepheids you found, assuming they are of Type I? Just select the closest to X 0 L sun, 0 L sun, X 0 L sun, or 0 L sun. (More blanks may have been provided than are necessary there may be less than five Cepheid candidates)