Astro 210 - Project # 2
Observations of Long Period Variable Stars

The objects of the exercise are to:

1. appreciate that the sky is not unchanging;
2. examine directly part of the way in which most stars die;
3. explore how scientific data are acquired and used.

To these ends, you will look at the variations of a "long-period variable" star, otherwise known as a "Mira" variable (named after the first such star discovered). These are giant stars that undergo huge variations in brightness over a period of a year or so (different ones from about 100 to 1000 days). Mira variables are dying stars with carbon-oxygen cores that have lost their equilibria and are pulsating and changing their brightnesses. They are in this state for 100,000 years or so. At the same time they are losing matter through massive winds, and will eventually lose their entire outer envelopes, nearly exposing their old nuclear-burning cores. At the end, they will produce planetary nebulae that are seen as shells of gas surrounding hot stars, and then will die as white dwarfs.

Your job is to use Stardial to observe the Mira star RR Aquarii (in the constellation Aquarius).

All the images Stardial has collected since 1996 are available on-line: you can browse them by date, or by location on the sky. For this experiment, you will need to examine images near the location Right Ascension = 21h 15m, Declination = 0. Here's how to find them:

When you select any particular image, your WWW browser should show a picture something like this (but without the red box):

Finding the variable star

The red box in the picture above outlines an area in the constellation Aquarius which contains our variable star RR Aqr. Your first job is to figure out which of the stars is the variable. Here are two Stardial images of the field, one taken when the variable was at its brightest, the other when it was at its faintest:


Can you find the star which changes its brightness?

Astronomers use a method called "blinking" to search for variable stars: they alternate rapidly between two images, displaying registered versions of each for just a second or two. You can "blink" the two images above by selecting the link below. You will see one image by itself; click on it to display the other image. Keep clicking (or using the Alt-Left and Alt-Right buttons) to alternate the images until you find the variable. Click on the text at the bottom to return to this exercise when you have found it.

Click here to reach blink pages

Note that the star RR Aqr is varying while the other stars are not varying. (If all the stars varied together in synchronism, we'd suspect that clouds and/or equipment malfunction were the cause.)

Making a light curve

You will to construct a "light curve" for RR Aqr, in which you make a graph of apparent magnitude plotted against time. Magnitude measurements are to be made using the oldest device, the human eye.

Now that you've found the variable star, you must measure its change in brightness over an entire season. You can compare the appearance of RR Aqr against those of stars nearby to gauge its apparent magnitude. Below is a chart of stars inside the red box (perhaps you'd prefer a PDF version of the chart.)

The chart has reversed the usual color scheme: astronomers often use a "negative" portrayal of the sky as white and stars as dark in publications, both because it's easier on printers, and because most people can discern faint details more clearly.

The chart provides apparent magnitudes in the "V" passband for eight stars in the area. As you examine images from the Stardial archive, compare the appearance of RR Aqr to these eight stars. If it looks just like one of them, then its magnitude must be close to that of the star; so if RR Aqr looks just like star "D", it would have a magnitude of 8.1. On the other hand, if RR Aqr seems to fall between two of the marked stars, its magnitude must be between those of the two stars; for example, if it looks fainter than star "E", but brighter than star "F", then its magnitude must be between 9.4 and 10.0: perhaps 9.7.

RR Aqr is found in the field with the right ascension of 21 hours and 15 minutes, or 2115. Go to the
Stardial web page
find the archive that is organized by location (the right ascension, RA, mode, under "web" and "jpg") and find your the "2115" field (the one that contains your variable star). Pick data from 2005, 2004, and 2003 (and 2000 too, if you wish to add more data points). Also be sure to pick clear nights (note: if the other stars look very different in an image, that means it was not a clear night). Continue observing the star until roughly the end of the term!

This is not a project with canned data. We do not know what the star will do, whether it will brighten, fade, or how fast it will change. You will determine that by observation as the data arrive.

You should have a minimum of 20 observations spaced throughout the three years (or more than that for four years). Begin with data from the archive, that is, this semester, and then keep track of your star during the remainder of the semester. This is actually the way variable stars are examined, except that professionally, electronic measuring devices are used; generations of amateurs, however, have made useful observations using the "naked eye" technique at the telescope. For each image you choose,

Now, turn your table of measurements into a graph. As you observe, record your data in a table and then plot your data on a graph with the date on the bottom axis (the x-axis) and the magnitude increasing downward (so fainter is down) on the side (the y-axis). Plots should be neat, and the use of a computer graphing package to plot your data is strongly recommended. At the end, connect your observations with a smooth curve; this may be done by hand.

  1. You will notice that there are several months of each year with no data recorded for RR Aqr. Explain why this is the case. Hint: this is not an error in the system, or an issue of computer disk space, but rather to do with issues related to the celestial sphere. (For further inspiration see the first part of the first Stardial project.)
  2. What do you estimate the period of the star's oscillations to be? Note that the data gaps mentioned in Question 1 complicate this estimate. Is there a way to get around this problem?
  3. Based on this period, estimate how bright RR Aqr will be on August 3, 2005.
  4. What is the amplitude of the variation in RR Aqr -- that is, by how many magnitudes does it vary from minimum to maximum?
  5. Convert the amplitude from magnitudes to intensity: how many times brighter is RR Aqr at maximum light than minimum?
  6. Pretend for a moment that the outer layers of RR Aqr don't heat up and cool off, but maintain a constant temperature as they expand and contract. If that were the case, then the brightness of the star would depend simply on its surface area: the larger the diameter, and larger the surface area, the brighter the star. If RR Aqr varied only in size, what would be the ratio of its diameter at maximum light to its diameter at minimum light? Would a citizen of a planet around RR Aqr find the change in the angular size of his/her/its star noticable?
  7. No measuring device is perfect, and all measurements necessarily contain errors. When you plot your graph you will see that the points do not exactly follow a smooth path. The deviations of your points from the smooth curve indicate your typical "error of measurement," which should always be cited. Estimate your typical errors from the graph before turning it in. There are formal ways of assigning errors; you need only make your best estimate.

Reports are due on April 29th. Include in your report:
  1. a table of measurements that includes the date and the magnitude;
  2. a graph with magnitudes increasing downward;
  3. your error estimate (the size of a typical error);
  4. your answers to questions 1 through 7 above.

Leslie Looney
Last modified: Fri Apr 8 14:49:22 CDT 2005