The American Association of Variable Star Observers

25 Birch Street · Cambridge, MA 02138 · U.S.A. · 617-354-0484 · aavso@aavso.org

Observing Variable Stars

Measuring Delta Cephei

1. Using an all-sky chart, locate the constellation Cepheus in which Delta Cephei lies. Below is an all-sky chart. (You can download a copy from the AAVSO's FTP site.) Face north, and lift the chart over your head so that the northern horizon is at the bottom. Use the pointers of the Big Dipper to find the North Star Polaris, and Cassiopeia beyond. Cepheus lies among Cassiopeia, Polaris and the star Deneb in the constellation Cygnus. The apparent size of Cepheus is about the same as the apparent size of your clenched fist held at arm's length.

All-sky chart

Pictured below and to the right is a chart of Cepheus (also available via FTP), showing the variable and several non-variable comparison stars that forn the "frame of reference" for the measurements. The numbers beside the stars are their magnitudes--the astronomers' way of specifying the apparent brightness of the star. The brighter the star, the smaller the magnitude. This is because the magnitude system evolved from one in which the brightest stars were classified as "first magnitude" and the faintest as "sixth magnitude." Chart of Cepheus;
The strange case of Polaris:
Cepheids are actually rare supergiant stars.  They have completed most of their
life cycle, having used up most of their hydrogen thermonuclear fuel.  
Supergiants with surface temperatures of about 9,000 K undergo pulsations, due
to an instability of the gases created by the star's radiation passing 
through them.  Some Cepheids are changing so fast in size that their period of
pulsation is changing at a measurable rate.  A good example is the North Star,
Polaris, which is a Cepheid with a period of about 4 days.  However, its 
range of brightness variation is unusually small, and getting smaller.  Thus 
the best-known star in the sky is a Cepheid variable with unique behavior!

2. Locate Delta in Cepheus, and estimate its brightness relative to the comparison stars. Record the exact time and date. In the case of Delta Cephei, there are two convenient comparison stars: Zeta at magnitude 3.6 and Epsilon at magnitude 4.2. Delta varies from slightly brighter than Zeta to slightly fainter than Epsilon. If Delta appears to be midway between Zeta and Epsilon in brightness, its magnitude would be 3.9. If it appeared only very slightly fainter than Zeta, its magnitude would be 3.7.

Based on experience with other beginning variable star observers, we estimate that the accuracy of students' measurements will be 0.2 magnitude, depending on their skill and experience, and on their sky conditions.

It may be helpful to practice identifying and measuring Delta Cephei and the comparison stars using a 35mm slide of the constellation. An excellent set of constellation slides can be obtained from: Astronomical Society of the Pacific, 390 Ashton Avenue, San Francisco CA 94112.

3. Measure the brightness of Delta Cephei on each clear night for a month. The measurements can be entered into a computer to form a convenient database for analysis.

4. If possible, compare your results with those of two or more observers who independently measure the brightness of Delta Cephei at roughly the same time (within a few hours). Determine the average of the individual measurements and the deviation or difference of each individual measurement from the average. Then determine the average deviation of the individual measurements from the average. This is an important indication of the accuracy of the measurements.

5. Convert the time and date of each measurement to Julian Date. First, convert the time to Standard Time by subtracting one hour if you are on Daylight Time (This is not the case in Europe in November 1996). Then convert to Universal (Greenwich) Time (UT) by adding or subtracting the appropriate number of hours. For instance, Universal Time is one hour behind of Central European Time (CET) in Europe. Retard the date if necessary: 00:30 November 19 CET is 23:30 November 18 UT. For this reason, it helps to record a "double date" when you make a measurement: 00:30 November 18/19, 1996, CET.

Astronomers use the Julian Date (JD) to specify the date and time of the measurement. The JD is the number of days which have elapsed since January 1, 4713 BC. You may wish to investigate the significance of this date! A new day using the Julian system begins at noon, Greenwich Mean Astronomical Time (GMAT) which very nearly corresponds to UT. Thus midnight (UT) on January 1, 1995, corresponds to JD 2449718.5. Noon (UT) on November 10, 1996, corresponds to Julian Date 2450398.0.What is the advantage of the JD system?

Graph 6. Plot the magnitude of Delta Cephei against time in JD. Such a graph is called a light curve. Be sure to plot smaller magnitudes at the top, since they represent greater brightness. This is easy when graphing by hand, but more difficult when graphing by computer. It is also important to choose appropriate vertical and horizontal scales.

Light Curve

AAVSO logo For more information on the Hands-On Astrophysics curriculum, please write to aavso@aavso.org or write to Dr. Janet A. Mattei, Director, AAVSO, 25 Birch Street, Cambridge, MA, 02138-1205.

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Return to: Astronomical Times, Observing Delta Cephei, or Learning to Observe Variable Stars.