Variable Stars and Zeta Geminorum

Spring 2005

Astronomy 110L

Thurs. 7:00 - 10:00 pm

WHAT CAUSES VARIABILITY in STARS?

Over the course of one human lifetime, the vast majority of stars appear to be constant in both location (relative to other stars) and brightness. A few special stars, however, have been known even since ancient times to vary in their brightness, either periodically or sporadically. These stars, collectively termed variable stars, number well over 30,000 in our part of the Milky Way alone, and as stellar observations become increasingly sensitive, the number of known variable stars in both our own Galaxy and other nearby galaxies continues to grow.

Variable stars are classified according to the physical mechanism believed to produce their observed variation in brightness. It is believed that virtually all stars will exhibit some level of variability as their internal structure changes in their old age; these are called intrinsic variables, and it is to this class that Zeta (z) Geminorum belongs. Other stars appear to brighten and dim because their light is physically occulted by an orbiting companion; this second-most common class of periodic variables is eclipsing variables. Finally, a host of less common phenomena can also cause a star’s brightness to vary, either periodically or sporadically; these include rotating variables, eruptive variables, and cataclysmic variables.

HOW INTRINSIC VARIABLES WORK

Most young and middle-aged stars, like our own Sun, are in a state of equilibrium: gravity tries to make the star smaller, but the heat released by nuclear reactions at its center tries to make the star expand. These two forces balance at some equilibrium size (radius), and that is the constant radius that we see for a non-variable star. As stars reach old age, however, their nuclear reactions slow down, and this initiates changes in the star’s internal structure. Initially, the star’s radius R decreases in response to the cooling center. Then…

as R decreases, the surface area SA of the star also decreases;
as SA decreases, the luminosity L (total energy given off by the surface of the star) decrases;
as L decreases, the star’s energy loss rate slows, and heat is allowed to build up inside the star: its internal temperature T increases;
as T increases, the gas (of which the star is made) expands, and R increases.

Now, the reverse steps occur:

As R increases, SA increases;
As SA increases, L increases;
As L increases, the star’s energy loss rate increases, and T decreases;
as T increases, the gas contracts, and R decreases.

…and the cycle begins again! As R varies, L varies, and it is luminosity L that we see as “brightness” with our eyes and telescopes. R swings widely around some average equilibrium value, but on each pulsation the star first overshoots, then overcorrects the other way. This can continue with amazing regularity for thousands of years, although most variables eventually show gradual changes in their period (the time it takes for one cycle) and average brightness. The period can be anywhere from hundreds of days down to a few hours — the latter is especially amazing, considering that a star’s typical radius is roughly a million miles, and it can more than double during one pulsation!

Here are some web sites with pulsation animation and other variable star information: http://faculty.rmwc.edu/tmichalik/pulsvar.htm
http://ftp.nofs.navy.mil/projects/npoi/science/cepheids.htm (fundamental vs 1st overtone still picture; Polaris)
http://www.astronomynotes.com/ismnotes/s5.htm (great graphs)

CEPHEID VARIABLES and the PERIOD-LUMINOSITY RELATIONSHIP

In the early 20^th century, a great debate raged within astronomy about whether the spiral Andromeda “Nebula” and others like it were objects close to or within our own Galaxy, or that they were very distant and comprised “island universes” unto themselves. The first view was put forward by the accomplished American astronomer Harlow Shapley in 1918 and had many supporters, while those who disagreed were led primarily by Heber D. Curtis. In 1920, the now-famous Shapley–Curtis debate was held before the National Academy of Sciences in Washington, D.C., but the existing observational evidence at the time seemed not to decisively favor either side. That uncertainty lingered until Edwin Hubble’s 1923 discovery of a Cepheid variable in the Andromeda galaxy, a remarkable achievement unto itself, considering how difficult it still is today to observe individual stars in other galaxies! Using Henrietta Leavitt’s 1908 period–luminosity relationship, Hubble was able to assign it a distance of 2,000,000 ly. This lay well beyond the 100,000-ly outer limits of our own Galaxy, and (correctly) settled the debate. To this day, measurement of Cepheid variables remains our most precise and reliable method of deducing distances to nearby galaxies.

PROCEDURE for ZETA GEM EXPERIMENT

Using the finder chart supplied, locate zeta Gem at the center (between gamma and delta Gem). Also locate the other stars in Gemini whose magnitudes are given: lambda at magnitude 3.56, iota at 3.75, upsilon at 4.03, nu at 4.12, rho at 4.15 and tau at 4.40. Zeta Gem varies in a range that is spanned by these stars. For each observation, compare Zeta to the other stars. It may be identical to one of the others, or it may fall between two of them in brightness. You should be able to estimate its brightness to about 0.1 magnitude. This observation is probably easiest naked-eye, that is without optical aids. But you may want to try it with binoculars too, in case that works better for you. You can work out your own best technique, but try something like this: Is zeta brighter than tau? It ought to be, it's not expected to get that faint. Then, is zeta brighter than upsilon? Keep making comparisons until you find a pair of reference stars, one of which is brighter than zeta and the other fainter. Then you can estimate zeta's magnitude---is it closer to one of the references than the other? You'll have to check back repeatedly until you're pretty confident of your measurement. It takes about ten minutes, and your eyes need to be dark-adapted. Record the date and time, and the observed brightness. It will work best to just write the data in your log, then do the plot at the end of the project. That way you don't have to keep track of the plot in the field or try to figure out the scale in the dark. Repeat the observation over a period of six weeks, every day that you can. Get at least twelve measurements, and as many as possible. It will be easier for the first two and the last two weeks of the period, since the moon won't be a problem.

Plot the magnitudes for each day on the chart provided, trying to be accurate about the time of day for each measurement. Note that smaller magnitudes are at the top of the vertical axis, since they represent higher brightness. You should see the entire cycle of variation on your plot. Estimate the period (time from one maximum to the next maximum) of the star.

Draw a smooth curve through the data points. If there are several days in a row with no date, leave out that section of the curve. Estimate, from the scatter of the data, the accuracy of an individual measurement.

Copy or trace the plot onto a transparency and place it over the original. Shift the overlay sideways until the curves match. The amount of shift required is equal to the period of the oscillation.

Write a short report, including your plot and a description of the observations. Estimate the uncertainty for a single measurement, and also the uncertainty for the smooth curve you drew. State the oscillation period you derived, and estimate the uncertainty in this number. Suggest some ways that the measurement of the period could be improved.

Donald L. Mickey (mickey@ifa.hawaii.edu)

Last modified: March 3, 2005
http://www.ifa.hawaii.edu/users/mickey/ASTR110L_S05/zetagem.html