Beverly Smith
Department of Physics and Astronomy,
East Tennessee State University.

Our Sun is a relatively stable star, and does not vary much in brightness. Many of the other stars in the sky are not constant, but vary dramatically in brightness with time, sometimes by a factor of 1000 or more in brightness.

An Hertzsprung-Russell (H-R) Diagram, a plot of the surface temperature of a star vs. its luminosity (total energy emitted per second). The diagonal strip down the middle of this chart is the main sequence. In the core of main sequence stars, hydrogen fusion is occuring, producing helium. Our Sun is currently a main sequence star, in the middle of the range of temperature and luminosity.

After the hydrogen in the core of our Sun runs out, in about 5 billion years or so, the outer layers of the Sun will expand and cool off, and the Sun will become a luminous red giant star.

At the same time the outer layers of the star are expanding, the core of the star is shrinking and getting hotter. Eventually it gets hot enough for a new nuclear region to occur: helium fusion. This new source of energy stabilizes the star, and the outer layers contract back in and heat up, and the star moves back to the left on the H-R diagram, to hotter temperatures. But the helium doesn't last forever. When it runs out, the star will again expand even larger, and get even more luminous. The star moves up to the right on the H-R diagram. This section of the H-R diagram is called the Asymptotic Giant Branch (AGB). AGB stars are often pulsating, changing their sizes rapidly with time.
 
 

A Hubble Space Telescope image of the IC 418 planetary nebula (the Spirograph Nebula). Eventually AGB stars will completely blow off their outer layers and become planetary nebula, like the one shown here. Planetary nebula are simply shells of ejected gas clouds surrounding the hot inert cores of dead stars.

Perhaps the best-known type of AGB stars are the Mira variables, named after the star Mira in the constellation of Cetus. This is a plot of the visual brightness of Mira as a function of time for a five year period. This plot came from data from the American Association of Variable Star Observers (AAVSO). A Mira variable is a star whose brightness varies by at least a factor of 10 (i.e., a magnitude change of at least 2.5), with a period of between 100 and 1000 days. As can be seen in this plot, Mira variables are not perfectly regular; their periods can vary a bit with time, as can their maximum and minimum brightnesses.

Mira variables are often surrounded by shells of dust. This dust is produced in the cool outer layers and blown outwards by radiation pressure from the star. This dust can be observed directly at infrared wavelengths.

To investigate how this dusty circumstellar shell varies with changes in the photosphere of the star, it is important to observe variations in the infrared brightnesses of the star, and compare with changes in visible light. To this end, we extracted infrared light curves for a sample of 38 Mira variable stars from the archives of the Diffuse Infrared Background Experiment (DIRBE) instrument on the Cosmic Background Explorer (COBE) satellite.

The Cosmic Background Explorer (COBE) satellite.
This NASA infrared satellite was designed to study the Cosmic Background Radiation. It also detected many AGB stars, since these stars are extremely bright at infrared wavelengths.

COBE light curves for the mira variable R Hor at two infrared wavelengths, 1.25 microns (near-infrared) and 4.9 microns (mid-infrared), compared to that in the visual. Note that the amplitude of variation is less at 1.25 microns than in the visual, and even less at 4.9 microns. In general, we found that, for Mira variables, as the wavelength increases, the amplitude of variation decreases. This is consistent with theoretical models of circumstellar shells around Mira variables.

Also note that the peak brightness in the infrared occurs later than that in the visual. Also note that the peak in the mid-infrared (at JD = 2447959) occurs slightly before than (JD = 2447987), but still after that in the visible (JD = 2447934). Similar lags were also found in a few other stars in the sample. The near-infrared-to-visible lag can be explained by variations in the strength of various molecular absorption features in the atmosphere of the star, because different molecules form at different depths in the atmosphere. At present, the time offset between the mid-infrared and near-infrared maxima is unexplained.

COBE 1.25 microns and 4.9 micron light curves for R Car, compared to those in the visual. Note again the decreasing amplitudes with increasing wavelength. Also note the inflection points in the rising portion of all three light curves. The simultaneous observations of secondary maxima at infrared and optical wavelengths supports the hypothesis that these features are caused by shock waves in the stellar atmosphere, rather than newly formed dust layers in the shell, an alternative hypothesis.

For more information and more light curves, see Smith et al. 2002, Astronomical Journal, volume 123, 1411.