Delta Cephei is the prototype Cepheid variable, a class of giant stars that pulsate with periods proportional to their luminosity. This relationship is exploited by astronomers to determine the brightness — and thus distance — of Cepheids in other galaxies.

Delta's magnitude ranges from 3.5 to 4.4 in a cycle of 5.37 days. The fade from maximum to minimum is slower than the rise back to maximum, which takes less than two days.

Zeta Geminorum, Eta Aquilae, and Others

Zeta Geminorum is another Cepheid variable. But its light curve is more symmetrical than the preceding two, with the declining and rising phases each taking half of the 10.15-day cycle. The magnitude range is 3.6 to 4.2. According to my light curves, all three Cepheids reached maximum light at the times predicted by the GCVS. Many Cepheids do have slightly variable periods, but the deviations from prediction are usually smaller than those often seen in eclipsing binaries.

Among the naked-eye variables are several red giant or supergiant stars that change irregularly or semiregularly, with transient or multiple periodicities. Mu Cephei (magnitude 3.4-5.1, periods 2 and 12 years) and Alpha Herculis (2.7-4.0 with rough cycles of about 100 days and 6 years) show noticeable variations if you observe them patiently for long enough.

Eta Geminorum is a binary star whose bright component is a semiregular red giant. Most of the time it varies only slightly from magnitude 3.2. But every 8.2 years the bright component is eclipsed by its companion star, causing the system's total light to drop to about 4.0. The next of these eclipses is expected in October 2012.

Eta Aquilae, a Cepheid of summer and fall, closely resembles Delta Cephei in its magnitude range, 3.5 to 4.4, and the general shape of its light curve. But its period is 7.18 days. About halfway down the decline there is a temporary reversal, visible as a small hump in my light curve.

Mira, Gamma Cassiopeiae, and Betelgeuse

When it comes to pulsating giants we can hardly pass up Mira, Omicron Ceti. With a declination of -3° it doesn't quite meet our criterion of being in the north celestial hemisphere, but this seems like splitting hairs. Mira had an unusually brilliant maximum in the winter of 1996-97. At a typical peak of its cycle Mira reaches magnitude 3.4, but in early February 1997 it topped out at about 2.5 and stayed there for the rest of the month.

Mira is the brightest of the red long-period variables, and (again barring novae and supernovae) it presents the most radical changes that can be seen with the naked eye beyond the solar system. Mira's period of 332 days means its maxima come one month earlier each succeeding year. In 2009, maximum brightness occurred in late November; in 2010 maximum is predicted for late October. But the date, like the peak brightness, is never exactly predictable.

The unstable hot star Gamma Cassiopeiae is generally low in the north. Previously magnitude 2.25, it rose to 1.6 for many months in 1937 when it ejected a shell of gas. The familiar W pattern of Cassiopeia looked noticeably different. After fading to 3rd magnitude in 1940, Gamma slowly brightened to 2.2 by 1966. Since then it has shown little visible change, but there is no telling when it might again act up.

AAVSO: The Variable-Star Experts

The American Association of Variable Star Observers (AAVSO) keeps track of all these stars, but isolated estimates of Algol and Lambda Tauri made at random times are of little value. For these eclipsing stars, the AAVSO prefers to receive series of estimates made during the course of an eclipse, from which the time of minimum can be determined. In the case of Lambda Tauri with its long eclipses, this means observing the fade into an eclipse on one occasion and the rise from another eclipse on a different night. Several nights' observations can be combined into a single graph if the star's period is well known. For more information, charts, and observing techniques, contact the AAVSO at 49 Bay State Road St., Cambridge, MA 02138 USA

Most bright naked-eye variables have small magnitude ranges, so care is needed in making estimates. Above all, avoid using comparison stars whose heights above the horizon differ greatly from that of the variable, as they will then be seen through different thicknesses of atmosphere. If circumstances force you to use such stars, apply atmospheric extinction corrections to each one.

These corrections are especially important with Betelgeuse, Alpha Orionis, the brightest noticeably variable star of all. It fades and brightens slowly and semiregularly with a suggested underlying period of about 6 years.

How many skywatchers know that Betelgeuse can grow nearly as bright as Rigel or as faint as Aldebaran? Its visual magnitude has ranged from about magnitude +0.3 (in late winter 1988 and early winter 1990-1991) to as faint as +0.9 (in late winter of 1989 and 1993 and early spring of 1995).