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

Observing Delta Cephei

Up until the mid-1920s, astronomers debated about the nature of galaxies (or"spiral nebulae," as they were called back then): were these objects part of our own galaxy, the Milky Way, or were they independent of our galaxy and thus "island universes" in their own right? Astronomer Edwin Hubble proved that the "spiral nebulae" were galaxies similar to our own-yet located at distances almost too great for the human mind to comprehend. The keys to Hubble's discovery were Henrietta Leavitt's painstaking study of variable stars and Harlow Shapley's groundbreaking method for determining the distance to a variable star.

Variable stars ("variables" for short) are stars which vary or change in brightness. Over 30,000 variables are known and catalogued, and tens of thousands more are being discovered every year. Most stars (including the Sun, and the North Star) turn out to vary in brightness if measured precisely. Variables provide astronomers with unique and important information about the properties, processes and evolution of the stars.

Variables are numerous, and often unpredictable, so skilled amateur astronomers can make important contributions to astronomy by measuring variables in a systematic way. The American Association of Variable Star Observers (AAVSO, 25 Birch Street, Cambridge MA 02138-1205) is the largest organization of variable star observers worldwide. It coordinates variable star observing, mostly by amateur astronomers, and archives over 300,000 of their measurements each year. These measurements are much in demand by professional astronomers and educators.

Variable star measurement and analysis is also well suited to student activities and projects in high school and beyond. While simple, it is challenging--requiring the development and integration of a wide variety of science, math, and computer skills.

Picture of John Goodricke The following activity (Measuring Delta Cephei) illustrates many of the aspects of the study of variable stars. It requires little or no equipment. (Binoculars are helpful, though not essential.) It enables the student to experience the excitement of doing real science, with real data which they and their fellow students obtain from the real sky. It deals with one very famous variable: Delta Cephei. This star is the prototype Cepheid variable. Its variability was discovered by John Goodricke (1764-1786) of Yorkshire, England--a deaf mute who, before his untimely death at the age of 22, made many of the discoveries that established variable stars as an important topic for research.

Delta Cephei is a pulsating variable star: it expands and contracts rhythmically, heating and cooling due to an internal instability.

Image of Virgo Cluster and link to 
 http://bozo.lpl.arizona.edu/messier/more/virgo.jpg In autumn of 1994, two groups of astronomers reported that they had discovered Cepheid variable stars in a distant cluster of galaxies (the Virgo Cluster) and had used these stars to determine the size scale and age of the universe. One group of astronomers used the Hubble Space Telescope (HST), and their work received the most publicity. The other group actually reported their results first and used innovative techniques with the ground-based Canada-France-Hawaii telescope (CFHT).

The size scale and age of the universe. Astronomers observe that distant galaxies appear to be receding from us at a velocity (V) which is proportional to their distance (D). This is known as Hubble's Law. This effect is interpreted as being due to the expansion of the matter and space in the universe, following the Big Bang which occurred about 15 billion years ago. All parts of the universe are receding from all other parts. One effective analogy demonstration is to inflate a balloon with galaxy dots marked on it.

Hubble's Law can be written: V=HD, where H is a constant called the Hubble Constant. H can be determined by measuring both the distance and velocity of distant galaxies such as those in the Virgo Cluster. The velocity is measured from the spectrum of the galaxy using the Doppler effect. Thereafter, the distance of any distant object in the universe can be estimated by measuring its velocity and dividing by the Hubble Constant. How do Cepheid variable stars figure in all of this?

The period-luminosity relation for Cepheids. The period of a Cepheid (the time required for one complete cycle of variation) is correlated with the power output of the star. This is because

By measuring the period of a Cepheid variable, astronomers can infer the power output. By comparing this with the apparent brightness or magnitude of the star, they can determine the distance to the star by the inverse square law of brightness. This states that the apparent brightness (B) of a light source is proportional to its power output (P) and inversely proportional to the square of its distance (D): B ~ P/D2. This law is a consequence of the fact that light travels in straight lines. As the light moves further away from its source, it spreads over an increasingly large area. For the Cepheids in star clusters, the luminosity can be determined from the known distance and the measured (average) apparent brightness.

We therefore have a tool for measuring the size scale of the universe. If we discover a Cepheid, measure its period and its average apparent brightness, we can

From the distance of the Cepheid, and the velocity of the galaxy in which it is located, the Hubble Constant can be determined: H=V/D.

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Did you read the Astronomical Times' profile of John Goodricke?
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