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Time (days)

-10 12 Log period (days)

The period of the oscillations of such a variable star is directly measured, and this yields the luminosity from Fig. 6b, or its equivalent. Comparison to the measured mean flux then yields the distance.

Knowledge of the absolute mean luminosities of the cepheid variables is required if they are to be used as distance indicators. In other words, the luminosity must be calibrated. This was a difficult observational problem. Historically, the period-luminosity relation was first noted in 1912 by Henrietta Leavitt. She identified 25 cepheid variables in the Small Magellanic Cloud (SMC), a small satellite galaxy of the (MW) Galaxy, and noted that the brighter stars had longer periods. All stars in the SMC are presumed to be, more or less, at the distance of the SMC which was unknown at that time. (It is ~200 000 LY.) This allowed a curve such as Fig. 6b to be constructed but without an absolute calibration of the luminosity.

The luminosity calibration was accomplished through measurements of the nearer brighter cepheid variables in the Galaxy. This could not be done with trigonometric parallax studies because the cepheids were too distant. However, some cepheids lie in open clusters of known distance. Also the statistical methods described above were used. The RR Lyrae stars are also calibrated with such methods.

The relationships in Fig. 6b were well established by ~1939 for the classical cepheid variables. Prior to this, in 1923, Edwin Hubble identified several cepheid variables in the Andromeda nebula (M31). Their extreme faintness established for the first time the great distance of this nebula, now known to be ~2.5 MLY. This demonstrated its great size and luminosity and hence that it is another galaxy like our own. Previously, it was not clear whether such objects were smaller nebulae within the Galaxy or large nebulae outside it.

The cepheids are so luminous that, as noted, they can be identified in very distant open clusters that contain the rare high-mass stars in the Galaxy and in nearby galaxies. In turn this gives us the luminosities of these high-mass objects.

The physics that governs the oscillations of size and luminosity of cepheids is interesting; it is sketched briefly here. The degree of ionization of hydrogen and helium near the surface of the star controls the opacity to radiation and hence the rate of energy radiated into space from the star. The periodic variation of stellar radius (atmospheric height), density and temperature of the cepheid variables affects these ionization levels leading to periodic opacity changes. In cepheid variables, the periodic opacity releases or holds in energy at phases that cause the oscillations to be reinforced rather than damped.

It is not unlike a child on a swing who pumps energy into the swinging motion or takes energy out depending on the phase with which he leans back and forth. In a cepheid star, the gas elements of the stellar atmosphere serve as heat engines that do work on their surroundings. The work varies with the phase of the oscillation so as to sustain it. Many stars enter this state of instability during a late stage of their evolution.

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