The last major instability region in the HR diagram is the one in the upper right. It is occupied by a variety of interesting objects, known collectively as RED VARIABLES. These occupants include numerous small-range variables with periods of a few weeks, conspicuous large-range variables with periods of a few months and rare supergiant variables with periods of several years.

The large-range variables in this region are known as MIRA STARS after the prototype o Ceti. Their periods are 100 to 500 days and their ranges can be as much as ten magnitudes, partly because at minimum brightness they are coolest, and most of their radiation is shifted from the visible portion of the spectrum into the infrared. The light variations are so large that they can easily be measured visually, and much of what we know about these stars has been learned from visual observations by amateur astronomers. Figure 4.15 shows the light curve of Mira itself, determined from visual observations by members of the American Association of Variable Star Observers. The period is 332 days and the range is about 8 magnitudes, but Mira can be as bright as 2 magnitudes at maximum or as faint as 4. Such irregularity is even more pronounced in some other red variables. Mira, at 3000 K, is one of the coolest stars known, and it is several hundred times larger than the Sun. However, the mass of material in this enormous volume is little greater than the mass of the Sun, so the density of the outer layers of Mira must be extremely low. When pulsation waves travel through these layers, they produce shock waves (like a supersonic aircraft does) and a characteristic emission-line spectrum. Mira is classified as a cool giant star. Cool supergiant stars also vary in brightness, by as much as a magnitude on a timescale of several years, but the variation is quite irregular. If any periodicity is evident, the variable is called SEMI-REGULAR ; if no periodicity is evident, it is called IRREGULAR.

? Orionis (Betelgeuse) is a prominent example of an irregular variable. It is not easy to detect periodicities in semi-regular variables. To begin with, we need many years of observations, and we also need sophisticated methods of mathematical analysis. ?, Cephei is the best-studied, semi-regular variable; it has under lying periodicities of two and ten years. Incidentally, we have now met ? ? and ? Cephei is a ? Cephei is a ? Scuti variable and y, o and u are suspected of small-range variations. This indicates how abundant variable stars are among the bright stars of a typical constellation.

Luminous variables like Betelgeuse are massive young stars, but less luminous variables like Mira are older, with ages and masses similar to those of our Sun. Some red variables are found in globular star clusters, and must therefore be among the oldest stars known. In the HR diagram, they lie at the tip of the giant branch which, according to our theoretical evolutionary tracks, means that they have almost exhausted the hydrogen fuel in their core. Other than that, we understand very little about the nature and cause of the pulsation in these stars. That is because their energy is transported outward, from the core to the surface, by convection, and convection is a poorly-understood process in astrophysics.

Convection refers to the transport of energy by material motions. Usually these motions occur in CELLS, in which hot material rises in the centre, cools and falls at the periphery. On the surface of the Sun, these cells are visible and are called granules; they are a few hundred kilometres in size. On a star like Betelgeuse, they may be much larger: almost as large as the star itself. The distinguished astrophysicist Martin Schwarzschild has suggested that there may only be about a dozen cells on the surface of Betelgeuse, giving it a faceted appearance. Observations of Betelgeuse, using the technique of speckle interferometry, have shown a hint of such faceting.

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