Variable Stars Help (page 2)
Introduction to Variable Stars—Eclipsing Binaries
Some of the fluctuating “stars” are actually binary systems (pairs of stars in mutual orbit) that eclipse each other. If one of the stars is large and dim and the other is smaller and brighter, and if the orbital plane of the stars appears edge-on to us, we will see a decrease in the brilliance of the system when the dimmer star passes in front of the brighter one. These eclipsing binaries are characterized by steady brilliance with periodic sharp dips. The dips always have the same depth; that is, the minimum brilliance is always the same. The dips occur at regular intervals.
Eclipsing binaries can be recognized in another way. The absorption-line spectra of the two stars alternately shift slightly toward the red and blue ends of the spectrum as one star recedes from us and the other approaches. When an object moves away from us, the spectral lines are red-shifted (they move toward longer wavelengths); when an object approaches, the spectral lines are blue-shifted (they move toward shorter wavelengths). This is a result of the well-known Doppler effect , the same phenomenon that makes a car horn sound higher in pitch as the car comes at you and lower in pitch as it passes and then moves away from you. Dual red-blue back-and-forth spectral shifting is a dead giveaway that a variable “star” is an eclipsing binary.
Certain variable stars, known as Cepheid variables or Cepheids , are intriguing because of the clockwork regularity of their changes in brilliance. These stars get their name from the fact that one of the first-discovered and most well-known of them is in the constellation Cepheus .
Individual Cepheids change brightness at a consistent rate. However, two different Cepheids can have different periods (lengths of time from one peak of brilliance to the next). Some Cepheids have periods of less than 1 Earth day; others have periods of several weeks. Some Cepheids vary greatly in brightness, whereas others vary only a little. Polaris, the familiar North Star that has been used by navigators for centuries, is a Cepheid variable. Its brilliance does not fluctuate enough to be noticeable to the casual observer.
After tirelessly searching for coincidences and patterns, astronomers discovered that the periods of Cepheids are correlated with their absolute visual magnitudes. This correlation is so precise that these stars can be used as distance-measuring beacons for determining distances in interstellar and intergalactic space. The longer the period, the brighter the star, averaged over time. Cepheids are massive stars that, when plotted on an H-R diagram, fall in the upper middle region, off the main sequence. These are called yellow supergiants . Not all yellow supergiants are Cepheids, but all Cepheids seem to be yellow supergiants.
RR Lyrae Variables
There are other types of variables besides eclipsing binaries and Cepheids. RR Lyrae variables are bluish stars and are on average, about 40 times as bright as the Sun. The term comes from the location, in the constellation Lyra, of one of the best-known stars of this kind.
RR Lyrae variables have regular, constant cycles of pulsation, usually with periods of about half an Earth day. They tend to be found in large clusters of stars and in the halo of stars surrounding the Milky Way. Because of their locations, they are always far away and require a telescope to be observed. They, like Cepheids, can be used as distance-measuring beacons.
Both the Cepheid and RR Lyrae variable stars physically expand and shrink in size as their brightness changes. Another sort of variable, called a Mira variable , oscillates without any apparent change in size. Mira variable stars are named after a certain red giant, Mira , in the constellation Cetus. Mira’s brightness varies with a period of about a year and fluctuates between the eighth and the third visual magnitudes. Thus, at its peak, it is about 100 times as bright as it is at the minimum in its cycle. Because of their long periods, Mira stars are sometimes called long-period variables (LPVs).
Astronomers think that Mira variable stars do not expand and contract in radius, as do the Cepheid or the RR Lyrae variables. The increase in brilliance occurs faster than the decline. While Mira, the first variable of this type to be discovered (in 1596), varies by 5 visual magnitudes, some Mira variables have brightness ranges of only 2 or 3 magnitudes, whereas others can change by up to 10 magnitudes. Mira variables are believed to be old stars that have depleted much of their hydrogen and are fusing helium atoms. These stars contain heavier elements as well; most of them are rich in elemental carbon, and some contain large amounts of elemental oxygen.
Practice problems of this concept can be found at: Stars and Nebulae Practice Problems
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