Skip to main content
Physics LibreTexts

13.20 Variable Stars

Astropedia Image
David Fabricius. Click here for original source URL

 

Astropedia Image
John Goodricke. Click here for original source URL

 

In 1595, the amateur astronomer and Lutheran pastor David Fabricius noticed that a bright star in the constellation Cetus (the Sea Monster) was fading. Within two months it had vanished from the sky. Fabricus was amazed as the star recovered its former brilliance several months later. The star, called Mira (meaning wonderful), was found to vary in brightness with a period of 11 months. This was the first discovery of a variable star. Nearly two centuries later, the 17-year-old English astronomer, John Goodricke, discovered brightness variations in the star called Algol. While still a teenager, Goodricke found that Delta Cephei varies with a regular period of 5 days and 8 hours. The Royal Society of London awarded him a medal for his work. Goodricke overcame considerable odds in his short but brilliant career. He was born deaf and unable to speak, in an age when most deaf-mutes"" were hidden away in mental asylums. Tragically,he caught pneumonia while observing Delta Cephei and died at the age of 21.

Both Fabricus and Goodricke had observed variable stars; stars that vary in brightness on a time scale of hours to years. Variations can come from a number of different things. Some stars, Algol included, are in binary systems, where the dance of one star in front of and then behind the other causes us to see varying amounts of light. In other cases, such as Mira, the star is intrinsically variable. For a whole variety of reasons, stars can become unstable and pulsate or give off observable flares. Variable stars are found in all stages of stellar evolution, but most lie in two areas of the HR-diagram: a narrow band called the instability strip that includes pulsating white dwarfs, RR Lyraes, and Cepheid variables. Additionally, old red giant stars tend to become unstable and pulsate in semi-regular ways.

Why do some stars vary? We have seen that main sequence stars like the Sun are stable and do not vary except with a few, very low amplitude exceptions. Main sequence stars are in a state of hydrostatic equilibrium — pressure and gravity are in balance at every point, and the energy smoothly flows out through the balanced system. You can think of stable stars as having a thermostat. If you compressed a main sequence star, the density and pressure would rise, resulting in an increased nuclear reaction rate that would counter the compression. As long as energy flows smoothly and easily out of the star, this equilibrium is maintained.

Giant stars that evolve into the instability strip become unbalanced because they have atmospheres that trap a portion of the energy radiated by the core. When energy "dams up" in this way, the outer layers heat up and expand. The expansion cools the gas, which drops the pressure and allows gravity to pull the outer layers in again. The newly compressed gas once again dams up energy, which starts the cycle over again. Pulsation is not caused by any variation in the rate that energy is generated in the core of a star; it is caused by a variation in the rate that energy can escape from the star. Now think about a boiling pan of water with a lid on it. The lid traps steam and raises the pressure under it. At some point the lid will tip and release the steam. The pressure then builds up and the cycle continues. Meanwhile, the energy flowing into the water from the stove has not varied.

What determines the pulsation period of a star? Just like a bell (or any other object), each star has a frequency or time period in which it tends to vibrate in response to a disturbance. Just as a pitch of a bell varies with size, the period of a variable star varies with the size and density of the star. John Goodricke discovered the Cepheid variable class. Cepheids have regular variations in brightness with periods from one to 50 days. (Polaris is in fact a Cepheid variable. Shakespeare was taking artistic license when he declared a love to be "as constant as the Pole star.") RR Lyrae stars vary with periods in the range of an hour to over a day. Outside of the instability strip, it's not always clear what causes the variations. The exact pulsation mechanism behind stars like Mira, for instance, still aren't understood.

Cepheid and RR Lyrae variables are important for two reasons. First, because their variations are regular, they are somewhat better understood than stars whose brightness changes are unpredictable (called irregular variables). Second, and more important, the period of variation of each Cepheid directly correlates with its average luminosity. This relation was discovered in 1912 by one of the most famous women astronomers, Henrietta S. Leavitt, who measured hundreds of images of Cepheid variables in the first years of this century at Harvard Observatory. Both Cepheid and RR Lyrae variables were eventually found to have distinct period-luminosity relationships. These relationships allow astronomers to determine the luminosity of any Cepheid at any distance simply by measuring its period. This, in turn, leads to a new way to measure the distances of stars: find a Cepheid or RR Lyrae, measure its period and hence its luminosity, then measure its apparent brightness and derive its distance by the inverse square law.

Astropedia Image
Hertzsprung-Russell diagram. Click here for original source URL.

", he caught pneumonia while observing Delta Cephei and died at the age of 21.

 

Both Fabricus and Goodricke had observed variable stars; stars that vary in brightness on a time scale of hours to years. Variations can come from a number of different things. Some stars, Algol included, are in binary systems, where the dance of one star in front of and then behind the other causes us to see varying amounts of light. In other cases, such as Mira, the star is intrinsically variable. For a whole variety of reasons, stars can become unstable and pulsate or give off observable flares. Variable stars are found in all stages of stellar evolution, but most lie in two areas of the HR-diagram: a narrow band called the instability strip that includes pulsating white dwarfs, RR Lyraes, and Cepheid variables. Additionally, old red giant stars tend to become unstable and pulsate in semi-regular ways.

Why do some stars vary? We have seen that main sequence stars like the Sun are stable and do not vary except with a few, very low amplitude exceptions. Main sequence stars are in a state of hydrostatic equilibrium — pressure and gravity are in balance at every point, and the energy smoothly flows out through the balanced system. You can think of stable stars as having a thermostat. If you compressed a main sequence star, the density and pressure would rise, resulting in an increased nuclear reaction rate that would counter the compression. As long as energy flows smoothly and easily out of the star," this equilibrium is maintained.

Astropedia Image
Polaris, the North Star, and its companion as seen by the Hubble Space Telescope. Click here for original source URL.

Giant stars that evolve into the instability strip become unbalanced because they have atmospheres that trap a portion of the energy radiated by the core. When energy ""dams up"" in this way", the outer layers heat up and expand. The expansion cools the gas, which drops the pressure and allows gravity to pull the outer layers in again. The newly compressed gas once again dams up energy, which starts the cycle over again. Pulsation is not caused by any variation in the rate that energy is generated in the core of a star; it is caused by a variation in the rate that energy can escape from the star. Now think about a boiling pan of water with a lid on it. The lid traps steam and raises the pressure under it. At some point the lid will tip and release the steam. The pressure then builds up and the cycle continues. Meanwhile, the energy flowing into the water from the stove has not varied.

What determines the pulsation period of a star? Just like a bell (or any other object), each star has a frequency or time period in which it tends to vibrate in response to a disturbance. Just as a pitch of a bell varies with size," the period of a variable star varies with the size and density of the star. John Goodricke discovered the Cepheid variable class. Cepheids have regular variations in brightness with periods from one to 50 days. (Polaris is in fact a Cepheid variable. Shakespeare was taking artistic license when he declared a love to be ""as constant as the Pole star."") RR Lyrae stars vary with periods in the range of an hour to over a day.

Outside of the instability strip", it's not always clear what causes the variations. The exact pulsation mechanism behind stars like Mira, for instance, still aren't understood.

Cepheid and RR Lyrae variables are important for two reasons. First, because their variations are regular, they are somewhat better understood than stars whose brightness changes are unpredictable (called irregular variables). Second, and more important, the period of variation of each Cepheid directly correlates with its average luminosity. This relation was discovered in 1912 by one of the most famous women astronomers, Henrietta S. Leavitt, who measured hundreds of images of Cepheid variables in the first years of this century at Harvard Observatory. Both Cepheid and RR Lyrae variables were eventually found to have distinct period-luminosity relationships. These relationships allow astronomers to determine the luminosity of any Cepheid at any distance simply by measuring its period. This, in turn, leads to a new way to measure the distances of stars: find a Cepheid or RR Lyrae, measure its period and hence its luminosity," then measure its apparent brightness and derive its distance by the inverse square law.