Dr. Jason Lisle
[Originally published as the first section of Stellar Astronomy: Part 5 – Variable Stars]
How do stars change over time? Secular astronomers have proposed various scenarios for stellar evolution, including the now-discredited idea that stars evolve along the main sequence from blue to red and modern ideas of giants and supergiants being aged stars. Unfortunately, such long-term changes cannot be observed and therefore are beyond the scope of operational science.
Nonetheless, some stars change in ways that have been observed in history, and some types of changes are even observable in the present. In particular, stars can change in luminosity, appearing either brighter or fainter over time. These are called variable stars.
Eclipsing Binaries
The change in apparent magnitude1 of a star can be either intrinsic to the star itself or merely due to our perspective on Earth. In the latter category are eclipsing binary stars.
These are two stars that orbit their common center of mass and in which one star passes in front of the other (as seen from our solar system). Since the star in front is blocking some of the light from the background star, we see the combined light drop for a short while. The main dimming occurs when the fainter star passes in front of the brighter star. This is called the primary eclipse. Half an orbit later we perceive a less noticeable secondary eclipse when the fainter star passes behind the brighter one.
For us to perceive an eclipsing binary, the orbital plane of the two stars must be nearly edge-on relative to our solar system. For this reason, the two stars in an eclipsing binary are usually very close to each other. This allows a greater range of angles of tilt where one star can still eclipse the other as seen from Earth. The greater the distance between the two stars, the closer to exactly edge-on the system must be relative to us in order to see an eclipse.
Since most eclipsing binaries have a very tight orbit, their orbital period tends to be small, usually a matter of days. This also means that most eclipsing binaries cannot be visually distinguished in even our most powerful telescopes; they appear as a single point of light. Nonetheless, we can use spectroscopy to confirm that two stars are present and indeed orbit with a period matching their mutual eclipses.
One of the most well-known eclipsing binaries and the first to be discovered is Algol. Astronomers have known that it is variable since 1667 (and perhaps much earlier), but they did not initially know why. Algol drops in brightness by a noticeable 1.3 magnitudes every 2.86 days for a period of about ten hours.2 Its name is Arabic, meaning “head of the demon,” and it is nicknamed the “demon star.” Perhaps ancient people called it this because of its habit of “winking” every 2.86 days. Algol is easy to see with the unaided eye in the northern constellation Perseus.
The two eclipsing stars of Algol are class B8V (blue main sequence) and K0IV (red subgiant), respectively. This is perplexing from a secular perspective because the main sequence star is more massive than the red subgiant. But the maximum lifespan of a star on the main sequence is inversely related to its mass. In other words, the blue star should have left the main sequence before its less massive companion.
This problem is called the Algol paradox. The standard explanation is that the blue star was once less massive. However, when the other star entered the subgiant phase, it transferred some of its mass to the less massive star via accretion, converting it into a blue main sequence star. This explanation is plausible but is difficult to prove.
Pulsating Variables
Many other stars change their true brightness by pulsating — by changing their physical size. Recall that size and temperature determine the luminosity of a star. If a star swells in size, its surface area increases. Furthermore, its surface temperature changes as well (due to the ideal gas law). This results in a change in luminosity. Depending on the size of the radial pulsation, the change in brightness can be dramatic.
Cepheids
There are many varieties of pulsating variable stars. Depending on the mechanism, such pulsations can be regular or irregular. They can be rapid (on the order of a day) or long-term (years). Cepheids are one of the most well-known (and scientifically useful) regular variable stars. They are named after one of the first members to be discovered: Delta Cephei, a fourth-magnitude star in the constellation Cephus. Each Cepheid has its own highly regular pulsation period. Depending on the star, the period can be between 1.5 and 50 days. The North Star (Polaris) is a low-amplitude Cepheid with a period of about 4 days.
What makes Cepheids particularly useful scientifically is that there is a relationship between their pulsation period and their average luminosity. The brighter the Cepheid, the longer its pulsation period.3 This mathematical relationship was discovered in 1912 by Henrietta Leavitt.
It is easy to measure the pulsation period of a Cepheid by observing the star’s brightness over time. Once we know its period, we can compute its true luminosity. And by measuring its apparent brightness, we can compute its distance.
This is what makes Cepheids so useful in astronomy — they are “standard candles” (objects whose intrinsic brightness is known) that can serve as distance markers. And this method of measuring distance works far beyond those distances obtainable by the parallax method. Indeed, Cepheids are particularly luminous stars and can therefore be seen to great distances. A sufficiently large telescope can detect them even in other galaxies. This was how the distance to the Andromeda galaxy was first measured.
RR Lyrae
Likewise, RR Lyrae stars are pulsating variable stars, similar to Cepheids, but not as luminous and with a more rapid period which is between 7 and 14 hours.4 They are named after the first star of their type to be discovered, RR Lyrae, which is also the brightest (as seen in our sky).
Like Cepheids, RR Lyrae stars are useful as standard candles because all RR Lyrae stars are approximately the same (average) luminosity. Refinements in the estimated luminosity can be obtained by analyzing their light curves (the measure of brightness over time) in multiple wavelengths, although this is more complex than with Cepheids. These RR Lyrae stars are often found in globular star clusters and are therefore helpful in determining the distance to such clusters.
Why Pulsate?
Today, we have a pretty good understanding of why Cepheids and RR Lyrae stars (and other similar rapidly pulsating stars) pulsate as they do.
It is due to the ionization of helium. When helium is non-ionized, it has two electrons that can orbit only at certain distances/energy levels from the atomic nucleus. Thus, neutral helium can only absorb those specific frequencies of light that correspond to an energy difference between two electron levels (see my article on spectroscopy). Otherwise, neutral helium is essentially transparent, allowing the light to flow freely from the lower layers of the star to the surface and into space.
However, RR Lyrae and Cepheid stars are at the right size and temperature that helium is ionized below the surface. Since the electrons have been stripped away from the nucleus, they are free to absorb light of any energy, converting it into thermal energy which heats the ionized gas. In other words, ionized helium is opaque, which absorbs light, heating the gas.
The heated gas expands (due to the ideal gas law), causing the outer layers of the star to swell up. This increased volume causes the gas to cool, which results in the electrons rebinding to their nuclei, and the helium becomes neutral. This causes it to become transparent, and the light flows freely through the gas. The helium acts like a release valve. Without the extra pressure due to the energy of absorbing light, the outer layers of the star contract under the force of gravity. This contraction reheats the gas (again due to the ideal gas law), causing it to re-ionize. The gas again becomes opaque, which allows it to absorb light, heat, and thereby re-expand. And the process repeats. This method of pulsation is called the kappa mechanism because kappa is the Greek letter used by physicists to indicate opacity.
References
- Recall that apparent magnitude refers to the brightness of a star as it appears in our sky on Earth. The system is backward in the sense that brighter stars have a lower magnitude. The faintest stars visible to the unaided eye have an apparent magnitude of around 6, whereas the brightest stars are around 0 or even slightly negative.
- This is the primary eclipse. The secondary eclipse is not noticeable to the unaided eye but can be detected by instrumentation.
- We now know that there are two families of Cepheids: classical Cepheids and type II Cepheids. Each family obeys a period-luminosity relation, but the relation is different for the two families, with type II Cepheids being somewhat fainter. Several subcategories also exist.
- I have done photometric observations on RR Lyrae, measuring its brightness as a function of time. In a field like astronomy where most things look exactly the same night after night and century after century, it is amazing to see a star change its brightness on such a rapid timescale.
