Cepheids and the Standard Candle Technique


By Emily Levesque, University of Washington

Why would a star seem to get brighter and dimmer over time? Why would this happen so regularly? And why should this be connected to the star’s luminosity? We know today that Cepheids appear to vary because they are pulsating, growing and shrinking radially, and appearing to get brighter and dimmer as a result.

An image of a Cepheid called Delta Cephei (left), and a diagram shows how Delta Cephei's bow shock was formed (right)
The standard candle technique is used to determine and study very distant objects. (Image: NASA/Public domain)

The Standard Candle Technique

The standard candle technique is particularly valuable when studying very distant objects. Eventually, the effects of parallax stop working because things get too far away (if you try the left-eye, right-eye trick with a distant building or tree on the horizon, odds are you won’t see it move at all). However, since a standard candle depends on the inverse square law, it can reach much further as a result. 

As long as we have instruments that can detect a standard candle and measure its brightness, it can be used to measure a distance. For bright stars like Cepheids, the Leavitt law meant that if we could measure a Cepheid’s variation period, we could infer its true luminosity. We could then compare that to its apparent brightness and use the inverse square law to calculate how far away it was, giving us unprecedented reach when it came to measuring the distances of stars.

The Similarities between Cepheids and Two-stroke Combustion Engines

The Cepheids that Henrietta Leavitt discovered were born with four to twenty times as much mass as our own Sun. Temperature-wise, they’re surprisingly similar to our own Sun, around 5,000 to 8,000 Kelvin (8,500 to 14,000° Fahrenheit) at their surfaces; Annie Jump Cannon would have classified them as F, G, or K type stars, and our own Sun as a type G2. These temperatures give rise to the specific conditions that make these stars pulsate. 

An illustration of a two-stroke combustion engine
How a Cepheid works is very similar to how a two-stroke combustion engine works. (Image: Snehalata/Shutterstock)

The physics of a Cepheid’s pulsation is similar to the physics involved in two-stroke combustion engines. Combustion engines generate power by the motions of pistons set in cylinders. For an engine to work properly, it needs to inject heat into the cylinder at exactly the right moment, when the fuel above the piston is compressed. In a gasoline engine, this is accomplished by producing a spark during compression. 

This spark ignites the fuel, which expands and pushes the piston downward, turning the crankshaft. In a two-stroke engine, as exhaust gases escape through an outlet pipe, fuel enters the cylinder, and the piston rises, ready to begin another cycle of compression.

The key here is producing the spark at the moment of maximum compression of fuel, creating the explosion that will drive the piston downward to power the crankshaft.

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How Cepheid Variables Pulsate

The same basic principle applies in the outer layers of a Cepheid variable. As the outer layers of the star shrink and become compressed, the density of the gas increases. At the temperatures of a Cepheid variable, more atoms in the gas will become ionized, ejecting electrons and making the gas more opaque to the radiation trying to pass through it. 

An illustration of a Cepheid pulsation
A Cepheid variable pulsates because of some interactions that happen in its outer layer. (Image: Urutseg/Public domain)

Unable to pass properly through the gas, the radiation is trapped and the energy of the layer rises. This increases the energy at a moment of maximum compression, just like in our internal combustion two-stroke engine. The trapped energy then drives the star’s outer layers to expand again. 

When the gas expands, the density decreases, and atoms in the gas recombine, reuniting with their electrons and decreasing the opacity of the gas. With radiation now able to pass through the gas, the formerly trapped energy escapes, releasing excess heat so that the layers can settle and begin a new compression phase.

If the Outer Layer of a Cepheid Is Too Cold or Hot

If the outer layers of the star are too cold, this mechanism won’t work. The layer where gas is ionized will be too low and won’t be able to lift the layers above it. This mechanism also won’t work when the star is too hot; there, the layer where gas is ionized is too close to the surface of the star, and there won’t be enough gas above it to produce an apparent pulsation. 

As a result, this type of pulsating behavior is restricted to that 5,000 to 8,000 Kelvin temperature range, typical of Cepheids. If we look at Cepheids, and other types of stars that pulsate like this, on the Hertzsprung-Russell diagram, plotting surface temperature against luminosity, it’s clear that they fall along what we call the instability strip. 

Henrietta Leavitt’s discovery revealed that more luminous Cepheids, outputting more energy at their surfaces, take longer to complete a pulsation cycle.

Today, Cepheids are just one of several standard candles that astronomers use. All standard candles share a common thread of making remarkable distance estimates possible and changing what we know about the very structure of our universe. Henrietta Leavitt’s discovery of the period-luminosity relation for Cepheids was no exception.

Common Questions about Cepheids and the Standard Candle Technique

Q: How does the standard candle work for measuring the distances of the stars?

The standard candle technique is used to study very distant objects because it depends on the inverse square law. For example, by measuring the period of variation of a Cepheid, its true luminosity can be deduced. Then the true luminosity can be compared to the apparent brightness, and the distance of the star can be measured using the inverse square law.

Q: How does a Cepheid variable work?

The density of the gas increases when the outer layers of the Cepheid are compressed. Atoms in this gas ionize and release electrons. Therefore, radiation isn’t able to pass through the gas, and the energy of the layer increases. This trapped energy causes the outer layers to expand. At this point, the density of the gas decreases again and the atoms reunite. The energy that was previously trapped can now pass through the gas and release excess heat. The layers are then precipitated again and a new compression phase begins.

Q: What happens when the outer layers of Cepheids are too cold or too hot?

When the outer layers of a Cepheid are too cold, the layer in which the gas must be ionized will be too small to lift the top layers. On the other hand, if the outer layers of the star are very cold, the process of pulsating doesn’t take place as well. This is because in this case the layer in which the gas must be ionized is very close to the surface and, therefore, can’t create an apparent pulse.

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