Cepheid Variables in the Universe

Cepheid variable stars are very much like our own star, the sun, except these stars are 500-30,000 times as luminous as our own. Currently, there are around 1,400 known Cepheid variable stars, with 400 of these residing in our Milky Way galaxy and the remainder found in our two neighbor galaxies, the large and small Magellanic Clouds. Having regular pulsations of their radii, these stars change in brightness with a period of one to one hundred days. In this general group called Cepheid stars there exists two distinct types called Type 1 and Type 2. It was discovered by Henrietta Leavitt that this special variety of stars has a specific relationship between their luminosities and periods. Using this discovery, Harlow Shapley used Cepheid variable stars to find our place in the galaxy, and further diminished our solar system’s place in the universe. One extremely important law also was produced via this discovery when Edwin Hubble used what we know about Cepheids when he discovered what we now call Hubble’s Law. To this day astronomers are still using Cepheid variable stars to unlock the mysteries of the universe.

To understand what Cepheids are, the Hertzsprung-Russell diagram is a useful tool. The Hertzsprung-Russell diagram is a plot of stars’ luminosity versus surface temperature. Along with surface temperature, a specific letter can be given for each class of stars based on their temperature, called spectral class. This plot is very useful in visualizing the lives of stars. Plotted diagonally across the diagram is the main sequence where stars live most of their lives’ fusing hydrogen into helium. Stars that have main sequence masses of one to two times our sun’s mass with spectral classes of A, F, G and early K will evolve in a particular way. Once these stars are finished fusing hydrogen in their cores they will start to evolve into what is called the instability strip region of the Hertzsprung-Russell diagram. This region is where pulsating variable stars of the RR Lyrae, Delta Scuti, W Virginis, and Cepheid variable stars live. As evolve through the instability strip they begin to pulsate seemingly randomly and maybe quit pulsating from time to time. Because of the location of the instability strip, the types of stars that Cepheid variables can be is limited, and therefore easier to search for. These stars exert interesting qualities as they travel through the strip.

The location of the instability strip on the H-R diagram allows for an easy prediction of the evolutionary tracks of Cepheid variable stars for both before and after instability. It has been found out that Cepheids have a mass range of five to twenty-five solar masses after the main sequence stage of their live cycles’. This means that Cepheids are either giant or supergriant stars. Once these stars finish fusing hydrogen into helium in their cores they follow the Kelvin-Helmholtz time scale and cross through the instability strip for the first time. Importantly, Cepheids can and do cross the strip multiple times during their lifetime. This crossing causes Doppler Shift effects called red and blue loop excursions. Red excursions represent a fast crossing of the instability strip and are associated with red shifts in the Doppler Effect. Since these are fast and therefore short lived, not many stars are observed towards the red edge of the instability strip. Blue loop excursions are just the opposite. They are slower movements and are associated with blue shift. Since blue loop excursions are slower, it is thought that Cepheid variable stars are thought observable here near the blue edge of the instability. In fact, this is indeed where they are mostly observed. Even though we have been observing these stars for a long time, it was not long ago that it was first discovered how useful these stars can be.    

Back in the late 1800’s, Harvard University wanted to find out the position, color, and brightness of every star in the night sky. In the days before electronic computers there was a human computer. One of these computers, Henrietta Leavitt, was given the job to calculate the brightness of stars comparing them to what at the time was thought to be a constant star, Polaris. However, early in her career, Miss Leavitt had asked to switch to finding variable stars which were of special interest of her for an unknown reason. After discovering twenty-five new variable stars in the Small Magellanic Cloud in just a short span of time, Henrietta Leavitt discovered a relationship between the periods of the variable star compared to how its brightness changes over time. These results were published under the name Edward Pickering, her boss, in 1912 in a Harvard Circular. Consequently, Henrietta Leavitt discovered the rule that now allows us to measure the universe. Starting in 1914 a gifted astronomer by the name of Harlow Shapley took the scene. Harlow Shapley was interested in looking at globular clusters and at the time very little was known about them. Using the sixty inch reflecting telescope at Mount Wilson Observatory, he conducted his research by first looking for Cepheids is the nearest globular clusters to us. Miss Leavitt’s relationship proved useful for Harlow Shapley because he could use the Cepheids’ period to find how far away these clusters actually were. For farther away globular clusters where Cepheid variable stars were not observed other methods were used to determine distance. The overall picture of the Milky Way galaxy came into view when he then plotted all of these globular clusters on a graph, in the process revealing the real location of the Sun, the Solar System, and, ultimately, us. Many were probably surprised to see that we are in no special place in the galaxy. We are located in the galactic disk about two-thirds of the way out of one of the spiral arms coming from the galactic center. The year Harlow Shapley finished his work find our place in the galaxy, 1919, was the same year that Edwin Hubble was hired to work at the Mount Wilson Observatory. The big controversy of the day allured Edwin Hubble to the topic of the nature of the cloudy patches in the sky called nebulae. During this time, it was not known if these nebulae were a part of the Milky Way galaxy or on their own. After taking several images of the now called Andromeda galaxy, Edwin Hubble observed a Cepheid variable star. Observations over a period of many months are needed for the period of a Cepheid to be determined, but once this had been obtained, Hubble calculated that based on its period the Cepheid variable star must be 900,000 light years away. Along with his other discoveries, Harlow Shapley determined the size of our Milky Way galaxy to be about 100,000 light years in diameter, much too small to have this nebula in it. Later it was found out Hubble was comparing two different types of Cepheids, and the distance to the Andromeda galaxy was actually two million light years away. Edwin Hubble was not done there; he used what he learned about Cepheid variable stars in Andromeda galaxy to discover that the universe is expanding in an accelerated manner, with the help of this assistant Milton Humason. In the past, Cepheid variable stars was been used to discover some of the most important pieces of information known to humans. Nobody knows what other contributions Cepheids will have in the ongoing task of understanding the universe around us. 

In astronomers’ quest to understand the universe, they have come across two types of Cepheid variable stars Type 1, or classical, and Type 2. Classical Cepheids often are more massive than our own sun, and thought to be up to ten million years in age. This variety of Cepheid has a strong concentration towards the plane of our galaxy with low space velocities. The Magellanic Cloud Classical Cepheids reviled that these stars occupy a small and narrow strip in the period-luminosity diagram. This would indicate that most Classical Cepheids are similar when compared to each other. Looking at the type 2 Cepheids, they are fainter than type 1 Cepheids when compared at the same period. These stars are less massive than their counterparts and are estimated to be fifteen billion years old. This is indicated in their presence in globular clusters and in the galactic halo. Type 2 Cepheids also have a different shaped light curve compared to type 1. 

One indication of a Cepheid variable star is its light curve. If plotted on a luminosity versus time graph, Classical Cepheid variable stars have an asymmetrical curve. Often, these curves have a quick spike up to the maximum light level followed by a slow decrease in luminosity level. It seems that a process known as the Hertzsprung Process is responsible for a bump along the light curve of Type 2 Cepheids with periods from six to sixteen days. This bump is on the descending part of the light curve for six day periods and in the ascending part for longer than ten days. The Hertzsprung Process can be quantitatively described by Fourier decomposition parameters taken from the light curves themselves, and the results are expressed as Fourier amplitude ratios. It is thought that these sudden changes in amplitudes are echoes of the first pulsation from the deep interior of the star. With less than six days for a period, short period stars have smooth light curves with no noticeable bumps like the others. These smooth curves are often very sinusoidal in nature and are associated with small changes in amplitude. A natural question to ask might be, how are they pulsating?

An interesting point of discussion is how Cepheid variable stars pulsate. Cepheid variables pulsate by what is called the “Eddington Valve” or more commonly, the κ (Kappa)-mechanism. This mechanism depends on the opacity of the star itself. A specific part of opacity that contributes to the pulsation mechanism is the fact that the outer layer of the matter that makes up the star is ionized, or it contains free electrons. These free electrons scatter and absorb throughout the star and this is the driving force behind the κ-mechanism. The ionized matter can be pictured as a shell inside the star with the center of the star being the center of the shell. Below this shell contains the normal matter expected in stars, and outside of the shell contains the free electrons that drive the pulsation. As the star compresses the energy produced contributes the higher ionization of the matter, and therefore increasing the opacity. This increased opacity traps in radiation and in turn increases the exerted pressure. This process is called the у (Gamma)-mechanism. At some point, the outward pressure pushes out the shell in a radial fashion causing the shell to cool and increase the opacity further. After a time of further cooling, the outward pressure drops and the shell sinks back towards the center of the star. A cycle is produced by the increasing and decreasing of opacity and pressure and as a result, pulsations occur. One might wonder how these stars initiate this pulsation mechanism. It seems that the initialization pulsation cycle is random in a sense that a star has to be perturbed from its hydrostatic equilibrium, and then if the situation allows for it, the star will overshoot hydrostatic equilibrium when trying to reestablish this position and then continue to over shoot this position for the remainder of its pulsating lifetime.

There exists a subset of Cepheid variable stars known as beat Cepheids. Beat Cepheids are classical Cepheids that pulsate in two ways at the same time instead of the usual one. The first beat Cepheids were discovered by Pieter Oosterhoff in 1957, when he saw that there was a variation in the amplitude of light curve in the stars U TrA and TU Cas. Two other men, Worley and Eggen, observed the same results for the star TU Cas. Because of these two modes of oscillation, there are two periods for these beat Cepheids. One is longer and is considered the primary period, and the shorter is considered the secondary period. These stars, at first, showed only the total period and the primary period so the secondary period had to be determined based on the first two. Today, the primary and secondary periods are most commonly observed only. This has resulted in beat Cepheids being more commonly called double-mode Cepheids. So far, not too many beat Cepheids have been discovered in our galaxy, but, by using gravitational microlensing, more than two hundred of these stars have been observed in the Large and Small Magallenic Clouds. A period with one mode oscillation can reveal a lot about the physical properties of the star, but if a star has two modes of oscillation then the problem can be a little bit more complex. It seems that understanding these beat Cepheids is important in the understanding of stellar structure and evolution in large mass stars. One study used the presence of beat Cepheids in the Large and Small Magallenic Clouds to try to determine the general metallicity of the clouds. There have been previous studies done to find the metallicity of the clouds using other methods, so the study compared their results of the metallicty of the beat cepheids in the clouds to the previously determined metallicty to determine if beat Cepheids can be used as a general indication of the metallicity of their galaxy. The results say, that in a general sense beat Cepheids can be used to determine a rough estimate of the metallicty of their galaxy that they are living in. If these beat Cepheids are useful in determining the metallicity of galaxies, there is no telling what we will find Cepheid variable stars, in general, will be able to tell us. 

In the future, maybe telescope will keep getting better and better and our observations of Cepheids will be farther and farther away until we can observe these special stars in galaxies many light years farther away from where we can currently observe them. With how much we currently know about the universe, I can only imagine what wonders we will discover using these constantly brightening and dimming stars will yield for the human race in the future. Until then, we can keep observing them in our own galaxy and in our neighbors’ in hopes of deciphering nature itself.    

Thank you,
Philip
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Image Source: https://en.wikipedia.org/wiki/Cepheid_variable