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THE KEY TO A DISTANCE SCALE OF THE UNIVERSE

Some of the most important, but often most challenging, measurements for astronomers to make have been the distances to extremely remote objects— which includes most celestial objects aside from the moon, sun, and other planets of the inner solar system. Nothing in the light coming from distant stars and galaxies gives any direct indication of how far that light has traveled through space to reach Earth.

For several hundred years, scientists realized that it should be possible to measure the distances to relatively nearby stars by a method called parallax. This is based on comparing the position of a nearby star against the background of more distant stars from two perspectives—usually Earth’s different positions in space six months apart in its orbit around the sun. Although many others had tried (and failed) before him, the first astronomer to measure a star’s distance accurately using this method was Friedrich Bessel, in 1838. However, even with increasingly powerful telescopes, measuring star distances by parallax proved difficult and, by the year 1900, the distances to only about 60 stars had been measured. Furthermore, the parallax method could be applied only to nearby stars. The difference in perspective for more distant stars over the course of a year was too small to be accurately determined. New methods were therefore needed to measure large distances in space.

“A remarkable relation between the brightness of these (Cepheid) variables and the length of their periods will be noticed.” Henrietta Swan Leavitt

Measuring brightness

In the 1890s and early 1900s, the Harvard College Observatory in Massachusetts was one of the world’s leading astronomical research institutions. Under the supervision of its director, Edward C. Pickering, the Observatory employed many men to build equipment and take photographs of the night sky, and several women to examine photographic plates taken from telescopes throughout the world, measure their brightness, and perform computations based on their assessment of the plates. These women had little chance to do theoretical work at the Observatory, but several of them, including Williamina Fleming, Henrietta Swan Leavitt, Antonia Maury, and Annie Jump Cannon, nevertheless left a lasting legacy.

Henrietta Swan Leavitt, who had originally joined the Observatory as an unpaid volunteer in 1894, eventually became the head of the photographic photometry department. This mainly involved measuring the brightness of stars, but a specific aspect of Leavitt’s work was to identify stars that fluctuate in brightness—known as variable stars. To do this, she would do a comparison of photographic plates of the same part of the sky, made on different dates. Occasionally she would find a star that was brighter on different dates, indicating that it was a variable.

“One of the most striking accomplishments of Miss Leavitt was the discovery of 1,777 variable stars in the Magellanic Clouds.” Solon I. Bailey

The Cepheid variable stars that Leavitt studied are in the Magellanic Clouds, known today to be galaxies outside the Milky Way. The Large Magellanic Cloud is about 160,000 light-years away; the Small Magellanic Cloud is about 200,000 light-years away. Both are part of the Local Group galaxy cluster that includes the Milky Way.

Cluster variables

A specific task that Leavitt took on was to examine some of the photographic plates of stars in the Small Magellanic Cloud (SMC) and the Large Magellanic Cloud (LMC). At the time, the SMC and LMC were thought to be very large star clusters within the Milky Way, which itself was assumed to comprise the entire universe. Today, they are known to be relatively small, separate galaxies that lie outside the Milky Way. The Magellanic Clouds are visible to the naked eye in the night sky of the southern hemisphere, but are never visible from Massachusetts, where Leavitt lived and worked. Therefore, although she examined numerous photographic plates of the LMC and SMC obtained by astronomers at an observatory in Peru, it is highly unlikely that she ever physically observed them in the sky.

After several years’ work, Leavitt had found 1,777 variables in the SMC and LMC. One particular kind that caught Leavitt’s attention, representing a small fraction of all the variables she had found (47 out of 1,777), was of a type called a Cepheid variable. Leavitt called them “cluster variables”—the term Cepheid variable was introduced later. These are stars that regularly vary in brightness with a period (cycle length) that could be anything from one to more than 120 days. Cepheid variables are reasonably easy to recognize because they are among the brightest variable stars, and they have a characteristic light curve, showing fairly rapid increases in brightness followed by a slower tailing off. Today, they are known to be giant yellow stars that “pulsate”—varying in diameter as well as brightness over their cycles—and are very rare. As a class of stars, they also have an exceptionally high average brightness, which means they stand out even in other galaxies. In examining her records of Cepheid variables in either the LMC or SMC, Leavitt noticed something that seemed significant. Cepheids with longer periods seemed to be brighter on average than those with shorter periods. In other words, there was a relationship between the rate at which Cepheids “blinked” and their brightness. Furthermore, Leavitt correctly inferred that, since the Cepheids she was comparing were all in the same distant nebula (either the LMC or the SMC), they were all at much the same distance from Earth. It followed that any difference in their brightness as viewed from Earth (their apparent magnitude) was directly related to differences in their true or intrinsic brightness (their absolute magnitude). This meant there was a definite relationship between the periods of Cepheid variables and their average intrinsic brightness or their optical luminosity (the rate at which they emit light energy).

Leavitt published her initial findings in a paper that first appeared in the Annals of the Astronomical Observatory of Harvard College in 1908. Then, in 1912, after further study, which included plotting graphs of the periods of Cepheid variables in the SMC against values for their minimum and maximum brightness, she confirmed her discovery in more detail. It became known as the “period−luminosity” relationship. Formally, it stated that the logarithm of the period of a Cepheid variable is linearly (i.e., directly) related to the star’s average measured brightness.

“A straight line can readily be drawn among each of the two series of points corresponding to maxima and minima, thus showing that there is a simple relation between the brightness of the variables and their periods.” Henrietta Swan Leavitt

A Cepheid variable belongs to a class of star called a pulsating variable. These stars expand and contract over a regular cycle, at the same time regularly varying in brightness. They are hottest and brightest shortly after reaching their most contracted phase. The graph of the star’s luminosity (light output) against time is called its light curve.

Building on Leavitt’s work

Although it is possible that Leavitt did not realize the full implications right away, she had discovered an extremely valuable tool for measuring distances in the universe, far beyond the limitations of parallax measurements. Cepheid variables were to become the first “standard candles”—a class of celestial objects that have a known luminosity, allowing them to be used as tools to measure vast distances in space.

One of the first people to appreciate the significance of Leavitt’s discovery was Danish astronomer Ejnar Hertzsprung. Due to the period−luminosity relationship discovered by Leavitt, Hertzsprung realized that by measuring the period of any Cepheid variable it should be possible to determine its luminosity and intrinsic brightness. Then by comparing its intrinsic brightness to its apparent magnitude (measured average brightness from Earth), it should be possible to calculate the distance to the Cepheid variable. In this way, it should also be possible to determine the distance to any object that contained one or more Cepheid variable star.

However, there was still a problem to be solved: although Leavitt had established the important period−luminosity relationship, initially all this promised was a system for measuring the distance to remote objects relative to the distance to the SMC. The reason for this is that Leavitt had no accurate information about the distance to the SMC, nor indeed any accurate data about the intrinsic brightness of any Cepheid variable.

“I should be willing to pay thirty cents an hour in view of the quality of your work, although our usual price, in such cases, is twenty five cents an hour.” Edward C. Pickering

Calibrating the variables

To turn Leavitt’s finding into a system that could be used to determine absolute distances, not just relative distances, it needed calibrating in some way. In order to do this, it would be necessary to measure accurately the distances to and intrinsic brightness of a few Cepheid variables. Hertzsprung therefore set about determining the distances to a handful of Cepheids in the Milky Way galaxy, using an alternative complex method called statistical parallax, which involves calculating the average movement of a set of stars assumed to be at a similar distance from the sun.

Having obtained the stars’ distances, it was a straightforward step to figure out the intrinsic brightness of each of the nearby Cepheids. Hertzsprung used these values to calibrate a scale, which allowed him to calculate the distance to the SMC and the intrinsic brightness of each of Leavitt’s Cepheids in the SMC. Following these calibrations, Hertzsprung was able to establish a system for determining the distance to any Cepheid variable from just two items of data—its period and its apparent magnitude.

“Leavitt left behind a legacy of a great astronomical discovery.” Solon I. Bailey

Further applications

It was not long before Leavitt’s findings, tuned by the work of Hertzsprung, led to further important results in terms of helping to understand the scale of the universe. From 1914 to 1918, the American astronomer Harlow Shapley (who was also the first person to show that Cepheid variables are pulsating stars) was one of the first to use the newly developed concept that the distances of variable stars could be found from knowing their periods and apparent brightness. Shapley found that objects called globular star clusters— all part of the Milky Way—were distributed roughly in a sphere whose center lay in the direction of the constellation of Sagittarius. He was able to conclude from this that the center of the Milky Way galaxy is at a considerable distance (tens of thousands of light-years) in the direction of Sagittarius and that the sun is not, as had previously been supposed, at the center of the galaxy. Shapley’s work, which led to the first realistic estimate of the true size of the Milky Way, was an important milestone in galactic astronomy.

Right up to the 1920s, many scientists (including Harlow Shapley) maintained that the Milky Way galaxy was the whole universe. Although there were those that believed otherwise, neither side could conclusively prove their argument one way or another. In 1923, however, the American astronomer Edwin Hubble, using the latest in telescopic technology, found a Cepheid variable in the Andromeda nebula, allowing its distance to be measured. This led directly to the confirmation that the Andromeda nebula is a separate large galaxy (and is now called the Andromeda galaxy) outside the Milky Way. Later, Cepheids were similarly used to show that the Milky Way is just one of a vast number of galaxies in the universe. The study of Cepheids was also employed by Hubble in his discovery of the relationship between the distance and recessional velocity of galaxies, leading to confirmation that the universe is expanding.

The star RS Puppis is one of the brightest Cepheid variables in the Milky Way. It is about 6,500 light-years from Earth and has a cycle of variability lasting 41.4 days

Revising the scale

In the 1940s, the German astronomer Walter Baade was working at the Mount Wilson Observatory in California. Baade made observations of the stars at the center of the Andromeda galaxy during the enhanced viewing conditions afforded by the wartime blackout. He distinguished two separate populations, or groups, of Cepheid variables that have different period– luminosity relationships. This led to a dramatic revision in the extragalactic distance scale—for example, the Andromeda galaxy was found to be double the distance from the Milky Way that Hubble had calculated. Baade announced his findings at the International Astronomical Union in 1952. The two groups of Cepheids became known as classical and Type II Cepheids, and started to be used for different purposes in distance measuring.

Today, classical Cepheids are used to measure the distance of galaxies out to about 100 million light-years—well beyond the local group of galaxies. Classical Cepheids have also been used to clarify many characteristics of the Milky Way galaxy, such as its local spiral structure and the sun’s distance from the plane of the galaxy. Type II Cepheids have been used to measure distances to the galactic center and globular clusters.

The measurement of distances to Cepheid variables for more accurate calibration of period–luminosity relationships is still considered extremely important, and it was one of the primary missions of the Hubble Space Telescope project when it was launched in 1990. A better calibration is crucial, among other things, to calculate the age of the universe. Leavitt’s findings from over a century ago are still having significant repercussions in terms of truly understanding the scale of the cosmos.

“Hubble’s underwhelming acknowledgment of Leavitt is an example of the ongoing denial and lack of professional and public recognition that she suffers from, despite her landmark discovery.” Pangratios Papacosta

A simplified version of the mechanisms that cause Cepheid variables to fluctuate in size is shown here. The pressure forces inside a star include gas pressure, maintained by heat output from the star’s core, and radiation pressure. Another mechanism that may be involved is a cyclical change in the opacity (resistance to the transmission of radiation) in gas within the star’s outer layers.

HENRIETTA SWAN LEAVITT

Henrietta Swan Leavitt developed an interest in astronomy while studying at Radcliffe College, Cambridge, Massachusetts. After graduation, she suffered a serious illness that caused her to become increasingly deaf for the rest of her life. From 1894 to 1896 and then again from 1902, she worked at Harvard College Observatory. Leavitt discovered more than 2,400 variable stars and four novae. In addition to her work on Cepheid variables, Leavitt also developed a standard of photographic measurements, now called the Harvard Standard.

Due to the prejudices of the day, Leavitt did not have the chance to use her intellect to the fullest, but she was described by a colleague as “possessing the best mind at the Observatory.” She was remembered as hardworking and serious-minded, “little given to frivolous pursuits.” Leavitt worked at the Observatory until her death from cancer in 1921.

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