The Cepheids of Henrietta Leavitt

There is a category of stars, known as the cepheid variables, that grow bright from a relatively dim state within a fixed period of days and then revert to a dim state in the same period—only to do it again. Their name derives from the first of these discovered, the Delta Cephei, in the Constellation of Cepheus in 1784. These suns are big—five to twenty times the size of our sun. They expand as they grow brighter, grow small again as they go dim. The following graphic, from the European Space Agency (link), illustrates the process.

The mechanism of pulsation is explained by doubly- or singly-ionized helium in the stars. Doubly means that two electrons are missing, singly that one is missing. Doubly ionized helium is more opaque. When the cepheid is dim, its outer atmosphere is high in doubly-ionized helium; it holds radiation in. As the sun heats, it expands and cools; as it cools the helium becomes less ionized and more transparent; the expanded star is bigger and brighter; more light escapes. Expansion is countered by the sun’s gravitational pull, and the process reverses.

Henrietta S. Leavitt (1868-1921) discovered an interesting relationship between these stars’ change in luminosity and the period (measured in days) it took them to go from peak-to-peak or trough-to-trough: the brighter the star, the longer the period. This news surfaced in 1912—and Leavitt appeared in my own telescope again yesterday when I was looking back to that year. Ah, yes! An interesting story. The paper in question was by the Harvard astronomer Edward Pickering (1846-1919); Leavitt worked for Pickering at Harvard with other women studying and cataloging photographic images of the sky. She turned sixty-six that year. The paper was called “Periods of 25 Variable Stars in the Small Magellanic Cloud”; it was published in the Harvard College Observatory Circular and cited Leavitt’s work. Leavitt had written an earlier paper, but it was only available in the Annals of Harvard College Observatory. It was dated 1908 and titled “1777 Variables in the Magellanic Cloud.” (Image from Wikipedia here.)

The ladies who worked for Pickering did the mind-numbing “clerical” work so that their male betters could do the “serious thinking.” My own conviction, to the contrary, is that real discoveries are made when creative people study the actual raw data—whatever form they take. And Leavitt was one of these. She began to record the luminosity and periods of the cepheids—and as any awake mind will do, she began to chart them. Soon she discovered the highly predictable relationship between period and luminosity. The longer the period, the brighter the peak. Leavitt had made a very fundamental discovery—used to this day to measure stellar distances.

So how does this work? The apparent magnitude of a star is provided by its luminosity as observed from the earth. If the two variable stars have the same regular periodicity, they can be assumed to be the same size, wherever they are. As for their absolute magnitude, that all depends on how far away they are. Leavitt made the simplifying assumption that the Cepheids in the Small Magellanic Cloud (SMC) were roughly at the same distance from us. Therefore, their absolute magnitudes could be measured as soon as the distance to the SMC became known. Thereafter, the periods of the stars alone, no matter how dim or bright they were at peak, could yield their absolute magnitude. And then, in turn, those two values (M for absolute, m for apparent) could be used to calculate the distance. And, indeed, that turned out to be true. The formula is D = 10^(m-M+5)/5 .

Absolute magnitude needs a little more unpacking. It is the brightness that a stellar object would have if it were observed at a distance of 32.6 light years (10 parsecs) from the surface of the sun. The star nearest to us, Proxima Centauri, is 4.2 light years (1.3 parsecs) from us.

The distance to the SMC was first estimated by Ejnar Hertzsprung in 1913. He used the cepheid variables in his method. His estimate, of 30,000 light years, was way off, but the method was later perfect. Now we know that the distance is 199,000 light years. The current method of calculating the absolute magnitude of a cepheid variable star is to:

• Measure its dimmest and brightest luminosity, calculate an average, and call that apparent magnitude (m).
• Calculate the absolute magnitude (M) from the period (P) using the following formula: M = -2.78 log(P) - 1.35. The constants used are built-in factors and adjustments necessary to indicate distance to the SMC.
• Use the distance equation (D = 10^(m-M+5)/5) to obtain the distance in parsecs.
• Multiply that number by 3.26 to get light years. 

Henrietta Leavitt thus, a hundred years ago, gave us what are called standard candles (they flicker, sort of, after all). Using them we can measure how far away they are. The art has made great advances since. Other categories of cepheids, with much longer periods, have been discovered. Methods of measurement have greatly improved. And the art is still somewhat iffy. But it’s good enough for astronomy work.