# Henrietta Leavitt and the Astronomical Cow Puzzle

RS Puppis, a particularly bright Cepheid variable star, imaged by the Hubble space telescope in 2010. Image: ESA, NASA, STScI/AURA

• Henrietta Swan Leavitt was one of the ‘Harvard computers’ – a team of women employed by Harvard University to process astronomical data.
• Leavitt was studying Cepheid stars, which periodically expand and contract in size. Different Cepheid stars have different pulsation periods.
• She found that if we know the period of a Cepheid star, we immediately know how much light it is sending out. This formula is called Leavitt’s law.
• It was a startling discovery that helped Edwin Hubble make his famous discovery – that nearby galaxies are moving away from each other.
• She got little credit for her work in her lifetime. If this bothered her, she did not show it. She was deeply religious, beloved among her colleagues for her joyful disposition.

There is a famous scene in the British comedy show Father Ted. Father Ted is explaining to a confused friend that cows that are far away are not, in fact, as tiny as they appear. ‘This is a small cow’, Ted says, holding a small toy cow, ‘the ones out there are far away.’

In astronomy and cosmology, one encounters a very similar puzzle. Except cows are now replaced by stars and galaxies. And unlike the comedic cow problem, we now have a serious riddle at hand. Suppose we want to estimate how far a far-away star is to us. But we have no way of measuring the distance directly, what we can measure is how bright the star appears, or in physics terms, how much light energy it is emitting. We all know that the further away a source of light is, the less bright it appears to our eyes. So we might think that we can use this fact to estimate the distance of a star: a fainter-appearing star must be further away than a brighter one.

But not so fast! Not all stars in the sky are equally bright. Think of them as a collection of bulbs of varying powers. If a star appears faint, it may be because it is far away. But it could also be because the star is just one of the low-power, dim stars. This is astronomy’s cow problem: how do we tell if a star is dim, or if it is far away.

A surprising discovery by Henrietta Leavitt resolved this problem.

Henrietta Swan Leavitt (1868-1921) was one of the ‘Harvard computers’. The Harvard computers were a team of women employed by Harvard to process astronomical data. At that time, unprecedented volumes of astronomical data were being collected and observatories needed a large number of employees to classify and categorise the astronomical data that was coming through.

The chief reason for hiring women for the job was that they could hire more for the same budget, as women were paid a pittance compared to men. Even though some of the Harvard Computers were astronomy graduates, they were paid the wages of an unskilled worker. Some of the Harvard computers like Henrietta Leavitt went on to make pioneering discoveries in astronomy.

Leavitt was studying Cepheid stars. Unlike our Sun, Cepheid stars don’t always stay the same size. They pulsate – that is, they periodically expand and contract in size. Their temperatures also go up and down during pulsations, making them alternately brighter and dimmer. Different Cepheid stars can have different periods of pulsation. Leavitt had measured these periods, which is the time it takes for a Cepheid star to go from its dimmest to its brightest.

Leavitt made a startling discovery about these periods. By making a plot of the light energy emanating from a Cepheid star and its period of pulsation, she found that the two could be linked by a linear formula. This means that if we know the period of a Cepheid star, we immediately know how much light it is sending out. This formula is referred to as Leavitt’s law.

Leavitt’s discovery provided a way to overcome the cow problem. Suppose we find two Cepheid stars in two different galaxies, which have the same period of pulsation. Then we immediately know that both should be sending out the same amount of light. If one appears less bright on the average, then it must be because one galaxy is further away from its counterpart. The key point here is that we have an independent way of ascertaining the light energy being radiated by a Cepheid star, from its period of pulsation. Using mathematical relations between distance and brightness in conjugation with Leavitt’s law (and some other factors), one can estimate the distance between different galaxies.

Leavitt got little credit for her work in her lifetime. If this bothered her, she certainly did not show it. She was a deeply religious person, beloved among her colleagues for her joyful disposition. After her passing, astronomer Solon I. Bailey wrote: “She had the happy, joyful, faculty of appreciating all that was worthy and lovable in others, and was possessed of a nature so full of sunshine that, to her, all of life became beautiful and full of meaning.”

Twenty years after Henrietta Leavitt’s passing, Edwin Hubble used Leavitt’s law to estimate distances of nearby galaxies and made the famous discovery that nearby galaxies were moving away from each other. As we now understand, this is a result of the expansion of the universe. Hubble always maintained that Leavitt deserved a Nobel Prize.

Since then, we have discovered other ways of estimating distances between galaxies. In astronomy terms, Cepheid stars are one example of a ‘standard candle’ — a distance sign on the sky. The criteria for being a standard candle is that we should have an independent way of determining the light energy it gives out. As we saw, this is true for Cepheid stars because of Leavitt’s law. Certain explosions in stars (called type 1 supernovae) are another example of a standard candle. Gravitational waves are also expected to become very useful for measuring cosmological distances. But those are stories for a different post.

This article first appeared on the author’s blog and was republished here with permission.

Nirmalya Kajuri is an assistant professor of physics in IIT Mandi.

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