Cosmic Staircase 6 - Cepheid Variables

Henrietta Swan Leavitt (1868 - 1921). Sorce - Wikimedia, American Institute of Physics

Henrietta Swan Leavitt was born in Massachusetts in 1868. At Radcliffe College she studied analytical geometry and calculus as well as classical Greek, fine arts and philosophy, graduating with a bachelor’s degree in 1892 at the age of 24. Towards the end of her studies she took a course in astronomy, then spent a year travelling, during which time she suffered a serious illness and became profoundly deaf. She began her career in 1893 as one of the ‘women human computers’ hired by Edward Pickering, the Director of the Harvard College Observatory. At that time women were not allowed to operate telescopes. In fact the attitude towards women in science at that time was particularly bad. They were given only mundane tasks and were only hired because they were cheaper than a male of equivalent skill. To add insult to injury the group of women she worked among was referred to as Pickering’s Harem. She was also paid a pittance and was unrecognised for her groundbreaking discovery in her own lifetime. Fortunately for the future of astronomy she was assigned to measure the brightness of stars captured in the observatory’s archive of photographic plates. She was assigned specifically to study stars that had variable brightness over time. Nobody expected anything significant to arise from this study, least of all that it would so radically change our approach to astronomy and launch us so dramatically into the cosmos. This is often how the knowledge journey goes. The most important discoveries can emerge from the most unlikely people and places.

I am writing this on Ada Lovelace Day to celebrate the contribution of women in science, technology, engineering and mathematics. At the time Henrietta Swan Leavitt lived, women were treated appallingly, not just in science, but also across all of society. In fact they didn’t even get the vote until the year before Henrietta died. The contribution women like Henrietta Swan Leavitt have made to science throughout history without getting recognition for their work is enormous. It is good that we are starting to give that recognition retrospectively, but much more still remains to be done about gender equality, and not just in the sciences.

There are several things that make her discovery one of the most important in astronomy:

Light curve of cepheid variable Delta Cephei. Source - Wikimedia, ThomasK Vbg

Although stars fluctuate in brightness for a number of reasons, there is a class of variable stars, the Cepheids, that have a highly regular period, the time between peaks (and troughs) of brightness are steady for an individual star. The curve (left) is for Delta Cephei from which this type of star gets its name. Among the Cepheids there is a wide variety of period lengths.

The period luminosity curve for two types of cepheid variable. Source - Wikimedia, Vedran V

Henrietta studied a large number of these stars in the Large Magellanic Cloud, so knew that they were the same relative distance from earth. Using this fact she found a direct relationship between a Cepheid’s period and its brightness (left). If you measure the period you can use the chart left to find the luminosity. A refinement since Henrietta's time identifies more than one class of variable with different curves.

The inverse square law. Brightness decreases by the square of the distance (twice as far away, four times fainter). Source - Wikipedia

Each of these stars has an actual brightness (intrinsic brightness) at its surface, and an observed brightness (apparent brightness) from earth. The difference between these two luminosities is a direct function of the distance between the earth and the star. The brightness of a star reduces by the square of the distance (left), so if the actual and observed luminosities are known, the distance can be calculated.

The most significant factor for our cosmic staircase is that there are over 46,000 Cepheids identified so far in the Milky Way. Henrietta herself identified over 2,500. This means we have a direct link between the Cepheids in the Milky Way and those we are able to also identify in galaxies up to over 100 million light years away.

So the distances of Cepheid stars in the Milky Way can be calculated by at least two distinct methods: Parallax and the period/luminosity ratio. This means that they are able to calibrate and validate each other. Both methods are being continuously improved. In the case of parallax it is by better instrumentation and noise reduction. For Cepheid Variables it is the recognition of different sub types that have slightly different ratios. This means that it is now possible to work out the distances to other galaxies, and is one of a handful of methods used to establish the distance of our nearest neighbour, the Andromeda galaxy.

The Milky Way Cepheids

The closest Cepheid to Earth is Polaris, the North Star. Its distance is 434 light years. Because these stars are so bright it is possible to see them even through the galactic centre to the other side. In 2014 five were found ranging from 72,000 to 99,000 light years away. This together with all the others identified and measured, means that we have a substantial catalogue of variables within our own galaxy, many of them validated by parallax. These stars get their name from the most famous of the Milky Way variables, Delta Cephei, in the constellation Cepheus the King. It is 887 light years away with a margin of error ±26 light years, or 2.9%.

Nearby Galaxies

The Hubble Space Telescope has played the biggest role in this task, but there are limitations. We are observing stars at great distances, and even though they are very bright we can only go so far before losing confidence in the results. Even so the accuracy of the closer distances is impressive. NGC 300, one of the closest galaxies to the local group (Milky Way and Andromeda), is 6.1 million light years away. Even at this distance the margin of error is only ±3%. The furthest galaxy we can measure this way is NGC 4603 in the constellation Centaurus. Over 40 Cepheids were found, with an average distance of 106.8 million light years away at ±5% margin of error.

This technique is the fourth in our cosmic staircase and more than doubles the distance we could measure, from 45 to 106.8 million light years.