HOW DID HENRIETTA DO IT?

Henrietta Swan Leavitt was a clerk at Harvard College Observatory. Her interest in astronomy made her go to Chile to study the mysterious Cepheid variables in the Magellanic Clouds which were not visible from the latitude of Harvard.

These stars have very regular periods of variability from brightest to dimmest and their rise to brightest is steeper than their decline to dimmest. 3y 1912 Miss Leavitt had come to the conclusion that there is a linear relationship between the apparent magnitudes of these stars in the Small Magellanic Cloud and their periods of variability. The apparent magnitude of a star is, of course, dependent on its distance from the Earth. Henrietta correctly concluded that the stars in the Small Magellanic Cloud are all very approximately equally far from the Earth if the Cloud is very far away. This must be so because the magnitudes of the stars in the Cloud are all 12, 13, 14...and dimmer. There is therefore a linear relationship between the apparent magnitudes and the absolute magnitudes of these stars, i.e. m - M must have a constant value for the stars in the SMC.

Miss Leavitt found that the brighter the Cepheid i.e. the smaller the magnitude number, the longer is the period of variation. This finding formed the basis of the Period Luminosity Law.

When Henrietta returned from the South and announced this relationship she was told by the astronomer in charge, one E C Pickering, that her job was to classify stars, not to formulate theories -- some men in authoritative positions are like that!

Henrietta's work was published in the Harvard Observatory Circular No 173 of 1912 under the title "Periods of 25 Variable Stars in the Small Magellanic Cloud". The two diagrams are tracings of Leavitt's original graphs. Diag 1 shows the distribution of apparent magnitudes against the periods of variability in days and diagram 2 shows the distribution of apparent magnitudes against the logarithms of the periods. From Diag 2 one can see at a glance that the apparent magnitudes of the Cepheid variables are proportional to the logs of the periods. This became known as the Period Luminosity Law. The periods of the Cepheids can be measured very accurately and once the period is known the corresponding brightness could be read off on the Y-axis... The apparent magnitude is then an indicator of the brightness of the particular star, provided the apparent magnitude could be converted into absolute magnitude

When the absolute magnitude of a star is compared to the apparent magnitude of the star, its distance can be calculated from the formula:

log P = (M - m - 5) ÷ 5,

where P is the star's parallax, M its absolute magnitude and m its apparent magnitude.

When the parallax is divided into 1, we obtain the distance in parsecs and when this is multiplied by 3,25, we get the distance in light years.

The Period Luminosity Law could therefore be used to determine stellar distances. Up to that time distances no further than 300 light years could be measured by the trigonometrical method, but no farther. Within that sphere there are about 5000 stars and of these about 1000 have had their distances determined. By using the Period- Luminosity Law distances of hundreds of thousands and even millions of light years could be measured.

It turned out that the distance of the Small Magellanic Cloud is 200 000 light years and that of the Large Magellanic Cloud 170 000 light years. Henrietta Leavitt was thus quite correct when she pointed out that the Magellanic Clouds must be very far away. In one leap astronomers' abilities for measuring distances had leapt from 300 light years to millions of light years.

If there were one or two Cepheid variables within a distance of 300 light years, its absolute magnitude could be calculated accurately, but there are none within this sphere of distance. The next article will explain how astronomers got around this problem of standardising the magnitudes of the Cepheid Variables.

Jan Eben van Zyl