At the age of nineteen, John Goodricke, an eighteenth century English astronomer observed that the star delta-Cephei brightened and dimmed in approximately 5-day cycles.
When you spend a few days in a dark place with clear skies, you can observe the same cycles that Goodricke did in 1784. delta-Cephei is a star in the constellation Cepheus, near the north star. By keeping a careful record of its brightness relative to nearby stars over the course of a few nights, you can trace out a curve like the one shown in the figure.
Since Goodricke's time, astronomers have discovered and catalogued thousands of stars whose brightness, or luminosity, like delta-Cephei's, undergoes cycles with periods of a few days. Such stars, called Cepheid variables, play an important role in determining the distances to nearby galaxies. This is because of a relationship, first noted by the American astronomer Henrietta Leavitt in 1912, between a Cepheid's period and its intrinsic brightness. If we know how much light a Cepheid in a distant galaxy gives off, we can calculate how far away it must be for it to appear as faint to us as it does. This lab explores this relationship and its application in detail.We cannot directly measure the distances to stars, and stars in other galaxies are much too far away for parallax measurements. We can, however, measure the periods of any Cepheid variable stars we can find in them. By assuming that these Cepheids obey the same period - absolute luminosity relation that their friends nearby have been observed to follow, we can compute how far away a galaxy must be in order that its Cepheids have their observed apparent luminosities. The distances to galaxies as far away as several million light years have been measured in this fashion.
Cepheids in the SMC
In 1522, a rag-tag crew of 21 sailed into the Spanish harbour of Seville. They were all that remained of Ferdinand Magellan's crew of 270 that had set sail from that same port three years before. Magellan and most of his crew hadn't survived the voyage, but those who had had sailed 'round the world. Among the stories they brought back to Europe was one of two fuzzy patches of starlight visible in the southern hemisphere's sky, which came to be known as the large and small Magellanic clouds.
|Star||Period (days)||App. Mag.||log(Period)|
Make a graph of apparent magnitude vs. log(Period) on a piece of graph paper. Draw a line through the data which represents approximately the period-luminosity relationship you observe.
m(delta-Ceph) = 4.0
much brighter than the apparent magnitudes of Cepheids in the SMC. This suggests that the SMC is much farther away than delta-Cephei. The distance to delta-Cephei has been determined using a variety of independent methods to be about
D(delta-Ceph) = 850 +/- 80 ly = 265 +/- 25 pc
Using the Magnitude equation:
M = m + 5 - 5log(d)
where d is in parsecs, compute the absolute magnitude(M) of delta-Cephei.
Distance to SMC =
Give your answer in parsecs and in light-years (1 parsec=3.2 light years). The SMC is the second CLOSEST galaxy to the Milky Way (just slightly farther away than the Large Magellanic Cloud).