A Cepheid is a very luminous variable star. It is also a very massive star, 5-20 M☉, with a high luminosity and of a spectral type between F and K. It obeys a strict period-luminosity relationship, whereby it rules that the later the spectral class, the longer its period is. This can be explained by the following: if the mass becomes higher, the luminosity increases and the more extended envelopes it will have. These envelopes have, because they are more extended, a lower density. This causes the period, which is proportional to the inverse square root of the density in the layer, to be longer.
Cepheids are variable because they oscillate between two states. At first there is a compact stage where a large temperature and pressure are build up. This causes the star to expand, causing the pressure gradient to become weaker. In this second stage the gravity is not compensated by the pressure gradient, which causes the star to contract and compress into its compact state.
Because of their strict relation between period and luminosity, Cepheids can be used to determine cosmic distances. If the period is measured and intrinsic brightness is compared with its apparent brightness, the distance to the star can be calculated. The distance to other galaxies, where individual Cepheids can be found, can be determined using these stars.
There are two kind of Cepheid stars. The first type, Type I, are known as Delta Cepheid stars, or classical Cepheids. With a typical period of 5-10 days they are around four times more luminous and metal rich than Type II. Type I is mostly found in the spiral arms of a galaxy. The Type II stars, also known as W Virginis stars, have a typical period of 10-30 days and can be found in globular clusters, galactic halos and elliptical galaxies.
δ-Cep has become the typical Cepheid star, with not only the variable star type named after it, but also the subclass of the Cepheids of which it is a part. Hence that we choose to study this star. We observed the star, after which we reduced the images with IRAF. With this data we could determine the magnitude using the method of Baade-Wesselink.
We measured a magnitude of 3.87, while the official magnitude is 3.7. But since the error margin was 10.5%, it was a very acceptable result.
Since there is a direct relationship between its luminosity and pulsation period, it can be used as a standard candle for establishing galactic and extragalactic distances. The best example of such a variable star is δ-Cep. In this project we determined the magnitude of this star.
In order to determine the magnitude of δ-Cep, we had to observe it first.
, we first studied the theory behind Cepheid stars, then observed δ-Cep and finally used the method of Baade-Wesselink and IRAF to determine the magnitude.
Observation of δ-Cep.
A demonstration of the magnification of the telescope.
Determining the magnitude of δ-Cep.
Computer programs used
In the research and writing process, we used several computer programs:
LaTeX: LaTeX is a document markup language and document preparation system. In contrast to wysiwyg text editors such as Word, you only see the result after compiling the source. But once you created a template or framework, you can reuse it and thus concentrate on the text and contents of the text, instead of having to trouble yourself with trivialities like the placement of illustrations or footnotes.
Gimp: Gimp is an image retouching and editing tool.
IRAF: IRAF (an acronym for Image Reduction and Analysis Facility) is a collection of software written at the National Optical Astronomy Observatory (NOAO) geared towards the reduction of astronomical images in pixel array form. This is primarily data taken from imaging array detectors such as CCDs..