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Observations of Delta Cephei

Chris Rowland, Jan Dell, Sarah Whittaker, John Fifield

Members of the Wycombe Astronomical Society made observations of the magnitude of the star Delta Cephei to determine its period and so its distance using the period-luminosity law for Cepheid variables.

Data Collection

Delta Cephei is a naked eye star in the Constellation Cephus. Its magnitude varies regularly over a period of a few days and there are two convenient comparison stars nearby. WAS members made a total of 116 observations from June 2005 to February 2006, giving magnitudes from 3.4 to 4.3. We made measurements using naked eye or binoculars. When measurements were made independently by several observers at the same time the magnitude estimates were within 0.1m or 0.2m of each other. The poor weather and light pollution made Delta Cephei difficult to see sometimes and on some occasions the fainter comparison star was not visible. This will make the fainter observations less reliable. The raw measurements are shown here; there is no obvious pattern to the data.

The data was analysed using the Anova method and a plot of the period shows a clear peak with a period of 5.3691 days

A plot of the data at this period gives a clear indication of the light curve:

This shows the characteristic Cepheid ?shark?s fin? light curve with a rapid rise followed by a slow decline. This is the official light curve:

The main difference seen in our data is that the amplitude is less than expected, especially at the low magnitude end. This could be due to a tendency to overestimate the magnitude when the star was only just visible.

Determining the distance to Delta Cephei

The absolute magnitude of a Cepheid variable is given by the function

M = -2.76 log(P) ? 1.4

Where M is the absolute magnitude and P is the period in days.

For our measurement of the period this gives an absolute magnitude of -3.41; in other words if Delta Cephei was at a distance of 10 Parsecs (32.6 light years) it would have a magnitude of -3.41 and so be the brightest object in the night sky, except the Moon and sometimes Venus.

The formula:

m = M + 5 * Log(D) ? 5
relates the apparent magnitude - m, the absolute magnitude - M and the distance in parsecs - D.

The average magnitude from our measurements was 3.92. This gives a distance to Delta Cephei of 294 Parsecs, or 958 Light years.

Comparison with Official values

The period of Delta Cephei is 5.366 days; our measurement is within 50 seconds of this. The average magnitude is actually 4.07m, our measurement is slightly higher, possibly because of a tendency to overestimate the brightness when the star is only just visible. The distance to Delta Cephei has been measured by the Hubble space telescope using parallax as 891 light years. Our measurement is within 10% of that, almost entirely because our mean magnitude is less than the actual value. This was an interesting and educational exercise, and we learned a lot about taking and recording observations.

Chris Rowland

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