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Magnitudes of Variable Star Cepheid 1

Keywords: time series, sum of sinusoids, discrete spectra


The data gives a sequence of observations on the magnitude of a variable Cepheid star made from the Mount Stromlo Observatory near Canberra in Australia. The observations were made as part of the MACHO project.

The MACHO project monitors millions of stars every night with a dedicated telescope at Mount Stromlo Observatory. The collaboration is probing the halo of our galaxy in order to detect dark matter in the form of Massive Compact Halo Objects -- MACHOs. These are astronomical bodies that emit negligible visible light, such as dwarf or neutron stars, large planets, and black holes. Detection of a MACHO is achieved by observing its gravitational lensing effect on a chance background star as the MACHO crosses near the line of sight between the observer and this star. In order to detect a sufficiently large number of MACHOs, the project collects observations on an large number of distant stars over an extended period of time. Data are being collected daily over a 4-year period (weather permitting), on approximately 8 million stars in the Large Magellanic Cloud (LMC) and the bulge of the Milky Way.

This database is a valuable resource for many other types of astronomical research. It is the most comprehensive catalog of stars in the LMC and contains stars much dimmer than those covered by previous surveys. Temporal coverage is unusually long compared to most star surveys, which permits a comprehensive study of star variability, including long periods and transient phenomena. About 40,000 variable stars have been observed in the LMC and a similar number in the galactic bulge.

Variable stars are stars for which the intensity of the emitted energy changes over time; for periodic variable stars the change of intensity is periodic over time. Common types of periodic variable stars include eclipsing binaries, RR Lyraes, and Cepheids. Cepheids are very bright stars with periods of 1-70 days. The light curve has an asymmetric shape, and rises more rapidly than it falls. Cepheids with periods of about 1 week tend to have a bump in the descending part of the curve. For periods of about 10 days, the bump is at the peak of the curve, and for longer periods it is on the rising part of the curve. The brightness changes are caused by periodic pulsation (contraction and expansion) of the stars and their outer layers.

There are numerous additional types of variable stars, and each of the categories above contains subcategories. For example, Beat Cepheids and Beat RR Lyrae oscillate at more than one frequency. Different classes of variable stars can be located in different regions of a plot of magnitude versus temperature or spectral type. For example, RR Lyrae and Cepheids lie on a strip called the "instability strip." Different types of variable curves are classified also on the basis of the shapes of their light curves and the relationships of shapes to period, for example. As well as being important for studies of stellar structure and evolution, these classes are used to determine distances on a cosmic scale by means of the relationship of their periods to their magnitudes.

Observations of these stars are typically made at rather irregular times, depending on observation schedules and sky conditions. Different observations have differing errors. All this makes determination of the periods and the shapes of the corresponding phased light curves an interesting statistical problem.

This particular star is a category 1 Cepheid (magnitude -9.166) at coordinates (1541.5,1395.1). Magnitudes were recorded in the blue band from 4500 to 6300 Angstroms.

Variable Description

Time Time of observation in days
Magnitude Differential Magnitude
SD Standard deviation of the magnitude observation. A value of -99 indicates missing and negative value indicate unreliable observations.


Data file (tab-delimited text)


Hall, P., Reimann, J., and Rice, J. (1999). Nonparametric estimation of a periodic function. Technical Report 562, July 1999, Department of Statistics, University of California, Berkely.
Reimann, J. D. (1994). Frequency estimation using unequally-spaced astronomical data. PhD Thesis, University of California, Berkeley.
The data and the description were down-loaded from the WWW page Variable Stars: A Brief Tour of the Menagerie, by John Rice, University of California, Berkeley. Data were originally provided by Kem Cook of the Institute of Geophysics and Planetary Physics at Lawrence Livermore National Laboratories.


The data are plotted below. There is a strong primary oscillation with a period of about 13 days.



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