The file binary59683 contains measurements of the light of an astronomical source as a function of time. Time is in units of days (Julian date), and brightness is measured as “magnitude.” According to this system of measurement, the brightest star has magnitude −1.4 and the faintest visible star has magnitude 6, so the larger the magnitude, the dimmer the light.
a. Plot magnitude versus time. Do you see any structure?
b. The object is actually an eclipsing binary system (two stars rotating around each other) with a period P = 0.407528 days. Define s = t mod P and plot magnitude versus s. Can you qualitatively explain the shape of the “lightcurve” you see?
c. The lightcurve contains a lot of information about the nature of the binary system. Use local linear smoothing to estimate the underlying lightcurve.
d. Change the period slightly and see how the lightcurve changes. Do this several times. Can you propose a method to find an unknown period? About how accurately can the period be estimated from this data?
This data comes from the Hipparcos mission. More information, more lightcurves, and interactive demos can be found at http://www.rssd.esa.int/SAgeneral/ Projects/Hipparcos/education.html.
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