# Light Curves

First, a bit of housekeeping: we apologize for the fact that this week’s post is slightly late, and unfortunately it will also be somewhat shorter, as we have both been insanely busy this week (we fear this will be a recurring theme), but ’tis a post nevertheless.

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Light curves are almost exactly what they sound like — they plot the brightness of an object over time. They’re typically used with all kinds of variable stars, in particular eclipsing binaries, pulsating variables, and supernovae.

If the light curve seems to repeat itself, like these idealized examples, you’ve got some kind of periodic variable. You can determine the period of the star simply by looking at how long it takes the light curve to start repeating a cycle.

Credit: Davison E. Soper at University of Oregon

If it looks something like this, you’ve got yourself an eclipsing binary — the brightness is mostly constant, except for the dips where one star passes in front of the other and blocks some of the light from it.

Credit: Institute for Astronomy at the University of Hawaii

If it looks like this, then you’ve got a cataclysmic variable star, more specifically, a supernova. Light curves from Type Ia supernovae are particularly important because they can be calibrated as standard candles to let us determine the distance to the exploded star (as for why this is possible, that is a topic for a future post). Furthermore, Type II supernovae are classified based on their light curves, with Type II-P having a “plateau” of relatively constant brightness shortly after maximum magnitude before decaying away, while Type II-L tend to just fade away in a relatively linear fashion.

Credit: University of Oregon

A very useful astronomy tool based off light curves is the O-C diagram, typically used for periodic variable stars. O-C stands for “observed minus calculated”, and (this seems to be another recurring theme today) it’s exactly what it sounds like. First, you look at collected data for a varstar, and then try to create a model that will be able to predict the future behavior of the star. To create an O-C diagram, you plot Time on the x-axis, just like for a light curve, but you subtract your calculated brightness from your observed brightness and plot that on the y-axis.

Credit: AANDA (“Starspots and photometric noise on observed minus calculated (O-C) diagrams” by A. Kalimeris, H. Rovithis-Livaniou and P. Rovithis)

If your O-C diagram shows a straight horizontal line at zero, like in the first half of the diagram above, then your model accurately predicts the behavior of the star, and you should pat yourself on the back. However, as always in science, you can be wrong. If the line has a positive slope (like in the second half of the diagram above), then the real period is longer than what you thought it was; if the line has a negative slope, the real period is shorter than your predicted period. And finally, if the O-C diagram shows a curved line, then the period is changing for some reason, which may warrant further investigation. Of course, there are more complicated ways in which you can be wrong, but we won’t address them here, in order to save time and minimize confusion.

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