# Lightcurves of Eclipsing Binary Systems

The variation in brightness of an eclipsing binary is described by its light curve. This is a graph of how its brightness changes with time. A light curve typically graphs some measure of brightness on the y-axis -- either flux or magnitude. The x-axis uses a variable called phase. This is a number between 0.0 and 1.0 that describes where an eclipsing binary is in its orbit. The purpose of this page is to develop a good understanding of how photometric data (measurements of brightness) are used to construct a light curve. Use the light curve simulator in following the discussion below.

There are four distinct sub-panels visible. The panel in the upper right depicts the eclipsing binary system. Click the Start Animating button to set the system in motion. Note that our line of sight is exactly aligned with orbital plane of the system (what astronomers call an inclination of 90°). The orbital period being simulated here is 3.65 days. The periods of most binary systems that have been observed are known to a much higher degree of accuracy. If one were to look up an eclipsing binary period in the General Catalogue of Variable Stars — it would likely be known to a high degree of accuracy — 3.650013 days. The periods of many eclipsing binary systems have remained constant for long periods of time over many orbital cycles.

The panel in the upper left shows the actual variation in brightness of the system. Note that these two upper windows are synchronized. The red dotted line labeled now indicates the present value of light curve brightness manifested by the binary system. The pattern of brightness values created by the binary system repeats itself over and over again.

- Estimate the temperatures of the two stars from their colors?
- Which star is obscured when the deeper eclipse occurs?

The panel in the lower right shows how phase is calculated. If one takes the total elapsed time (since some arbitrary starting time) and divides by the orbital period, one obtains a real number. The part to the left of the decimal tells you how many complete orbital cycles have passed since the starting time. If you watch the binary system progress over time you can watch this number of cycles slowly increment. The digits to the right of the decimal point indicate phase. This is a decimal between 0.00 and 1.00 that indicates how far along the binary system is in its present orbital cycle. Note that phase is the x-axis in a light curve.

- After 5.00 days have passed, what is the phase of the binary system?
- How long does it take the system to move through 6.5 revolutions?

When astronomers begin observing a binary system and taking photometric measurements, they ultimately want to determine the light curve of the system. However, they typically are not able to follow a binary through a complete cycle. Due to the object's availability, observing other objects, and the weather it often takes observations from many cycles to form a light curve (as shown in the animation below). However, until they know the orbital period of the system they can't determine the phase of a data point. A discussion of the method by which periods are determined must wait for another NAAP module and from here on we will assume that the period is known.