What is a Light Curve?
A plot that shows the changes in brightness with time is called a light curve. Brightness is a measurement of the intensity of electromagnetic energy, or "flux" from a star. Historically, and even now, astronomers often translate a star's brightness or flux into an "apparent magnitude", which describes how bright a star appears to be. A first magnitude star, like Aldebaran in the constellation Taurus, is 2.5 times brighter than a second magnitude star, like Polaris, in the constellation Ursa Minor. Counter-intuitively then, a dimmer star has a larger magnitude, and a brighter star has a smaller magnitude.
Different stars have different brightnesses, as measured by their magnitude, or energy flux. Brightness is affected both by the intrinsic luminosity of a star (for instance how large and hot the star is), but also by its distance from Earth. A star that is variable will show changes in its flux or magnitude over time. If astronomers measure the brightness of a variable star repeatedly across many nights, they may plot its magnitude against date. Instead of using day, month and year, a common way to note the date numerically is to use the Modified Julian Day or MJD. New Year's Day 2000 was MJD 51544. Two observations taken an hour apart will differ by one twenty-fourth of a day, or 0.041 MJD. Below is a sonified light curve of magnitude versus MJD for an RR Lyra variable star.
Some variability repeats itself in a reliable way, after a predictable amount of time called the period of variability. For example the RR Lyra d-type star whose light curve is plotted above gets brighter and fainter and then brighter again every 11 hours (or 0.458 days). Its period is 11 hours. That period can be detected from the raw observed light curve above by "folding" it at many trial periods (dividing every measurement time since the start by a candidate period), until a repeated pattern becomes clear in a "phase-folded" light curve. Below is a sonified phase-folded light for the same star above.
The phase-folded light curve can be fit with a mathematical function. In the simplest type of variability, that maye be a simple sinusoidal curve of a single period, amplitude and phase. More complicated variability patterns can be represented mathematically by adding together sine curves with different amplitudes and phases. The final best-fitting mathematical function allows a smooth theoretical depiction of the variability. Below is a sonified best-fit function for the same RRd star above.
Some variability is more random. or "aperiodic". Flare stars are a good example, where large eruptions analogous to solar flares can occur at random times. Quasars also show aperiodic variability, but the changes usually take years or decades, and trend slowly upward or downward. A supernova, represent the explosive destruction of a star, so is certainly not periodic. For aperiodic variables, we cannot find any period, phase the light curve on any period, or mathematically fit the light curve to any period, so we plot only brightness versus time.