Millions of stars twinkle in the night sky. A significant amount of this "stars", however, is rather a multiple system composed of two, three or even more stars forming a stellar system. Similar to our sun, stars may in addition be orbited by one or more planets. The astonishing precision of space telescopes such as TESS or Kepler allows for the identification of such system.
Let's assume we know of a stellar system, somewhere in the Milky Way. While we know that it exists, not much more is known about it. In essence, it seems like the stellar system is an opaque cloud of gas. Lucky enough, a space telescope observed this system for about 85 days, equivalent to three sectors of TESS observations.
The result of this observations is called a light curve. It shows the combined brightness of all elements of the stellar system as a function of time. One point every two minutes!
Look at this interesting behaviour! The brightness periodically drops down to 60-65%. This is typical for eclipsing binary stars. These are two stars that orbit each other in such a way, that the light of one star is periodically blocked by the other one. So, during the times the primary star blocks the secondary one, the brightness drops to about 65%. While the secondary star blocks the flux of the primary, the total brightness drops to about 60%!
This first look at the light curve already told us two things: First, we are dealing with a binary star. Second, since the eclipses are comparably deep, the luminosity of both components are comparable. We can hence already update our view on the stellar system (For simplicity, the animation does not show the eclipsing nature of the binary. The animation hence looks at it from a different direction than the telescope!).
To further enhance our knowledge of the stellar system, it is inevitably to remove the eclipsing binary signal from the light curve. Luckily, we have a very good understanding of how the light curves of such objects behave depending on the stellar and orbital properties. We can use scientific software such as Phoebe to create model light curves. Once we have obtained a model that reproduces the light curve of our system, we can remove this signal from it and investigate the residuals.
Once the signal of the eclipsing binary is removed, the light curve looks significantly different. We still see periodic dips in the light curves but if we compare this to the previous one, we see two main differences: On the one hand the brightness drops at every occation to the same level (about 97%). In addition, the light curve can be considered constant when no dip is occuring. This already gives a viable hint that this signal does not originate from both stars, but rather only one star. On the other hand, the periodicity of the signal (~3.75 days) differs from the orbital period of the binary (~1.7 days). The second and ensuring indicator tell us that the signal originates from one star only.
Indeed, what we observe in this light curve is the signal of stellar spots. The temperature of some area of the stellar surface is signifcantly lower than the temperature of the remaining stellar surface.
The amount of light radiated away from the stellar surface is directly dependent on its temperature. Hence, when the surface area we look at includes such a spot, the integrated light is less and the star seems less bright in our light curve. The time dependence of this phenomenon then originates from stellar rotation. When the star rotates, the spot will become gradually more visible until the star has rotated far enough to hide the spot on the side of the star we are not looking at.
We can now update our stellar system again. We now know that one star has a cool spot on its surface. Furthermore, we know the surface rotation period of this star. This now lifts the remaining dust of this component of our binary system. By removing the spot signal from our light curve, we can continue our search for more information and see, what additional signal we will encounter.
Wow! There is even more signal hidden in the light curve of our system. This new version of the light curve shows variability with much lower amplitude. The changes in brightness are only about 0.5%! The variability also happens on a very different time scale. The morphology of the light curves indicates multiple different periods far below one day.
Such a signal is typical for stars pulsating in pressure modes. Pulsating stars oscillate, which is similar to 1D strings on a guitar or 2d drumheads. Due to the oscillating behaviour, the surface area changes wie periodicities of a few hours to minutes. With more surface area the star is brighter and vice versa. This results in the rather complicated, but beautiful morphology of our light curve.
Since we now know that one component of the binary star is a pulsating variable star, we can once more update our stellar system. Stellar pulsations not only lead to specific light curves, they make it possible to look into the deep stellar interior and investigate the stellar structure in ways otherwise impossible. From its pulsational frequencies, one can obtain the star's parameters like the mass, radii, composition, rotation rate, and many more. By comparing rotation rates for example, we can make pretty sure that it is indeed the secondary component that undergoes the pulsations.
In most cases, the light curve of oscillating stars are well reproduced by a linear superposition of sinusoidal functions. That is, we can add up signal from every pulsation frequencies to obtain a very good model of the light curve. Here, we make again use of scientific software, in this case SMURFS. If we do so, we can investigate if there is even more signal hidden in the light curve of our system.
And yes, there is! There is a small dip in brightness every ~25 days with the duration being only a few hours! While it looks similar the signal from a spot, the short duration makes it impossible that the signal originates from one of these. It seems like a small objects periodically blocks the light emitted from the stellar system for a short time. Indeed, this case is very similar to our first light curve, the eclipsing binary system, but this time, the involved components are much more different!
The signal we see here is produced by planet orbiting the stellar system and eclipsing it every ~25 days. Since such exoplanets typically do not radiate much light themselves, they block the light from a small portion of the stellar surface when they make their way through our line of sight. In this case, the brightness drops by ~0.2%.
Similar to the light curve of eclipsing binaries, we have tools to model the light curves of such star-planet systems. This allows us to find for example the planet's mass, radius and sometimes even gives information about the structure of the planet's atmosphere.
With the addition of the planet, we have now completely identified all components of our stellar system. This hence also lifts the remaining dust from our animation. Let's shortly recapped what we have achieved in this example: We used the light curve of an otherwise unknown stellar system to completely identify all of its components. We have hence found a binary composed of a spotted primary star that rotates with a period of ~3.75 days and a pulsating secondary star. Even more, we found a planet, orbiting the system with a period of ~25 days.
Amazing, how much the observations of a space telescope allow us to find out about the stars in our night sky!