One star, two star, red star, blue star
Although our Sun is a single, isolated star - most stars actually come in pairs! In fact, 50% of all stars like our Sun have a gravitationally bound companion that it orbits around. These two star systems are known as binary stars.
When we look at a binary star system from Earth, the system has a given inclination with respect to how we see it. About 2% of all binaries in the night sky are oriented and aligned in a way that is just right so that we can see the stars pass in front of one another as they orbit each other. This causes the stars to __eclipse__ one another, causing regular (periodic) decreases in brightness. These special systems are known as eclipsing binaries, and they are powerful tools in astrophysics because they offer a rare opportunity to directly observe and measure the fundamental properties of stars. Specifically, the changes in brightness during these eclipses provide a wealth of information about the system.
Illustration of an eclipsing binary system (credit: Nora Eisner).
These pairs of stars come in several shapes and sizes and by modelling the shapes, depths, and separations of the eclipses - we can obtain highly precise measurements of stellar parameters! How exactly does that work? Well, according to Kepler’s Laws, we know that the orbit of a star is defined by an ellipse, where the size of the orbit (the semi-major axis a) is related to the period of the obit (P) and the total mass of the two stars (M_t = M1+M2), as seen in the relative orbit below.
Image credit: IJspeert (2024)
Doppler shifts
The movement of the two stars around one another in the “relative orbit” shown above means that the stars periodically move towards us, and then away from us. This produces a Doppler shift, whereby the light of the stars is shifted to shorter, bluer wavelengths when the star is moving towards us, and to longer, redder wavelengths when the star is moving away from us, as seen below.
Image credit: Spectral Atlas for Amateur Astronomers: A Guide to the Spectra of Astronomical Objects and Terrestrial Light Sources
Eclipses
As stated above, if the stars are oriented just right, we see eclipses as they pass in front of one another with respect to our line of sight. These eclipses hold a plethora of information on the sizes, temperatures, and separations of the two stars, as seen in the diagram below.
Image credit: IJspeert (2024)
The quantities d₁ and d₂ are the fractional area that cannot be seen from star 1 and 2, respectively. The quantities f₁ and f₂ are the amount of light blocked from the surface of star 1 and star 2, respectively, and the times t₁ and t₂ are the points in time where stars 1 and 2 are eclipsed, respectively. If times t₁ and t₂ are 1/2 period apart, then the star is in a circular orbit, if not, the orbit is eccentric!
By modelling these time series data, we can fully determine the orbit, masses, radii, and temperatures of the two stars to an extremely high precision - thus making binary stars of high value to astrophysics by providing high precision benchmarks for our evolution theories.
In this project post, I talk about the procedure that I use to model binary stars - however, eclipsing binaries produce some very strange signals in time series data (seen below) so sometimes, we have to get creative in how we model these signals.
Image credit: Prsa et al., 2022
