Multiple-Star System

About one third of all star systems in the Milky Way are multiple-star systems: star systems with two or more stars. There are several types of multiple-star systems, determined from the number of stars in the system (binary, triple, quadruple, etc.) and the separation of the stars (close orbiting P-type systems and far orbiting S-type systems).

Multiple-star systems can exist with any configuration of number of stars and distance, but for planet-forming purposes, either a close system of 0.15 AU to 6 AU or a far system of 120 AU to 60 000 AU is recommended. You can use any values you like, but for the purposes of this guide, we will work with these limits.

We will designate primary stars as A and secondary stars as B, with subsequent companion stars as C, D, E, etc. The primary star should be greater than or equal in mass to the secondary star.

Binary Systems
Binary systems (systems of 2 stars) orbit a common centre of mass, known as the barycentre. The stars, as well as any planets in the system (only in the case of close binary systems), will orbit this barycentre.

Given the average separation of the stars (a, in AU) and their masses (MA and MB), we can calculate the average distance between the primary star and the barycentre, using the following formula :

Therefore, the average distance between the secondary star and the barycentre is:

The orbits of the stars are not usually circular, but are instead elliptical. Eccentricity is a measure of just how "un-circular" an orbit is, where 0 is a perfect circle and 1 is a parabola. Both stars orbiting a single barycentre will have equal orbital eccentricity, which should ideally be between 0.4 and 0.7 for a close orbiting pair.

Given the eccentricity (e) of the orbit and the average distance between a star and the barycentre, the maximum and minimum distances between the star and the barycentre can be calculated as:

Using the above, we can calculate the maximum and minimum separation between the stars themselves as:





When determining the habitable zone, planetary limits and frost line of a close-orbiting pair (see Planetary Systems), all one needs to do is to add the masses or luminosities of the stars together. Far-orbiting systems follow the usual rules, as each star in the system may have its own planetary system.

In addition to the above, there are also limits on planetary formation due to the gravitational effects of the stars. No planets can form within these "forbidden zones", whose limits are given as:

Habitability
For close binary systems, we would like the outer planetary boundary to be less than the inner planetary limit if we wish the system to be habitable, so that the maximum area for planet formation is available to us. For a planet to be habitable, it must also orbit more than 4 times the outer forbidden zone from the barycentre.

For far binary systems, we would like the inner planetary boundary to be greater than the outer planetary limit of both stars, in order to have the maximum area for planet formation available to us.

The placement of planets in a binary system is identical to placing them in a single-star system, except that the above restrictions must be observed.

Systems of more than two stars
Stars in multiple-star systems tend to group hierarchically. In other words, triple, quadruple, quintuple, etc. systems will be grouped into single stars and close/far binary pairs, and then these pairs can be treated as a single effective star. For example, a quadruple star system (A, B, C and D) could be organised into two pairs of binary stars (A and B, C and D). We could create this system by first computing each pair individually, and then treating them as two single stars (AB and CD).

Remember that, just as the secondary must be less massive than the primary, the secondary system (C and D) must be less than the primary system (A and B).

Worldbuilding in Practice
"While binary systems are rather common in the galaxy, quintuple systems are rather rare. Yet they do exist, as evidenced by the perplexing Eta Rodriguez system, which is composed of Eta Rodriguez A, B, C, D and E. ER A orbits ER B at a distance of approximately 3 AU and ER C and ER D orbit each other at an approximate distance of 4.8 AU. In turn, the Eta Rodriguez AB and CD systems orbit each other at a distance of 18,931 AU (~0.09 pc). Finally, the lonely red dwarf Eta Rodriguez E orbits the barycentre of the AB/CD system at a staggering distance of 54,383 AU (~0.26 pc). At such distances, even observers within the system have difficulty noticing the relationship: from Eta Rodriguez Ac (a small terrestrial planet orbiting ER A), ER C and D appear as particularly bright stars, and ER E is invisible to the naked eye."