The next section of the star-system design sequence follows. Here, we determine whether the star system is a single or multiple star, and in the case of a multiple star we determine how many stellar components are present.

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Step Two: Stellar Multiplicity

This step determines how many stars exist in the star system being generated.

Our own sun is a single star, traveling through the galaxy with no other stars as gravitationally bound companions. Many stars do have such companions. Double stars, gravitationally bound pairs, are very common. Multiple stars, groups of three or more stars traveling together, are much less common but do occur. Most multiple stars are trinary stars, sets of three. Sets of four or more are possible – in fact, star systems with up to seven stellar components are known – but they are quite rare.

Multiple stars are almost always found arranged in a hierarchy of pairs. That is, the stars in a system can usually be divided into pairs of closely bound partners. Each pair circles around its own center of mass, and the pairs themselves follow (usually much wider) orbital paths around the center of mass of the entire system. Any odd star is usually bound with one of the pairs. This kind of arrangement is very stable over long periods of time.

Very young multiple star systems can form trapezia, in which three or more stars follow chaotic, closely spaced paths around the system’s center of mass. This arrangement is highly unstable, and is unlikely to last very long after the stars’ original formation. Some members of a trapezium will normally be ejected, to travel as singletons. The remaining stars soon settle down into a more stable hierarchy-of-pairs arrangement.

Procedure

To begin, select whether the system being generated is a multiple star. To determine this at random, roll 3d6 and refer to the Multiplicity Threshold Table.

Multiplicity Threshold Table
Primary star’s mass (in solar masses) is . . .	Then the star is multiple on a 3d6 roll of . . .
Less than 0.08	14 or higher
At least 0.08, less than 0.70	13 or higher
At least 0.70, less than 1.00	12 or higher
At least 1.00, less than 1.30	11 or higher
At least 1.30	10 or higher

If the star system is multiple, roll d% on the Stellar Multiplicity Table. Star systems with five or more components are possible, but so rare that they should not be selected at random.

Stellar Multiplicity Table
Roll (d%)	Number of Stars
01-75	2
76-95	3
96-00	4

Selecting for an Earthlike world: Earthlike planets can appear in single or multiple star systems, although the arrangement of components in a multiple star system (determined in the next step) will affect the presence of such worlds.

Examples

Arcadia: Alice determines the multiplicity of the Arcadia star system. She knows that multiple stars might still have Earthlike worlds, but decides not to take any chances. She determines that Arcadia’s primary star will be a singleton, and does not roll on the Stellar Multiplicity Table.

Beta Nine: Bob continues to work at random while generating the Beta Nine system. He rolls 3d6 to determine whether the Beta Nine system is multiple, and gets a result of 15. Even with the primary’s star’s low mass of 0.18 solar masses, this suggests that the system will, in fact, be a multiple star system. Bob rolls d% and refers to the Stellar Multiplicity Table. His result of 46 indicates that the Beta Nine system will be a double star system.

Modeling Notes

There has been considerable recent work on the frequency of multiple star systems, leading to the (rather surprising) discovery that most stars, especially low-mass stars, are not multiple. Two of the most useful sources for this are:

Lada, C. (2006). Stellar Multiplicity and the Interstellar Mass Function: Most Stars are Single. The Astrophysical Journal Letters, volume 640, pp. 63-66.

Duchêne, G. and A. Kraus (2013). Stellar multiplicity. Annual Review of Astronomy and Astrophysics, volume 51, pp. 269-310.

Step Three: Arrange Stellar Components

This step determines how the components of a multiple star system are arranged into a hierarchy of pairs, and the initial mass of each companion star in the system. This step may be skipped if the star system is not multiple (i.e., the primary star is the only star in the system).

Astronomers normally tag the various stellar components in a multiple star system with capital letters in the Latin alphabet: A, B, C, and so on. So, for example, the famous trinary star Alpha Centauri has three components: the bright yellow-white star Alpha Centauri A, its relatively close orange companion Alpha Centauri B, and a distant red dwarf companion Alpha Centauri C (also called Proxima Centauri, since it is noticeably closer to Sol than the A-B pair).

Unfortunately, astronomers are not always consistent about which component is given which alphabetic tag. In this book, we will always tag the primary star, the most star with the highest initial mass in the system, as the A-component. The other components will be tagged in order of their distance from the primary star.

 

Procedure

The procedure for arranging stars in a system varies, depending on the multiplicity of the system.

Stars other than the primary in a multiple star system are sometimes called companion stars. These stars can have any mass, from tiny brown dwarfs up to stars almost as massive as the primary, although there is a clear tendency toward the latter.

Binary Star Systems

There is only one possible arrangement for the two stars of a binary system. There are two components, A and B, and the primary star or A-component is in a gravitationally bound pair with the B-component.

Select the mass for the companion star. To generate its mass at random, roll d% on the Companion Star Mass Table to determine a mass ratio for the companion.

Companion Star Mass Table
Roll (d%)	Mass Ratio
04 or less	0.05
05-08	0.10
09-12	0.15
13-16	0.20
17-20	0.25
21-24	0.30
25-28	0.35
31-32	0.40
35-36	0.45
37-40	0.50
41-45	0.55
46-50	0.60
51-55	0.65
56-60	0.70
61-65	0.75
66-71	0.80
72-78	0.85
79-87	0.90
88 or more	0.95

In each case, feel free to select a mass ratio that is just above the result of the table, increasing the ratio by less than 0.05. For example, if the result on the table indicates a mass ratio of 0.60, it would be appropriate to select an actual ratio greater than 0.60 but less than 0.65. The mass ratio cannot be lower than 0.05 or higher than 1.00.

In a binary star system, the companion star’s mass will be equal to the mass of the primary star, multiplied by the companion’s mass ratio. Round the companion’s mass off to the nearest hundredth of a solar mass unit. You may wish to round the companion’s mass off further, to match one of the entries in the Stellar Mass Table (see Step One). In no case will the mass of a companion star be less than 0.015 solar masses; round any such result up to that number.

Trinary Star Systems

There are two possible configurations for the three stars (components A, B, and C) of a trinary system.

One possibility is that the primary star (the A-component) has no close companion, but the B and C components move some distance away as a gravitationally bound pair of close companions (A and B-C).

The other is that the primary star and the B-component move as a bound pair of close companions, with the C-component moving alone at a greater distance (A-B and C).

Both arrangements appear to be about equally common. When designing a trinary star system, select either one. To select one at random, flip a coin.

In a trinary star system which is composed of a single A-component and a close B-C pair, the mass of the B component is computed using the Companion Star Mass Table, based on the mass of the primary star. The mass of the C-component is computed based on the mass of the B-component. When rolling on the Companion Star Mass Table, add 30 to the roll for the C component.

In a trinary star system which is composed of an A-B close pair and a C distant companion, the mass of each of the B and C components is computed using the Companion Star Mass Table, based on the mass of the primary star. When rolling on the table, add 30 to the roll for the B component.

Quaternary Star Systems

There are many possible arrangements for the four stars (components A, B, C, and D) of a quaternary system. However, by far the most common arrangement, and the most stable over long periods of time, is one in which two binary pairs (A-B and C-D) orbit one another at a wide separation.

In a quaternary star system, the mass of each of the B and C components is computed using the Companion Star Mass Table, based on the mass of the primary star. The mass of the D-component is computed based on the mass of the C-component. When rolling on the Companion Star Mass Table, add 30 to the roll for both the B component and the D component.

Examples

Arcadia: Alice skips this step for the Arcadia star system, since she already knows that the primary star is a singleton.

Beta Nine: Bob continues to work at random while generating the Beta Nine system. Since he has already established that the system is binary, he knows that there will be an A component (the primary star) and a B component (its companion). To determine the mass of the companion star, he rolls on the Companion Star Mass Table, and gets a result of 27 on the d%, for a mass ratio of 0.35. The mass of the companion star will be:

In this case, rounding the companion star’s mass off to the nearest hundredth of a solar mass unit means that it will exactly match one of the entries for brown dwarfs on the Stellar Mass Table. Bob decides to accept this result as is. The companion “star” in the Beta Nine system will be a brown dwarf.

Modeling Notes

Studies have found that the ratio of mass between the components of a binary star appears to be evenly distributed, although there seems to be a statistically significant peak for ratios of 0.95 or higher in the data.

Mass ratios seem to be somewhat dependent on the orbital period. In particular, binary pairs which orbit one another at a short distance seem more likely to be close matches in mass. For simplicity’s sake, the model set out in this book largely ignores this effect, although in trinary and higher-multiplicity star systems we do assume that the close pairs are more likely to be matched. The paper by Duchêne and Kraus (cited under Step Two) discusses these statistical phenomena in some detail.